Session KP01 - Poster Session III.
POSTER session, Tuesday afternoon, March 23
Exhibit Hall, GWCC

[KP01.01] Principles of the Dual Noble Gas Maser

We describe principles of operation of the dual noble gas maser. This device can measure very small differential changes in the Zeeman transition frequencies of co-habitating ensembles of ^129Xe and ^3He atoms, and is useful for symmetry tests and precision measurements such as a search for a permanent electric dipole moment (EDM) of the ^129Xe atom. We present experimental techniques and theoretical analysis pertaining to the operation of the device as an active, stable oscillator and its resulting sensitivity to new physics.

[KP01.02] A Precise Measurement of the He^+ 2S Lamb Shift

There is now a ten standard deviation discrepancy between the measured value of the 2S Lamb shift in singly-ionized hydrogen-like helium [1] and the value calculated from quantum electrodynamics (QED) [2,3]. Recent Lamb shift measurements in atomic hydrogen [4,5,6] are not sensitive to the QED terms responsible for the discrepancy because of the uncertainty in the measured value of the proton charge radius, and measurements in hydrogen-like systems with Z higher than 2 do not have sufficient accuracy to address the problem. This serious situation is the motivation for a new experiment to determine the He^+ 2S Lamb shift using Doppler-free two-photon laser spectroscopy of the 2S-3S transition. We will report progress on this new measurement .

[1] A. van Wijngaarden, J. Kwela, and G.W.F. Drake, Phys. Rev. A43, 3325 (1991). [2] K. Pachucki et al., J. Phys. B 29, 177 (1996). [3] S. Mallampalli and J. Sapirstien, Phys. Rev. Lett. 80, 5297, (1998). [4] D.J. Berkeland, E.A. Hinds and M.G. Boshier, Phys. Rev. Lett. 75, 2470, (1995). [5] S. Bourzeiz et al., Phys. Rev. Lett. 76, 384, (1996). [6] Th. Udem et al., Phys. Rev. Lett. 79, 2646, (1997).

[KP01.03] Population dynamics of a triply driven, three-level atomic system

We report on interim results from an apparatus which allows us to monitor the time evolution of a triply driven, three-level system in atomic rubidium. Unlike lambda or ladder systems, this "delta" configuration (a closed loop of excitations) can exhibit T-asymmetric behavior. We prepare the system by optically pumping with a diode laser. At t=0 this laser is extinguished, and three standing wave fields start to drive the magnetic dipole transitions that constitute the delta system. Two weak probe lasers continuously excite a small fraction of the coherently driven atoms into a high-lying optical state, which quickly decays via emission of a blue photon. The intensity of the blue fluorescence signal has time-directional sensitivity and can be analyzed to set limits on T-violating effects in the delta system.

[KP01.04] Work on a Precision Measurement of Helium Fine Structure

We present a progress report on an experimental study of the 2P fine structure of atomic helium. The basic method has been demonstrated [1] and involves high speed modulation of a stabilized diode laser, using the resulting side bands to drive fine structure transitions in a beam of metastable helium atoms. Our data indicate a substantial increase in precision over previous work is possible. To help study and eliminate possible systematic errors, a number of improvements have been made, particularly to the interaction region and atomic beam. A discussion of these and the status of the experiment will be given.

[1] C. Koehler, D. Livingston, J. Castillega, A. Sanders and D. Shiner, 15th Int. Conf. Appl. Accel. Res. Ind. (AIP Conf. Proc.), to be published.

[KP01.05] Progess towards an Atomic PNC measurement in singly trapped Ba^+

Atomic Parity Violation experiments provide a powerful probe for possible new physics beyond the Standaed Model. A new experiment using a single trapped Ba^+ ion can provide improvements over existing atomic PNC experiments with increased sensitivity, easier analysis of systematic errors, and simpler atomic and nuclear structure.(Fortson, Phys. Rev. Let.) 70, 2383 (1993). The method involves measuring a parity induced splitting of the ground state magnetic sublevels in externally applied laser fields, and requires the ability to precisely manipulate and detect the spin state of a single ion. The techniques being developed to achieve this will be described, as well as recent results from their application to measuring light shifts in the 6S_1/2 and 5D_3/2 levels using either strong off resonant laser fields to generate dipole shifts that can be used to provide a precise test of atomic theory, or using light directly resonant with the S\to D transition to study the performance of the 2\mu m laser that will be used in the parity measurement, and to begin to investigate the ability to control certain classes of possibile systematic errors.

[KP01.06] Lamb Shift Measurement in He^+ by the Anisotropy Method

The Lamb shift continues to provide one of the most important tests of quantum electrodynamics. A previous measurement in He^+ by the anisotropy method yielded a value that is 70(12) parts per million higher than theory when two-loop binding corrections are included( K. Pachucki et al.), J. Phys. B 29, 117 (1996).. However, a recent test of the method in hydrogen gave results in agreement with theory and other measurements at the \pm15 MHz (15 ppm) level of accuracy( A. van Wijngaarden, F. Holuj, and G. W. F. Drake, Can.\ J. Phys.\ 76), 95 (1998).. The previous He^+ measurement is now being repeated with improved accuracy, and final results will be reported at the conference.

[KP01.07] Parity Non-Conserving Amplitudes in Francium and Barium Ion

We have written a separate code for the GRASP2 program to perform small-sized Configuration Interaction (CI) calculations for the Parity Non-Conserving (PNC) amplitudes. Our calculations of the amplitude arising from neutral weak currents in the even isotope of FrI agree well with an older calculation(Dzuba, et al, Phys. Rev. A, v. 51, num. 5, p. 3454, 1995). The importance of nuclear size, Breit and QED effects has been explored. These corrections play a crucial role in the precise calculation of the weak interaction amplitudes. Furthermore, the role of the dominant configurations is discussed in the investigation of the correlation effects for the PNC amplitudes. The result of parity nonconservation in FrI is 1.44 \times 10^-10 iea_o(-Q_W/N). We hope to improve low order results in the near future by performing larger-sized CI calculations to provide evidence of fundamental processes in the weak interaction sector as the progress in the PNC measurement in francium is made. We will also extend our approach to calculate PNC in other atoms and ions, such as Ba+.

[KP01.08] Proposed Test of Long-Range T-Violating Forces in Atomic Thallium

We present a new experimental proposal to search for time reversal-violating (T-odd, but P-even) forces in atomic thallium. Important modifications to the method originally proposed(M.G. Kozlov and S.G. Porsev, Phys. Lett. 142A, 233 (1989)) should lead to substantially increased sensitivity to possible `TOPE' effects. In our new scheme, a linearly polarized 1283 nm laser, tuned near the 6P_1/2(F=0)\rightarrow 6P_3/2(F^\prime=1) transition, is injected in both directions into a high-finesse ring cavity. A thallium atomic beam passes through the ring cavity, intersecting the laser beams at right angles. In the presence of a static electric field, \vecE, a `TOPE' signature is revealed by a cavity phase shift proportional to (\hatk_laser\cdot\vecE). We would search for a differential phase shift of the counterpropagating laser beam components correlated to electric field reversal. The cavity finesse both amplifies any TOPE effect and increases the precision with which it can be detected, while the differencing technique reduces sensitivity to common-mode laser frequency or mechanical fluctuations. An analysis of statistical phase shift resolution and consideration of potential systematic errors leads to predicted experimental limits on an atomic TOPE matrix element at the 10^4 Hz level or below. Preliminary results of new thallium calculations(S.G. Porsev, private communication), and a comparative discussion of direct vs. indirect (atomic EDM-based) limits on TOPE forces will be presented, as will further experimental details.

[KP01.09] Atomic Structure Measurements in Thallium using a 378 nm Frequency-doubled Diode Laser

Using a recently constructed atomic beam apparatus, we have undertaken a series of precise atomic structure measurements on the 378 nm 6P_1/2 - 7S_1/2 E1 transition in atomic thallium. This work complements ongoing vapor cell spectroscopy of the thallium 1283 nm M1 transition in this laboratory. These measurements will provide important, independent cross-checks on the accuracy of ongoing calculations of parity nonconservation in thallium. Our atomic beam apparatus consists of a multiple slit oven source and 20 cm oven-to-interaction region distance, which provides a favorable balance of beam density and modest Doppler narrowing. Using a 5 mW external cavity diode laser and an external resonant doubling cavity containing an LBO crystal, we have obtained 4 microwatts of light at 378 nm. In our experiment, we scan the diode laser via a PZT and measure the transmission of UV light through the atomic beam in the vicinity of the transition. With the aid of a calibrated Fabry-Perot cavity this will allow an improved spectroscopic determination of the \sim12 GHz 7S_1/2 state hyperfine splitting as well as the \sim1.6 GHz ^203Tl/^205Tl isotope shift within this transition. Using a precisely constructed electric field plate assembly, and an acousto-optic modulator to frequency shift the diode laser, we are also undertaking a precision Stark shift measurement within the 378 nm transition. Current experimental results will be presented.

[KP01.10] Trapping of Ytterbium Atoms for an EDM experiment

We are investigating the use of a magneto-optical trap (MOT) and optical dipole trap to search for a CP-violating permanent electric dipole moment (EDM) by nuclear spin resonance in Yb atoms.

Optical cooling and trapping of Yb atoms offers many advantages for an atomic EDM experiment, including long spin-relaxation lifetimes and a zero average motional magnetic field \vecv\times\vecE.

We have designed and built a new ultra-high vacuum apparatus for our atomic beam and MOT, including differential pumping and a Zeeman slower. We have slowed the Yb atomic beam with about 10% efficiency, using the ^1S_0 \rightarrow ^1\!\!P_1 (398.9 nm) transition.

We are currently improving the efficiency of our Zeeman slower, in order to effectively load the atoms into a MOT. We are also exploring the possibility of measuring the branching ratio of the decay from the ^1\!P_1 state into the D-states, ^3\!D_2 and ^3\!D_1. We will report the results of these experiments.

Further information can be found at \verb"http://www.phys.washington.edu/\~reinam/". This work is supported by NSF Grant PHY-9732513.

[KP01.11] Interaction Free Measurement with Coherent Light

We have investigated the efficiency of interaction free detection of a classical object using quantum interference with a coherent light source. This scheme is designed to detect the presence of an object using photon interference in an interferometer without the photon ever hitting the object. In the experiment, an interferometer is arranged so that incident light will not exit through one port (the dark port) if there is no object in the light's paths. However, if there is an absorbing object present, then light will exit through the dark port hence not be absorbed by the object. The efficiency is defined as the ratio of the probability of detecting a photon in the dark port to the probability of either the object absorbing a photon or detecting a photon in the dark port. Experiments were done using Michelson and Mach-Zehnder interferometers and detection was done with avalanche photodiodes operating in the Geiger mode. Previous experiments have determined the efficiency of this technique using single photons from a parametric down conversion. In our experiment we have measured the efficiency as a function of the average number of photons in light pulses from a 670 nm pulsed diode laser and also as a function of the reflectivity of the beamsplitter.

[KP01.12] Quasi-condensate formation in a gas of trapped atoms

We present a theoretical model of the formation of quasi-condensate droplets and apply it to recent measurements in an atomic hydrogen BEC. The formation of droplets of quasi-condensate is based on a first-order phase transition treatment. We consider a gas of weakly interacting trapped bosonic atoms in thermal equilibrium, and evaluate the probability of forming a droplet containing a given number of atoms from density fluctuations near the critical conditions. By determining the number of atoms in a droplet and its density as a function of the local gas density, we predict a global density profile that exhibits large distortion from the thermal density profile. We explore the effect of interaction between atoms using the scattering length. In order to compare the results from our model with experimental data obtained in the atomic hydrogen BEC experiment at MIT, we estimate the two-photon absorption lineshape under current experimental conditions, and predict the appearence of an asymmetric component due to the quasi-condensate droplets. The predicted behavior of the asymmetric component is in accordance with observations. We also speculate on the time evolution of the system: the droplets will coalesce to form larger droplets until the final condensate is formed in the center of the trap.

[KP01.13] Study of density-dependent loss and evaporative cooling of ^85Rb

We present the progress in our attmept to form a Bose-Einstein Condensate in ^85Rb. As part of our efforts to optimize the evaporation, we have studied both two- and three-body loss processes. These losses have very strong magnetic field dependences. Here we give a characterization of the losses, a comparison of the measured loss rate and structure with theoretical predictions, and the prospects for producing an ^85Rb condensate. This work is supported by the NSF and ONR.

[KP01.14] Real-Time Observation of Rabi Oscillations between Bose-Einstein Condensates

We explore a system of two Bose-Einstein condensates in different spin states of ^87\mathrmRb, coupled by a microwave driving field. We nondestructively observe both condensates with a state-sensitive phase contrast imaging technique that does not significantly affect the coherence between the condensates. With the coupling drive on, we observe Rabi oscillations in real-time that persist for the lifetime of the double condensate system. Under certain experimental conditions the oscillations also exhibit collapses and revivals. Recent results will be presented. This work is supported by NIST, the ONR, and the NSF.

[KP01.15] New system for creating a Bose-Einstein Condensate

We will discuss the progress in the development of a new and simple system to create BEC in ^87Rb. The design uses a single MOT and a spatially separated magnetic trap. The atoms are transferred between traps by means of moving magnetic fields. This magnetic transfer method will reduce the alignment problems associated with using a laser push beam. The efficiency of capturing the atoms in the final magnetic trap should be greater than laser transfer method because the atoms are transferred slowly between traps, and there is no heating from a transfer beam.

[KP01.16] The near-resonant condensate as a two-phase system

The interactions that create an intermediate quasi-bound molecule in the binary atom Feshbach resonance, create a second, molecular, condensate in the many-body Bose-Einstein Condensate (BEC). The coexisting condensates interact by coherently exchanging pairs of atoms. The contribution to the many-body energy of this novel type of inter-condensate tunneling depends on the relative phase of the atomic and molecular condensates, and reaches its minimum if the phases of the condensates differ by \pi. The population dynamics of the double condensate BEC reveals that the system has two distinct stationary states: the above mentioned state with condensates of opposite sign and a state with condensates of the same sign. The particular state that the experimental system finds itself in, depends on its history. If the BEC was brought near-resonance by adiabatically decreasing the detuning, starting from far-above resonance, the condensates will have the same sign. If, on the other hand the detuning was increased from below resonance, the atomic and molecular condensates can be of opposite sign. Interestingly, although the same sign mixture maximizes the energy, the corresponding system can nevertheless be stable. We discuss the implications of the molecule loss-processes, and we point out the similarities with an analogue in non-linear optics.

[KP01.17] Atomic condensates of with anisotropic interactions\ \ \ \

We study the properties of trapped Bose-Einstein condensates (BEC) of atoms with binary anisotropical interactions. We discuss interesting features not previously considered for condensates of non-spherical, e.g. electric field polarized, atoms. Our studies shed new light into the macroscopic coherence properties of dilute degenerate interacting quantum gas.

[KP01.18] Initiation of Bose condensation of atoms confined in magnetic traps

We present a model for the physics of the initiation of Bose-Einstein condensation of atoms confined in magnetic traps. We model the dynamics of the condensation process by a quantum mechanical master equation for the lowest energy modes, coupled to a quantum Boltzman type equation for the higher energy modes. The model and numerical results will be discussed.

[KP01.19] Light scattering from trapped degenerate fermi gas \ \ \

We study the signatures of fermi degeneracy as well as the BCS superfluidity of a degenerate fermi gas using the strong light scattering technique developed for bosons in Ref. (L. You, M. Lewenstein, and J. Cooper, Phys. Rev. A 51), 4712 (1995).

In our model, we consider a degenerate fermi gas confined in a three dimensional isotropic harmonic oscillator. Intense short laser pulses causes coherent Rabi oscillations of the degenerate gas. Atomic spontaneous emissions during the driving pulse is calculated perturbatively. The properties of the scattered light such as the angular distribution, coherence and total intensity reflects the the degree of degeneracy of the gas, i.e. its temperature.

[KP01.20] Time-Dependent Behavior of a Bose-Einstein Condensate in a 3D Trap

Excitation and decay of Bose-Einstein condensates in a 3D trap are studied by direct solution of the time-dependent nonlinear Schrodinger equation. The Hamiltonian is discretized on a 3D lattice using finite differences. The condensate wavefunction is partitioned on a distributed-memory parallel computer and then time evolved using an explicit leap-frog propagator. The nonlinear response of ground state alkali metal condensates in a fully anisotropic trap is studied using both single and broadband frequency probes. Comparison is made with previous theoretical results and experimental measurements of the excitation frequencies.

[KP01.21] An improved large N limit for Bose-Einstein condensates from perturbation theory

We present a perturbation solution of a model Bose-Einstein Hamiltonian derived by Bohn, Esry and Greene(J.L. Bohn, B.D. Esry, and C.H. Greene, Phys. Rev. A 58), 584 (1998).. In our solution we use 1/N as the perturbation parameter, where N is the number of particles in the condensate. Ground and excited state energies are reported for parameters approximating the J.I.L.A. ^87Rb experiments(M.H. Anderson, J.R. Ensher, M.R. Mathews, C.E. Wieman, and E.A. Cornell, Science 269), 198(1995).. We predict the critical number of atoms with negative scattering lengths that can be trapped using the effective trap frequency of the first-order equation. This effective trap frequency folds in interactions between the external trap and the interatomic term. The N\rightarrow\infty perturbation limit, which retains a single term beyond the conventional Thomas-Fermi limit, gives ground state energies that agree to three digits with converged results, thus providing a much improved limit for large N.

[KP01.22] Time-dependent GP equations for superpositions of macroscopically occupied states

We generalize the Bogoliubov prescription for the case of an initial macroscopically populated subspace and obtain the corresponding time-dependent Gross-Pitaevskii equations using the Castin--Dum(Y. Castin and R. Dum, Phys. Rev. A 57), 3008 (1998).--Gardiner(C. W. Gardiner, Phys. Rev. A 56), 1414 (1997). procedure. We show that the result is relevant for the analysis of the MIT interference experiment(M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275), 637 (1997)..

This work was supported by the NSF grant no. DMR-96-14133.

[KP01.23] A Mechanical Demonstration of Atomic Response to a Chopped Optical Field

In an effort to help students develop a clear picture of the physics of driven atoms, we have constructed a mechanical model. Using a mechanical mass-spring oscillator, a sonic ranger, and a voltage controlled stepper motor, we are investigating the oscillator's response to chopped forcing functions. The stepper motor coupling to the mass is designed so that the phase of the motor can be controlled from pulse to pulse. This allows for each pulse to be sent with the same phase, with a predetermined different phase or with a random phase. This system is analogous to the classical Lorentz model of the atom driven by a chopped optical field. This extreme amplitude modulation gives rise to a variety of interesting phenomena, including optical Ramsey fringes (large dipole atom response for detuning * cycle time = 2 pi). These results will be compared to numerical solutions of an isolated Lorentz model atom interacting with a similar train of short laser pulses.

[KP01.24] Manipulation of an ^87Rb Bose-Einstein Condensate

We have observed Bose-Einstein condensation of ^87Rb in a baseball Ioffe-Pritchard magnetic trap. The atoms are first collected from a vapor in a multiply-loaded double magneto-optic trap, then further cooled in optical molasses and transferred to the magnetic trap, and finally evaporatively cooled to the BEC transition temperature. We will describe recent experiments with the condensate, including attempts to manipulate it using time-dependent magnetic fields.

[KP01.25] Critical Velocity in Dilute Trapped BEC

Though vorticies in dilute trapped Bose-Einstein condensates may be unstable (R. J. Dodd, et. al.,) Phys. Rev. A 56, (1997) 587. \ (D. Rokhsar, Phys. Rev. Lett. 79), (1997) 2164. they yield a useful upper bound on the superfluid critical velocity. We describe some recent results of theoretical work using vorticies to compute the critical velocity for single component BEC at various density, coupling and geometry.

[KP01.26] Quantum kinetics of trapped Bose gases

We study numerically different aspects of the quantum kinetic time evolution of a model system that consists of an ideal Bose gas in a harmonic trap. The numerical integration of the appropriate quantum Boltzmann equation is accomplished using a trajectory method similar to that employed by Holland et al(M.~Holland, J.~Williams and J.~Cooper, Phys. Rev. A 55), 3670 (1997). One of our interests is to examine the relaxation to the condensate ground state from an initial distribution which contains a thermodynamically unstable macroscopically occupied state. This nonequilibrium situation is relevant to recent experiments at MIT with optically trapped multicomponent condensate systems. Using the same methods, additional insight into the nucleation dynamics of the condensate is gained.

[KP01.27] Fast Particle Confinement and Lost Ion Diagnostic in Low Aspect Ratio Tokamaks

Detailed understanding of energetic particle confinement, transport and losses in low aspect ratio tokamaks, such as NSTX and MAST, is necessary for understanding and planning future experiments. In this presentation requirements for plasma equilibrium to confine fast particles are analyzed and compared with ones in tokamaks. Beam ion losses are studied using the ORBIT code. Losses of fusion products (tritium and proton ions), having large gyro radius, and their distribution in pitch angle and poloidal angle are simulated by new code LARMOR. The opportunity to use the diagnostic of lost fast particles by measuring their energy spectrum and flux pitch angle distributions is discussed in order to be able to reconstruct basic plasma parameters, such as temperature profile, fusion products source profile, plasma current and others.

[KP01.28] TAE excitation in NSTX.

The unique features of NSTX, such as low aspect ratio, high plasma and energetic particle beta, low Alfvén velocity with the respect to beam ion injection velocity, and large Larmor radii present an entirely new regime for studying energetic particle physics, which need to be revisited. TAE stability is analyzed using the improved NOVA-K code, which includes finite orbit width and Larmor radiius effects and predicts the saturation amplitude for the mode using quasilinear theory. The analysis shows a broad spectrum of TAEs with different toroidal mode numbers. Most of eigenmodes are global because of strong toroidal coupling of the poloidal harmonics due to low aspect ratio. NBI ions are super Alfvénic producing a strong drive for TAEs. Trapped electron collisional damping is significant and can be shown to be of order \gamma / ømega \sim \beta_e for the ratio of the effective collisional frequency to the eigenfrequency to be \nu_\mathrmeff / ømega \simeq 0.1. ORBIT code is also used to study the effect of TAEs on beam ion confinement. It was found that the magnetic field well, which exists in high beta NSTX equilibria, provides a better confinement. Single TAE mode causes additional losses on the order of 5% for high beta case \beta_\mathrmav = 34 % and < 10% in low beta case \beta_\mathrmav = 10 %.

[KP01.29] Bootstrap Current in Anisotropic High-Beta Extremely-Low-Aspect-Ratio ( A \rightarrow 1 ) Tokamak Plasmas

The stability beta limit for low aspect ratio tokamak plasmas can be of the order of 50 % or higher. Equilibrium pressure in such plasmas is likely to be anisotropic, i.e., P_\parallel\ne P_\perp, due to strong auxiliary heating power, such as RF or neutral beam heating. Here P_\parallel is the parallel ( to magnetic field \mathbfB) plasma pressure and P_\perp is the perpendicular plasma pressure. A solution for the perturbed particle distribution of the linearized drift kinetic equation in the extremely low aspect ratio limit ( i.e. aspect ratio A \rightarrow 1 ) is obtained. It is found that bootstrap current <\tau J_bB > depends on parallel pressure gradient \partial P_\parallel/\partial\psi and magnetic field gradient \partial B/\partial\psi, where angular brackets denote flux surface average, \tau = 1 - ( 4\pi / B^2 ) ( P_\parallel - P_\perp), J_b is the bootstrap current, B =|\mathbfB| and \psi is the poloidal flux function. The Pfirsch-Schluter current is also calculated from the fluid momentum equation. Parallel plasma current in such plasmas is therefore completely determined.

[KP01.30] TST-2: The New Spherical Tokamak at the University of Tokyo

A new spherical tokamak TST-2 (R = 0.37\rm\,m and a = 0.23\rm\,m, corresponding to A = 1.6) is being constructed to replace the TST-M spherical tokamak at the University of Tokyo. Unlike TST-M, the new device will have a relatively thin-wall, toroidally continuous vacuum vessel (no toroidal break), and the coils (the toroidal and ohmic coils) are located outside the vacuum vessel. The vacuum vessel consists of a 1.4\rm\,m diameter, 6\rm\,mm thick stainless steel cylinder and top and bottom domes. The height of the vacuum vessel is 1.5\rm\,m. The inner wall of the vacuum vessel is made of a 0.23\rm\,m diameter, 2\rm\,mm thick Inconel tube. The new center stack consists of a 180-turn ohmic solenoid and the center legs of the 24-turn toroidal field coil. With the planned power supply upgrade in the near future, the flux swing capability of the ohmic solenoid will be increased up to 0.25\rm\,Vsec (compared to the presently available 0.025\rm\,Vsec). The ultimate field and current that can be achieved after power supply upgrade are B_T = 0.4\rm\,T and I_p = 0.2\rm\,MA. The new device is scheduled to start operation in the summer of 1999. The status of construction and the research plan will be presented.

[KP01.31] Interpretation of Energetic Particle--Driven Instabilities in the START Spherical Tokamak

Several distinct classes of energetic particle--driven instability have been observed during neutral beam injection in the Small Tight Aspect Ratio Tokamak (START). Possible interpretations of these observations are given. Shear Alfvén continuous spectra, computed for times of beam--driven wave activity, contain wide spectral gaps, extending up to several times the Alfvén gap frequency, in which shear Alfvén eigenmodes could, in principle, be driven unstable by energetic ions. Eigenfunctions are computed for the lowest frequency gap. Part of the instability drive in START is provided by positive gradients in beam ion velocity distributions, which arise from velocity--dependent charge exchange losses. It is shown that fishbone--like bursts observed at a few tens of kHz can be attributed to kink mode excitation by passing beam ions, while narrow--band emission at several hundred kHz may be due to excitation of fast Alfvén eigenmodes. The possibility of similar instabilities occurring in larger spherical tokamaks is discussed.

[KP01.32] Nonlinear Dynamics of Magnetic Islands in Low Aspect Ratio Tokamaks with Pressure and Curvature

In high temperature tokamaks, nonideal MHD instabilities limit the achievable plasma pressure through the production of long wavelength nonlinearly evolving magnetic islands driven by neoclassical bootstrap current effects. However, in low aspect ratio tokamaks, the neoclassical effect competes with the stabilizing effects of pressure and good average curvature [S. E. Kruger, et al, Phys. Plasmas 5, 455 (1998)]. Prior analytic calculations of pressure/curvature effects on the nonlinear resistive growth of magnetic islands implemented a small aspect ratio, small beta expansion which is not appropriate for tight aspect ratio applications. In this work, we revisit this analytic calculation by relaxing the small aspect ratio, small beta constraints by considering an asymptotic expansion based solely on a small island width assumption. Implications for beta limits in tight aspect ratio tokamak configurations will be addressed.

[KP01.33] Science of the National Spherical Torus Experiment (NSTX) Plasmas*

The Spherical Torus (ST) plasma has aspect ratio approaching unity and resembles a sphere with a modest hole through its center. The NSTX (National Spherical Torus Experiment) is currently being built at PPPL to investigate and prove the fusion physics principles of the ST plasmas at the MA level in current. The investigations will encompass a wide parameter domain of magnetized plasmas at high temperatures (\sim1keV) and densities (\sim10^20/m3). This domain promises high-performance fusion plasmas with large trapped particle fraction (up to 90% near edge) and Pfirsch-Schlüter current. Toward the outboard the plasma promises large magnetic well (\sim30%) with nearly omnigenous particle trajectories, dielectric constant (wpe2/wce2\gg 1), normalized gyroradius (ri/a\sim 0.03-0.01), supra-Alfvén fast ions (vfast > vA), diamagnetically driven flow shearing rate (\sim10^6), and magnetic mirror ratio (\sim4) and flux expansion (\sim10) in the Naturally Diverted (ND) outboard scrape-off layer of inboard limited plasmas. Investigations in this plasma domain will strengthen the scientific basis for magnetic fusion power. Detail of these properties and their implications for future fusion applications will be presented.

[KP01.34] Initial Operation of the National Spherical Torus Experiment (NSTX)

NSTX will be the first high-power, low aspect ratio device to operate in the U.S. It's multi-purpose mission is to explore physics in such areas as confinement and transport, MHD stability, non-inductive startup and current maintenance, and in the scrape-off layer and plasma edge in this new regime of operation. To accomplish it's mission, NSTX will be capable of operating with Ip=1 MA, Bt=0.3 T, R/a=0.86m/0.68m=1.3, and elongations up to 2.2. The device is outfitted with a set of close-fitting conducting plates to aid in plasma stability, and a divertor for handling escaping heat and particle flux. Up to 11 MW of auxiliary heating power will be provided by High Harmonic Fast Waves and Neutral Beam Injection. The HHFW and NBI will provide current drive for non-inductive current sustainment, and Co-axial Helicity Injection will be employed for non-inductive startup and sustainment. By operating at high-q (qpsi~10), high-betat (40%) discharges can be produced that also have high bootstrap current fractions (~70%), aiding in the non-inductive current sustainment. Furthermore, disruption effects are expected to be minimized with this high-q operation. The NSTX research program will be carried out by a nationally-based collaboration team. This poster will present details of the physics mission, device capabilities, and research plan for NSTX, along with results from initial plasma operation, scheduled for mid-Feb. 1999.

[KP01.35] Application of SVD to find coils for NCSX

The problem of ``reverse engineering'' suitable coils for the promising low-aspect-ratio quasi-symmetric configurations is important and challenging. A fast green's function method is often used (NESCOIL(P. Merkel, Nucl. Fusion 27, 867 (1987))) in the initial design of such coils. We present a modification of this method where we use singular value decomposition (SVD) techniques to obtain good coils even when the standard NESCOIL code fails to yield an answer. This

modification allows us to reduce the ``complexity'' of coils without significantly increasing the ``error'', i.e., the difference between the

initial plasma configuration and the plasma shape produced by these coils. This method has been successfully applied to both the quasi-axisymmetric

and the quasi-omigeneous configuration being studied for the National Stellarator Program.

[KP01.36] Calculation of resonant errors and their suppression for NCSX

The design of the National Compact Stellarator Experiment (NCSX) is being done in three steps. First, an optimized equilibrium is obtained using the VMEC(S.P. Hirshman and J.C. Whitson, Phys. Fluids \textbf26) 3553 (1983). code. Next, using the NESCOIL (P. Merkel, Nucl. Fusion \textbf27), 867 (1987) code, a surface current potential K is computed which minimizes (in a least-squares sense) the normal component of the magnetic field on the plasma surface. The coils are obtained from this potential. Finally, having obtained a coil set, the magnetic field generated by the coil set

is given as input to VMEC to see if the original equilibrium can be reconstructed. Often, if the field errors are small (<2%), the original equilibrium configuration can be recovered. Sometimes, even when the field errors are small, the reconstructed surfaces depart significantly from the physics target. This reconstruction error is thought to result from resonant components of the normal field errors introduced by the discretization of K. The calculation of these errors and their suppression for NCSX will be discussed.

[KP01.37] The theory of 3-D equilibrium

New, Reference Magnetic Coordinates (RMC), are proposed for 3-D MHD. Because of intrinsic anisotropy of high temperature plasma with respect to magnetic field, use of proper coordinates is of highest priority for both theory and numerical methods. While in axisymmetric case, the poloidal flux function \Psi(r,z)=const determines proper flux coordinates, in 3-D, such a function does not exist, and both theory and numerical methods have difficulties in describing 3-D magnetic fields. At the best, they rely on numerical technique of the field line tracing in order to describe the magnetic field. But this approach in incapable to resolve principal problems of 3-D MHD, such as a) self-consistent calculation of 3-D equilibria, b) the problem of S-parameter, and c) the problem of fast magneto-sonic waves. Here, we present the fast algorithm of construction of RMC, which are the most suitable for high-temperature MHD. As one of applications of RMC, the rigorous theory of 3-D equilibrium is formulated, which is not restricted by assumption of existence of the flux surfaces.

[KP01.38] Stellarator Coil Optimization in Three-Dimensions

The NESCOIL code [P. Merkel, Nucl. Fusion 27, 867 (1987)] can be used to determine both current sheets and discrete coils which can approximately match a prescribed distribution of | B |^2 on a plasma/vacuum interface, subject to the constraint B \cdot n = 0 (where n is the surface normal). The optimization of the coils in three dimensions is done by discretizing them into many connected filaments which are varied to match various physics and engineering constraints. This process is both time consuming and overly restrictive, since the coil topology is frozen-in and determining by the initial set of filaments. We describe a new optimization technique, in which the rapid (current-sheet) version of NESCOIL is embedded in a Levenberg-Marquardt numerical optimizer. This technique permits coil topology changes and can be used to find coils which satisfy engineering criteria of interest (current density limits, field on coil, coil-to-plasma separations, coil complexity and curvature). Application of this procedure to designing coils for the NCSX will be described.

[KP01.39] High Performance VMEC Optimizer

An MHD equilibrium solver which includes optimization for particle confinement and stability is being developed for parallel architecture. The VMEC (Variational Moments Equilibrium Code) code solves three-dimensional MHD (magnetohydrodynamic) equilibrium equations using Fourier Spectral (Moments) Methods. The optimizer version of VMEC takes this equilibrium and evaluates it relative to certain target goals (e.g., aspect ratio, \beta). Quasi-omnigeneous stellarator (QOS) configurations have been found using the VMEC optimizer.(S. P. Hirshman, et al., Phys. Rev. Lett.) 80, 528 (1998). QOS configurations achieve good confinement by alignment of J-surfaces with flux surfaces. Currently the code is being modified to include COBRA(R. Sanchez, et al., Bill. Amer. Phys. Soc.) 43, 1678 (1998). (COde for Ballooning Rapid Analysis) in order to include ballooning stability in the optimization procedure. Due to the increased memory and CPU requirements, a new version of the code is being developed for parallel architecture using High Performance Fortran. The parallel code will be implemented and tested on the Cray T3E's at NERSC (National Energy Research Scientific Computing Center).

[KP01.40] Ideal ballooning stability optimization of QOS equilibrium configurations

Recently, a ballooning code (COBRA, R.Sanchez, et al, Bull. Am. Phys. Soc. 43 (1998) 1678) has been developed and intensively benchmarked to evaluate fast and accurately the ideal ballooning stability of general three-dimensional configurations. A combination of matrix and variational techniques coupled to Richardson's extrapolation method is responsible for the noticeable increase in efficiency respect to other existing codes. COBRA has been now included into the optimization suite used in the design and optimization of the QOS concept exploration device planned as part of the US NCSX program (S.~P.~Hirshman, et al, to appear in Phys.Plasmas (1999)). By means of this new tool, the maximum average \beta is expected to be increased for existing configurations while, at the same time, new parameter regions of the optimization space could be identified and explored.

[KP01.41] Physics Issues in the Design of the National Compact Stellarator Experiment

This poster will discuss the status of the configuration design for the National Compact Stellarator Experiment (NCSX), and related physics issues. The NCSX design incorporates the following key physics features: 1) Optimized drift trajectories and low neoclassical toroidal viscosity in a low aspect ratio configuration via quasi-axisymmetry; 2) Good ballooning stability properties produced by strong n=0 components of triangularity and ellipticity; 3) Stabilization of the external kink mode in the absence of a conducting wall produced by externally generated shear and appropriate three-dimensional shaping; 4) Neoclassical suppression of magnetic islands (monotonically increasing iota); 5) Configurational robustness produced by a substantial externally generated transform. The trade-offs required for incorporating all of these features in a single configuration will be discussed, and the most recent optimized designs incorporating the features will be described. The impact of the constraints associated with retrofitting PBX to produce such a device will also be discussed.

[KP01.42] NCSX Calculations with the PIES Code

The PIES( Reiman, A.\,H., Greenside, H.\,S., Compt. Phys. Commun. 43), (1986). code has the ability to start its iteration scheme using VMEC(S. P. Hirshman, D. K. Lee, Comput. Phys. Comm. 39), 161 (1986). magnetic fields as the initial guess for its magnetic field. Using the VMEC fields as the initial guess significantly reduces the number of steps to convergence. We have recently modified PIES to be able to use the VMEC currents as the initial guess rather than the fields. This means that PIES can be used as a field line following code using coil currents and plasma current as the source function. We are hoping that this will aid us in resolving reconstruction problems that have surfaced in the design of NCSX. The results of this and other PIES applications to NCSX will be presented.

[KP01.43] Calculation of the Vertical Instability for Quasiaxial Stellarators

As part of a multifaceted effort to design an interesting high performance symmetric stellarator, MHD stability is being investigated with the CAS3D code(C.Schwab, Phys. Plasmas \bf3), 2401 (1996).. Instabilities and their stabilization are being studied in several quasiaxially-symmetric stellarator (QAS) configurations corresponding to a modest size experiment with R=145 cm, B=1-2 T. CAS3D has been used to calculate the internal mode structure and instability growth rates for a two field period QAS with 20% external transform(M.H.Redi, et al.,) Sherwood Theory Meeting, Atlanta, GA (1998).. The growth rates and the identification and ordering of the largest Fourier mode components, are in good agreement with calculations of the TERPSICHORE code( W.A.Cooper, et al.), Phys. Plas. \bf3, 275 (1996).. Results of benchmarking CAS3D for the external kink (N=1) against TERPSICHORE and the PEST code for a toroidally symmetric tokamak will be presented along with progress in calculating the vertical instability (N=0) for promising QAS designs.

[KP01.44] A 3D Newton MHD Equilibrium Code with Application to the NCSX Stellarator

A recent major extension of the PIES 3D MHD equilibrium code has enabled the use of a form of Newton's method, in (\mathbfJ, \mathbfB) space, to speed convergence. The new algorithm first solves the force balance equation for the current density \mathbfJ, given the latest approximation to the magnetic field \mathbfB. It then applies Newton's method to Ampere's Law by expansion of the functional \mathbfJ(B), which is defined by the first step. Thus the quantity (\partial \mathbfJ/ \partial \mathbfB)\cdot \delta \mathbfB is the gradient term analogous to \nabla \mathbff \cdot \delta \mathbfx in the standard Newton method for \mathbff(x)=0. The algorithm is computationally feasible because the Newton gradient term can be calculated analytically in magnetic coordinates, and is local to a magnetic flux surface when expressed in terms of a vector potential in the A_\rho=0 gauge. Newton's method is expected to provide a significant advantage over Picard (simple) iteration in the computation of finite \beta equilibria with net toroidal current, for the NCSX stellarator.

[KP01.45] Plasma Transport and Energetic Particle Confinement Studies in Low Aspect Ratio Quasi-Omnigenous (QO) Stellarators

Quasi-omnigenous (or drift orbit-optimized) stellarators have recently been designed at low field periods (N_fp = 3,4), low aspect ratio (A = 3 - 4), low bootstrap current fraction, and high ranges of rotational transform (i = 0.5 - 0.8). Continuing improvement of these devices is underway and is guided by accurate evaluation of their physics characteristics. For confinement studies, we use a Monte Carlo model (DELTA5D) which follows ensembles of guiding center trajectories through 5-dimensional phase space (\Psi,øminus,\zeta,v_\|/v, and energy). Different particle initializations appropriate to thermal plasma, ICRF heated tail ions, and alphas in reactors have been developed and diagnostics include: local diffusivities, global losses, bootstrap current (using low noise \deltaf weightings), and loss patterns of particles exiting the outer flux surface. Application of this model to QO devices has demonstrated that they can achieve good core transport (\tau_E^neo\approx 2-3 \times \tau_E^ISS95) and sufficient confinement of energetic tail populations for efficient heating. We will discuss the transport characteristics of a variety of QO configurations of current interest.

[KP01.46] Particle transport in three dimensional omnigenous equilibria

Omnigenity(J.~R.~Cary and S.~G.~Shasharina, Phys.~Rev.~Lett. \mbox78), 674 (1997). is a property where the bounce averaged drift trajectories lie on magnetic surfaces, implying small net radial particle transport. Compared with quasi-helical configuration where the magnetic field strength is constrained with a single helicity \exp i \left(m \theta - n \phi \right), omnigenous configurations allow greater freedom in the magnetic field spectrum. As a preliminary work, the formation of the magnetic surface is investigated by generalizing the method by Garren (D.~A.~Garren and A.~H.~Boozer, Phys. Fluids B \mbox3), 2805 (1991). to omnigenous systems, which compares the numbers of the free parameters and the constraints in Boozer coordinates, in each \epsilon \sim \sqrt\psi order expansion. The analytical results and neoclassical particle trajectories for corresponding magnetic structures will be presented. This research is supported by U.S DOE grant no. DE-FG003-95ER54297.

[KP01.47] Transport in Quasi--Axisymmetric Stellarators

We describe the current status of confinement studies of the quasi--axisymmetric stellarators (QASs) the NCSX physics team has been developing. We are evaluating two basic options to embody the QAS concept, (a) an aspect ratio A=3.4 design which would use the PBX vacuum vessel and TF coils, and (b) an A\sim 2.8 configuration which would not fit into PBX, whose lower A should enable it to regain the superior confinement performance of a very compact (A=2.1) family of QASs studied earlier, assisted by new tools the NCSX group has developed to at the same time achieve good stability and engineering characteristics. In this effort, we are beginning to make use of the GTC global gyrokinetic code,(Z. Lin, T.S. Hahm, W.W. Lee, W.M. Tang, R.B. White, Report PPPL-3302, (May, 1998).) which can be used both as a very fast guiding--center code to study 3D neoclassical transport, as well as self--consistent field effects.

[KP01.48] Bootstrap Current Resonances

Expressions for bootstrap current in stellarators commonly given in the literature possess resonances at rational surfaces, arising from large excursions of toroidally trapped particles in the low collision frequency regime. It is shown that these resonances are due to an improper neglect of particle collisions, and that for typical plasma parameters the excursions do not exceed the normal banana width. Simulations of bootstrap current using a Monte-Carlo \delta f technique are carried out in simple model equilibria and in a period two numerical stellarator equilibrium and the results are analyzed.

[KP01.49] Investigation of a kinetic energy principle in three dimensional geometry

To investigate the influence of fast particles on the stability of MHD equilibria kinetic effects have to be considered. Since it has been shown recently that the variational CAS3D code sucessfully describes Alfvén waves in three-dimensional equilibria this code will be extendend to include kinetic effects.

A drift kinetic equation is linearized and solved in three-dimensional geometry with a full electromagnetic perturbation. From this a generalized energy principle is derived. The time scale is drift-kinetic so that the resulting kinetic term contains resonances with bounce, transit and bounce-averaged drift frequencies of the hot particle population.

The energy principle is quadratic with respect to the perturbation and the force operator is not self adjoint and depends on ømega. This destabilizes otherwise stable MHD modes. Initially, growth rates and frequency shifts are estimated via a perturbative solution of the eigenvalue problem.

[KP01.50] Particle Transport Study with Tracer-Encapsulated Solid Pellet Injection

In order to promote particle transport studies, the concept of a tracer-encapsulated cryogenic pellet : TECPEL has been proposed. The concept is based upon the production of a both poloidally and toroidally localized particle source as tracers. After this, a tracer-encapsulated solid pellet : TESPEL is proposed. While TECPEL consists of a hydrogen isotope as an outer part and low Z material as an inner core, TESPEL consists of polystyrene as an outer part and LiH as an inner core. Therefore, TESPEL can be handled at room temperature. For proving the concept of the new diagnostics, TESPEL is injected into a neutral-beam-heated plasma of the Compact Helical System. The results from CHS have shown the successful local deposition of the tracer, and the behavior of tracer particles deposited locally in the plasma core region is also observed by a method of charge exchange recombination spectroscopy. Therefore, our new diagnostic concept has been proven for the first time from the viewpoints of both the production method of TESPEL and the observation of the tracer particle behavior.

[KP01.51] MHD Stability Calculations in Compact Quasi-axisymmetric Stellarators

This work investigates the key stability issue of beta limiting bootstrap current-driven external kink modes as well as pressure-driven ballooning modes in quasi-axisymmetric stellarators (QAS)(G.Y. Fu et al., the 1998 IAEA Fusion Energy Conference). The 3D MHD code TERPSICHORE(W.A. Cooper, Phys. Plasmas 3), 275(1996) is used to calculate the stability of low-n external kink modes. The results show that the external kink modes can be stabilized at high beta (\sim 5%) without conducting wall by combination of edge magnetic shear and 3D plasma boundary shaping. In contrast, the equivalent tokamaks with high bootstrap fraction have much lower beta limits. The physics mechanism for the kink stability is being studied by examining the contributions of individual terms in \delta W of the energy principle. Initial results show that the plasma current is the main driving force while the pressure gradient also plays a significant role. Methods have been successfully developed that enable us to simultaneously maximize the kink stability, ballooning stability and quasi-axisymmetry. High beta, MHD stable plasmas configurations have been obtained by the optimal choice of boundary shape as well as plasma pressure and current profiles. Details of parameter dependence of kink and ballooning stability and robustness of the stability limits will be reported.

[KP01.52] 3D MHD Simulation Studies of Pellet Injection, Halo Current, Runaways, and Stellarator Equilibrium

The MH3D++ unstructured mesh version of the MH3D code was used for tokamak disruption simulations. (H. Strauss et. al), IAEA-F1-CN-69/TH3/4, Yokohama (1998) We have studied the effect of 3D pressure perturbations caused by pellet injection on MHD stability. The pellet pressure perturbation can trigger ballooning like modes, which might explain recent experimental results (D.G.Whyte et. al), Phys. Rev. Lett. 81, 4392 (1998). It is found that pellets on the high magnetic field side require a higher beta for instability, as well as leading to more localized instabilities. We have also studied kink instabilities in the thermal quench phase of tokamak disruptions. We used a thin resistive wall boundary condition, and included an ITER relevant model of runaway electrons formed by avalanching. We will present calculations of halo current and runaway electron toroidal asymmetry due to nonlinear external kink modes. The MH3D++ code has been extended to have the capability of using a 3D mesh in configuration space, suitable for stellarator equilibrium and stability studies. Equilibria can be initialized with VMEC output or generated from initial data. Examples of stellarator computations will be presented.

[KP01.53] A Simple Model for Transport in an RFP

The present work describes a simple model for determining the energy confinement time in a reversed field pinch (RFP). The model is motivated by the idea that the region interior to the Bz reversal point is in a highly turbulent state resulting from tearing mode instabilities. It has been suggested, in fact, that the profiles adjust themselves so as to be in a state of nearly marginal stability against tearing modes. This conjecture further suggests that one approach to deduce the energy confinement time in an RFP is to determine the marginally stable profiles, consistent with MHD pressure balance, and use these profiles to evaluate tau using the standard definition. This somewhat heuristic approach is obviously less rigorous than a self consistent calculation of anomalous thermal conductivity and the resulting implied profiles, but is, nevertheless, much simpler to implement.

The original goal of the research was to develop the "marginally stable tearing mode" transport model. Even with such a simplified approach, it soon became apparent that a significant level of computational work would be required to determine profiles that were marginally stable to tearing modes. As a prelude to this work, it was decided to first develop a framework and formulation of the calculation based on a simpler local marginal stability criterion, the Suydam criterion. Once the analytic and computational machinery were set up, the more complicated, non-local tearing mode criterion would be implemented. The original expectation was that the Suydam criterion model, based on ideal MHD, would be more optimistic than the tearing mode model based on resistive MHD.

The calculation based on Suydam’s criterion has been completed. Somewhat to our surprise, the expression for tau agrees remarkably well with the existing experimental data in terms of both scaling and magnitude. This unexpected result is the motivation for the present paper. Details of the calculation and results will be presented at the meeting.

[KP01.54] Effects of DC Electric Field and Radial Transport on LHCD in the RFP

A series of lower hybrid (LH) experiments is being started on the MST RFP with an ultimate goal of improving plasma confinement via current profile control. To facilitate this endeavor, we are enhancing the capability of the RFP version of ray-tracing and Fokker-Planck simulation codes (GENRAY and CQL3D). This paper will focus on numerical studies of two physical effects: DC electric field and radial transport. The electric field may increase the current drive (CD) efficiency by a synergetic effect with LH waves, as well as by the knock-on, large-angle scattering process (V. S. Chan et al., in Proc. of ISPP, Varenna, Italy, 1998.). This is modeled with DC electric field and knock-on source terms in the bounce-averaged Fokker-Planck equation. On the other hand, moderately large radial transport in the RFP has adverse effects on LHCD. This is being studied by adding a velocity dependent radial diffusion term along with a pinch term which ensures particle conservation.

[KP01.55] The search for optimized RFP equilibria

To the present knowledge, the most fundamental issue for RFP confinement devices is, in a proper sense, the existence itself of such MHD quasi-equilibria [1]. The purpose of this paper is carry out a kinetic analysis of the conditions of their existence and analyze optimization criteria capable of extending their lifetime. In addition, the role played by toroidal and poloidal rotation, strong equilibrium drift, as well as of external sources (such as pellet injection, neutral beams, etc.) is investigated. References 1 - D.Gregoratto and M.Tessarotto, Bull.Am.Phys.Soc. 41, 1491 (1996).

[KP01.56] Single and multiple helicity states in the Reversed Field Pinch

This work unveils new features of the single helicity (SH) ohmic states of the cylindrical RFP in the framework of resistive MHD at zero pressure, and of their connection with the multiple helicity (MH) states. It is shown that since \mu = \fracj_\parallelB reverses in RFP SH states, the Grad-Shafranov equation in helical coordinates generally yields solutions with a minimum of \mu in the center of the plasma. The finite radial magnetic field associated with these helical equilibria turns out to be necessary to satisfy Ohm's law, as required by Cowling theorem. It is shown that there is no need for a dynamo acting at field reversal, in agreement with the dynamo velocity pattern found in SH resistive MHD simulations. The diagram of the bifurcation between MH and quasi SH (QSH) states controlled by the Prandtl number is revisited, and the importance of the Lundquist number is emphasized. The role of these QSH states in improving the transport properties of the RFP is analyzed by comparing the level of stochasticity of the magnetic field in the MH and QSH cases computed by numerical simulation.

[KP01.57] The Physics of Enhanced Confinement Regimes in the Reversed Field Pinch

We present a transition scenario for the spontaneous Enhanced Confinement (EC) regime observed in the Madison Symmetric Torus (Chapman, et al., Phys. Rev. Lett.) 80 2137 (1998) which is based on the combination of global magnetic turbulence and localized flow shear. It appears that the key physics leading to ECs is the spontaneous generation of a turbulence-suppressing shear flow outside the reversal layer. The stabilizing influence of this flow shear has been investigated both analytically and numerically for arbitrary current profiles, and thresholds for stabilization are obtained. We propose that the emergence of the shear flow is related to the generation of magnetic Reynolds stresses during the excitement of high n, ømega_*-tearing modes in a sawtooth crash. This effect could be explained and quantified using a model based on the reduced MHD equations.(Strauss, Phys. Fluids B) 4 (1) 3 (1992) The increase in Re \langle \tildeB_r \tildeB_\theta \rangle is related to the induction of a large imaginary part in the relevant eigenfunction by the combined effect of diamagnetism and shear flow. After the crash the role played by the Reynolds stress in driving the edge flow is taken over by the steepened pressure gradient created by suppression of turbulence, and the enhanced confinement is maintained. Key elements of the theory are compared with experimental observations.

[KP01.58] The Effects of Geometry and Current Drive on Turbulence in the Reversed Field Pinch

Using the initial value toroidal resistive MHD code, TRIM (D.~D.~Schnack, I.~Lottati, Z.~Miki\'c, and P.~Satyanarayana, \textbf140), 71 (1998), the nonlinear behavior of a plasma in the reversed field pinch configuration is simulated at several aspect ratios, elongations, and ellipticities. Convergences to the spheromak and infinite cylinder will be discussed. Variations in the number of excited modes and their amplitudes are compared with known results for cylindrical geometry(Y.~L.~Ho and D.~D.~Schnack, Phys. Plasmas, \textbf2), 9, 3411 (1995). Those results showed that the spectrum narrows at lower aspect ratio but neglected the toroidal coupling which becomes stronger at lower aspect ratios. In addition to geometric effects, we have begun a study on current profile control of RFP turbulence. A ray-tracing Fokker-Planck code package (GENRAY and CQL3D) (E. Uchimoto, et al., Proc. 1998 Sherwood Fusion Theory Conf., (March 23--25, 1998; Atlanta), paper 2C11) has been coupled to TRIM by means of an ad hoc term in the momentum equation. Preliminary results of current profile modification are presented.

[KP01.59] Spectroscopic Measurement of Plasma Flow Fluctuations and the MHD Dynamo in a Laboratory Plasma

The MHD dynamo has been directly measured in a high-temperature laboratory plasma. The MHD dynamo is a nonlinear mechanism by which correlated fluctuations in plasma flow velocity and magnetic field generate or sustain an equilibrium magnetic field. MHD dynamo activity has been proposed as the mechanism which produces the magnetic fields observed in starts, planets, and astrophysical plasmas. In laboratory reversed-field pinch (RFP) plasmas, the MHD dynamo is believed to be the primary mechanism which maintains the magnetic configuration against resistive decay. Plasma flow fluctuations have been quantitatively measured in the Madison Symmetric Torus (MST), a large RFP device, by time-resolved recording of Doppler-shifted impurity line emission. Well-correlated velocity and magnetic fluctuations are found to produce an emf which sustains the RFP magnetic field configuration.

Work supported by U.S.D.O.E.

[KP01.60] Control of Magnetic Fluctuations and Transport in the MST Experiment

A toroidal, magnetized plasma known as the reversed-field pinch exhibits fluctuations in the magnetic field which confines the plasma. Although the fluctuations are relatively small, about one percent of the equilibrium field, they can have two major macroscopic consequences: (1) the spontaneous generation of current and magnetic field (the dynamo effect) and (2) the production of energy transport across the plasma through the formation of chaotic magnetic field lines. The fluctuations are understood to be generated by spatial nonuniformity in the plasma current. Thus, it is expected that control of the equilibrium current profile will suppress magnetic chaos, and the transport associated with it. Suppression of magnetic chaos and transportis desirable to (1) controllably investigate the relation between fluctuations and transport and (2) advance the reversed-field pinch as a fusion energy concept. In the MST experiment current profile control has been implemented by inductive and electrostatic current drive techniques. To date the effects of current profile control are large - a two-fold reduction in fluctuation amplitude and a five-fold reduction in transport. A powerful link between magnetic chaos and transport is implied.

[KP01.61] The "Kinetic Tandem" Concept: Analysis and Computer Simulation*

Open-ended fusion systems have many desirable features. Their main disadvantage: end losses. In the kinetic tandem, with its solenoidal confining field tapering up from each end, plugging is accomplished in an intrinsically MHD-stable magnetic field configuration, one free from the cross-field drifts of non-symmetric fields: Operation is as follows: Ion beams from sources near the ends are compressed, stopped, and reflected part way up the magnetic gradient, forming density peaks. As in the TM, potential peaks arise, plugging ion losses. Electrons are confined by the same potential, in a situation where the field expansion ratio (out to the end wall) exceeds a critical value. In this case, studied by Mirnov and Ryutov [1], trapped electrons are decoupled from the ends and electron-channel losses are orders of magnitude lower than thermal conduction. Analyses and computer simulations of the generation of kinetic tandem plugs will be presented. 1) V. V. Mirnov, D. D. Ryutov, in Itagi Naukii Tekniki Fisika Plasmy, (V.D. Shafranov, Ed.) Moscow, Vol. 8, p. 77 (1988)

[KP01.62] High-Resolution Simulations of Merging Spheromaks

Fundamental properties of magnetic reconnection in merging co- and counter-helicity spheromaks are investigated using an implicit parallel resistive MHD code. Variable mesh spacing together with an implicit time-stepping algorithm allows resolution of both the global solution and reconnection layer in a single simulation. We present results of scaling studies of the dependence of the reconnection rate, the height and width of the current sheet, and the magnitude of the outflow velocity over a wide range of plasma resistivity and viscosity. The nature of the boundary layer and separatrix regions observed in the simulations are compared with recent theoretical models[1]. Particular attention is paid to the effect of the plasma pressure equation, the background toroidal field strength, and the associated plasma compressibility on the shape of the separatrix surface near reconnection layer. This work supported by DoE Contract DE-AC02-76CH03073.

[1] D. Uzdensky, R. Kulsrud, , Phys. Plasmas 4 (1997) pp. 3960-3973

[KP01.63] Simulation of Spheromak Edge Plasmas

The 2-D edge-plasma transport code UEDGE is being used in simulations of the SSPX spheromak(E.B. Hooper, et al., 17th IAEA Fusion Energy Conference, Yokohama, Japan, October 1998; to be published.) at LLNL. The code contains a classical model for field-aligned edge currents which are fundamental to forming the magnetic configuration(E.B. Hooper, R.H. Cohen, D.D. Ryutov, 13th PSI Conference, San Diego, CA, May 1998; to be published.). Initial simulations compute the edge currents in a fixed magnetic configuration to assess 2-D effects associated with neutral gas injection and recycling. Ion and neutral species are represented by fluid equations for mass, momentum and energy balance in the edge plasma. Hydrogenic and impurity radiation are included in the model. A detailed treatment of surface physics such as sputtering, secondary electron emission and sheath potentials will be implemented, together with a simple model for cross-field transport from the expected tearing-mode magnetic turbulence. Ultimately, the goal is to couple this edge model to a time-dependent MHD/core transport code such as CORSICA for a self-consistent description of spheromak configurations.

[KP01.64] Simulation of Pulsed Reflectometry in the SSPX Spheromak

A short-pulsed reflectometry system is being deployed on the Sustained Spheromak Physics Experiment (SSPX) at LLNL. Detailed computational modeling is presented addressing the use of pulsed reflectometry to reconstruct electron density and mod-B magnetic field profiles, and the use of linear mode conversion from extraordinary to ordinary modes induced by magnetic shear to infer the magnetic pitch-angle profile. The robustness of these diagnostics in the presence of plasma fluctuations is a key issue. Two-dimensional effects, e.g., microwave beam spreading and scattering and refraction due to plasma inhomogeneities are investigated. Data analysis techniques for use in both the simulations and SSPX are presented.

[KP01.65] Centrifugally Confined Plasmas: An Alternative Concept for Fusion

Magnetic confinement schemes in which the centrifugal forces of rotating plasma effect parallel confinement are assessed. The magnetic field is predominantly poloidal and could be mirror-like or multipole type. The rotation is toroidal. A supersonic rotation can effect complete parallel confinement, with the usual magnetic mirror force rendered irrelevant. The rotation, in addition, suppresses the flute mode. We show that supersonic rotation shear together with plasma elongation could result in almost complete or complete suppression. Any residual wobbles, observed in numerical simulations we will show, could be suppressed by a weak toroidal field. Likewise, the Kelvin-Helmholtz, at worst weakly growing in this geometry, could be suppressed by the weak toroidal field. The transport is also assessed. We show that at rotation speeds in excess of Mach 3.5, the parallel particle and heat losses can be minimized to below the Lawson breakeven point. The crossfield transport can be expected to be better than tokamaks on account of the large velocity shear. Broadly speaking, the plasma rotation constitutes an additional "knob" for purely magnetic confinement schemes with the result that centrifugal confinement schemes could feature four advantages over tokamaks: steady-state, disruption-free, superior confinement, and a simpler coil configuration. A disadvantage is the circulating power required to maintain the rotation. An exploratory experiment to test equilibrium, parallel detachment, and MHD stability has been proposed [1]. Earlier centrifugal confinement experiments - "homopolar generators", IXION, and experiments at Novosibirsk - will be discussed.

[1] MARYLAND CENTRIFUGAL TORUS: An Experiment to Test Centrifugal Confinement of Fusion Plasmas, R. F. Ellis and A. B. Hassam, ICC Workshop, PPPL, Princeton (1998).

[KP01.66] Profiles and Impurity Control in Advanced Fuel Levitated Dipole Reactors

The levitated dipole configuration offers the possibility of confining a high beta plasma in a configuration which is steady-state and disruption free. Classical confinement may be achieved, and it would permit ignition of advanced fuels in small devices. Other possible advantages of dipole reactors include the outward convection of ash and a natural low-power-density divertor. Convective flows could provide a low ratio of particle to energy confinement times, minimizing the ash accumulation that severely impacts other fusion concepts using advanced fuels. Because of the high-\beta, long energy confinement and good ash removal characteristics, this configuration is ideal for reactors burning hard-to-ignite advanced fuels. In this poster, calculated self-consistent plasma profiles (density, temperature and pressure) will be described. The plasma energy transport near the ring is assumed to be near classical (assuming that the limits of the universal instability are not violated). The outer plasma transport is determined from MHD stability requirements, assuming a marginally-stable pressure gradient. In addition, schemes to decrease the device size will be examined. D-^3He fuel will be emphasized.

[KP01.67] Plasma Confinement in a Levitated Dipole Configuration; the LDX Experiment

The levitated dipole configuration offers the possibility of confining a high beta plasma in a configuration which is steady-state and disruption free. The concept may permit the outward convection of ash and provides a natural low-power-density divertor. Additionally, we have shown that drift frequency fluctuations will be stable(Kesner, Phys Plasmas 4) (1997) 419; 5 (1998) 3675. so that we might expect near-classical confinement. The requirement of a superconducting ring internal to the plasma makes this approach compatible with an advanced fuel (i.e. D-^3He) fusion cycle.

We are in the process of constructing a small levitated dipole experiment, LDX as a joint project between MIT and Columbia University. The experiment will utilize a superconducting ring of approximately 0.8 m diameter and levitated within a 2.5 m radius vacuum chamber. MHD theory predicts that the peak pressure is related to the edge pressure by the flux expansion, i.e. p_max/p_edge =(V_edge/V_max)^\gamma with V=øint dl/B and \gamma=5/3 and we have designed LDX to obtain p_max/p_edge>10^4. We will also discuss schemes to further enhance the plasma pressure including H-mode-type pedestals and scrape-off-layer heating.

[KP01.68] Equilibrium of a Self-Gravitating Plasma in a Dipole Magnetic Field

We consider the equilibrium of a gravitating plasma in dipole magnetic configuration. Such a problem may be of interest for the study of the physics of accretion disks and galaxy formation. We derive an analog of the Grad-Shafranov equation describing the equilibrium of a self-gravitating plasma in a dipole magnetic field. We demonstrate that in some particular cases the form of the equation allows us to find solutions for the magnetic flux in a self-similar form. We discuss the solutions of Grad-Shafranov equation for the case of both weakly and strongly gravitating plasmas. In the former case we use the solutions found in Ref. 1 for a non-gravitating finite pressure plasma equilibrium in a magnetic dipole as a zero-order approximation. [1] P. J. Catto, R. D. Hazeltine, and S. I. Krasheninnikov, submitted to PRL.

[KP01.69] Two-Fluid Equilibria with Flow

The observation of significant flows in magnetic confinement systems has generated renewed interest in equilibria with flow. Improved stability and transport have been variously attributed to these flows. This may be the result of equilibria near the minimum state of magnetofluid (magnetic + flow) energy, as predicted by two-fluid theory.* To facilitate future studies of the stability and transport of axisymmetric two-fluid equilibria, the formalism for such equilibria is developed. The characteristic surfaces are found to be the guiding center surfaces, which differ slightly (particle inertia) from the magnetic surfaces (constant magnetic stream function). Each species has its own family of surfaces. Assuming a reasonable equation of state (either barotropic or isothermal surfaces), quasineutrality, and massless electrons, it is shown that two-fluid equilibria are governed by a system of equations composed of two second order partial differential equations for the magnetic and ion flow stream functions, plus an auxiliary “Bernoulli” equation for the density. The system includes six arbitrary surface functions (three for each species). This system is more complicated than the Grad-Shafranov system (one-fluid, nonflowing equilibrium) which has one second order equation for the magnetic stream function and only two arbitrary surface functions. In the case of states of minimum energy, the six surface functions are no longer arbitrary, but take on a particular forms that depend on the Lagrange multipliers that are introduced in the constrained minimization procedure. Examples of two dimensional equilibria are presented for a compact (singly-connected) geometry. These examples apply to compact toroid configurations such as spheromaks and FRCs. In addition, astrophysical examples are considered. This very high-beta case requires only the inclusion of the gravitational potential in the system of equations.

*L.C. Steinhauer and A. Ishida, Phys. Rev. Lett. 79, 3423 (1997); Phys. Plasmas 5, 2609 (1998)

[KP01.70] Kinetic Studies of the Formation and Stability of Field-Reversed Configurations

Field-Reversed Configurations (FRCs) are compact toroidal plasmas confined by poloidal fields. The external field is reversed on axis by diamagnetic current carried by either thermal particles or energetic ions. The latter configuration is known as the Ion Ring Configuration (IRC). Hybrid systems have also been proposed. One of the distinct FRC features is the existence of a magnetic null point in the vicinity of which ion Larmor radii are finite. Thus, kinetic effects play an essential role in the formation and equilibrium of such configurations. Since the typical Alfvén and ion cyclotron frequencies in the FRC are comparable, ions can be modeled as full-orbit macroparticles. Using a \hbox3-D, hybrid, Particle-in-Cell code, FLAME(Y.A. Omelchenko and R.N. Sudan, J. Comp.\ Phys.\ 133), 146 (1997).\ we have studied the formation and compression of an IRC under experimental conditions.(Y.A. Omelchenko and R.N. Sudan, Phys.\ Plasmas 2), 2773 (1995). We also report results obtained by simulating the field-reversed theta-pinch formation and kinetic tilting of FRCs.

[KP01.71] Dynamical stabilization of the internal tilt mode in field-reversed configuration plasmas by rotating magnetic fields: a physical picture

It is suggested that rotating magnetic fields (RFM) can provide dynamic stabilization of high-s reversed-field-configuration (FRC) plasmas against the internal tilt mode. The approximate stability criterion is (w B_w L)/B_a > V_A, where w is the angular frequency of the RMF, B_w is its amplitude,B_a is the amplitude of the static axial field, L is the length of the FRC, and V_A is the Alfven speed. This is compared with constraints set by current-drive and magnetic field penetration and circulating power power requirements.

[KP01.72] 3D, Two-Fluid Simulation of FRC Plasmas

First results of 3D, two-fluid, nonlinear simulations of FRC plasmas are presented. The runs are aimed at investigating the FRC stability in connection to previous theoretical work, based on a two-fluid formulation, that predicts a relaxed equilibrium state with flows [1]. The NIMROD code is applied to low-s FRC plasma (where s is the ratio between the FRC "minor radius" and the ion gyroradius) both in the MHD and two-fluid mode. The MHD calculation is intended as a benchmark with previous results that show the development of tilt instabilities [2], [3]. The tilt modes have not been observed in laboratory FRC's, however experiments at larger "s" (reactor scale range) are needed. Simulation results analyzing different FRC scenarios that include variations of the "s" parameter and the effect of plasma rotation are presented.

[1] L.C. Steinhauer, A. Ishida, Phys. Plasmas 5, 2609 (1998)

[2]A. Tarditi, D.D. Schnack, Proc. US-Japan Work. on Phys. of High Beta Fus. Plasmas, Seattle, WA, March 1998

[3]R. D. Milroy et al., Phys. Fluids B 1 (6), p. 1225 (1989)

[KP01.73] FRC stability study using hybrid MHD/kinetic simulations

A nonlinear 3D code in cylindrical geometry is being developed forthe stability studies of FRC.Two numerical schemes have been implemented: a hybrid scheme with particle ions and fluid electrons, and MHD/particle scheme in which background plasma is described by MHD equations and energetic ions are treated using particle simulations. MHD equations are advanced on a finite difference mesh in a cylindrical coordinate system, while particle pushing is done on a 3D Cartesian grid. Full ion dynamics is retained in order to include large-orbit effects (with s \sim 1), which are important for the tilt mode stabilization in FRC. In contrast to the previous work\delta f method is utilized to reduce numerical noise in the simulations. The code will be applied to the study of 2D axisymmetric equilibrium configurations and for 3D simulations of kinetic stabilization of the tilt mode in FRC.

[KP01.74] Kinetic Calculations for POPS

Previous work(D. C. Barnes, R. A. Nebel,Physics of Plasmas 5, 2498 (1998)) has demonstrated the existence of a self-similar oscillating ion solution which remains in local thermodynamic equilibium at all times during an oscillation. These solutions have flat temperature profiles and Gaussian density profiles as a function of radius.Here we show that these solutions are unique for a one-dimensional spherical plasma However, in a real device the Gaussian will be truncated due to the presence of a wall or conductor. Here we present PIC simulations which compare this truncated Gaussian with the Gaussian solutions as well as a second self-similar sharp boundary solution.(R. A. Nebel, D. C. Barnes, Fusion Technology 38, 28 (1998)) Results show a favorable comparison between the truncated Gaussian and the Gaussian profile, but substantial differences between these two and the sharp boundary solution.

[KP01.75] Charge Exchange Modeling in a Spherical IEC Device

The spherical Inertial Electrostatic Confinement (IEC) device produces neutrons from the fusion of an electrostatically confined deuterium plasma. Charge-exchange collisions are an important energy sink in this fusion plasma. During these collisions, fast become high-energy neutrals, leaving behind thermal energy ions. These resulting thermal ions re-gain some energy due to the local accelerating potential field. Still, the collisions represent a net transfer of energy from ions to neutrals, decreasing the fusion rate and the efficiency of the system.

A computer model of charge exchange in a spherical IEC device was developed to describe the effects of voltage, pressure, and cathode radius on the process, and hence on the fusion rate. The results indicate that a significant fraction of charge-exchange collisions occur at low energy. When the re-acceleration of thermal ions is taken into account, the ion population retains, on average, 70-80 their initial potential energy. Results yield a fusion scaling with cathode radius that generally matches experimental results. This information is important for the design of future, high-yield, IEC fusion neutron sources.

[KP01.76] Virtual Well Formation in a Spherical Inertial Electrostatic Confinement Device

The formation of a double-well potential structure in a spherical inertial electrostatic confinement (SIEC) device has received considerable theoretic study by various researchers. High ion densities in the center core are generally attributed to the resulting potential trap. We present a simple theoretical model to explain virtual well structures, despite the divergent ion beam produced by the finite structure of the accelerating grid. A simple analysis shows that the localization of charged particles is approximated by the device radius multiplied by the beam divergent angle. The divergence angle for electrons can be much smaller than for ions. Consequently ion-electron charge variations are localized, producing a virtual well. This model will be compared with parametric data obtained from experiments.

[KP01.77] Energy Gain Studies of Spherical IEC Devices using the BAFP Code

In the spherical IEC concept, ions are focused radially inwards by a kV potential well, and converge to a dense central core where fusion may occur. However, ion diffusion in velocity space may prevent a satisfactory energy gain in the system. BAFP is a fully implicit code developed to analyze IEC physics under a wide range of conditions, without requiring the approximations that limited earlier studies by various researchers. Ion-ion collisions are handled by the bounce-averaged Fokker-Planck collision operator. A two-group electron model has been implemented to simulate both high-energy electron effects (ion confinement) and low energy effects (ion space charge neutralization). The electrostatic potential profile within the electron population is obtained self-consistently every time step. Preliminary BAFP results for non-Maxwellian steady-state solutions will be presented, as well as parametric studies of associated fusion energy gains.

[KP01.78] The Penning Fusion Experiment

As part of the innovative confinement concepts initiative, a series of experiments is being conducted at Los Alamos to determine the suitability of Penning traps as fusion confinement devices. Early experiments concentrated on achieving enhanced densities by inducing spherical flow in a nonthermal, nonneutral plasma confined in a traditional Penning trap. The present experiment seeks to overcome the limitations of this method by forming a well for positive ions from the space charge of a uniform cloud of electrons confined in a modified Penning trap. The radial well thus provided will allow spherical convergence in a multi-species plasma. After a brief summary of the first-stage experiments, we will present results on electron recirculation in the present experiment.

[KP01.79] Penning Fusion eXperiment - Ions: Diagnostics and Preliminary Results

The Penning Fusion eXperiment – Ions (PFX-I), part of the Innovative Concepts Initiative of the Office of Fusion Energy (OFE) is a unique magnetic confinement concept based upon the traditional Penning trap. To produce fusion relevant conditions, high voltages (\geq100kV) and small sizes are required, making electrical breakdown a critical technology and science issue. The trap itself has an ID of less than 40mm, with access to the center restricted through ports less than 15mm in diameter. The small trap size and relatively low electron density discounts several diagnostics. We are developing a diagnostic based upon the Stark splitting of the Hydrogen \alpha-line when neutral H_2 gas is added to the electron cloud confined in the trap. For our experimental conditions (n_e \geq 10^10 cm^-3), calculations indicate that \sim10^13 photons/sec^.cm^3 should be emitted from the plasma and the H_\alpha \pi-lines should be separated by more than an angstrom. We will present the specifics of the optical assembly and magnetic field flux-shaping. Results to date will be presented, including the electron lifetime data.

[KP01.80] Flow Shear Stabilization of a Z-Pinch

A 3D numerical MHD simulation of a flowing Z-pinch is presented. The code UMMHD, the fluid code at the University of Maryland (Guzdar, et al; 1995), is used. The code includes explicit viscosity and resistivity, as well as applied E fields and particle and momentum sources. There are conducting walls. The system is set up so that an axial electric field drives the Z-current and sets up the equilibrium in 2D. This state is then disturbed by random noise. The discharge is seen to go unstable to a combination of m=0 (sausage) and m=1 (kink) modes. The plasma hits the walls and swirls in the chamber with complete mixing of the pressure. A momentum source is now turned on to force a Z-flow with no-slip boundary conditions at the wall. At low forcing (subsonic flows), the turbulence continues. At higher forcing (sonic flows), the discharge recovers quite nicely. The turbulence is largely ironed out and the laminar pressure profile is recovered to a large degree (at least by 70%). There is, however, a residual wobble left in the discharge with low level turbulence on the axis. Thus, complete stabilization is not attained, at present, and the transport may be substantial. The effect of plasma elongation is considered and shown to help the stabilization. The addition of an axial field is also considered.

[KP01.81] Helically symmetric ideal magnetohydrodynamic equilibria with incombressible flows

A recent study on axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 5, 2378 (1998)] is extended to the generic case of helically symmetric equilibria with incompressible flows. It is shown that the equilibrium states of the system under consideration are governed by an elliptic partial differential equation for the helical magnetic flux function \psi containing five surface quantities along with a relation for the pressure. The above mentioned equation can be transformed to one possessing differential part identical in form to the corresponding static equilibrium equation, which is amenable to several classes of analytic solutions. In particular, equilibria with electric fields perpendicular to the magnetic surfaces and non-constant-Mach-number flows are constructed. Unlike the case in axisymmetric equilibria with isothermal magnetic surfaces, helically symmetric T=T(\psi) equilibria are over-determined, i.e., in this case the equilibrium equations reduce to a set of eight ordinary differential equations with seven surface quantities. In addition, it is proved the non-existence of incompressible helically symmetric equilibria with (a) purely helical flows and (b) non-parallel flows with isothermal magnetic surfaces and the magnetic field modulus being a surface quantity (omnigenous equilibria).

[KP01.82] A Kinetic-Fluid Model for High-\beta Plasmas

The study multiscale coupling phenomena in which particle kinetic physics involving small spatial and fast temporal scales can strongly affect the plasma global structure and long-time behavior is a major challenge especially at high-\beta. The difficulty of modeling such multiscale coupling processes stems from the disparate scales which are traditionally analyzed separately: the macroscale phenomena are generally studied using the fluid MHD framework, while microscale phenomena are best described by kinetic theories. To study multiscale coupling phenomena effectively, we have developed a new nonlinear kinetic-fluid model for high-\beta plasmas with multiple ion species. The model embeds important kinetic effects due to finite ion Larmor radii (FLR), wave-particle resonances, magnetic particle trapping, etc., in the framework of simple fluid descriptions. For ømega << ømega_ci, the kinetic-fluid model takes a simpler form in which the fluid equations of multiple ion species collapse into one-fluid, density and momentum, equations and a low-frequency generalized Ohm's law. The particle kinetic effects are introduced via plasma pressure tensors which are computed from particle distribution functions that are governed by kinetic equations. Ion FLR effects provide a parallel electric field, a perpendicular velocity that modifies the E \times B drift, and a gyroviscosity tensor, all of which are neglected in the usual MHD description. Applications of the kinetic-fluid model to laboratory and space plasmas will be demonstrated.

[KP01.83] Axisymmetric Hall equilibrium of a toroidally rotating plasma

Stationary toroidal rotation of plasma in an axisymmetric magnetic field is studied in the frame of Hall magnetohydrodynamics (HMHD) both analytically and numerically. The HMHD-analogue of Grad-Shafranov equation is derived for an axisymmetric magnetic confinement configuration (like a tokamak) in the form, which allows for the simple transition to the limit of ideal MHD(E.Hameiri, Phys. Rev. A 27), 1259 (1983). It is shown that HMHD restricts a freedom of stationary plasma parameters more than ideal MHD does. The stationary solutions of the certain class are optimized to reach the higher values of the ratio \beta of the plasma pressure to the magnetic field pressure.

[KP01.84] Nonlinear MHD modeling of Marginally Stable Modes in DIII-D Plasmas with the NIMROD Code

The evolution of marginally stable global MHD modes in DIII-D type plasmas is studied with the nonlinear MHD/multifluid code NIMROD. The initial plasma equilibrium is a model DIII-D discharge with beta value just below the marginal stability limit. By increasing "self-similarly" the pressure profile (heating), slowly compared to the time scale of the unstable mode, it is possible to drive "smoothly" a marginally stable mode through its instability threshold, beyond the beta critical. The relatively slow initial growth of the unstable modes immediately past the threshold allows to diagnose the change in growth rate vs. time caused by the heating process. A theoretical analysis of this process based on ideal MHD [1] predicts the onset of an unstable mode with a hybrid time scale between the MHD and transport time scales. A comparison of the NIMROD simulation results with theory-based calculation is presented.

[1]J.D. Callen et al., Bull. APS Vol.43 (1998), p. 1762

[KP01.85] Future Of Plasma Simulations = Chapman-Enskog-like Approach?

There are two main strategies for simulating plasmas --- particle based and fluid moment based (e.g., magnetohydrodynamics, MHD). These two approaches may be converging: particle-based delta-f simulations are evolving from electrostatic to electromagnetic turbulence simulations where the electron momentum balance equation (Ohm's law) will become a very important, nonlinear player, particularly for magnetic reconnection processes; and MHD-like simulations are adding ''two-fluid" kinetic effects through kinetically-deduced closure relations. We propose that a natural framework for unifying these approaches for the future is to adopt an extended Chapman-Enskog-like approach [1] in which the (nonlinear) fluid moment equations are the basic equations and the needed closure relations are obtained from relevant moments of kinetic simulations of the non-fluid distortions of the distribution function. Some cases where such an approach may or may not be useful will be presented.

[1] J.P. Wang and J.D. Callen, Phys. Fl. 4, 1139 (1992). Z. Chang and J.D. Callen, Phys. Fl. B 4, 1167 (1992); 1182 (1992).

[KP01.86] Stabilization of wall modes by poloidal rotation

It is well known that the combined effects of dissipation and toroidal rotation suppress resistive wall modes in tokamaks. There are two classes of resistive wall modes: the resistive-wall tearing modes (RWTMs) and the ideal-plasma resistive-wall modes (IPRWMs). The RWTMs are stabilized by a slow plasma rotation with a frequency greater than the inverse wall magnetic diffusion time while the IPRWMs require a fast toroidal rotation frequency of a few percents of the Alfven frequency. In this work, we have studied the effect of poloidal rotation on the stability of the IPRWMs. The analysis is carried out using the sharp boundary model of Ref. [1] including high beta, plasma resistivity, toroidicity and sound wave continuum resonances. It is shown here that poloidal rotation can suppress the IPRWMs and its stabilizing effect is q(a) (safety factor at the plasma edge) times greater than toroidal rotation. The effect of multiple resonances with the Alfven and sound wave continuum is also investigated by increasing the edge safety factor above three while keeping the central q equal to unity. This work was supported by the Department of Energy under grant No. DE-FG02-93ER54215.

[1] R. Betti, Phys. Plasmas 10, 3615 (1998)

[KP01.87] Non-Ideal Effects on the Stability of Ballooning Modes

Ideal ballooning modes are believed to be responsible for high beta disruption observed on TFTR and DII-D. Recent 3D MHD simulations of the disruption phenomenon further support this point of view. Thus it is important to understand the role of non-ideal effects, like finite electron inertia as well as electron pressure gradients and ion-diamagnetic effects on the stability of these modes and establish more realistic threshold conditions. We have modified our one-dimensional eigenvalue code based on the ballooning mode formalism, to include these non-ideal effects and will systematically investigate the changes in the beta threshold for ballooning modes. We will present results of the modification of the stability boundary in the standard s-\alpha diagram due to each of the non-ideal effects that we incorporate in our studies.

[KP01.88] Influence of background plasma flow on stationary states and spectrum of MHD waves

A general review is given of how flow changes the structure of stationary equilibrium states and the MHD wave spectrum. Axisymmetric stationary ideal MHD equilibria are shown to be derivable from a single variational principle which facilitates the construction of transsonic MHD flows. Particular self-similar solutions are constructed which exhibit almost all of the intricacies of transsonic flow, like limiting line singularities and shocks. The relationship between the specific classes of self-similar flows and the more general flows obtained from large-scale 3D MHD codes is discussed. The second part is a sequel to the static results that appeared in Physics of Plasmas (September 1998). In that paper old and recent misunderstandings on the spectrum of MHD waves were clarified by the explicit construction of the Green's dyadic and the solution of the initial value problem. In the present contribution this issue is extended to plasmas with flow.

[KP01.89] Singular Modes of Ideal Magnetohydrodynamics

Under certain conditions related to the frequency, the linearized equations of ideal magnetohydrodynamics have singular solutions in space that are signatures of a continuous spectrum. An important issue concerns the mathematical nature of the spatial singularities. The specific form of the singularity depends on the geometry of the plasma configuration and the plasma variables. A self-consistent expansion scheme that can be used to identify the singularity is presented. The expansion scheme is based on power series representations about magnetic surfaces \psi(\bfr) = const. The well-known logarithmic singularity \ln|\psi-\psi_0| coupled with the 1/(\psi-\psi_0) singularity is found if the plasma is compressible and the geometry is either planar or cylindrical. New results appear for axisymmetric toroidal geometry. It has been found that an essential singularity (\psi-\psi_0)^i\tau coupled with (\psi-\psi_0)^i\tau-1, where \tau is a real constant, is the general rule. This contradicts previous results of other authors. The logarithmic singularity appears only under special circumstances. An important toroidal configuration with the \ln|\psi-\psi_0| and 1/(\psi-\psi_0) singularities is a pressureless plasma with a purely poloidal magnetic field. Extension of the results to nonaxisymmetric toroidal geometry is discussed.

[KP01.90] Feedback Stabilization of Rotating Resistive Wall Modes

MHD instabilities that limit the attractiveness of tokamaks and reversed field pinches as fusion systems grow on a time scale that is set by the resistivity of the conducting chamber that surrounds the plasma. These instabilities are called resistive wall modes and can be feedback stabilized or in some cases stabilized by plasma rotation. In earlier work [Phys. Plasmas \underline5, 3350 (1998)] a method was given for treating each MHD mode of a plasma as a circuit element. Jim Bialek has developed a code, VALEN, which simulates the currents in the plasma chamber and the feedback circuits and incorporates the plasma modes as circuit elements. To provide stabilization, plasma rotation must supply sufficient torque applied to an unstable mode to make the mode rotate faster than the time scale set by the resistivity of the chamber. A method of incorporating plasma rotation in the VALEN code has been developed and will be described.

[KP01.91] Vertical Displacement Events and Nonlinear External Kink Modes during Major Disruptions in Tokamaks.

Understanding the evolution of plasma currents, and halo and induced eddy currents in the vacuum vessel during a major disruption is important for present and future tokamak designs. Here we present first, three dimensional studies of these disruptive events where the plasma, the vacuum region around it, and the resistive vacuum vessel are treated self-consistently using our MHD code CTD. Single or double-null equilibria, consistent with an assumed set of transport coefficients and distribution of external vertical field and shaping currents are also obtained with CTD and used as initial conditions. Subsequent nonlinear calculations exhibit a wide range of phenomena, determined by the time scales for the thermal quench, current quench, and the large-scale displacement of the plasma column. Even with an assumed axisymmetry, in addition to the poloidally localized halo currents, large nonuniformities in the induced toroidal currents are seen, driven by the combined effect of the plasma column motion and the field induced by the current quench. With no symmetry assumptions, an n=1 external kink that becomes significant in late stages of the displacement, coupled to the VDE, produces also toroidal nonuniformities both in the halo currents, and the induced toroidal currents. In the benign environment of a numerical simulation, conditions can be easily generated in which a factor of two or more toroidal nonuniformity is seen in the vacuum vessel currents.

[KP01.92] Simulation of neoclassical tearing modes with NIMROD.

Neoclassical tearing modes (NTM) have been observed on the DIII-D tokamak to be triggered by the magnetic perturbation of a sawtooth crash and to inversely scale with the Lundquist number.(R. J. LaHaye and O. Sauter, Nuclear Fusion, Vol. 38, (1998), 1.) Since NTMs require a seed island for excitation, secondary islands that are driven by the coupling of poloidal harmonics in toroidal geometry to the unstable internal resistive kink and its harmonics are presumed to be responsible for producing an island of sufficient width to exceed the NTM threshold. The physics of such secondary island formation is a complicated forced reconnection problem, where the amplitude of the secondary islands is determined by layer physics.(C.C. Hegna and J.D. Callen, CPTC Report 98-5) NTM simulation results will be presented and compared with analytic theory for DIII-D shot 86144 based on the NIMROD code. Simulation results of the secondary island formation will also be presented and compared with scalings for both the Lundquist number and differential rotation.

[KP01.93] Particle and Heat Transport in the Presence of Magnetic Islands

A fundamental problem for bootstrap current-driven magnetic islands is to understand the dynamics and profile properties of density and electron temperature. To study the evolution of density and electron temperature in a helical island geometry, we solve the coupled parallel momentum and continuity equations in the presence of a slowly growing magnetic perturbation that simulates the evolution of a neoclassical tearing mode. It is assumed that sound wave propagation along field lines is primarily responsible for equilibration of density over perturbed flux surfaces. Electron temperature equilibration, on the other hand, occurs on perturbed flux surfaces as a result of a rapid parallel heat flux. An analytic closure for this heat flux is constructed based on a multiple time and spatial scale, Chapman-Enskog-like analysis. This heat flux is then inserted into a temperature evolution equation which is solved in the presence of an evolving helical magnetic island.

[KP01.94] Implications of JET ICRH sawtooth data for kinetic MHD theory

There is a wide consensus that sawtooth instabilities in tokamaks are a direct consequence of the destabilization of the m=n=1 internal kink mode followed by a relaxation process enabling the plasma core to stabilise. The stability properties of this mode have been calculated using a state-of-the-art expression for the kinetic-MHD energy principle in the presence of an energetic ICRH minority ion population. Comparison with measurements of giant sawtooth duration in recent ICRH pulses from the JET DTE1 campaign suggests that energetic ions contribute significantly to countering the destabilizing effect that results from higher plasma pressures. It is found that the stabilising influence of the hot ions increases in parallel with sawtooth period, whilst the destabilising toroidal effects, notably the gradient of the Shafranov shift, also increase. This further suggests that analytical expressions for the perturbed generalised MHD energy can play a useful role in assessing the sawtooth stability of JET and predicting the performance for Next Step devices.

[KP01.95] Effect of Plasma Rotation on the Stability of the Internal Kink Mode in the Banana Regime

The stability of the internal kink mode is calculated taking into account the kinetic response of the trapped thermal ions. Subsonic sheared toroidal rotation and diamagnetic effects at the mode-resonant layer are included. The trapped ion instability, characterised by a mode frequency of the order of the toroidal precessional drift frequency of the trapped thermal ions, is strongly modified through the inclusion of sheared plasma rotation. For increasing levels of toroidal plasma rotation, the calculated critical pressure for internal kink displacements can be varied by a factor of two.

[KP01.96] Oscillatory Model of the Sawtooth Phenomena in Tokamak Plasmas

One of the most generic instabilities in tokamak plasmas is the so-called sawtooth instability, which occurs in the core of the plasma column. It is associated with the safety factor (q) taking on the value of q=1. Recently, also off-axis sawtooth instabilities have been observed at q=3/2, 2 and 3 values [1].

Based on the general mathematical background of the relaxational oscillations [2], an oscillatory model has been developed, which is capable of describing the majority of the signal forms generated by those oscillations. Results of the numerical- and analytical study of the so-called, generalized Van der Pol oscillator (Ref. [2]) are presented. It is conjectured, that the instability, known as 'negative resistivity' [3] offers a plausible way to interpret the model in terms of plasma physics.

In particular, a new dynamics is proposed to solve the open problem of triggering the crash. It is shown, that the ratio of the energy, stored in the long- and short wavelength spectrum of fluctuations defines different types of trigger events. It is equally possible to get crashes with or without precursors, and with the appropriate trigger event, significant postcursor activity can be observed.

[1] R. Meulenbroeks, et al.: submitted to Phys. Rev. Lett. [2] J. Grasman: Applied Math. Scienc. Vol.63. (Springer, New York, 1987). [3] A.J. Pouquet: J. of Fluid Mech. (1978), 88, p. 1.

[KP01.97] Improved Numerical Technique to Solve the Linear Resistive MHD Problem

A new approach to construct the linear resistive MHD modes criterion for toroidal plasma was proposed.(S. Galkin et al.), Bull.\ Am.\ Phys.\ Soc.\ 43 (1998) 1751. This approach does not require extraction of infinite solutions a priori. A special transformation converts the original system of Euler equations into a new one, where the infinite non-integrable solutions become finite functions and all solutions can then be found numerically. A weak form of new equations is used in place of the second variation of the potential energy functional. Resistive MHD criterion: (1) Numerical solution of the modified Euler equations; (2) Extraction of Frobenius series coefficients and estimation of \Delta' for each resonance surface; and (3) Solution of the dispersion relation to determine growth rates on the basis of a wide class of different inner layer models. This approach was tested on 1D Sturm-Liouville problem with singular points and excellent accuracy and robustness were shown. A new version of the TWIST-R code had been developed to study resistive modes of the axisymmetric toroidal plasma. Convergence results for 2D toroidal plasma equilibria are presented and physical issues are discussed.

[KP01.98] Ideal MHD Stability of High Performance Tokamak Plasmas with Finite Edge Pressure Gradient and Current Density

High performance \hboxDIII--D plasmas are presently limited by ideal MHD edge instabilities. In VH Mode and Negative Central Shear (NCS) H Mode plasmas, these edge instabilities appear as large ELMs which terminate the high performance phase. In standard H Mode, however, Type~I ELMs result only in a temporary relaxation of the plasma edge. Low and intermediate n stability calculations have identified edge peeling modes driven by edge pressure gradient and current density that are correlated with the observed modes. The VH--mode termination instability, however, is much more global than edge instability in standard \hboxH--mode. A study of the dependence of the edge stability on the edge profiles is described. The role of the self consistent bootstrap current in driving the instabilities and in opening access to second stability for ballooning modes is evaluated. Cross-section shaping also plays an important role as a result of its effect on second stability access and this is also discussed.

[KP01.99] Plasma Simulation Studies using Multilevel Physics Models

The question of how to proceed towards ever more realistic plasma simulation studies using ever increasing computing power is addressed. Our answer is the M3D(Multilevel 3D) project, which has built a code package with a hierarchy of physics levels that resolves increasingly larger extent of phase-spaces, and therefore with increasing realism.( W. Park, E.V. Belova, G.Y. Fu, X. Tang, H.R. Strauss, L.E. Sugiyama (submitted to Phys. Plasmas, 1998). ) The existing physics levels are fluid models (3D configuration space): MHD and Two-fluids, hybrid models: Gyrokinetic-energetic-particle/MHD (5D energetic particle phase-space), Gyrokinetic-particle-ion/Fluid-electron (5D ion phase-space), and Full-kinetic-particle-ion/Fluid-electron level (6D ion phase-space). Resolving electron phase-space (5D or 6D) remains a future project. Phase-space-fluid models are not used in favor of \delta f particle models. An unstructured mesh option is also available for efficient representations of geometric effects. The examples of simulation studies are high-\beta disruptions, neoclassical magnetic islands, nonlinear TAE mode saturation, fishbones, pellet injection, runaways, and stellarator studies.

[KP01.100] Resistive Wall Mode Feedback Control Analysis Using Circuit Equations

The modeling of Resistive Wall Mode(RWM) feedback stabilization with lumped circuit parameters in cylindrical geometry[1] has been useful for comparing the various feedback schemes. Here, we extend the modeling of RWM feedback with lumped parameters to toroidal geometries. PEST with the VACUUM code provides the eddy current toroidal pattern and the induced magnetic field on the stabilizing shell due to excitation by the ideal external kinks. With the assumption that the pattern structure does not change during the feedback process, it is possible to introduce lumped parameters similar to the mutual inductances of the cylindrical case. Again, the effective self inductance of the plasma surface represents the growth rate of the external kink without the shell. [1]M.Okabayashi, N. Pomphrey and R. Hatcher, ``Circuit Equation formulation of resistive Wall Mode Feedback Stabilization Schemes'' (Nuclear Fusion, Nov. 1998)

[KP01.101] Theory of Resistive Instabilities in 2-Dimensional Plasma Configurations with a Magnetic Separatrix

Within the framework of the reduced resistive MHD model, we present an analytic theory of axisymmetric linear perturbations whereby a current sheet develops along the magnetic separatrix of a 2-dimensional equilibrium. This requires consideration of several asymptotic regions, namely ideal MHD domains outside the separatrix, a resistive layer along the separatrix but away from the X-points, and the vicinity of the X-points. Analysis of the resistive layer away from the X-points determines the functional form of the perturbed current along the separatrix. A complete solution of the resistive MHD equations in the vicinity of the X-points is obtained by separation of variables. Matching this to the outer solutions yields the normal mode growth rate, which is proportional to the cubic root of the resistivity and to a single parameter determined by the global solution for the perturbed magnetic flux in the ideal MHD domains. The latter is evaluated for the specific example of Gajewski's equilibrium(R. Gajewski, Phys. of Fluids 15), 70 (1972)..

[KP01.102] Stability limits for unity beta ET equilibrium using NIMROD.

Time evolution of low m/n MHD instabilities, particularly the internal kink, is studied using NIMROD in preparation for learning to operate the Electric Tokamak (ET) well beyond the Troyon limit with beta Troyon approaching 20. The code has performed remarkably well in ingesting numerical equilibrium data from a home made equilibrium solver exhibiting extreme Shafranov shift as unity beta (p(0)/B(a)^2 \sim 1) is approached with bootstrap aligned current profiles. Overall "NIMROD" stability is achieved above beta(0) of 60% without any plasma EXB rotation. There is no stability between BETA(0) of 5% and 60%. Here we are studying the effect of poloidal rotation, and rotation shear, on macro stability. NIMROD's portable design enables applications from scalar to massively parallel computers. In our case, the code is used in the low m/n regime on a PC cluster. Scans are made in 10 concurrent computations on 10 separate PC's. We find that it is efficient to use NIMROD in a "distributed computing" environment and on the ET PC-based data acquisition system. We are tooling up to run the ET tokamak and a fledgling Numeric Tokamak, using the same initiation files and graphic interfaces. NIMROD turned out to be a good test case for the MHD component for this development. Rotation stabilized/destabilized operating boundaries for ET will be presented.

[KP01.103] Comparison of Experimental Diagnostic Signals with Stability Code Predictions

A new code has been written to compare experimental diagnostic signals with those predicted by stability code output using experimental equilibrium diagnostic signals. Comparison of expected and actual diagnostic signals will help distinguish or identify modes by the signals they produce, and will also help validate stability codes.

Comparisons of predicted and actual signals for negative central shear and wall stabilized discharges in DIII-D show reasonable agreement. Also, theoretical predictions for linear growth of disruption precursors is compared with data.

[KP01.104] Robustness Studies of High-\beta Plasma Configurations on the National Spherical Torus Experiment^1

We study the effect of local variations of the equilibrium profile shaping on the stability properties of NSTX high-\beta plasmas. The reference set of profiles used are a monotonic q (q_0 \simeq 2.8; q_edge \simeq 12) and a pressure profile with peakedness P(0)/

\equiv F_p=1.7 (marginally stable at \beta=40%)^2. Initial results from ballooning calculations show a robustly stable plasma for variations of q_0 up to 30%. A variation in q of -40% at mid-radius combined with a +20% edge increase produces a reversed shear profile which is marginally second-stable to ballooning at \beta=34%. Assuming the pressure profile shape of a high-\beta beam-heated plasma from the START experiment (F_p=2.4), and a slightly reversed shear q profile (q_0 \simeq 2.8; q_min \simeq 2.3), the calculated ballooning \beta-limit is reduced to 25%. TRANSP calculations using the NSTX NBI geometry yield an F_p=4.2 resulting in a high-n \beta limit reduction to 18%. Relatively broad P profiles (F_p=2.4) yield stable access to second stability. Low-n kink stability calculations results will complete the reassessment of the NSTX operational limits. ^1USDOE Contracts: DE-FG02-89ER53297 ; DE-AC02-76CH03073. ^2J. Menard, et al., Nucl. Fusion, 37, 595 (1997).

[KP01.105] Fishbones involving magnetic reconnection in toroidal plasmas*

"Fishbone oscillations" have long been observed(K. McGuire et al., Phys. Rev. Lett. \bf50\rm, 891 (1983)) and correlated with energetic nuclei originating from auxiliary heating systems. Theoretical considerations(B. Coppi and F. Porcelli, Phys. Rev. Lett. 57 \rm, 2272 (1986)) have shown that these ions can excite m=n=1 modes that do not involve magnetic reconnection. Subsequently, the excitation of modes involving magnetic reconnection by high energy particles was predicted. Recently, fishbone-type oscillations with higher mode number (e.g.\rm, m=3 and n=2) have been observed(K. Toi et al., 17th IAEA Fusion Conf., \rm(Japan), paper EXP1/19 (1998)), often in configurations with negative magnetic shear in the plasma center. The simplest relevant theory is based on the two-fluid approximation, for the background plasma, including finite diamagnetic frequency effects and an electrical resistivity that allows reconnection and the removal of the mode singularities. The contribution of the high energy ion population is evaluated from kinetic theory. The conditions for the mode localization and stability are pointed out.

*Supported in part by the U.S. Department of Energy

[KP01.106] The Application of the NIMROD Code to Resistive Interchange Instabilities

We apply the NIMROD code to the study of linear and nonlinear resistive interchange instabilities (g-modes) in the D-IIID tokamak. NIMROD advances the linear or nonlinear, time-dependent, MHD or 2-fluid equations, using bilinear finite elements in flux coordinates in the poloidal plane; a pseudo-spectral Fourier representation in the toroidal direction; and a semi-implicit time step. New features of the code have been developed to allow accurate treatment of these modes, which pose major challenges to numerical simulation due to their sharp radial gradients about multiple mode rational surfaces, very small parallel gradients, and very small growth rate. Parallel additive Schwarz preconditioning of conjugate gradients, supplemented with a coarse-grid correction, has been developed to accelerate linear system solution, the most time-consuming component of the code. This is essential because of the exceptionally large condition number of the linear system, which is close to ideal MHD. Packed gridding about singular surfaces is used to improve spatial resolution while avoiding excessive grid size. Techniques have been developed to minimize \nabla \cdot B with minimum effect on physical behavior. Comparisons are given to analytical theory and other numerical computations. New visualization techniques are presented.

[KP01.107] A Common Interface to MHD Equilibrium Solvers

Under the combined auspices of the National Transport Code Collaboration (NTCC) and the Strategic Simulation Initiative (SSI), a common interface module called CEO -- Common Equilibrium Object -- has been developed to standardize access to MHD equilibrium solvers. The CEO module, written in C++, will be available for download with documentation at the NTCC modules library web site (http://w3.pppl.gov/NTCC). CEO provides a shared, standardized front end to several 2d fixed boundary solvers (J-SOLVER, ESC, VMEC, etc). The benefits of standardization are increased flexibility, reduced code maintenance and development costs, and ease of use. Extensions to the CEO module will include an MDSplus front end, providing a method for channeling data from US tokamaks to analysis codes over the network. The CEO module will be used in TRANSP data analysis to give users greater flexibility in choice of MHD solver, and in codes such as PEST to access and prepare data for stability analysis.

The status of this work is described. Thoughts on the generalization of the approach to free boundary codes will be presented.

[KP01.108] Time-scales for Non-Inductive Current Drive in Toroidal Geometry

There is considerable interest in using non-inductive current drive to establish, maintain, control, and modify the current distribution in toroidal fusion experiments. This includes RF current drive, bootstrap current, and NB current drive. Here we address what are the time-scales associated with this. We have used the TSC code to model a full non-inductive startup of the NSTX experiment, using a combination of RF and bootstrap current drive. If the non-inductive current drive term exceeds the plasma current by too great an amount, an unstable current distribution will develop with very low inductance, and the current on axis can actually attempt to reverse sign. These results are reproduced and parameterized using a simple one-dimensional model. The characteristic time is set by the central resistivity. Attempts to increase the plasma current faster than this time will results in severe transients, especially when the bootstrap current fraction is high. In general, acceptable time-scales for non-inductive current ramp-up are 4-5 times longer than those for inductive ramp-up. This work supported by DoE Contract DE-AC02-76CH03073.

[KP01.109] Toroidal Alfvén and energetic particle modes excited by ICRF-produced energetic particles

We have developed a magnetohydrodynamic(MHD) - gyrokinetic hybrid simulation code to study shear Alfvén instabilities excited by trapped energetic particles in toroidal plasmas. Since the energetic particles are treated non-perturbatively, both MHD Alfvén eigenmodes and energetic-particle mode, could be destabilized. The simulation employs the \delta F scheme to solve for the linearized trapped-particle response. The equilibrium distribution function is taken to be Maxwellian in energy, but anisotropic in the pitch angle. The results of the simulation will be compared with the analytical theories, as well as experimental observations in TFTR.

[KP01.110] Destabilization of "Counter Propagating" TAE Modes by Particle Anisotropy

The resonant wave particle interaction which taps the "universal" instability drive is destabilizing for co-propagating modes (with respect to the energetic particle diamagnetism), but stabilizing for counter-propagating modes. Nonetheless, sometimes only self-excited counter-propagating TAE modes have been observed in experiments on C-mod when resonant energetic particles are produced by ICRF heating (then anisotropy is another source of free energy). However particle anisotropy can produce a larger linear growth rate for counter-propagating modes when the mode frequency is close to critical frequencies corresponding to where there is "merging" of two "Landau" poles. The frequency of the observed counter-propagating mode is at one discrete frequency and close to the predicted critical frequency, supporting the hypothesis that pole "merging" and anisotropy explain preferred destabilization of counter-propagating TAE modes in tokamaks.

[KP01.111] Diffusion of Fast Ions by Driven Contained Modes

Apparently, extremely high quasilinear diffusion rates for energetic beam ions can be deduced from TFTR mode conversion experiments. Comparison of the experimentally inferred loss rates with the theoretical prediction of the interaction of energetic ions with MCIBWs shows a discrepancy in the calculated diffusion coefficient of a factor of 30-70. This enhanced loss of energetic particles under the influence of intense imposed waves does enhance the prospect of advantageously channeling energetic alpha particles in a tokamak reactor. Resolving this discrepancy is thus of clear importance both from the standpoint of academic interest in basic wave-particle theory and from the standpoint of practical interest in an improved tokamak reactor. An attempt is made here to determine if this accelerated diffusion might be explained by the excitation of a contained mode, possibly similar to that used in explaining the ICE phenomenon, near the edge of a tokamak. A simple model is developed and compared with more complete numerical simulations of the growth of contained modes. The mode parameter space is explored to determine if such a mode could dramatically enhance particle diffusion.

[KP01.112] Grafting of End-Functionalized Chains at Immiscible Polymer Interfaces

The normalized grafting density (z/R_g) of amine-terminated deuterated PS chains at the interface of bilayer films of the immiscible polymers polystyrene (PS) and poly(styrene-r-maleic anhydride) (PSMA) was determined after various reaction times t from the interfacial excess z^* using dynamic secondary ion mass spectrometry (SIMS). As z^*/R_g increases with t, the interfacial tension decreases to zero and and the interface becomes unstable, leading to surface roughening and possible microemulsion formation. Interface topology was measured by scanning force microscopy (SFM) after the unreacted PS(dPS-NH_2) had been washed off the PSMA. The experiments show clearly that two regimes exist, at low and high normalized grafting density. The low grafting density regime is characterized by z^*/R_g values less than one and shows a smooth interface. The high grafting density regime, on the other hand, reaches z^*/R_g values as high as forty. SFM results show a strong increase in the interfacial roughness with t, an increase resulting from the interface instability.

[KP01.113] Rhythmic Crystal Growth in Polymer Blends

Crystallization behavior and morphological development in miscible blends of polyvinylidene fluoride (PVDF) and polyvinyl acetate (PVAc) have been investigated by using optical microscopy. At high crystallization temperatures, a spiral growth in spherulites of PVDF has been observed in PVDF/PVAc blends rich in PVDF contents. At a lower supercooling, a target (i.e., concentric rings) pattern, often called "banded or ringed spherulites", is emerged. A closer examination on growth dynamics of the bands in the spiral and target spherulites reveals that the band periodicity increases in a step-wise fashion with elapsed time, suggestive of a rhythmic crystal growth which may be ascribed to the peridic energy dissipation accompanying crystallization. A theoretical model based on time-dependent Ginzburg-Landau equation (Model C) has been developed for polymer crystallization in which the conserved compositional and the non-conserved orientational order parameters are coupled. The simulation truly captures the trend of the observed rhythmic crystal growth.

[KP01.114] Single-Crystal Morphology of Electro-Optically Active Poly(nonylbithiazole) (PNBT)

Polybithiazoles are a family of n-dopable, soluble, conjugated polymers of interest as cathodes in solid-state batteries and as electron-injection layers in light emitting diodes (LEDs), among other applications.^1 The nonyl-substituted polymer, poly(nonylbithiazole) (PNBT), displays an interesting variable bandgap behavior and can adopt three distinct colors in the solid state: yellow, red and metallic-green.^2 These changes have been correlated with differences in the nature and extent of crystalline order in the polymer. We have studied the morphology of PNBT single crystals by means of selected area electron diffraction (SAED) and transmission electron microscopy (TEM). Polymer crystals were prepared by slow solvent exchange between dilute solution and non-solvent. Sheaf-like crystal bundles were commonly observed. Chain orientation, folding, and crystal growth will be discussed in the context of previous high-resolution electron microscopy (HREM) studies of PNBT thin films.^3 ^1Curtis et al, Macromolecules 1998, 31, 205 ^2Nanos et al, Chem. Mater. 1995, 7, 2233 ^3Gonzalez Ronda and Martin, Macromolecules 1997, 30, 1524

[KP01.115] Effect of Pattern Dimensions on Morphology of Thin Films of Diblock Copolymers on Chemically Patterned Surfaces

The morphology of thin films of diblock copolymers on chemically patterned surfaces was investigated using AFM, TEM, and optical microscopy. Self-assembled monolayers (SAMs) of octadecyltrichlorosilane on SiO_x substrates were patterned with regions of different chemical functionality and different pattern dimensions by exposure to X-rays. Thin films of symmetric poly(S-b-MMA) (lamellar period = L_o) were deposited on the patterned surfaces and annealed. On patterned surfaces with feature dimensions of 10\mum to 50\mum, the surface of the film was featureless above exposed SAMs and exhibited topography (islands or holes) above unexposed SAMs, or vice versa, depending on the initial film thickness. The lateral dimensions of the islands or holes are typically greater than 2\mum. If the dimensions of the patterned SAM were less than 2\mum, then the surface of the film was smooth over both unexposed and exposed regions. The maximum difference in thickness over the exposed and unexposed regions was ½L_o, and the grade between peaks and valleys was as little as 1.5

[KP01.116] Kinetics and Morphology of Phase Separation in Filled Polymer Blends

The effects of addition of filler particles on the phase separation kinetics and morphology development of polystyrene/polybutadiene (PS/PB) blend films are investigated. Optical and atomic force microscopy are used to image the surface structure of blends with fumed silica particles and buckminsterfullerene (bucky balls). The fumed silica apparently modifies the polymer-surface interaction thereby changing the kinetics of the phase separation process. In contrast, addition of fullerenes to the blends primarily affects the morphology of the phase separation patterns and additionally acts in shifting the blend phase boundary. These results are used to draw conclusions on how polymer-filler interactions affect the kinetics and morphology of filled systems.

[KP01.117] Origin of the High Temperature TSDC Peak in Poly(\epsilon-caprolactone)

The technique of thermally stimulated depolarization currents is used to obtain the dielectric relaxation peaks of Poly(\epsilon-caprolactone). The spectra measured in samples with different molecular weights, ranging between 10000 and 83000, reveal a complex high temperature peak above the \alpha mode, which is the dielectric manifestation of the glass transition. This \rho peak is found to be the only one dependent in its position, profile and magnitude, on the molecular weight of the sample. This particular behavior could be a characteristic of the dielectric response originated by normal modes, related with the existence of an electric dipole moment parallel to the main chain. As these samples have a relatively high cristallinity (between 78% and 53%) as determined by DSC, the high temperature peak could also be due to capture-release processes of free charges between the amorphous-crystalline interphases. In order to clarify the physical origin of this peak, a series of curves with variable polarization temperatures, around the temperature of the maximum are obtained, using the thermal sampling method with null width windows. The curves obtained are fitted with a general kinetic order model, to describe the trapping levels distribution of Poly(\epsilon-caprolactone). The quality of the fit, as well as the numerical values of the kinetic order, activation energy, and pre-exponential factor, are discussed in order to clarify the origin of the \rho peak.

[KP01.118] Analysis of LCOT Transition Parameters in Diblock Copolymers using X-ray Reflectivity

Diblock copolymers of styrene and n-butyl methacrylate exhibit a lower critical ordering transition (LCOT), a first order phase change driven by the temperature dependence of excess mixing volume. In-situ high pressure SANS shows that this transition from a disordered to an ordered state upon heating is markedly influenced by the application of hydrostatic pressure, with coefficients exceeding 100 K/kbar. We report experiments to measure the volume change associated with this transition using X-ray reflectivity studies of the temperature dependence of thin film thickness. We also measure the enthalpy of transition using differential scanning calorimetry. This yields a consistent thermodynamic analysis of the LCOT.

[KP01.119] Phase Separation Dynamics of a Binary Polymeric Mixture containing Hard Particles

We study the pattern evolution of a binary mixture in the presence of hard particles which have a preferential attraction for one of the components of the mixture. Local interactions between the hard particles and the mixture are included in the model. Numerical results for the morphology of the phase separating mixture and the motion of the hard particles are presented.

[KP01.120] Interferometric Imaging of Hydrogels: Observation of the Gel Interior in Contraction and Swelling

Jamin interferometry combined with digital image analysis of the fringe pattern is applied to in-situ characterization of a cylindrical polyacrylamide gel undergoing a volume change. Spatial resolution of the method provides the distribution of the gel matrix and/or the penetrant concentration at various times after the fluid immersing the gel is changed from pure water to a water-methanol mixture or a solution of low- and high-molecular-weight penetrants and vice versa. It was found that the penetrant distribution changes with time according to the diffusion equation, but the change in the density profile of the gel matrix does not always follow the equation derived originally Li and Tanaka and then refined by Wang, Li, and Hu. It was also found that the gel contraction that begins in the near-edge portion accompanies initial swelling in the core. Likewise, there is initial contraction in the core when the gel swells.

[KP01.121] Structural relaxation of PET by dielectric spectroscopies.

Structural relaxation of amorphous and semi-crystalline PET has been studied through dielectric relaxation by means of ThermoStimulated Currents (TSC) and Dynamic Dielectric Spectroscopy (DDS). In TSC experiments, physical ageing has been induced by two procedures : one is isothermal, the second implies various cooling rates under DC field from the rubbery state to temperatures lower than Tg. TSC studies show the existence of two relaxation modes in semi-crystalline samples corresponding respectively to the free and constrained amorphous phases glass transitions. The relaxation mode at lower temperature is shifted to higher temperatures and its magnitude increases upon ageing, and is well described by relaxation times following a compensation law. The compensation parameters remain constant while the maximum activation enthalpy increases with ageing. This evolution is analogous in the case of amorphous or bi-oriented semi-crystalline PET. Moreover, the relaxation mode at upper temperature is due to quasi-isoenthalpic processes whose magnitude is decreasing with physical ageing. These data will be compared with DDS results.

[KP01.122] Structures and Optical Band Gaps of 1,2-phenylamino Squaraine Polymers

Symmetric ground state polymers incorporating squaric acid moieties in the polymer backbone are of interest as low band gap materials. This work focused on 1,2-phenylamino-squarine polymers having either aromatic or quinoidal bonding.The geometries, ground and first excited state electronic structures for oligomers up to 6 repeat unit were investigated.The polymer structures and band gaps were extrapolatied from the oligomer properties. Semi-empirical and ab initio SCF method were used to characterize the polymer and electronic structures. The CIS method was employed to calculate the excitation energies between ground singlet state and ground triplet state for a series of oligomers and the band gaps of either aromatic or quinoidal polymers were then extrapolated. The quinoidal polymer is highly polarizable with dipole moment per unit cell of 6.95 D while the aromatic polymer has a dipole moment per unit of 2.47 D. In the ground electronic state, the two configurations have almost same stabilities, the difference of energy per unit cell is less than 1.7 kcal/mol. Both types of polymers show narrow band gaps which are close to 1.0 eV.

[KP01.123] Simulation of Pattern Formation Dynamics in Liquid Crystalline Polymer Fibers

Although periodic structures are a common feature of liquid crystal polymer systems, the mechanisms by which these features form are often unknown. New explanations for many of these phenomena have been offered by considering the dynamic behavior of liquid crystalline polymers as a pattern forming process. As an example, the development of two distinct morphological features found in fibers made from liquid crystal polymers is examined. First, the presence of a zig-zag director trajectory along the fiber direction is shown to be the result of the reorientation of the director after cessation of flow if an extended version of the Frank free energy is used to describe curvature elasticity in the material. Second, the concentric ring patterns shown in etched fiber cross sections is found to be a consequence of the coupling between orientational ordering and density changes during crystallization. In both cases, the development of these morphologies has been shown to be an expected part of the pattern forming process in these systems using both analytical methods and computer simulations of the structure formation process.

[KP01.124] Controling the Orientation in Thin Film Blockcopolymers by Means of Electric Fields

Achieving precise control over the ordering and orientation of block copolymer microdomain structures is an important step towards the usage of these materials for creating nanostructures. We report about the alignment behavior of Polystyrene-block-Polymethylmethacrylate with cylindrical microdomains in a thin film geometry under the influence of an electric field. The resulting structure is characterized by Small Angle Scattering and Transmission Electron Microscopy. As a function of electric field strength we observe two regimes with different orientation which are separated by a sharp transition. At low strength the electric field leads to an improved ordering of the cylindrical domains parallel to the substrate, as it is caused by the interaction of the material with the surfaces. In this regime the cylinders are oriented perpendicular to the applied electric field. Above a threshold field strength the interaction with the electric field forces the cylindircal domains to orient parallel to the electric field and perpendicular to the substrate. This effect demonstrates a new way for a quantitative determination of interface interaction energies.

[KP01.125] Rear Earth Metallorganic Polymer Self-Assembled Structures for Electroluminescence Applications

The terbium chelating self-assembly of poly (urethane urea) (2,6-MCPU-4/200) based on 2,6-diaminopyridine and 1,4-diisocayanato butane metal chelating unit that has been chain extended with poly(ethylene glycol), with a molecular weight of 200, to facilitate solubilization is presently reported. These assemblies were characterized with UV/VIS and fluorescence spectroscopy, spectroscopic ellipsometry, and ATR FTIR. These films exhibit a green photoluminescence emission with peaks at 490, 545, 585, and 620 nm while the UV-VIS showed absorbance maxima at 218, 250, and 310 nm. The fluorescence emission pattern is typical of the lanthanide chelated center. The film growth was monitored by both UV/VIS spectrophotometry and spectroscopic ellipsometry. The index of refraction, n, for a 57 nm thick film was determined to be 1.52 +/- 0.01 at 633 nm. ATR FTIR confirmed the chelation from shifts in the carbonyl stretching frequencies. The film properties confirm a material with polymeric properties evident from the observed micro-structured phase separation by optical microscopy. To the best of our knowledge this is the first reported anhydrous block copolymer based self-assembly of a terbium based polymeric chelate.

[KP01.126] Influence of Flow Field and the Minority Phase Microdomain Structure on the Crystalline Block Morphology of a Terpolymer

A structural transformation was observed from a spherical polystyrene microdomain to a cylindrical one by causing microphase separation to take place under an applied flow field. using both SAXS and TEM. The semicrystalline terpolymer polystyrene-b-polyethylenepropylene-b-polyethylene displayed a spherical PS microdomain structure when quiescently cast from decalin solution maintained above the melting point of the PE block. When roll cast, also at a temperature above the melting point of the PE block, a hexagonally packed cylindrical structure of PS well oriented along the flow direction formed. This is an example of the suppression of the spherical domain structure by an applied field. We also investigated the subsequent crystallization behavior of the PE block within the microphase separated state. Temperature dependent SAXS was used to monitor changes accompanying crystallization and TEM was employed in order to directly visualize the morphology of the PE crystals. In the case of the roll cast sample, the PS domains severe to align the fast growth direction of the PE crystals along the cylinder axis.

[KP01.127] Phase segregation of PS and PMMA under confinement

We studied phase separation phenomena of polystyrene (PS) and polymethyl methacrylate (PMMA) confined between hydrophobic Si wafers as a function of annealing time, weight fraction and molecular weight. Polymer thin films were obtained from toluene solution casting and its thickness was carefully measured by ellipsometry. Two film-spun substrates were pressed parallel to each other and annealed at above Tg of each polymer. To ensure the confinement, we used a homebuilt device engineered to produce uniform pressure. To analyze morphology, we used scanning probe microscopy (SPM), Scanning Transmission X-ray Microscope (STXM) and neutron reflectivity (NR). STXM and SPM both show for mixtures of asymmetric molecular weights (PS-PMMA, 62K-25K) 2-dimensional phase segregation occurs with a well-defined wave vector. For the symmetric case (90K-90K) there is no lateral segregation detected. The result of further studied with NR on the surface induced orientation will be presented.

[KP01.128] Spinodal Dewetting of Block Copolymers on Surfaces

The stability of thin films of a symmetric diblock copolymer of polystyrene-b-polymethylmethacrylate (PS-b-PMMA) and a random copolymer of styrene and acrylonitrile (SAN)) on an SiOx/Si substrate was studied using atomic force microscopy. Ultrathin films of thickness h(0)<200 A were observed to undergo an instability consistent with spinodal dewetting. We measured the overall thickness of the fluctuation, dh/h(0), and the wave vector of the instability q(m). A two-stage breakup process involving increasing fluctuations and decreasing wave vector was observed. The two regimes correspond respectively to the time where the rupturing process begins,t(d), and the time, t(b), when dh/h(0) approached 1 (rupture of the film). The SAN completely dewet the surface whereas part of the PS-b-PMMA (thickness of about half a lamellar period L/2) remained stable. The dominant dewetting modes were a function of h(0). dh/h(0) increased as exp[-(t-t(d))/tau] from a value of dh/h(0)=1 to an equilibtium value when t>t(d). A model, based on the lubrication approximatiion and on volume conservation, shows that (dh/h(0)~K/(h(0)^i*q(m)^j) where K is a constant, i and j are exponents. q(m) was observed to decrease exponentially with time.

[KP01.129] The Diffusion of an Alternating Copolymer to the Biphasic Interface of an Immiscible Polymer Blend

The use of copolymers is a practical method to reinforce the interface of immiscible polymer blends. However, to be useful in industrial applications, the copolymer must diffuse to the biphasic interface within a blend during processing. Thus, the process of getting to the interface can be a limiting step in the utilization of copolymers as interfacial modifiers. Moreover, the role of copolymer sequence distribution on its ability to compatibilize blends is of current interest. Pursuant to this, the rate at which an alternating copolymer of polystyrene (PS) and poly(methyl methacrylate) (PMMA) diffuses to a biphasic interface has been examined. Neutron reflectivity has been used to investigate the time dependence of the diffusion of poly(methyl methacrylate-alt-styrene) to the interface between deuterated PMMA and deuterated PS from the d-PMMA phase. Qualitatively, the results show that the diffusion of an alternating copolymer at 10% loading is slower than the diffusion of a similar 50/50 random copolymer to the bilayer interface. Future experiments are in progress to verify this result.

[KP01.130] Genetically Engineered Protein Hydrogels: Biological Activity & Gel Structure

A series of genetically engineered triblock copolymers of the general form ABA have been synthesized using recombinant DNA methodologies. The center block is a water soluble poly(amino acid) flanked by two poly(amino acid) sequences that exhibit alpha-helical conformation in solution and have been specifically designed following a leucine zipper motif. Under proper conditions of pH and temperature, physical gelation occurs in solutions with polymer concentrations as low as 5% (w/v). Furthermore, gelation is reversible in response to changes in temperature and pH. Site specific biological activity has been introduced into the polymer backbone by the incorporation of discreet amino acid sequences allowing precise control over enzymatic degradation. Gel structures have been investigated by x-ray and neutron scattering.

[KP01.131] Near-Surface, Parallel Orientation of Lamellae in Shear-Aligned Diblock Copolymers

Subjecting lamellae-forming poly(styrene-b-isoprene) (SI) diblock copolymers to large amplitude oscillatory shear (LAOS) offers a route to microstructural alignment. This study examines the spatial uniformity of both isotropic (unaligned) and LAOS-aligned states of an SI diblock copolymer and its blend with homopolystyrene. Unlike typical studies in this vein, we do not restrict our examination to the bulk, but characterize the state of alignment near the shearing surfaces. Small angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) results reveal that lamellae near the surfaces adopt a parallel orientation, regardless of bulk orientation. This near-surface parallel region is uniform and extends ca. 2 um into the bulk. In the case of perpendicular bulk alignment, the mutually orthogonal bulk and surface lamellae are separated by a transition similar to a +1/2 disinclination. Our results indicate that the near surface parallel region is created upon quenching through the order-disorder transition temperature, and persists while LAOS creates the perpendicular orientation in the bulk.

[KP01.132] Gelation and Phase Separation in Equilibrium Polymerization with Trifunctional Branches

We consider a model of equilibrium polymerization in the presence of trifunctional branches. The phase separation is caused by the interaction with the solvent. The density of branches is controlled by an activity. The model is solved exactly on a Bethe lattice of coordination q and exhibits both gelation and phase separation that compete with each other. We consider various values of q and the branching activity and numerically investigate the phase diagram. We pay special attention to the interplay between gelation and phase separation.

[KP01.133] Polyelectrolyte Electrophoresis: (I) Oligomers and (II) Polycations

Two problems involving the dependence of electrophoretic mobility on the degree of polymerization N have been investigated for flexible polyelectrolytes: separation by N of oligomers in free solution and fractionation by N of high molecular weight polycations in dilute, neutral polymer solutions. A maximum of the free solution electrophoretic mobility in the oligomer range, previously suggested by capillary electrophoresis experiments with poly(styrene sulfonate), has been confirmed by experiments with poly(deoxythymidine); the maximum, in the range N=10-50, appears only at low ionic strength. The presence of this theoretically unexplained maximum confounds the analytical separation of oligomer mixtures by free solution electrophoresis. Conventional electrophoretic methods fail to separate high molecular weight polycations. Here, we report on the electrophoretic separation of polycations, such as quaternized poly(vinyl pyridine), in dilute solutions of pullulan. This success will facilitate the study of polyelectrolyte electrophoresis in nonaqueous media and an accurate electrophoresis examination of counterion condensation.

[KP01.134] A Molecular Dynamics Simulation Study of PEO/Water Solutions.

We have performed extensive molecular dynamics simulations of PEO/Water solutions using a quantum chemistry based atomistic force field. The composition, temperature and molecular weight dependence of structural, conformational and dynamical properties of the solutions will be discussed, and compared with available experimental data. These comparison provide important new insights into the structure and dynamics of PEO/Water solutions. For example, the anomalous conformational behavior of short PEO oligomers observed experimentally in the dilute solutions can be explained through analysis of intramolecular dipole-dipole correlation obtained from simulation. The influence of different water potentials on simulation predictions for the structural,conformational and dynamic properties of the systems is also discussed.

[KP01.135] Liquid Crystalline Characteristics Through Hydrogen Bonding Interactions in Benzoic Acid Containing Materials

Benzoic acid containing materials are particularly interesting because they can self-associate to form "dimers" that exhibit liquid crystalline characteristics (the "monomers" do not). DSC, FTIR, and optical miscroscopy have been used to study the phases that exist in the pure materials, as well as in blends with amorphous polyethers. It was initially believed that only three forms of benzoic acid associated species exist in either the pure state or in blends, a monomer, a dimer, or molecules that inter-associate with the polyether. However, two other bands in the FTIR spectra of the pure benzoic acid were discovered which are believed to be due to open chain hydrogen bonded acid groups and the open chain ends. The chain-like associated species may be stabilized by other interactions in the liquid crystalline state.

[KP01.136] Stark Shifting of Surface States in Silicon Field Emitters and its Impact on the Electron Tunneling Probability

Silicon field emitters are capable of providing a emission current density and they might be used Field Emission based display devices. For this reason one needs to calculate correctly, theoretical value for emission current density. In silicon, there is a continuum of surface states in the band gap at the surface. These states are very highly localized and attenuate rapidly towards both the bulk and the vacuum direction. At room temperature electron can jump into these surface states by absorbing long wavelength surface acoustic phonons. Electron tunneling probability has an exponential dependence on the width of potential barrier. Threrfore electrons in the surface states have a greater tunneling probability. Surface extraction electric fields in field emission are on the order of 0.6V/Angstrom. At these high electric fields, there would be significant distortion of surface states. This Stark shifting of states would move the maxima of surface states a small distance (approximately 0.5 Angstrom) towards the vacuum region, thereby effectively reducing the width of the potential barrier. This would have a significant impact on the tunneling probability. In this paper we are theoretically investigating these issues which involve calculating the Stark shift of the surface states produced by the extraction field and the subsequent increase in the tunneling probability. This would lead to a higher calculated tunneling current density.

[KP01.137] Diffusion of PS Into Filler-Reinforced Matricies

We have studied by dynamic Secondary Ion Mass Spectrometry (SIMS) the diffusion of monodisperse deuterated polystyrene (molecular weight = 94K) into matrices of polystyrene (molecular weight = 575K) reinforced with various fillers. These fillers include Carbon particles (approx. 300A diameter), Colloidal Silica and Organotrol Clay particles. Concentrations of the filler ranged from 1% to 5% by weight. Bilayers were made by blending the filler into the PS matrix in solution, spin casting a layer approximately 1000A to 1500A thick onto a HF stripped silicon wafer and floating a 500A DPS layer on top. Diffusion of the DPS was determined from SIMS depth profiles as a function of temperature, annealing time and filler concentration. This work is supported by the NSF under NSF DMR-9732230 (MRSEC Program).

[KP01.138] Numerical Investigation of Monodisperse Polymer Solution Next to a Surface

We numerically investigate a monodisperse polymer solution next to a surface, by using a recently developed numerical method by Chhajer and Gujrati that has been successfully applied to investigate polymer systems containing polydisperse species next to a surface. We replace the original cubic lattice by a modified tree structure of the same coordination number. The modification allows us to capture some of the correlations produced by the surface. The model is then solved by recursive technique. The monodisperse polymers require distinguishing a monomer by its distance from the end-point. This makes computations more time-consuming than the polydisperse counterpart. We report the results of our computation of various density profiles as a function of distance z from the surface (z=0) and the surface density as a function of surface interaction. We also look at the effect of chain length.

[KP01.139] Control of Adhesion and Friction between Self-Assembled Monolayers of Alkylsiloxanes in Liquid Environments

We investigated control of adhesion and friction between surfaces in liquid with molecularly thin self-assembled monolayers (SAMs) of alkylsiloxanes as boundary lubricants. To probe the effects of the surface free energies of the solvent and surfaces, SAMs with either -CH_(3) or -COOH terminal groups were contacted in hexadecane, ethanol, 1,2-propanediol, 1,3-propanediol and water using chemical force microscopy. -CH_(3)-CH_(3) and -CH_(3)-COOH interactions in simple n-alcohols most effectively reduced both adhesion and friction. To better understand the SAM/alcohol system, we studied the frictional behavior of SAMs of octadecytrichlorosilane on Si/SiO_(2) surfaces immersed in a series of n-alcohols, n=1-12, as a function of the solvent quality, applied load, sliding velocity and temperature with lateral force microscopy. Frictional maxima with respect to sliding velocity were observed for normal loads of 20-40 nN and sliding velocities of 1-100 \mum/s for n-alcohols with n=2-9. This behavior is similar to maxima observed for monolayers of surfactants within 40 ^oC of the bulk melting temperature, which have been interpreted as temperature-induced phase transitions. We interpret the maxima observed in our systems as phase transitions in the SAM related to solvent partitioning in the monolayer.

[KP01.140] Use of Self-Assembled Monolayers to Control Interface Bonding in a Model Study of Interfacial Fracture

The relationships between the extent of interfacial bonding, energy dissipation mechanisms, and fracture toughness in a glassy adhesive/inorganic solid joint are not well understood. We address this subject with a model system involving an epoxy adhesive on a polished silicon wafer containing its native oxide. The extent of interfacial bonding, and the wetting behavior of the epoxy, is varied continuously using self-assembling monolayers of octadecyltrichlorosilane (ODTS). The epoxy interacts strongly with the bare silicon oxide surface, but forms only a very weak interface with the methylated tails of the ODTS monolayer. We examine the fracture behavior of such joints as a function of the coverage of ODTS in different loading geometries. Various characterization methods are applied to the ODTS-coated surface before application of the epoxy, and to both surfaces after fracture. The fracture data are discussed with respect to the wetting of the liquid epoxy on the ODTS-coated substrates, the locus of failure, and the energy dissipation mechanisms. In addition, the effect of the distribution of bonding sites is examined by applying the ODTS monolayers in domains on the silicon wafer surface using photolithography.

[KP01.141] Thermal and Dielectric Characterizations of Fluorinated Aromatic Polyimide Films

Eight fluorinated aromatic polyimides were developed as novel dielectrics. Their molecular packing was disrupted by the bulky fluorinated substituents on monomers, yet the backbone rigidity and linearity were maintained. Consequently, these polyimides were quite soluble. They formed flexible, tough, transparent, and thermally stable films with low permittivities and loss factors, low moisture absorption, low CTEs, and high Tgs. These amorphous polyimides exhibited multiple mechanical and dielectric relaxations. The structural in-plane orientation within films was characterized by the optical birefringence and the anisotropic dielectric relaxations in directions parallel and perpendicular to the film surface. Small pre-tilt angles were found in thin films after rubbing, and surface enhanced Raman scattering was used to study the chain alignment.

[KP01.142] Microscopic Model of Craze Thickening in Amorphous Polymers

A process of craze thickening in a polymer glass is theoretically investigated. Craze microstructural parameters are calculated and craze thickening stress is determined as a function of temperature and entanglement density. Craze-to-shear transition is analyzed and its dependence on the temperature and entanglement density is presented. The obtained results are in good agreement with experiment.

[KP01.143] Primary and Secondary Crystallization in Fractions of Bisphenol-A Polycarbonate

A commercial grade PC (GE lexan) was fractionated through a solution-precipitation process and 11 narrow molecular weight distribution fractions ranging from 5,000 to 55,000 g/mol were obtained. The effect of molecular weight on the glass transition temperature and on the amorphous density of PC have been characterized. The kinetics of primary and secondary crystallization in some of these fractions have also been investigated. Particular attention was placed here on understanding the effect of primary crystallinity on the nature and extent of the secondary crystallization process. The kinetics of crystallization of PC from a completely amorphous state (melt or glass) is known to be considerably slow. In comparison, the secondary crystallization process occurs at a relatively higher rate, suggesting entirely different mechanisms for primary and secondary crystallization. Finally, the effects of annealing temperature and time on the evolution of the topological constraints during secondary crystallization of PC were examined. The secondary crystallization of PC follows the same universal laws, which were discovered in previous studies of PEEK, PET, it-PS and ethylene copolymers.

[KP01.144] The Sectorization and Metastability of Syndiotactic Polypropylene Crystals

Sectorized lamellar single crystals of syndiotactic polypropylene (sPP) show two regions, each with different thicknesses. In these different sectors, the chain folding directions appear to be different. Using melting experiments, the existence of two melting temperatures (two metastabilities) in one single crystal has been proved. Crystals with two melted thinner sectors and two unmelted thicker sectors have been observed under transmission electron microscopy (TEM). The crystal structure of the unmelted sectors is the same as before the melting experiments were performed. Recently, dark field images of sPP have been obtained by multi-image and normal TEM methods. The observations obtained by these two methods (each with advantages and disadvantages) show the same morphological features. Sectorization in these single crystals is also clearly shown in dark field images. Also, the submorphological orientations within each single crystal sector are different. This work is supported by NSF DMR-9617030.

[KP01.145] Structure Development in Side Chain Liquid Crytsalline Diblock Copolymers

The confinement of liquid crystalline mesophases within block copolymer microdomains affords the development of hierarchical structure in one material, developed under the influence of multiple driving forces. Here, we study a series of styrene-isoprene diblocks in which the isoprene is side functionalized with an azobenzene based mesogen using a C5 spacer. Smectic A mesophases are observed with homogeneous anchoring of the mesogens at the inter-material dividing surfaces. The high surface to volume ratio of nano-scale cylindrical microdomains results in the production of mesophases of low defect density, as gauged by the order parameter. The influence of liquid crystallinity on the structure of these materials in the bulk, in thin films, and on their orientation by oscillatory shear is explored.

[KP01.146] Structure and Crystallization behavior of Nylon 6/Vectra blends.

We have prepared blends of nylon 6 and the liquid crystal copolyester Vectra from the melt, and with different compositions, in order to analyze the influence of the anisotropic component in the crystallization behavior of the thermoplastic polymer. The structural transformations that take place during the crystallization processes, under isothermal and no isothermal conditions, have been studied combining differential scanning calorimetry, and small and wide angle X-ray diffraction real time experiments using synchrotron radiation. The polymorphic behavior of nylon 6 has been observed to be strongly affected by the presence of the liquid crystal. The relative amounts of the crystalline forms of nylon 6 depended on the copolyester concentration. In spite of the thermal treatment imposed on the blends, Vectra enhanced the formation of the alpha crystalline form of the polyamide. It has also been observed significant differences in the crystallization rates of the blends measured in the isothermal studies. These results have been correlated with the structural properties of these systems and will be discussed.

[KP01.147] Static and Dynamic Properties of Free Volume : Phantom Bubble Model and Dynamic Free Space

Two approaches to study the static and dynamic properties of voids in atomistic simulation were devised. First, a phantom bubble is defined as an empty sphere, which contacts four or more hard spheres of atoms simultaneously in 3 dimensional space and does not overlap with any atom in the structure. Phantom bubbles are only allowed to overlap with other phantom bubbles. Phantom bubbles were constructed in the various fully atomistic structures using the hard sphere atomic radii. Small changes in the atomic radii had little effect on the shape of the distribution function. Second, a methodology to investigate dynamic character of the voids was devised. Illustrative fully atomistic amorphous structures were prepared at various temperatures, and MD calculation was done for 2 ns. A number of small boxes with the dimension of (3 A)^3 were located at the random positions. Each box was used as a probe to calculate the local free volume with changing time using the hard sphere atomic radii. Normalized autocorrelation function of the local fractional free space showed that the voids had roughly two kinds of movements. One had a short memory that lasted for several ps. The other was extremely slow and showed a memory longer than 2 ns.

[KP01.148] Time-Resolved Small- and Wide-Angle X-ray Scattering Study of Crystallization of Poly(ethylene oxide) and Model PEO Blends

Time-resolved SAXS and WAXS experiments were used to investigate the crystallization kinetics and microstructure development of poly(ethylene oxide) and four model PEO blends at various crystallization temperatures and compositions. Average long periods and crystal layer thicknesses decreased at early crystallization times for both neat PEO and the blends: PEO and blends containing low Tg polymers exhibited an initial change of 2 - 3 nm, while blends containing high Tg diluents often exhibited an initial decrease of about 9 nm. The latter reduction appears to result from additional restrictions placed on the growing lamellae by the stiff, high Tg diluents. The increase in final long period was found to be 2 - 4 nm for the weakly-interacting blends as opposed to as large as 9 nm for the strongly-interacting blends. In the former case, the changes are associated with interlamellar diluent placement, while in the latter they are the result of increases in crystal thickness.

[KP01.149] Crystallization and Structure of Ethylene/Styrene Interpolymers as Compared to Ethylene/alpha-Olefin Copolymers

Ethylene/Styrene Interpolymers can be considered as statistical copolymers of ethylene and styrene-ethylene moieties. In this presentation, we compare the morphology, crystallization and melting behavior of these new materials with conventional ethylene/alpha-olefin copolymers. We are particularly interested in understanding the correlation between the rate of cooperative segmental motions associated with the alpha relaxation and the secondary crystallization kinetics. At the same co-unit content, the glass transition of ethylene/styrene interpolymers is at least 40°C higher than that of alpha-olefin copolymers. In all cases, the ethylene comonomers crystallize over a large temperature range and the co-units are excluded from the polyethylene orthorhombic lattice. These copolymers exhibit an extensive range of morphologies: from lamellae at low branch content to fringed micellar structures at the highest counit content. We will focus here on the determination of the kinetic parameters associated with the formation and melting of secondary crystals and on the the variation of these parameters with distance from the glass transition temperature.

[KP01.150] Polydiacrylate network formation in dilute solution: the influence of polymer solubility and solvent liquid crystallinity

Polydiacrylate networks formed by polymerization in dilute solution are composite structures whose morphology, which influences their performance in liquid crystal displays or membranes, depends on monomer structure and polymerization conditions. The network formation and structure was investigated by in situ phase contrast optical microscopy and, after drying in supercritical CO2, by scanning electron microscopy (SEM). The monomer and polymer solubility provide a facile means to control structure, through the competition of gelation and phase separation processes. In the limit of poor solubility, microgel particles precipitate at a very early stage and the network is assembled through the aggregation of tiny polymer grains or particles. The size of the polymer aggregate grows with time until gelation. The size and shape of the aggregate can be adjusted by reaction kinetics and solvent liquid crystallinity. When the monomer and polymer are more soluble (i.e. when the difference in solubility parameter between monomer and solvent is less than 1.5), phase separation is delayed, and gelation and solidification prohibit coarsening of the phase-separated structure. These conditions produce fibrous and sheet-like networks. The authors gratefully acknowledge the financial support of the Royal Thai government and NSF ALCOM grant # DMR89-20147.

[KP01.151] Studies on the Crystalline Structure of Poly(aryl ether ketone ketone) Copolymer

Recent crystallographic studies have been performed on the Poly(aryl ether ketone ketone) copolymer containing alternating terephthalic acid (T) and isophthalic acid (I) linked phenylene units [PEKK(T/I)]. When the copolymer is crystallized at high temperatures, only one orthorhombic unit cell (form I) is found. At crystallization temperatures below 210 oC, another orthorhombic crystal unit cell (form II) forms. However, evidence for an intermediate form (form III) was identified in the copolymer in the temperature range between 200 and 280 oC. Attempts to resolve the unit cell structure of this new polymorph were unsuccessful. To help answer these questions a [PEKK(T/I)] oligomer was prepared via a Friedel-Crafts acylation reaction. Through studies on this oligomer via TEM, ED, WAXD, and DSC, direct evidence was found for the existence of these three different crystal forms. Aknowledgements: This work was supported by the NSF DMR-96-7030.

[KP01.152] Low Voltage Transmission Electron Microscopy of Polymer Single Crystals

Bright field images of polyethylene (PE) lamellar single crystals have been obtained with a novel low voltage transmission electron microscope (LVTEM). The compact microscope design incorporates a Schottky emitter source, permanent magnetic condensor and objective lenses, side-entry goniometer, and electrostatic projector lenses. The image is formed on a YAG crystal screen, and is acquired with the optics of a conventional light microscope. The LVTEM images clearly show the well-known lozenge morphology of the PE crystals, and demonstrate that the \sim5 kV LVTEM beam can penetrate through more than 40 nm of this all-hydrocarbon polymer. Examinations of the polymer lamellae crystalline edges gives an estimate of the resolution of the instrument as \sim2 nm.

[KP01.153] Comparative Studies of Homogeneous and Heterogeneous Branched Polyethylenes

Commercial branched polyethylenes prepared with metallocene and Ziegler-Natta catalyst systems, of similar melt flow indexes, were compared using differential scanning calorimetry, transmission electron microscopy and by density measurements. The polymers were characterized, previously, by nuclear magnetic resonance, fourier transformed infrared spectroscopy and viscometry. The crystallization and melting behaviors as a function of cooling and heating rates, respectively, were studied. Preliminary results show that lamellar reorganization during heating depends on how homogeneous is the distribution of branches along the polyethylene chain. By looking at the lamellar morphologies of the samples, information about crystal thicknesses is obtained and related to their melting behaviors.

[KP01.154] Morphology and Property Development in Mixed Metallocene/Ziegler-Natta Isotactic Polypropylene Homopolymer Drawn Film

Morphology/property development in biaxial drawn isotactic polypropylene (BOPP) film of mixed metallocene regio-specific iPP (r-iPP) and Ziegler-Natta iPP (ZN-iPP) homopolymer compositions are evaluated. DSC and SAXS/WAXS synchrotron x-ray experiments show co-crystallization of ZN-iPP/r-iPP components at high undercooling, and r-iPP as morphological "diluent" at low undercooling. Structure/property relations of ZN-iPP/r-iPP BOPP blends are compared with ZN-iPP of varying isotacticity. ZN-iPP/r-iPP blends exhibit reduced biaxial yield stress, \sigma_y(T). A "fractional crystallinity" model collapses the \sigma_y(T) data into a common normalized form over a range of draw temperature, ZN-iPP tacticity, and blend composition. The model is extended to define universal interrelationships of yield activation and strain hardening behavior into regimes differentiated by characteristic crystallinity levels. A morphological model is developed to explain the effect of draw temperature and resin/blend microstructure on draw behavior, film stiffness, barrier, elongation, and BOPP film processability/ property/barrier balance synergies.

[KP01.155] A Study of Melting Kinetics of Isotactic Polypropylene Crystals

An unusual profound effect of melting kinetics has been observed in the fusion behavior of monoclinic (alpha) Ziegler and metallocene type isotactic polypropylenes (iPP). Profound melting kinetics are unique to poly(propylene) crystals and are found to be related with the epitaxial crystallization of this polymer. The radial mother lamellae become unstable after melting the daughter lamellae, and melt at temperatures lower than the characteristic melting endotherm of the mother lamellar structure. This system is relevant for representing a clear example where the usual methods of extrapolation to determine the equilibrium melting temperature fail. The Arrhenius-type activation energy of the kinetics is related to the initial crystallite morphology. The apparent melting temperatures, extrapolated to infinite annealing time, are significantly lower than conventional Hoffman - Weeks extrapolations. The melting kinetics of iPP crystals formed preferentially in the gamma polymorph (> 85%), with negligible contents of cross hatching, will also be discussed.

[KP01.156] Morphology and Dynamics of \alpha-Cyclodextrin/Poly(ethylene oxide) Polyrotaxanes

Small-angle and quasielastic neutron scattering, along with solid-state ^2H nuclear magnetic resonance were used to explore the microstructure and rotational molecular dynamics of some polyrotaxanes prepared by the inclusion complexation of perdeuterated polyethylene oxide (PEO) by \alpha-cyclodextrin (CD). Samples were examined as a function of PEO molecular weight, and as a function of CD threading ratio. The included backbones were found to exhibit faster motions as compared to the uncomplexed PEO at the same temperatures. In addition, PEO motions of the complex were anisotropic and remained so even at temperatures where uncomplexed PEO motion became isotropic (>T_m). While it was already known that low-molecular-weight (e.g., 1.5k g/mol) backbones thread completely, efforts were focused on determining microstructures for the complexes formed with high-molecular-weight backbones (e.g., 25k g/mol).

[KP01.157] Morphology Evolution in Polytetrafluoroethylene as a Function of Melt Time and Temperature

Heating of dispersed PTFE dispersion particles for 2 hours at 350 ^oC was shown^1 to lead, during crystallization, to the growth of folded chain, lamellar, single crystals and banded structures resembling those observed on free surfaces of bulk samples treated similarly^2. Examination of the evolution of the morphology of dispersed particles (Teflon* 5070 and 3170) as a function of time in the melt indicates that substantial molecular motion on the substrate occurs, large, angular particles, considerably larger than the original dispersion particles, form first for short melt times, followed by development of single crystals and banded structures with parallel double striations oriented along the long axis of the band. The molecules in the bands are parallel to the substrate, an individual striation appearing to consist of a "double edge" lamella more or less normal to the substrate. Correlations with the development of related structures on free and fracture surfaces of bulk samples will be described. *Registered trademark of the DuPont Co. ^1. N. K. J. Symons, J. Polym. Sci., 1, 2843 (1964). ^2. P. H. Geil, Polymer Single Crystals, Chap. IV, Interscience-Wiley, New. York (1963)

[KP01.158] Percolation in electrically conductive Polyepoxy-Polypyrrole blends

The aim of this work is to realize electrically conductive structural composites by using conductive polymeric blends as matrix. Polyepoxy-PPy blends are prepared by mixing PPy particles (0 to 20 percent in weight for PPy). these blends show percolation threshold around 11 percent in weight for PPy. In such conditions, electrical conductivity is 1E-3 S/cm. The glass transition temperature, as defined by DSC, increases with PPy concentration due to hydrogen bonds between PPy particles and epoxy matrix. Around the percolation threshold, a drop of Tg is observed probably due to a poorer crosslinking of the resin. Mechanical properties are practically unmodified except around the percolation threshold. Carbon fibres reinforced composites with blend of 13 percent in weight of PPy as matrix has electrical conductivity of 1E-4 S/cm without modification of the mechanical properties. This work has been suported by the Conseil Regional de Midi-Pyrenees, France, contract AMSA.

[KP01.159] Effect of Thickness on Morphology of Thin Films of Diblock Copolymers on Chemically Patterned Surfaces

The morphology of thin films of diblock copolymers on chemically patterned surfaces was investigated using AFM, TEM, and optical microscopy. Self-assembled monolayers (SAMs) of octadecyltrichlorosilane on SiO_x substrates were patterned with regions of different chemical functionality by exposure to X-rays. Thin films of symmetric poly(S-b-MMA) (lamellar period = L_o) were deposited on the patterned surfaces and annealed. Symmetric wetting (thickness quantized as nL_o) was observed on unexposed regions, and asymmetric wetting (thickness quantized as (n+½)L_o) was observed on exposed regions. If the initial film thickness was close to (n+½)L_o, the surface of the film was featureless over exposed regions and exhibited islands or holes over unexposed regions. Contrarily, for initial film thickness close to nL_o, the surface of the film was featureless over unexposed regions and exhibited islands or holes over exposed regions. In both cases, the topography of the film exhibited more complex structures over the transition region between exposed and unexposed SAMs.

[KP01.160] Synthesis amp; Characterization of Transparent Barrier Urethane Elastomers Based on Polyethylene Soft Segments

A series of polyurethane elastomers have been synthesized through copolymerization of polyethylene soft segments and MDI or H12MDI. Polyethylene soft segments were prepared by hydrogenation of polybutadiene polyols, either before or after copolymer synthesis. Polyols from three different suppliers were used as precursors, and ranged in branch content from 15 to \sim90%. Flexible, transparent materials were produced. The mechanical and barrier properties of these urethanes were evaluated for comparison with the performance of traditional flexible barrier materials (i.e., butyl rubber). Solvent uptake and swelling measurements were used to evaluate barrier performance. Branch content in the soft segment was found to affect both mechanical properties and solvent resistance, with low branch content leading to superior performance. Solvent diffusion coefficients for the materials were in the 10-8 range, comparable to those exhibited by flexible high barrier materials.

[KP01.161] Molecular Dynamics Study of a Tethered Polymer Chain in a Flow

It is now possible to observe the deformation of a single polymer chain in a flow using videomicroscopy. We have used Molecular Dynamics computer simulations to study the non-equilibrium static and dynamic properties of a single tethered polymer chain under a strong flow. Other computer simulation or numerical algorithms based on the worm-like chain have been developed to study the deformation of DNA chains. Our results are compared with experimental results as well as with previous theoretical predictions. Furthermore, our simulations provide very detailed information (even at the monomer scale) about the polymer conformation and dynamics, and the solvent flow around the polymer. The effect of excluded volume interactions and strong confinement is also examined.

[KP01.162] Near-Field Scanning Optical Microscopy Studies of Alkyl-substituted Polyfluorene Thin Films

Polyfluorene is an excellent candidate for the luminescent material in polarized light-emitting devices because of its rigid rod structure and thermotropic liquid crystalline properties. The fluorescence behavior of polyfluorene thin films is related to interpolymer interactions which are influenced by polymer ordering and chain aggregation. Both of these can be dramatically affected by annealing conditions and film thickness. While the fluorescent properties of rigid rod polymers have recently been investigated on a macroscopic scale, little is known about the structure on the sub-micron scale. We have used near-field scanning optical microscopy (NSOM) to study the fluorescence properties of a series of alkyl-substituted polyfluorenes as a function of film morphology in order to determine how the length of the alkyl chain affects local ordering and aggregation. Polarized fluorescence NSOM images of annealed and pristine films of various thickness show sub-micron ordering that can be correlated with emission from aggregate versus non-aggregate species. The length of the alkyl chain is observed to directly affect the degree of sub-micron liquid crystalline ordering and aggregation.

[KP01.163] Mechanochemical Alteration of Ethylene Copolymers

Pulverization of a series of commercial ethylene copolymers (Ziegler-Natta LLDPE, metallocene LLDPE, LDPE, HDPE) creates a small, but significant, amount of altered chains in these materials. These alterations are the result of mechanochemistry induced by the intense shear associated with the patented process, Solid State Shear Pulverization (S^3P). During S^3P chains are cleaved in the vicinity of every fracture of an in-process particle. Calorimetry, viscometry, and NMR data reveal how much long- and short-chain branches are created and consequently how much bulk properties are affected for each of these grades of polyethylene.

[KP01.164] Rotational and Translational Diffusion of a Rodlike Virus in Linear and Highly-Branched Polymer Solutions

Probe diffusion of polymer solutions is a popular technique to study the motion of polymers in solution at small distance scales. Such studies can provide insight into the nature of polymer entanglements in solution, which is still not fully understood. Described here is the use of depolarized dynamic light scattering to measure translational and rotational diffusion of tobacco mosaic virus in solutions of random coil ("entangling") polymers and highly-branched ("non-entangling") polymers, taken separately.

[KP01.165] Investigating the Effects of Size-Disparity in a Compreesible "Athermal" Blend

We use a recently development lattice theory [1] of a compressible blend to investigate an "athermal" polymer blend of two monodisperse species A and B having no exchange enrgy of interaction. Despite this, there are interactions in the system because of the presence of voids. The two polymers have different sizes. The present study complements a recent study by Chhajer and Gujrati [2] on the efects of size disparity in an "athermal" solution of polydisperse polymers. We extend this work to a polymer blend of monodisperse polymers. We will report the analytic and numerical results of our investigation.

[1] P. D. Gujrati, J. Chem. Phys. 108, 6952 (1998). [2] M. Chhajer and P. D. Gujrati, J. Chem. Phys.(to appear, Nov. 22, 1998).

[KP01.166] Measuring Scaling Laws in Polymer Reaction Kinetics

Theory has found universal scaling laws in polymer reaction kinetics. Many of these have never been tested experimentally. Here we present novel radical-based methods which can measure long and short time polymer-polymer reaction rates. These methods are able to overcome problems which severely limit the use of phosphorescence quenching at high concentrations. We present: (1) a theoretical analysis of our methods and (2) preliminary data.

To measure the long time rate constant k_\infty, macroradical-radical pairs are created by laser flashing a solution or melt containing chains carrying photolabile end groups. It is shown that after an initial transient, only the macroradicals survive. The subsequent kinetics are of simple second order with rate constant k_\infty.

A related method entails the creation of macroradical pairs from photocleavable groups at interior backbone locations. We demonstrate that the reaction kinetics which follow are governed by the time-dependent short time rate coefficient k(t).

[KP01.167] Integral Equation Theory of Polymer Melts and Blends

Polymer Reference Interaction Site Model (PRISM) calculations were performed on realistic models of polyolefin melts including: polyethylene, polyisobutylene, isotactic and syndiotactic polypropylene. In these calculations, both the intra and intermolecular structure of the polymer liquid were determined in a self-consistent manner. The multiple chain problem is mapped onto an equivalent single chain Monte Carlo simulation by representing the effects of the other chains through a medium-induced potential calculated from PRISM theory. The intra and intermolecular structure and the medium-induced potentials were obtained numerically from a series of Monte Carlo simulations and PRISM calculations performed iteratively until a self-consistent solution is obtained. The resulting structure factors are in close agreement with wide angle x-ray scattering experiments. The intermolecular pair correlation functions were used to calculate the solubility parameters of the melts and to study the heats of mixing of the various binary polyolefin blends.

[KP01.168] Molecular orientation in Langmuir monolayers studied by surface second harmonic generation

We used surface second harmonic generation (SHG) to study molecular orientation in a smectic-C liquid-crystal Langmuir monolayer at an air/water interface. The molecules under investigation are 4-octyl-4’-(3-carboxytrimenthyleneoxy) azobenzene (8AZ3). Because water is inversion symmetric, the SHG signal comes only from the surface. Furthermore, the magnitude of the surface SHG signal depends on the orientation of molecules, which makes SHG a sensitive probe of the phase of the monolayer. We measured the response of the SHG signal as we compressed the monolayer from a smectic-C phase to a more condensed phase and determined the average polar angle in each phase. The SHG probe samples an area roughly the size of a monolayer domain. As a result, the SHG technique combined with the depolarized reflected-light microscope enables us to extract further information about the local molecular orientation.

[KP01.169] Transmission Electron Microscopy of Electric-Field Induced Alignment in Liquid Crystalline Polymers

We have been examining the influence of electric fields on the in-plane alignment of lyotropic liquid crystalline polymers by transmission electron microscopy. The orientation is induced by solution casting onto electron transparent, self-supported (75 nm) silicon nitride substrates on which patterned arrays of interdigitated gold electrodes (5 microns wide) have been lithographically defined [1,2]. The geometry of the our devices includes variable electrode spacings (6-50 microns), average radii of curvature (10-550 microns), and field gradients (at a constant angle of 9 degrees) in order to systematically explore the influence of such spatially variable fields on the local microstructural evolution of ordered polymer thin films. The materials we have examined include poly(alkylisocyanates) and poly(benzyl glutamates), both of which can be conveniently processed from organic solvents and are of interest for such applications as electrorheological fluids and optoelectronically active devices. 1. T. L. Morkved, et al., Science, 273, 931, (1996). 2. T. L. Morkved, et al., Polymer, 39(16), 3871-3875, (1998).

[KP01.170] Neutron Reflectivity and Scanning Force Microscopy Studies on the Reinforcement of Rubbers by Silica and Carbon Black Fillers

Carbon black and silica are widely used fillers in the rubber industry. In numerous applications the mixture of the two fillers are used to reinforce elastomers. Therefore, it is of interest to study the differences between the two fillers on polymer rheology and to determine whether the two fillers are distributed uniformly in the polymer material. NR (neutron reflectivity) data show that the proximity of a planar HF-etched hydrophobic Si surface can slow down the dynamics of a dPB (d6-1, 4-polybutadiene) film. When dPB is reinforced with hydrophobic silica particles, a narrowing of the interface with BIMS ( Brominated poly (isobutylene-co-4-methylstyrene) ) is observed. When hydrophilic silica particles are used, almost no effect on the interfacial width is observed. Scanning force microscopy shows that when carbon black and silica particles are mixed, annealing causes the film to segregate into two distinct layers. The silica-rich layer is present at the air interface. The carbon-rich layer is located below the silica-rich layer. The results of further studies with XPS and SIMS will be presented.

[KP01.171] Spinodal Decomposition in a Sub-surface Layer of a Polymer Blend

We have studied phase separation in off-critical mixtures of poly(ethylene propylene) (hPEP) and perdeuterated poly(ethylene propylene) (dPEP) inside the metastable and unstable region of the phase diagram but under the influence of a surface which attracts the majority component (dPEP). In the adjacent depletion region nucleation barriers are eliminated and the film starts to phase separate long before phase separation occurs in the bulk. The hPEP-rich domains are confined to grow anisotropically within the unstable region. The growth gives rise to the formation of a regular roughness pattern on the surface when the domains relax into a more circular shape driven by surface tension. The volume fraction versus depth profiles are obtained using time-of-flight forward recoil spectrometry (TOF-FRES) while the roughness pattern that mirrors the phase morphology in the depletion layer can be monitored by scanning force microscopy (SFM). Depending on the initial dPEP volume fracti! on, the lateral bicontinuous phase pattern within the unstable region develops into different morphologies.

[KP01.172] Transient Dewetting in Thin Bilayers of Polymer Blends

For a polymer blend of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN), which exhibits a lower critical solution temperature (LCST), bilayers of PMMA-rich (M) and SAN-rich (S) films were prepared at their co-existing compositions and annealed at a temperature (T_a) above the LCST. Using confocal optical microscopy, the top M film was observed to dewet from the S substrate. For all the systems and temperatures (180^oC to 210^oC), hole growth in the M layer was observed only at early times (< 5 hours). Using atomic force microscopy, we found that the interface between M/S broadens during hole growth. We relate this transient dewetting to the relaxation time of the interface.

[KP01.173] Molecular mobility from the glassy state to the liquid state of Poly(n-butyl methacrylate)

The study of the crossing of the glassy state to the liquid state of poly(n-butyl methacrylate) has been performed by Thermo-Stimulated Current (T.S.C.) The T.S.C. complex spectrum shows two peaks above 273K. The first one, the \alpha-mode, which is located around T\alpha = 303K, has been associated with the glass transition, consistent with Differential Scanning Calorimetry results. The second one, the \alpha'-mode, which is localized near 363K, is also due to a dipolar relaxation process. The fractional polarizations technique allowed us to study the relaxation times distribution of these modes. The \alpha-mode is characterized by a broad distribution of relaxation times well described by an Arrhenius equation. Below T\alpha, the activation enthalpy increases and relaxation times follow a compensation law; for T between T\alpha and T\alpha+50, the activation enthalpy decreases. As for the \alpha', relaxation times follow a Vogel-Tammann-Fulcher equation. The evolution of activation parameters highlights three zones from the glassy state to the liquid state. The intermediate zone might reflect the existence of inter or intra molecular interactions in the liquid state.

[KP01.174] Dynamics of Water in Poly(ethylene oxide)/Water Solutions from Molecular Dynamics Simulations and Quasi Elastic Neutron Scattering

Molecular dynamics (MD) simulations and Quasi Elastic Neutron Scattering (QENS) studies were performed on low molecular weight poly(ethylene oxide)/water systems at two PEO weight fractions corresponding to Ether Oxygens:water=1:2.3 and EO:water=1:10 from room temperature to 450 K. QENS data were nalyzed by a random-jump-diffusion model, which assumes decoupling of rotational and translational motion. Water self-diffusion coefficients from MD simulations and QENS experiments were found to be in satisfactory agreement, but those from MD simulations were systematically higher. Direct comparison of intermediate structure factors for QENS experiments and MD simulations was also made. Hydrogen bonds between ether oxygen atoms and water molecule were found to have a short lifetime (less then 5-10 ps).

[KP01.175] Local Segmental Dynamics of a Copolymer in Dilute Solution Studied by Carbon-13 Spin-Lattice Relaxation

Local segmental dynamics of a styrene-butadiene copolymer in dilute solution were measured using carbon-13 magnetic relaxation spectroscopy. In recent literature, local segmental motions of polystyrene homopolymers have been reported to be significantly slower than for polybutadiene hompolymers. Hence, this copolymer system allows an experimental measure of the length scale of segmental motions. The copolymer used is random in structure with 20 percent of the monomers being styrene. On average, there are four butadiene monomers for every styrene monomer. Spin-lattice relaxation times for the butadiene monomers were obtained over a range of temperatures and solvent viscosities. All measurements were made in the extreme narrowing limit. The data are analyzed in terms of Kramers and Grotes-Hynes theories. The results are compared to similar measurements on polybutadiene homopolymers. It is seen that the styrene monomers do not significantly modify the dynamics of the butadiene monomers which is consistent with the length scales of segmental motions seen in recent simulations.

[KP01.176] Influence of Nanoscale Inorganic Layers on the Structure of Semi-Crystalline Polymers

Inclusion of 1-5 wt. in a polymer matrix (e.g., polymer-silicate nanocomposites) not only results in substantial improvements of mechanical, thermal, and barrier properties with respect to the pure polymer, but also provides a new means to evaluate structure and dynamics of polymers near surfaces using conventional bulk analytical techniques. Because of the nanoscale dimensions (1 nm) and the large aspect ratio (>100) of the layers, the material is comprised of polymer-inorganic interfaces in which each polymer chain is nominally less than Rg from an inorganic surface. Isothermal crystallization of nylon 6 containing dispersed aluminosilicate layers is examined in-situ using simultaneous small and wide angle x-ray scattering. Specifically, the influence of silicate content, interfacial interactions and layer size is considered. In addition to a change in crystal form (\gamma v. \alpha), the presence of the layers substantially alter nucleation rate and growth kinetics. These observations are attributed to the layers disturbing the crystal lamellae organization. Control of these processes is critical to process optimization of the properties of these semi-crystalline nanocomposites

[KP01.177] Crystallization by Surface Roughening: Nylon 66

The crystallization and melting of nylon 6,6 has been studied using thermal analysis, small angle x-ray scattering, and optical microscopy. A steady increase in melting temperature with crystallization temperature was observed for isothermally crystallized samples. However, the lamellar thickness remained essentially constant at between 1.5 and 2.0 chemical repeat units. The increase in the melting temperature is suggested to be a result of changes in the fold surface free energy. With a relatively constant lamellar thickness, the size of the critical nucleus for the secondary nucleation model could be obtained assuming a three dimensional nucleus, rather than the conventional monolayer nucleus. It was found to be between 14 and 260 stems in size, suggesting that another crystallization mechanism is operating. Calculations of the surface free energy of the hydrogen-bonded surface (the known growth face) suggest that it is the high energy surface, rather than the folded surface. An earlier model of Lovinger, which placed the fold direction into the melt, generating a rough surface, is consistent with the results.

[KP01.178] Micro-thermal Analysis of Macromolecules

A newly developed micro-thermal analyzer affords thermal images such as thermal conductivity, thermal diffusivity, and thermomechanical analysis on a sample of a few square micrometers area by combining the imaging ability of AFM and the thermal characterization ability of temperature-modulated DSC. By varying modulation frequency, one can obtain depth profiles of the thermal diffusivity since the thermal penetration depth depends on the frequency. Also, it can be used to characterize phase-transition temperatures such as the glass and melting transitions of such small sample regions with a precision of about 3 K. Heating rates can be varied from 1 to 6000 K/min. Modulation frequencies can be applied up to 100 kHz. We applied this new type of instrument to characterize micro-thermal and structural properties of various polymer systems. The operation principle and application examples will be presented.

[KP01.179] Orientation and non linear optical properties of 2-methyl-4-nitroaniline crystals grown on highly oriented PTFE substrates

The orientation of MNA on highly oriented PTFE substrate is investigated by optical microscopy, grazing incidence X-ray diffraction and FTIR spectroscopy. The MNA crystals grow on the substrate with two definite orientations. The low and high substrate temperature modes of growth correspond to a deposit of the aromatic ring flat or edge on the substrate. At low temperature, the orientation proceeds via an epitaxial growth which exhibits a good agreement between overlayer and substrate lattices. Without considering reconstruction, the lattice mismatch is equal to 3.9. However, at high temperature, the orientation mechanism corresponds to a grapho-epitaxy. This assumption is in agreement with the drastic decrease in the nucleation rate and the larger lattice mismatch for this crystallographic plane (6.2). Finally, the non linear optical properties of the deposited layers were determined from second harmonic generation experiments.

[KP01.180] The Local Structure of Polyolefin Melts from X-ray Diffraction

The local structure of atactic and head-to-head polypropylene melts have been examined with wide angle X-ray scattering methods. The local molecular architecture of linear macromolecules lead to unique intra and intermolecular packing which has important consequences for the properties of polymers and polymer blends. We examined a-PP and hh-PP to determine the effect of tacticity on the local and intermediate-range structure by comparing to the results for isotactic and syndiotactic polypropylene reported earlier. The stereo polypropylenes show unusual short-range order which may point to reasons for their peculiar behavior in blends with other polymers. In particular, the local structure of hh-PP is of interest, since this polymer shows unusual miscibility behavior with other polymers, such as PIB. The results will be compared to PRISM integral equation theory calculations.

[KP01.181] Thermal Stability of Electroactive Properties of Polyamide 11

Our objective in this work is to determine the limit working conditions for stable pyroelectric properties in Polyamide 11. Pyroelectric properties of ferroelectric films of Polyamide 11 have been investigated. The temperature dependence of the pyroelectric coefficient has been analyzed in the temperature range -180^oC up to +160^oC. Changes of slope in the temperature variation of the pyroelectric coefficient reveal the existence of transitions. A study of the influence of thermal history on ferroelectric films has been carried out by means of DSC. The breaking of hydrogen bonds at the glass transition does not affect pyroelectric properties. Broadband Dielectric Spectroscopy revealed the presence of secondary relaxation processes \beta and \gamma in the low temperature side. The \beta mode is dependent on hydratation and has an influence on the pyroelectric activity. Pyroelectric properties are mildly reduced after annealing at relatively high temperatures. This feature allows to envisage the use of this class of ferroelectric polymeric materials in new applications as sensors.

[KP01.182] Modeling the Phase Behavior of Binary Mixtures of a Nematic Liquid Crystal and Multifunctional Acrylates

Liquid crystal (LC)/polymer composites formed by polymerization induced phase separation process (PIPS) have found many applications in the field of electro-optics. The thermodynamic state of the LC and monomer mixtures (starting components of the composites), influences the final morphology, and therefore has a direct effect on the performance of any potential device. We have investigated the phase behavior of a series of binary mixtures, composed of the liquid crystal 4-n-pentyl-4'-cyanobiphenyl (5CB), and multifunctional acrylates with varying functionality. In particular, we report studies using molecular simulations to discern the effect of changing monomer functionality on the miscibility of the binary mixtures.

[KP01.183] Local pH and Ionic Strength in a Polyelectrolyte Solution

To probe the local pH and ionic strength in a polyelectrolyte solution, we contrasted the ionization of 1-4 quaternized poly-(vinylpyridine), PVP, in several environments. The PVP was 50quaternization was possible according to the local pH and ionic strength. The measurements were made by FTIR-ATR (Fourier transform infrared spectroscopy in attenuated total reflection), performed for technical reasons in D20 rather than H20. It emerged that ionization was decidedly different according to the environment. In particular, we find strong differences according to whether PVP is present (i) in free solution, (ii) adsorbed to oxidized silicon, (iii) in monomeric form in free solution. The main difference is the LOCAL ionic strength, analyzed in this poster.

[KP01.184] Fluorescence Sensor Development for In Situ Characterization of an Epoxy/Anhydride/Tertiary Amine System

Fluorescence methods have been developed for in situ characterization of cure at high temperature in a system consisting of an epoxy based on diglycidyl ether of Bisphenol A, methyl tetrahydrophthalic anhydride (MTHPA), and methyl imidazole as accelerator. This system undergoes reaction at an active site, unconventional for step growth monomers, and is the first of its type to have intrinsic fluorescence used to monitor reaction and properties. The excitation spectrum shape and intensity are strong functions of conversion, and a ratio of excitation intensities at different wavelengths yields a robust method for monitoring conversion. While the emission spectrum intensity increases upon cure, it changes little in shape, making it less suitable for in situ monitoring. MTHPA is largely responsible for the observed fluorescence during cure; the roles of chemical reaction and system viscosity and polarity during cure in modifying MTHPA fluorescence will be detailed. The ability of intrinsic fluorescence to provide sensitivity to physical aging and sorption in a cured system will also be discussed.

[KP01.185] Computer Simulation of Polyolefin Interfaces

Interfaces, thin films and amorphous cells of several hydrocarbon polymers are studied with atomistic computer simulation. Solubility parameters, surface tensions and interfacial tensions are evaluated from the computed structures. These structures are constructed using Molecular Dynamics (MD) and Molecular Mechanics (MM) techniques. The various components of the energetic interactions (torsional, vdW, etc.) are examined in detail in order to gain insight into the nature of the regular and anomalous interactions between these films. The polymers studied are all are atactic linear hydrocarbons and have approximately 200 carbons in the backbone chain. The primary difference between the polymers studied is the type of side group (ethyl or methyl) and the location, frequency and spacing of that group. Interfaces formed with the same polymer type yield a surface tension close to zero as expected. Attractive interactions between some of the pairs of films is found in the simulation results. The distribution among the energetic terms seems to indicate that this attractive interaction is brought about by favorable local intramolecular energetic terms rather than simply by van der Waals interactions alone.

[KP01.186] Structure of Poly(silylenemethylene)s

The structures of poly(silylenemethylene)s (PSMs) with n-alkyl side chains, namely, poly(di-propylsilylenemethylene) (PDPSM), poly(di-butylsilylenemethylene) (PDBSM), poly(di-pentylsilylenemethylene) (PDPeSM) and poly(di-hexylsilylenemethylene) (PDHSM) have been studied by X-ray and molecular modeling. The fiber X-ray pattern of PDPSM shows reflections that can be indexed by a monoclinic cell with dimensions a=10.26Åb=8.39Åc=4.88Åand g=83.25^o. The fiber repeat of PDPSM indicates that the backbone has an all-gauche conformation which is in contrast to polysilaethylene (PSE) which has all-trans conformation. Similarly, the reflections of PDBSM, PDPeSM and PDHSM can be indexed by a monoclinic cell with simple dilation of the a and b dimensions. Conformation and packing energies have been investigated using molecular mechanics methods with a force field based on ab-initio (6-31G** basis set) calculations. Comparison of the inter- and intra- molecular energies have been used to understand change of the backbone conformation from the all-trans to all-gauche with side chain length.

Supported by NSF grant DMR-9731345

[KP01.187] Nascent Liquid Crystal Polymers*

Lamellar single crystals have been grown for poly(p-phenylene terephthalate) (PPT), poly(p-phenylene naphthalate) (PPN) and poly(9-(2-oxy-5-carboxy)phenyl-10-phenylanthracene) (PPAOBA) using our CTFMP technique^1 and bulk melt polymerization. The properties and structure of PPT and PPN, with symmetric backbones, are of interest for comparison with the directional poly(p-oxybenzoate) (PpOBA) homopolymer and poly(p-oxybenzoate/2,6-naphthoate) copolymer. Characterization of PPAOBA extends our prior study of bulky side group rigid polymers. As for the phenyl branched 4,4’-oxybibenzoate and 2,6-oxynaphthoate polymers with the phenyl branch at a specific location,^2 the PPAOBA has a higher transition temperature than the corresponding non-side-group polymer; here 420^oC (T_g=311^oC) compared to 320-360^oC for PpOBA depending on its morphology.^3 Crystal structures have been determined by electron diffraction and simulation using Cerius2. For PPN, e.g., the phase I unit cell is monoclinic, a=7.76, b=5.71, c=14.99Å\alpha=\gamma=90^o, \beta=99.7^o. *Supported, in part, by NSF (Polymers Program) and KOSEF. ^1 F. Rybnikar et al., Macromol. Chem. Phys., 195, 81 (1994). ^2 J. Liu et al., Polymer, 37, 2205 (1996). ^3 E. g., Rybnikar et al., this meeting

[KP01.188] A Critical Comparison Between Time and Frequency Domain Relaxation Functions

A critical comparison is made between time and frequency domain relaxation functions. The issue of what defines equivalence between two functions is addressed. It is demonstrated that the appropriate measure for distinguishing between two functions is the maximum residual. Using this measure, we delineate the cases where the Kohlrausch-Williams-Watts (KWW) and Havriliak-Negami (HN) functions are indistinguishable and where they are decidedly different. The high and low frequency limiting power laws are examined for the Laplace transformed KWW function. Conclusions are presented regarding the ability to reach the limiting power law behavior experimentally as a function of the magnitude of the loss and as a function of frequency range, i.e., how broad a frequency range must be examined to observe the limiting power law behavior. This work is an extension of our previous work on distinguishing between representations of relaxation data over narrow frequency ranges: C.R. Snyder and F.I. Mopsik, J. Appl. Phys., 84 (8), 4421 (1998).

[KP01.189] Non-Linear Optical Polymers Studied by Positron Annihilation

Positron annihilation lifetime spectroscopy has been used to measure sub-nanometer defects (free volumes and holes) properties in a series of chromophore-doped polymers as a function of temperature and of electric field. The lifetime results vary as a function of electric field poling. Current positron results show the important role of free volumes in the generation of non-linear optical properties of chromophore-doped polymeric systems.

Supported by AFOSR. Chia-Ming Huang et al, J. Phys. Chem. B, 102, 2474(1998).

[KP01.190] Polyelectrolyte Adsorption onto Polyelectrolyte Brushes of Opposite Charge

Polyelectrolyte brushes of variable surface density and charge density were grafted to single solid surfaces of oxidized silicon, then exposed to solutions of poly(acrylic acid), PAA, at pH such that the PAA was negatively charged. The mass adsorbed and the ionization of the adsorbed chains were measured by FTIR-ATR (Fourier transform infrared spectroscopy in attenuated total reflection). It emerged that ionization of the adsorbed chains was very different from that of these same chains in bulk solution. The deviations were both positive and negative, depending upon the amount adsorbed. Positive deviations -- near-complete ionization of the poly(acrylic acid) -- was observed when the surface coverage was low. Negative deviations -- ionization less than one-half that characteristic of these same chains in bulk solution -- was observed when the surface coverage was near full coverage. This poster discusses why the sign of deviation depends on surface coverage.

[KP01.191] A Novel Technique for Polymer Blend Compatibilization

Solid-state shear pulverization is a continuous, environmentally benign technique in which chain scission results in a powder containing a free radical population. Evidence of chain scission includes changes in the molecular weight distribution and melt flow rate. Characterization of the glass transitions (Tg) of polystyrene in a PP/PS 25/75 wt% blend has revealed a 10°C reduction in Tg for the polystyrene-rich phase upon pulverization. Additionally, the PP-rich phase exhibits a reduced ability to crystallize as compared to the PP homopolymer. Mixing studies show that pulverization of PS/PE 92/8 wt% blends reduces phase inversion and long mixing times despite the components’ unmatched viscosities. The crystallinity and glass transition studies coupled with the mixing studies indicate intimate mixing upon pulverization and microstructure stabilization, i.e., compatibilization. In addition, some pulverized blends of PP/PS and PS/PMMA exhibited mechanical property improvements, including a factor of four increase in elongation, up to a 30up to a 15% increase in flexural strength.

[KP01.192] Diffusion Coefficients of Linear and Cyclic n-Alkane Melts

Monte Carlo simulations of alkane melts are performed on a high coordination lattice which is formed by connecting every other site on a tetrahedral diamond lattice. Local interactions and long range interactions are calculated by the rotational isomeric state (RIS) model and by a Lennard-Jones potential, respectively. The simulations are performed by moving randomly chosen single beads using a Metropolis Monte Carlo algorithm. Diffusion coefficients, D, can be calculated either from the time dependence of the motion of the center of mass (Einstein) or from the integral of the velocity autocorrelation function (Green-Kubo). Both of these methods should yield the same result at infinite time. The results of these two methods approach each other in our finite time simulations. The main subject of this study is to find the better method for estimation of D in the simulation of large polymeric systems. The diffusion coefficients of linear chains of C_12H_26, C_60H_122, C_100H_202 and C_316H_634 and cyclic chains of C_60H_120 and C_100H_200 are calculated at 473K. The results indicate that the D from the Green-Kubo equation approaches its limiting value faster than the D from the Einstein equation. The difference is more pronounced at high molecular weights where computation time is extremely high. Therefore, D can be estimated for large polymeric systems with smaller simulation lengths with Green-Kubo equation.

[KP01.193] Poyleletrolyte-Protein Complex in Synovial Fluid

Synovial fluid is essential to the lubrication and cushioning of our joints. Hyaluronic acid (HA), a high molecular weight polyelectrolyte, and albumin are found in sizable quantities in synovial fluid (3 mg/ml and 11 mg/ml, respectively). We propose a soluble complex between HA and albumin is formed from multiple albumin molecules binding to a single HA chain, and that this complex strongly influences the mechanical, and therefore, lubrication properties of synovial fluid. We investigated the rheological properties of the following solutions: 1) HA as function of concentration; 2) HA at 3mg/ml with various anti-inflammatory drugs, such as aspirin, methotrexate, and D-penicillamine; 3) HA (3 mg/ml) with albumin (11mg/ml); and 4) the HA-albumin solution with various anti-inflammatory drugs. The complex, time dependent rheology of the HA-albumin solutions will be discussed.

[KP01.194] Large-strain steady shear of lamellar diblock copolymers

Most studies of shear-induced alignment in lamellar diblock copolymers have focused on alignment processes using oscillatory shear with 40% to 100% strain. We explore larger strain effects on the morphological development of a lamellar diblock copolymer, poly(styrene-b-ethylene propylene), by focusing on the evolution of defect structures such as kink bands. A well-aligned parallel starting state was produced with less than 10 cycles of large amplitude oscillatory shear using a strain amplitude of 200%, indicating the efficiency of large strains in producing parallel alignment. A series of large-strain steady shear experiments were carried out, with strain amplitudes varying from 100% to 1000%. Small-angle X-ray scattering showed that an asymmetric intensity distribution developed around the parallel starting state, qualitatively consistent with our model of lamellar rotation at small strains. Electron microscopy was also used to characterize morphological changes caused by large-strain steady shear.

[KP01.195] Thermodynamics of Confined Semidilute Polymer Solutions: Computer Simulation and Effective-Medium Gaussian Chain Theory

Thermodynamics of nondilute solutions of chain molecules confined to a slit was studied in lattice simulations and the effective-medium Gaussian chain theory. The latter extends the eigenequation formulation of de Gennes to a Gaussian chain in an effective interaction potential determined by the local monomer density. The concentration dependence of the chemical potential, determined in the insertion method, and the chain dimension, determined in the canonical ensemble simulation, showed a crossover from three- to two-dimensional characteristics as the slit narrowed. The density profile across the slit showed a slightly concave pattern at the plateau and was consistent between the simulation results and the theory.

[KP01.196] Physical characteristics of a swelling gel

The study concerns a cross-linked PolyAcrylicAcid (PAA) synthesized by inverse emulsion polymerization. The principal chemical property of this material is related to COOH groups which are able to absorb an important amount of liquid. This justifies its use for biomedical applications. Thanks to Differential Scanning Calorimetry (DSC) technique, it is possible to determine glass transition temperature (Tg), the influence of different parameters like annealing, water and N, N' MethyleneBisAcrylamide (MBA), which is at the origin of polymeric network. Thermally Stimulated Current (TSC) allows us to analyze the dielectric relaxation mode (\alpha) associated with the glass transition below 273K and due to delocalized molecular mobility. More localized molecular mobility gives a secondary dielectric relaxed mode (\beta) at very low temperature. The dielectric mode will be compared with the anelastic modes as obtained by Thermally Stimulated Creep (TSCr). A discussion of the value of the activation parameters will be presented.

[KP01.197] Structure Change from Smectic to Columnar Phases in a Series of Liquid Crystalline TPP Copolyethers

A series of liquid crystalline copolyethers was synthesized from 1-(4-hydroxy-4'-biphenyl)-2-(4-hydroxyphenyl)propane and various *,*-dibromoalkanes [coTPP(n/m)]. These coTPPs possess a varying odd-number (n = 5, 7, 9 and 11) and a fixed even-number (m = 12) of methylene units in an equal molar ratio. The coTPPs show multiple phase transitions during cooling and heating, which are close to thermodynamic equilibrium. The periodicity order along the chain direction is increasingly disturbed when the length of the odd-numbered methylene units decreases from 11 to 5. This leads to a structure change from smectic and smectic crystal phases in coTPP(11/12) to a hexagonal columnar phase in coTPPs(5/12 and 7/12) as based on wide angle X-ray diffraction results. Such structure change also occurs in coTPP(9/12) when the temperature is increased. The overall structual changes are attributed to disorders introduced into the layer structure by the dissimilarity of the comonomer lengths.

[KP01.198] Measurement of Fracture Toughness and Hydro-thermal Fatigue Resistance of Polymer Interfaces

We have measured the fracture toughness and hydro-thermal (HT) fatigue crack growth resistance of an epoxy (both silica filled and unfilled)/polyimide interface which is of interest in microelectronic assemblies. An asymmetric double cantilever beam testing method was used to quantify the critical strain energy release rate for crack growth along the interface as a function of the mechanical phase angle. The critical energy release rate is also compensated for the effect of thermal residual stresses in the specimen. We have also developed a new technique based on a fiber optic displacement sensor for rapid determination of crack growth rate per cycle (da/dN) of an interfacial crack under HT fatigue conditions. The relation between da/dN and the maximum strain energy release rate characterizes the HT fatigue resistance of the interface, which depends on the mechanical phase angle of the interfacial crack and the relative humidity.

[KP01.199] The Effects of Relative Viscosity on Phase Segregation in PS/PMMA Blends

The effects of relative viscosity on phase segregation were studied. Symmetric blend films of Polystyrene (PS) and Poly Methyl(Methacrylate)(PMMA) were spun cast onto HF etched Silicon wafers and annealed at 165 C for various times. The relative viscosity of the polymers was adjusted by changing the molecular weights. Annealing sequences with PS/PMMA blends of 27k/27k, 90k/27k, 27k/90k, and 90k/90k were examined. Results show that when the viscosity of the two components are comparable, unique flow patterns are observed. These patterns persist when the PS viscosity becomes larger than that of PMMA. If the PMMA viscosity is much less than PS, then a frustrated system is observed. In all cases, PMMA forms the continuous phase that wets the silicon surface. Consequently, the mobility of the PMMA becomes the limiting factor in the phase segregation dynamics.

[KP01.200] Thin Film Anomalies in the Glass Transition of Polymer Brushes

The glass transition in confined geometries such as small pores or thin films has recently attracted a lot of interest. Cooperative relaxation mechanisms which are believed to underlie the glass transition may well be affected by geometric constraints. Significant differences between the glass transition of bulk materials and thin films have been found. While the glass is most often induced by temperature, addition of low molecular additives constitutes an alternative approach. Organic solvents act as plasticizers and decrease the glass transition temperature Tg. Provided that the film of interest is in diffusion equilibrium with an adjacent phase of solvent vapor, the glass transition in the film can be driven by the solvent vapor pressure. The solvent driven glass transition proceeds analogously to the temperature driven transition. The sorption curve (solvent volume fraction vs. solvent activity) displays a characteristic kink at the solvent content which is just sufficient to lower the glass transition temperature to room temperature.

[KP01.201] Selective Etching of PS/PB Diblock Copolymer Thin Film by Oxygen Plasma

In an attempt to fabricate nano-patterns in polystyrene/polybutadiene(PS/PB) diblock copolymer films, we characterize oxygen plasma etching properties under various conditions. The PS/PB copolymer thin films with thickness of 50nm were prepared by spin-coating method on silicon wafers. The PB cylinder domains were formed in the PS matrix after phase separation. Oxygen plasma operated in a parallel-plate RF discharge system was used to etch PS/PB thin films. Etching selectivity of PB versus PS was found in oxygen plasma, so that selective removal of PB domains was realized. Optimal conditions of etching were searched. Further the crossover from the ion etching mechanism to that of reactive neutral etching was studied with the aid of different methods for plasma diagnostics.

[KP01.202] Conformations and Density Profile in Electrophoretic Deposition of Polymer Chains on Adsorbing Surface

Conformation of polymer chains and their density profile are studied using a Monte Carlo simulation of polymer chains driven by an electric field toward an impenetrable wall/surface. A discrete lattice of size L_x \times L_y \times L_z is considered with a large aspect ratio L_x/L_y(L_z). Polymer chains are released from the source end (X=1), far from the wall (X=L_x). In addition to excluded volume, nearest neighbor polymer-polymer repulsive and polymer-wall attractive interactions are considered in presence of a field (E) along x-direction. Kink-jump dynamics is used to move the chain nodes with the Metropolis algorithm. Polymer density grows as the chains are deposited on the wall. Growth of the density profile is studied in detail along with the conformation of chains. Attempts are made to study the variation of conformations of polymer chains in different regions (at/near the wall, soft-bulk, interface, and fluid regimes) as a function of field and temperature.

[KP01.203] High Temperature Conductivity and Glass Transition Relaxation Processes in Polyarylates

Thermal-stimulated polarization and depolarization experiments with and without blocking electrodes are performed on Tyrosine-Derived Polyarylates with different backbone lengths. The experiments on the different samples are carried out using the same thermal history throughout the entire characterization process. The high temperature current rise due to the conductivity of the samples is studied comparatively with a simple model that employs an approximation for the WLF^1 relaxation time used for the characterization of the dielectric constant in polymers. The Glass Transition Peak is modeled with a phenomenological expression valid near Tg, which describes the glass relaxation with a minimum numbers of parameters^2. The zero and first order parameters obtained for the conductivity are compared and discussed as well as the parameters of the glass transition peak for the different samples chosen. The redistribution peak observed due to the presence of blocking electrodes is also presented and compared with the conductivity results. Departure of the conductivity data at low temperatures is discussed on the bases of results obtained for polymer dynamics. ^1 M.L. Williams, R.F. Landel and J.D. Ferry, J. Am. Chem. Soc.\/, 77\/, 3071 (1955). \vskip 18pt ^2 M. Puma, Polym. Adv. Technol.\/, 8\/, 39 (1997).

[KP01.204] Environmental stress-cracking of polyolefin nanocomposites

Polypropylene (PP) clay nanocomposites have been produced with conventional improvements in modulus and strength, and with ductility that exceeds conventional composites. In addition, the resistance to environmental stress cracking (ESC)is significantly better than either pure polypropylene or conventional composites. These exceptional properties originate from the small size and high aspect ratio of the particles, and from strong interactions with the polyolefin matrix caused by the tethering of chains to the particle. Tethering reactions were confirmed by NMR and DRIFT spectroscopy, and by X-ray diffraction (XRD) analysis, which showed intercalation of both coupling agent and polymer. The nanofiller was then dispersed in unmodified PP by conventional melt-mixing procedures, and the resulting morphology was examined by XRD and TEM analyses. Double-notched rectangular pieces were tested under constant load, while immersed in a 20% aqueous solution of a surfactant that is known to have a high affinity for polyolefins. At 10% filler loading, the time to failure was increased by a factor of three. Conventional talc filled PP specimens showed only 20% improvement in ESC resistance. The authors gratefully acknowledge the financial support of ACS PRF grant #31333-G7 and NSF CMMC grant #EC9108700.

[KP01.205] Rigidity of the Backbone for Poly(bis(4-butoxycarbonylphenyl)) carbodiimide and Poly(bis(4-butylphenyl))carbodiimide studied by Solid State ^13C T_1\rho Measurements

The structure and rigidity of backbone of the two polycarbodiimides as a function of the side chains was studied by the ^13C CP/MAS NMR. From these results, the structures of the polycarbodiimides were determined, and the ^13C spin-lattice relaxation times in the rotating frame were measured. Based on our findings, we discuss the mobility for backbone of the two polycarbodiimides with and without ester linkage between the aromatic and aliphatic side chains. The backbone carbon of polycarbodiimide (I) with ester linkage has a lower activation energy, 18.63 kJ/mol, than the polycarbodiimide (II) without ester linkage, 23.20 kJ/mol. Also, the activation energies of the aliphatic side chains show gradually increasing values. We think that this increase results from the greater mobility of the alkyl chain toward its free end.

[KP01.206] Generation of Elastomeric Nanofiber by Electrospinning

Electrospinning utilizes electrical force to produce polymer fibers with nanometer scale diameters. Nanofibers of a commercial styrene-butadiene-styrene tri-block copolymer (Kraton D1101) were electrospun from solution. Solvent evaporation occurred on a sub-millisecond time scale, while the nanofibers were being stretched by the electrical force. The nanofibers were elastic, birefringent and had diameters around 200 nanometers. After staining with osmium tetroxide, the nanofibers were examined using transmission electron microscope. In the as-spun fibers, the shapes of the separated phases were very irregular and somewhat elongated along the fiber axis. Annealing the as-spun fibers at 100°C for five minutes caused the separated phases to grow larger and adopt more regular shapes. Longer annealing time made the phase boundaries sharper, and produced polystyrene domains that were not precisely aligned along the fiber axial direction. Electrospun elastomeric nanofibers may find use in polymeric composites for improving the toughness.

[KP01.207] Supramolecular Comb-Coil Diblock Copolymers with Two Length Scales: Transmission Electron Microscopy

Flexible polymers complexed with low molecular weight amphiphilic molecules form highly organized supramolecular structures with typical layer thickness of 20-50Å. Amphiphiles can be bonded to the polymer using either hydrogen bond or ionic interaction.[1-3] Order-disorder transition temperature can be tailoring by balancing the interaction strength and the polarity difference between the polymer and amphiphile. These structures can be combined with block copolymers to construct self-organized hierarchical nanostructures consisting of two length scales[4]. In this work TEM is used to construct morphology diagram and to study the structure-inside-structure morphology in the lamellar, cylindrical and spherical case.

(1) G. ten Brinke, O. Ikkala Trends in Polym. Sci. 1997, 5, 213. (2) M. Antonietti, C. Burger, A. Thünemann Trends in Polym. Sci. 1997, 5, 262. (3) C. Ober, G. Wegner Adv. Mat. 1997, 9, 17. (4) J. Ruokolainen, R. Mäkinen, M. Torkkeli, R. Serimaa, T. Mäkelä, G. ten Brinke, O. Ikkala Science 1998, 280, 557.

[KP01.208] Polymeric Material Limitations to the Spatial Resolution of Confocal Microscopy

Confocal microscopy is popular for identifying the 3D spatial location of structures in biological materials. It has recently been used to study skin/core effects in fibers and the composition of polymer blend phases. This article describes how the mismatch between the design refractive index of the microscope objective and that of many polymeric materials greatly limits the spatial resolution of the confocal microscope. The resultant error is caused by the spherical aberration induced by the refractive index mismatch. It can result in a defocusing by more than half of the thickness of the object. Experimental results are shown to agree with the simple geometric optics analysis of the confocal microscope. This problem is inherent in all polymeric materials to a greater or lesser extent and can greatly limit the utility of confocal microscopy in the study of polymers.

[KP01.209] Molecular Mobility Ranges in Poly(\epsilon-caprolactone): from Local to Segmental Dynamics

Dielectric measurements were carried out on undiluted poly(\epsilon-caprolacone) (PCl) over wide frequency and temperature ranges, 10^-3 \leq \nu \leq \ 3 \times 10^6 Hz and 110 \leq T \leq 318 K, respectively. The results indicate clearly the presence of several relaxation processes in the dielectric loss curves. In the low temperature region there are at least two processes corresponding to local mobility, the \gamma and \beta modes. In the medium temperature range, i.e. 210 K, the \alpha mode which is the dielectric manifestation of the glass transition corresponds to the segmental mobility. At higher temperatures a fourth relaxation process appears as a shoulder on the steep increase due to the conductivity. The molecular weight dependence of the molecular mobility is apparent only in this highest temperature mode, the local and the segmental mobility do not show any changes when the molecular weight ranges from 10,000 to 83,000 gmol^-1. As this polymer has a dipolar moment along the chain, this very intense mode could be due either to the charge accumulation at the interphases or to a restricted normal mode. The degree of crystallinity determined by WAXS shows an important increase in the crystallinity of the material as the molecular weight decreases which does not affect the dynamics for the local and segmental modes.

[KP01.210] Non-Contact Measurement of the Viscosity of Water as a Function of Temperature

Surface tension and viscosity govern the propogation and attenuation of capillary waves on the surface of fluids. Hence a detailed knowledge of the dispersion and attenuation behavior of capillary surface waves may be used to obtain the surface tension and viscosity of fluids. We employ a novel non-contact method to determine the viscosity of water as a function of temperature by a precise measurement of the extinction coefficient of the capillary waves.

[KP01.211] Phase Diagram of water/2,6-dimethyl pyridine/nanoparticle Complex Fluids

We report measurements of the phase diagram of complex fluids consisting of stabilized dispersions of gold and silica nanoparticles in water/2,6-dimethyl pyridine binary liquids. We will discuss both a classical thermodynamic interpretation of our results and also the possible influence of critical fluctuations of the binary fluid on nanoparticle interactions. Our results will be compared and contrasted with previous work by other groups on similar binary-liquid based complex fluids having larger particle diameters.

[KP01.212] Molecular Dynamics Simulation of Bubble Formation in Micropores

Molecular dynamics simulations are carried out to study the molecular mechanism of bubble formation of confined liquids in slit microscopic pores. Three kinds of wall were selected: weakly adsorbing wall (WAW), moderately adsorbing wall (MAW) and stronly adsorbing wall (SAW). The width of the slit pore ranges from about five (the narrow pore) to twenty-four (the wide pore) molecular diameters. Markdely different bubble formation behavior is found in pore with WAW, MAW and SAW, for both the narrow pore or wide pore. For the wide pore, the stability limit of confined liquids is also analyzed and compared with that of the bulk liquid.

Part K of program listing