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 lim