Session CP1 - Poster Session.
POSTER session, Monday afternoon, November 15
Grand III, The Westin Seattle

[CP1.01] Three-dimensional magnetic field and energetic particle measurements and simulations on SSX

Three-dimensional magnetic field measurements in the reconnection layer of the SSX experiment are underway. Magnetic probes (B_x, B_y, B_z) are arranged in a 5 by 5 by 8 array with 2 cm resolution (600 separate measurements on a single shot). Probe signals are integrated and multiplexed at 10 MHz in groups of 8 so the effective digitization rate is 1.25 MHz. At the same time, energetic particle flux will be monitored by sets of identical retarding grid energy analysers (calibrated in a separate cw plasma facility). We have observed jets of magnetofluid at the Alfvén speed in the reconnection plane and super-Alfvénic ions accelerated normal to the plane. These measurements appear to be correlated with formation of a magnetic o-point. Coordinated with the experimental effort is an MHD/particle simulation effort. Results from the TRIM MHD code will be used as input for a precision particle orbit code. Finally, temperature and density are monitored with a combination of VUV spectroscopy and electrostatic probes.

[CP1.02] First Measurement of Local Ion Heating During Magnetic Reconnection in a Laboratory Experiment

Magnetic reconnection is believed to play an essential role in accelerating and heating plasma particles to high energies in solar, magnetospheric, and laboratory plasmas. This process has been studied on MRX, which creates a stable, quasi steady-state, and toroidally axisymmetric 2D reconnection layer and an environment in which the MHD approximation (\rho_i \ll L, S\gg 1, v_A\ll c) is valid globally. Local values of T_i are obtained using a miniature, fast-swept (100~kHz) retarding-field gridded energy analyzer and a multi-chord spectroscopy-CCD system. Ion flows are measured using a Mach probe and calibrated with Doppler shifts of ion line emission. T_i is observed to be 2--3T_e (measured with a triple probe) inside the reconnection layer, indicating efficient conversion of magnetic field energy to ion thermal energy. The downstream ion outflow velocity is only approximately 0.2--0.3v_A, in contrast with the Sweet-Parker model. Indications are that the ion toroidal velocity is larger, around 0.5v_A, making up a substantial fraction of the current. Therefore, primary energy conversion occurs not through the thermalization of a downstream Alfvénic outflow jet but through a different mechanism possibly involving the more energetic toroidal ion flow and wave-particle interactions. Comprehensive results will be presented and discussed.

[CP1.03] Resistivity and Fluctuations in the Current Sheet of MRX

The electrical resistivity in the current sheet of the Magnetic Reconnection Experiment (MRX) has been measured to be larger than the Spitzer value by as much as an order of magnitude(H. Ji, et al), Phys. Rev. Lett., 80, 3256 (1998). The drift parameter, V_d = j/(e n v_th,i), in these experiments has been determined from measured current density, density, and temperature. This parameter was found to be constant and of order unity over a wide range of operating parameters. An explanation for these observations is the existence of a current-driven instability which limits the relative drift speed and enhances the resistivity. The order of the drift parameter implies that lower hybrid waves are unstable, and that they have a sizable growth rate (\gamma \approx ømega_r). Theoretical calculations show that the instability can produce the observed level of anomalous resistivity if the density fluctuation level reaches a few percent. Measurements of fluctuations in the MRX device are in progress, using Langmuir probes and pick-up coils to investigate electrostatic and magnetic fluctuations. We will present measurements of fluctuations in floating potential, density, and magnetic field in the current sheet.

[CP1.04] Numerical Study of Two-Fluid Effects on Magnetic Reconnection in Merging Spheromaks

The investigation of magnetic reconnection in merging spheromaks with an implicit parallel resistive MHD code is extended into the low-viscosity and low-resistivity regimes. The scaling of the reconnection rate in the nonviscous limit is presented. The physical model is refined with the addition of two-fluid effects, requiring the resolution of finer spatial scales within the current sheet. The effects of the added terms on the reconnection rate scaling are described.

[CP1.05] Experimental Investigation of Non-MHD Fast Magnetic Reconnection in TS-3

Cause and mechanism for fast magnetic reconnection event have been investigated using spheromak/tokamak merging experiment in the TS-3 device. We have reported that the effective resistivity of the current sheet increased significantly, when the sheet width \delta is compressed shorter than ion gyroradius \rho_i. However, \rho_i is almost equal to ion collisionless skin depth c/ømega_pi in the current-sheet with ion beta \approx 1. We scanned the ion beta by varying field component B_X parallel to the X-line from 0.5 B_// to 5 B_//, where B_// is the reconnecting field component. A new finding is that this anomalous increase in resistivity depended clearly on the relationship between current sheet width \delta and ion gyroradius \rho_i, not on that between \delta and ion collisionless skin depth c/ømega_pi. Ion motion effect is concluded to cause the fast magnetic reconnection observed in low-B_X discharge.

Current-sheet ejection was also found as another fast magnetic reconnection mechanism in high-B_X and low density discharge. The current sheet was ejected rapidly outside of the X-point region by large external compressing force and this global instability of the current sheet caused a significant increase in reconnection speed, while the high-B_X tokamak reconnection is much slower than the low-B_X spheromak reconnection.

[CP1.06] Current-Sheet Structure in TS-3 Merging Experiment

Detailed spatial structure of current sheet has been measured experimentally by use of magnetic reconnection of two merging toroidals. In our TS-3 merging device, two spheromaks or tokamaks were merged together in the axial direction and a toroidally-closed current-sheet was produced on the midplane during their merging process. We installed three-types of probes to know its detailed spatial structure: Mach probes, triple electrostatic probes, Faradey cup and magnetic probe. The Mach probe composed of two double probes was used to measure 2-D plasma velocity on r-z plane. This measurement identified both of plasma inflow and outflow in 2-D and its maximum velocities turned out to be Mach 3 whose absolute value was calibrated by Faradey cup measurement. A triple probe was installed on the midplane to measure ion density and electron temperature. A new finding is that the electron density falls shapely around both ends of the current-sheet length. Around the same points, the magnetic field strength increases sharply and the plasma velocity was annihilated, suggesting formation of fast shock in the plasma outflow regime. Those parameter is consistent with the Ranking-Hugoniot equation within 30% error. Further 2-D study of plasma velocity, ion density, ion temperature and magnetic fields near the X-point will conclude whether the observed fast reconnection is equipped with the famous shock structure or not based on the Ranking-Hugoniot equation and what type of 2-D structure the current sheet has.

[CP1.07] Alfven Wave Instability of Current Sheets in Force-Free Collisionless Plasmas

We show that inertial or kinetic Alfven waves can be spontaneously emitted by sufficiently thin current sheets in low \beta force-free collisionless plasmas. Such current sheets are associated with the abrupt change in magnetic field direction at the interface between adjacent twisted flux tubes. When the current sheet is thin enough for the electron flow velocity to be comparable to the Alfven velocity, the electron flow becomes susceptible to Landau instability (i.e., beam instability). However, for global instability the narrow instability region must pump enough power into the plasma to overcome both ion Landau damping within the current sheet and electron Landau damping of the radiated Alfven waves outside the current sheet. By calculating the net wave power injected into the global plasma, the instability threshold is calculated for both the inertial and the kinetic Alfven wave regimes. For moderately strong shear, emitted kinetic Alfven waves can resonantly accelerate current sheet ions to energies much higher than T_e , providing a direct mechanism for conversion of magnetic field energy into an energetic ion beam.

[CP1.08] Wave Steepening and Current Sheet Formation in EMHD Turbulence

A large, nonuniform laboratory plasma has been generated with electron \beta \geq 5. Its diamagnetism completely expels the weak external magnetic field (B_0 = 5~G) from the plasma center. A strong instability near the lower hybrid frequency is observed on the density/magnetic field gradient. It produces flute-like density perturbations (\delta n / n \geq 30%), propagating near the sound speed in the electron diamagnetic drift direction, coupled to magnetic fluctuations, which form flux-ropes of predominantly negative helicity. The nonlinear waves form asymmetric density cavities with steepened fronts where thin current sheets are located. The EMHD turbulence is analyzed via magnetic hodograms, amplitude statistics, and conditional averaging.

[CP1.09] Vortex Collisions in Electron MHD Plasmas

Three-dimensional Hills-type vortices in the electron fluid or perturbed magnetic field are generated in a large, weakly magnetized laboratory plasma in the parameter regime of electron MHD. The vortices propagate in the whistler mode along a uniform dc magnetic field B_0 where the propagation direction determines the sign of their helicity. The collision of two oppositely propagating vortices is studied. For vortices of opposing toroidal fields, the head-on collision produces a single poloidal vortex of zero helicity. The lost toroidal field energy is converted into poloidal field energy. After the collision, the vortices continue to propagate without energy/momentum loss due to the collision. Likewise, no nonlinear interactions occur in glancing collisions. These results are explained by the fact that vortices are force-free structures and imply a lack of wave-wave interactions among whistler wave packets. The observations suggest that there is no cascading in EMHD turbulence spectra.

[CP1.10] Lack of Helicity Conservation and Field Line Tying During Vortex Reflection

A magnetic field vortex is created with a pulsed loop antenna in a magnetized laboratory plasma (1~m diam, 2.5~m length, 10^12~cm^-3, 3~eV, 5~G). The vortex is strong enough to modify the local ambient field (B_z,max \approx 1.5~G, B_\perp,max \approx 2~G). Because we operate in the EMHD regime, the magnetic vortex causes a similar structure in the electron fluid velocity, both propagating in the whistler mode against the ambient magnetic field towards a conducting boundary. With magnetic probes, the field topology is measured during the reflection process and found, at the boundary, to be radial, i.e., tangential, satisfying the boundary conditions. The incident and reflected axial fields have the same direction, while the azimuthal field reverses sign, consistent with the EMHD requirement that the helicity of a magnetic vortex be reversed when the direction of propagation is changed. This leads to non-conservation of helicity because the frozen-in condition is violated at the sheath between the conducting boundary and the plasma. This implies that no field line tying occurs between plasma and boundary. Energy dissipation at the boundary layer is negligible.

[CP1.11] 3D Magnetic Null Points in a High-Beta Plasma

In a large, high-beta laboratory plasma (1~m diam, 2.5~m length, B_0 = 5~G, \beta \approx 5), a strong dipole field is generated with a pulsed loop antenna. It is directed opposite to the dc field and creates two 3D magnetic null points whose topology (improper spiral nulls) is measured with magnetic probes. A Taylor series expansion of the measured magnetic field at the null points yields all twenty-seven components of the second order expansion matrix. In this EMHD plasma, the field penetration is controlled by the propagation of whistlers. The nonlinear propagation of whistlers with magnetic null points is studied. It leads to a breakdown of the field symmetry and rapid topological changes involving 3D reconnection.

[CP1.12] Three-Dimensional Kelvin-Helmholtz Instability and Magnetic Reconnection

We present results from an ongoing computational investigation of a three-dimensional Kelvin-Helmholtz instability and the ensuing magnetic reconnection under conditions similar to those in the dayside magnetosphere [1]. The equations of compressible, resistive, magnetohydrodynamics are solved using the FLIP-MHD, particle-in-cell method [2]. The dynamical equations are integrated implicitly using a Jacobian-free Newton-Krylov method [3]. In the 3-D configuration of this study we consider the low-latitude conditions, where the flow is nearly perpendicular to the magnetic field. In the direction parallel (or anti-parallel) to the initial magnetic field the imposed velocity shear has a maximum at the center (i.e the equator), and decreases to zero at the two ends of the geometry. This configuration will drive a differential rotation in the magnetic field since the initial Kelvin-Helmholtz instability will have the largest growth rate at the equator. Even though the configuration is a simplified representation the day side of the earth's magnetopause, one can make connections between the time dependent reconnection observed in the simulations, and observations. In particular, we will draw analogies between our simulations and the phenomena referred to as a flux transfer event (FTE) [4], which is observed in the magnetopause region.

[1] J.U. Brackbill and G. Lapenta, 16th Int. Conf. Numerical Simulation of Plasmas, 1998, Santa Barbara, CA. [2] J.U. Brackbill, J. Comput. Phys., vol. 96, pp. 163-192 (1991) [3] D.A. Knoll, J. Comput. Phys., vol. 142, pp. 473-488 (1998) [4] C.T. Russell and R.C. Elphic, Geophys. Res. Lett., vol. 6, pp. 33-36 (1979)

[CP1.13] Nonlinear Magnetic Reconnection in Three Dimensions

With CELEST3D, an implicit PIC code, we study reconnection in current sheets with and without a perpendicular component of the magnetic field and with realistic values for the current sheet thickness, 1/2 to 1 ion gyroradius, temperature ratio, 1 < Ti/Te < 10, and mass ratio, mi/me=180. Three types of modes interact in reconnection: kinetic drift kink modes parallel to the current, collisionless tearing modes parallel to the magnetic field, and oblique modes. First, the rapid growth of the drift-kink mode alters the equilibrium, and in a Harris equilibrium, delays the growth of the tearing mode until the drift-kink mode saturates. This non-linear interaction is not observed in 2D simulations, since the drift-kink and tearing modes cannot both be present, or in 3D simulations with low mass ratios, where the tearing mode outgrows the kink mode. Second, a new oblique mode is observed. In a pure Harris sheet, the oblique mode is unaffected by non-linear interaction with the drift-kink mode. In magnetotail-like equilibria with perpendicular magnetic fields, which suppress the tearing mode, the oblique mode still grows, leading to plasmoid formation and ejection.

[CP1.14] Generalization of the Harris sheath

A novel, exact solution to the Vlasov-Maxwell system, with self-generated magnetic field and non-uniform plasma flow, is constructed. It is shown that a gyrotropic distribution function (independent of gyrophase) is not consistent with equilibrium flow shear. The agyrotropic solution presented includes that of Harris [E. G. Harris, Nuovo Cimento 23, 1167 (1962)] as a special case, but in its general form allows for shear in the flow speeds of both plasma species. The resulting equilibrium appears relevant to magnetic reconnection experiments on the MRX device at Princeton.

[CP1.15] Nonlinear Dynamics of a Current Sheet Formation System in Magneto-hydrodynamics

This abstract not available.

[CP1.16] 3D Collisionless Magnetic Reconnection

The theoretical understanding of collisionless magnetic reconnection in the context of 2D systems (systems in which there is one ignorable coordinate) has undergone a revolution over the past several years with the advent of large-scale numerical simulations that include a key physical element: the Hall effect. These simulations have shown that models which properly account for this effect in the electron dynamics, eg those based on Hall-MHD, full particle, or hybrid models, yield similar rates of reconnection that are dramatically faster than the predictions of conventional resistive MHD. In the 2D limit, strong, relatively stable gradients in the current as well as the electron and ion pressures are observed in the simulations, with characteristic scale-lengths ranging from the electron skin depth near the x-line and along the magnetic separatrix to larger than ion skin depth across the outflow region. Recent Hall-MHD simulations of collisionless magnetic reconnection in 3D, however, indicate these sharp gradients in fact break up due to the onset of secondary instabilities, leading to a strongly turbulent configuration in the full 3D system. Two distinct secondary modes have thus far been identified: an electron shear flow instability and the lower-hybrid drift instability. The former mode, driven by gradients in the current transverse to the reconnection plane, leads to a turbulent broadening of the electron skin depth scale structure in the current profile. The latter (the lower-hybrid drift instability), driven by cross-field gradients in the pressure/density, can generate order-unity fluctuations in the plasma profiles. The strong onset of the the lower-hybrid drift instability in the simulations requires an ion to electron mass ratio on the order of 300 or more. Comparisons of the Hall-MHD model to fully kinetic descriptions of the secondary modes will be discussed.

[CP1.17] Theory of Collisionless Reconnection: Effect of the Hall Current and Electron Pressure Gradient

A five-field model is developed for collisionless reconnection dynamics in a 2.5-dimensional plasma, including the effects of the Hall current and electron pressure gradient via the generalized Ohm's law. The equilibrium magnetic field is taken to be the Harris sheet solution B_x = B_0 \tanh z/a, B_y \neq 0. The shear-Alfvén mode dominates the exterior region, |z| > d_i, where d_i is the ion skin depth. In the interior region, |z| < d_i, the shear-Alfvén mode transforms to a whistler-like mode for high-beta plasmas (B_y = 0), but a kinetic Alfvén mode for low-beta plasmas (B_y \neq 0). In both cases, a parallel electrical field E_\parallel \sim (d_iV_A/Lc)B is obtained, where L is the length of the current sheet bridging the island tips, V_A is the Alfvén speed, and B is the reconnecting magnetic field. Analytical results are tested with Hall MHD simulations.

[CP1.18] Nonlinear Magnetic Reconnection in a Nonperiodic Slab Geometry

Magnetic reconnection in regimes where electron inertia in important in Ohm's law can be described with a two-fluid model, which takes into account electron and ion temperature effects. Electron inertia enters the equations through the electron skin depth while the electron and the ion temperatures are related to the sound Larmor radius and to the ion Larmor radius respectively. In Ref. [1] the nonlinear phase of the reconnection process was studied in a doubly periodic magnetic configuration, in the 2D cold ion limit. In order to avoid the limitations that arise from the double periodic conditions, here we solve our two-fluid model in the 2D cold ion limit, over an integration domain corresponding to the Harris pinch equilibrium. The typical cross structure in the vorticity and current density layers formed in the early nonlinear phase persists in the full nonlinear phase. After a faster than exponential growth rate in the nonlinear phase convection cells start to grow inside the magnetic island, near the O-points of the magnetic flux. At saturation the velocity cells are confined within the island separatrix which therefore ceases to grow.

[1] E. Cafaro, D. Grasso, F Pegoraro, F. Porcelli and A. Saluzzi, Phys. Rev. Lett, 80, 20 (1998).

[CP1.19] Linear growth rate of the EMHD reconnection instability

The onset of spontaneous magnetic reconnection in a collisionless plasma in the whistler frequency regime is investigated in a 2-D slab geometry. This is a first step in the direction of simulating the nonlinear phase of kinetic reconnection using a single species Vlasov code. The linear growth rate, previously studied in the framework of the so-called costant-\psi approximation [S.V. Bulanov, F. Pegoraro, A.S. Sakharov, Phys. Fluids B 4, 2499 (1992)] is extended to finite values of the stability parameter d_e \Delta^\prime. A boundary layer approach is used together with a matched asymptotic expansion technique. In order to match the inner solution, the (stabilizing) effect of frequency must be included in the external region. The dispersion relation shows a substantial increase of the reconnection rate in the intermediate wavelength region with respect to the standard costant-\psi solution, while in the long wavelength region the growth rate vanishes. Scaling laws of the growth rate and of the width of the layer with respect to the inertial skin depth are drawn and compared with those obtained in standard MHD theory.

[CP1.20] Bernstein-Greene-Kruskal chain of drift-tearing vortices

Collisionless magnetic reconnection in the drift\--wave plasma regime is studied using a drift\--kinetic description of electrons and fluid ions. A fully nonlinear Bernstein-Greene-Kruskal (BGK) stationary solution is constructed which has the form of a quasi three\--dimensional chain of electron holes coupled to hydrodynamic vortices. This stationary structure is obtained by setting up a plateau in the electron distribution function, followed by the trapping and consecutive depletion of resonant particles, and by the removal of the singular current layers by their short\--circuiting via electron gyrations. This new coherent structure is expected to play an important role in collisionless reconnection in high temperature toroidal plasma experiments.

[CP1.21] Structural Stability and Magnetic Field Line Reconnection

The problem of magnetic field line reconnection is closely related to the problem of the structural stability of vector fields. We investigate the nonlinear dynamics of magnetoacoustic and Alfvèn-type magnetohydrodynamic (MHD) perturbations in structurally unstable magnetic configurations analytically and numerically. The nonlinear evolution of the perturbed electric current turns structurally unstable configurations into structurally stable ones. This transformation is forbidden in the framework of the ideal MHD equations, but can occur in the process of magnetic field line reconnection. MHD simulations of the transformation of configurations with two null lines (X-lines) under perturbations imposed from the boundaries show that the change in the magnetic field topology due to the magnetoacoustic perturbations is accompanied by the redistribution of the electric current curried by the Alfven perturbations.

[1] S. Bulanov, E. Echkina, I. Inovenkov, F. Pegoraro, V. Pichushkin. Phys Plasmas, 6, 802, (1999)

[CP1.22] Collisionless Reconnection by High Energy Particle Populations

Following indications of recent experiments (K. Toi et al., in Fusion Energy 1998 (IAEA, Vienna, 1999), F1-CN69-EXP1/19.), we show that macroscopic modes involving magnetic reconnection can be stimulated(B. Coppi \emphInternational Symposium on Magnetic Reconnection) (Turin, Italy, 1999). by a ``high energy" population of nuclei that resonate with the modes considered. The mode frequency is comparable to the ion diamagnetic frequency and can equal the magnetic curvature frequency of the high energy particles. Since modes producing magnetic reconnection by the effect of a finite resistivity cannot have a frequency near ion diamagnetic and still be localized, it is shown that collisionless modes that could be classified as ``inductive" instead have the proper frequency. These modes would be purely oscillatory if the wave--particle resonance was absent. This resonance with the high energy particles can be simulated with an effective ion viscosity. An effective mutual ``inductivity" is introduced to replace the effects of finite electron inertia as this would lead to unrealistically small reconnection layers.

[CP1.23] Hamiltonian Description of Vlasov Dynamics: Action-Angle Variables for the Continuous Spectrum

The linear Vlasov-Poisson system for homogeneous, stable equilibria is solved by means of a novel invertible integral transform that is a generalization of the Hilbert transform. The integral transform provides a means for describing the dynamics of the continuous spectrum that is well-known to occur in this system. The results are interpreted in the context of Hamiltonian systems theory, where it is shown that the integral transform defines a canonical transformation to action-angle variables. A means for attaching Krein signature to a continuum eigenmode is given.

[CP1.24] Weakly Nonlinear Vlasov-Poisson Hamiltonian Dynamics

We extend techniques from finite-dimensional Hamiltonian perturbation theory to study weakly nonlinear dynamics around Vlasov-Poisson equilibria. This approach lets us examine the role of the continous spectrum in the dynamics, including the part it plays in transient phenomena. These techniques, in particular the use of a so-called resonance Hamiltonian, also provide a framework for systematically deriving weakly nonlinear models.

[CP1.25] Phase space analysis of wave-plasma interaction

The dynamics of a beam plasma system is described by a Hamiltonian treatment.The structure of the 2N dimensional phase space, and the stability of the critical points are investigated, and it is found that different regimes are characterized by different phase space topologies. In particular, the instability is related to the coalescence of two fixed points in the 2N phase space. The long time behavior of the system has been identified as due to trapping around the only elliptic point. The analysis is extended to the investigation of the nonlinear behavior of Langmuir waves.

[CP1.26] Nonlinear Landau damping and particle trapping in non-relativistic and relativistic regime

The evolution of the nonlinear Landau damping of an electrostatic perturbation is analized for different regimes in a collisionless plasma by solving the Vlasov-Poisson system numerically. First, the non-relativistic case is considered. Starting from a Maxwellian plasma, the long-time evolution (up to 2000 inverse electron plasma frequencies), the modification of the electron distribution function, the onset of the sideband instability, and the role of the ions are investigated for different initial electric field amplitudes.

The asymptotic time behaviour of the electric field is found to be modified by the excitation of the sideband instability and to depend, through the onset conditions of this instability, on the number of modes allowed by the simulation box. The transition between two different time asymptotic regimes is discussed as a function of the initial field amplitudes.

In the relativistic regime, the Juttner-Synge distribution function is perturbed in order to obtain the dispersion relation of a relativistically hot plasma numerically. This is compared with the analytical results that are available in the literature in special limits. The transition from the weak relativistic (v_ph < c) to the ultra-relativistic regime (v_ph \to c) is also investigated.

[CP1.27] Vacuum Propagation of a Super-Critical Electromagnetic Wave

The propagation of an electromagnetic wave in free-space is considered for intensities above the Schwinger critical field, where vacuum nonlinearities, including electron-positron pair creation, become important. The pair production rate is equivalent to vacuum absorption, and the Kramers-Kronig relations are used to derive the corresponding vacuum refraction. The wave envelope is governed by a nonlinear Schroedinger equation, which is solved numerically. The vacuum is found to behave like a nonlinear plasma and a saturable absorber; self-diffraction is studied within this context.

[CP1.28] Modulational Interaction of the Lower Hybrid Waves with ELF Density Perturbations

A modulational interaction of the lower hybrid waves and slow density perturbations in aurora is investigated in the paper, It is shown that a main mechanism responsible for the interaction is so called vector nonlinearity produced by electron drift on the background of density perturbations as well as creation of these density perturbations by the lower hybrid Reynolds stresses. Two types of the density perturbations are considered in the paper resulting either from quasineutral ion acoustic or kinetic Alfven mode. In both cases the structures have a form of field aligned filaments, their transverse structute could be either unipolar (a density well) or dipolar (the density well and hump) type. The lower hybrid waves are trapped inside these structures and are rotating over azimuthal phaze. Direction of rotation is determined by a sign of density perturbation. Presented here theoretical model is compared with the auroral observations.

[CP1.29] The Effective Dielectric Tensor for Non relativistic Inhomogeneous Plasmas in Inhomogeneous Magnetic Fields

We discuss the derivation of explicit expressions for the effective dielectric tensor to be utilized in the dispersion relation for weakly inhomogeneous plasmas. The general expressions obtained are useful for situations with simultaneous existence of weak inhomogeneities in density and magnetic field. The particular case of a Maxwellian distribution in velocity space for the electron population is discussed, and relatively compact expressions for the dielectric tensor are obtained, which display the correct symmetry/antisymmetry properties in the off-diagonal terms and correctly describe the energy exchange between waves and particles. A discussion is made on a future application of this formalism to the problem of cross-field instabilities generated in the magnetotail of Earth's magnetosphere, which can play a significant role in triggering current disruption in the magnetotail, leading to a magnetospheric substorm.

[CP1.30] Laser Initiation and Radiofrequency Sustainment of Seeded Air Plasmas

Seeded gas plasmas and air constituents have been created by a 193 nm laser and radiofrequency sources. We have obtained 10^14/cm^3 plasma densities with initial electron temperatures of 0.3 eV in TMAE (tetrakis (dimethylamino) ethylene) by laser photoionization. We developed a fast Langmuir probe analysis of plasma decay independent of ion species mix. Langmuir probe and optical emission data illustrating the density and temperature decay with TMAE mixed with nitrogen is presented. Simulations of antenna coupling, wave frequencies, wave propagation, and power absorption are compared with experimental observations for radiofrequency plasma sources. The source produces plasma densities of 2 \times 10^13/cm^3in an 8500 cm^3 volume at electron temperatures of 5 eV in 10 mTorr Ar in a nonuniform magnetic field. Radiofrequency plasma production at pressures from 2-760 Torr using Ar and laser initiated TMAE plasmas as seeds will be discussed.

[CP1.31] Particle Energization Due to Mass-Loading

The microphysics of mass-loading of the plasma flows with newly born ions is investigated. Special attention is paid to the analysis of wave activity in the mass-loading process. It is shown that in the superalfvenic plasma flows the dominant wave excitation mechanism is an ion cyclotron instability leading to excitation of the mainly parallel propagating Alfven waves. In the subalfvenic flows (e.g. inside the bow shock), the most important mechanism is the so-called modified two-stream instability leading to excitation of the lower hybrid waves. Particle interaction with both types of waves is investigated in the quasilinear approximation. In the case of lower hybrid waves, their feedback on the particles results first of all in particle heating. Waves are very efficient in organizing an energy exchange between electrons and ions. In the case of ion cylcotron instability of Alfvenic waves the dominant quasilinear process is a pitch angle diffusion of pick up ions. Energy diffusion of ions develops much slower and results in the formation of exponential tails of energetic ions.

[CP1.32] Longitudinal Kinetic Modes in a Weakly Collisional Plasma

In our experiment, we study the ion kinetics of a weakly collisional, magnetized Ar plasma (n \approx \rm1\times 10^9cm^-3,T_i\approx \rm0.07eV, T_e\approx \rm3eV,B=\rm1kG) in the presence of electrostatic ion cyclotron (EIC) waves. Using laser induced fluorescence (LIF) spectroscopy, we have measured the perturbed distribution function, f_i1(x, v,ømega), synchronously with the wave excitation. We have also measured the time-averaged total ion distribution function, f_i(x,v), as well as the time-resolved total ion distribution, f_i(x_o,v_o,t), at selected positions and ion velocities. Our measurementrs show that there exist modes for f_i1 in addition to the classical EIC mode. Since the work of Case and van Kampen, it has been known that there exist other solutions for the Vlasov-Maxwell equations beyond those found from the classically derived dispersion relations. However unlike the Case-van Kampen modes for a collisionless plasma, these new modes are not very strongly damped. Recent improvements to our apparatus have enabled us to measure f_i1(x_\parallel,v_\parallel,ømega) with unprecedented scope and precision. We use this data set to help elucidated the full spectrum of longitudinal ion kinetics in the presence of collisions.

[CP1.33] LIF Studies of Three Wave Interactions in a Weakly Collisional Plasma

Three wave interactions have been studied in a linear magnetized RF discharge plasma device. Laser induced flourescence is used to monitor the ArII ion response to electrostatic ion cyclotron waves launched by a four-ring phased antenna. Waves are launched at two parent frequencies ømega_1 and ømega_2 and measurements are taken of the plasma response at the daughter frequency ømega_3 = ømega_1 + ømega_2 . We present analyses of the energy and momentum partition between the waves, and explore the role of wave-particle resonances in mediating the exchange of energy and momentum between the waves.

[CP1.34] Effects of High Frequency Waves on the Dynamics of Hot Electron Interchange Instability in the Collisionless Terrella Experiment

An m = 3 broad-band magnetostatic antenna installed at one of the magnetic poles of the Collisionless Terrella Experiment (CTX)(H. P. Warren and M. E. Mauel, \textitPhys. Plasmas), \textbf2 (1995) 4185. is used to excite waves in the range of 10-1000 MHz. To date, we have examined the application of coherent waves at powers up to a 100 W. Waves are detected with movable electric and magnetic probes. In CTX, electron cyclotron heating (ECRH) is used to create a population of energetic electrons (1-20 keV). These electrons become unstable to hot electron wave interchange instabilities which saturate non linearly. We discuss the effects of externally induced high frequency waves on saturation of these instabilities, as well as on plasma parameters. For example, it was found that 153 MHz wave has the most dramatic effect on the instability growth rate and nonlinear saturation processes--including influence of frequency chirp rates. The applied waves also appear to influence plasma confinement and floating potential.

[CP1.35] Mode Structure of Natural and Induced Plasma Waves in the Collisionless Terrella Experiment

Measurements of radial and azimuthal mode structures of plasma waves excited by both the hot electron interchange (HEI) instability and by a broad-band antenna with m = 3 symmetry located at one of the magnetic poles of CTX(H. P. Warren and M. E. Mauel, \textitPhys. Plasmas), \textbf2 (1995) 4185. are presented. The hot electron population, produced via electron cyclotron heating, becomes unstable to HEI instabilities which saturate nonlinearly. These instabilities are also associated with inward transport of phase space holes as well as frequency chirping. The structure of both the natural and excited waves is observed with the use of movable high-impedance floating potential probes as well as a small magnetic probe.

[CP1.36] Kinetic Eigenmodes and Discrete Spectrum of Langmuir Oscillations in a Weakly Collisional Plasma

The damping of plasma oscillations in a weakly collisional plasma is revisited using a Fokker-Planck collision operator. Eigenfrequencies and eigenmodes are calculated numerically for a very small value of the collision frequency. It is shown that the Case-Van Kampen continuous spectrum is eliminated in the limit of zero collision frequency and replaced by a discrete spectrum. The Landau-damped solutions are recovered in this limit, but as true eigenmodes of the weakly collisional system. For small but non-zero collision frequency, the spectra and eigenmodes are qualitatively different from their counterparts in the collisionless theory. These results are consistent with recent experimental findings.

[CP1.37] Using ion motion in waves to determine kinetic equations.

We study the role of ion motion in an electrostatic perturbation using laser induced florescence in a magnetized Agron II plasma. Study of the relative metastable fraction is used to determine the metastable quenching crossection and then to determine terms of the ion kinetic equation by direct calculation from the data. Consistency checks are performed on the quenching model as well as on the kinetic equation.

[CP1.38] Spectral Properties of Low-Frequency Electrostatic Waves in the Ionospheric E Region

The spectral properties of low frequency electrostatic waves in the polar cap E region over northern Scandinavia were studied experimentally by instruments on the ROSE rockets. Fluctuations in plasma density were detected as well as potential differences between boom mounted probes. By comparison of the spectral index for fluctuations in the potential signal and plasma density, evidence is obtained for deviations from Boltzmann distributions in the electron dynamics, which would predict fluctuations in density and potential to be proportional, with the same constant of proportionality at all frequencies. Investigations of the cross-correlation between density and potential signals demonstrate that the phase between the two increases approximately linearly with frequency. Empirical relations are obtained for the frequency dependence of the amplitude and phase relations between fluctuations in density and potential.

[CP1.39] Experiments in Suppression of Electrostatic Waves Using Non-linear Feedback Controllers Based on Three-wave Coupling Model

We have shown in the past that using an ion/electron beam in the Columbia Linear Machine (CLM), simple linear feedback controllers can be constructed to suppress electrostatic modes. However, it is difficult to design a purely linear controller that provides good uniform suppression for all modes, because the coupling of the modes prevents us in finding an appropriate setting to suppress all modes simultaneously. This experiment attempts to add a nonlinear element to the feedback controller, namely the multiplication (modulation) of two fluctuation signals, mimicking the nonlinear terms present in the three wave coupling equation. While the linear part of controller reduces the linear drive of a particular mode, the nonlinear feedback term will provide additional control freedom to couple/decouple the modes, such that the overall fluctuation spectrum can be reduced even further. Results will be presented on the effectiveness of this feedback scheme, in particular investigating the effect of the nonlinear part of the controller on the coupling of the modes using bispectral analysis techniques. This work is supported by NSF grant ECS-93-7179 and DOE grant DE-FG-02-87ER.

[CP1.40] Temperature Equilibration via Electrostatic Waves

Nonequilibrium fluctuations in both electromagnetic and electrostatic fields due to spatially localized perturbations in the electron distribution function can play an important role in energy transport and current spreading in magnetized plasmas. They also can play an important role in the thermal equilibration of unmagnetized plasmas. The present study uses one- and two-dimensional unmagnetized particle (PIC) simulations to explore the general question of how fast (nonequilibrium) electrons equilibrate with the background plasma, and the role played by the electrostatic waves that are emitted by the fast electrons. The results are compared with classical predictions, and with the velocity-space transport theory of two-dimensional ``point'' particles. [1] It is found that the rate agrees with the classical value if the plasmas are in approximate thermal equilibrium, but that nonequilibrium fluctuations play an important role when high-energy tails are present on the electron distribution functions.

[1] Reynolds et al., Phys. Plasmas, 4 1286 (1997).

[CP1.41] Nonlinear Saturation of the Bump-On-Tail Instability

We carry out an investigation of the nonlinear saturation of a ``linearly unstable" electrostatic mode in a collisionless plasma. By applying a recently introduced new approach [based on the so-called A-T decomposition followed by ``transient linearization" of the Vlasov equation, see C. Lancellotti and J.J. Dorning, Phys. Rev. Lett. 81, 5137 (1998)] we obtain analytical solutions for the electric field and the particle distribution function under the familiar single-mode approximation. In particular, we are able to obtain the time-asymptotic field amplitude as a function of the initial amplitude of the perturbed mode. In the limit of vanishing linear growth rate our results are consistent with previous analytical and numerical results that yield a ``trapping scaling" of the field amplitude in terms of the linear growth rate.

[CP1.42] Are "collisionless electrostatic shocks" moving double layers?

In previous work describing single ion species plasmas, collisionless electrostatic shocks have been argued to be moving double layers. Double layers have potential structures similar to sheaths and ion velocity at both sheath and double layer potential steps can be provided by Bohm presheaths. For collisionless cold plasmas, all ions will have the same energy range at the double layer or sheath boundary. In the shock frame, all ions approach the shock at the same speed, somewhat greater than the Bohm velocity, so for a sheath, the ion energies match, while for a shock, the ion velocities match. For single ion species plasmas the Bohm velocity is equal to the ion acoustic velocity. When two or more ion species are present, it is usually assumed that each ion species is lost at their individual Bohm velocity. However, neither of these velocities is equal to the ion sound velocity of the combined system. Riemann has derived a Bohm criterion for systems with multiple ions which depends explicitly on the individual ion densities at the sheath edge. Possible solutions include one with each ion species lost at its own Bohm velocity, the sheath or double layer solution, and another for which all species are lost at one velocity, the shock solution.

[CP1.43] Alfvén wave propagation in a helicon discharge

Alfvén wave propagation in a helicon plasma is being studied in the Auburn Linear Experiment for Space Plasma Investigations (ALESPI). The helicon discharge provides the high-density background plasma necessary to propagate Alfvén waves. Shear Alfvén waves are produced in this discharge by means of a 225 turn, 6 mm diameter solenoid positioned to oscillate the magnetic field perpendicular to the background field lines. The waves are detected by means of a 100 turn, 4.5 mm diameter solenoid aligned in the same way as the emitter and positioned 19 cm down the plasma column. Initial investigations show the existence of shear Alfvén waves within the plasma due to the localization of the oscillations along the magnetic field lines. We will present investigations of the dispersion relation for these waves as a function of driving frequency and density of the plasma. The helicon wave used to produce this discharge is launched be a helical twist antennae with 900 W of radio frequency power at 10 MHz into a fill pressure of 9 mTorr and a background magnetic field of \sim0.1 T. A chord average density of 6x10^18m^-3 across the plasma and a core electron temperature of 8 eV are measured.

[CP1.44] Helicon Wave Excitation at a Uniform Arbitrary Magnetic Field

A self-consistent theory of helicon waves in a cylinder requires the inclusion of Trivelpiece Gould (TG) waves to satisfy the boundary conditions^1. Many authors have employed a simplified theory that neglects TG waves and assumes that the helicon waves are approximately transverse electric. Antenna coupling for both theories is compared for an arbitrary static magnetic field B_0. For a radially uniform density exact solutions are employed. For a nonuniform density the differential equation describing the fields is singular in the large magnetic field limit ømega/ømega_c = \delta << 1, and a novel approach to its solution is used. At moderate magnetic fields (\delta ~ 0.1) the TG waves produce small but measurable modifications to the wave magnetic field shape and large changes to the current and electric field shapes (see D. D. Blackwell, et al, elsewhere at this meeting). At large B_0 the TG amplitude decreases rapidly radially inward from the surface, and has little direct effect on the observable wave shape. However, it significantly affects the spectrum of waves generated and thereby the fields and antenna impedance.

^1 D. Arnush and F. F. Chen, Phys. Plasmas 5, 1239 (1998)

[CP1.45] Radially localized helicon modes in nonuniform plasma

A radial density gradient in a cylindrical plasma column forms a potential well for nonaxisymmetric helicon modes whose wavelength in the direction of the equilibrium magnetic field is much larger than the radius of the plasma column. In contrast to conventional helicon modes, these new modes are peaked around the steepest gradient and do not propagate radially. Their distinctive feature is a lower phase velocity than that of conventional helicon modes. Closely associated with the new modes are narrow current layers and localized enhancements in the parallel component of the electric field. These singular layers should cause a resonant-type absorption of rf power in helicon discharges. In addition, the low phase velocity of the localized modes should facilitate their Landau damping. It is plausible that such an absorption is responsible for unusually high efficiency of the helicon plasma sources, especially at frequencies below the typical helicon frequency for a uniform plasma.

[CP1.46] Group Velocity Resonance Cone Measurements in a Large Volume Helicon Source

We report a series of experiments in which earnest attempts were made to launch Trivelpiece - Gould modes in a 9cm radius, 50 cm length helicon source. Waves were excited using a small electrostatically coupled auxiliary antenna, scanning frequencies from 1 to 30 MHz. Maps of the wave amplitude and phase were made within the source by scanning the position of a dog - leg electrostatic probe and b - dot probe. At low densities, we found amplitude maxima corresponding to the group velocity resonance cone angle that decay as the distance from the antenna was increased. Although there were some indications of reflections when the resonance cone peaks intersected the radial boundary of the source, the observed radiation pattern in most cases was consistent with that of a point source in an unbounded plasma. No global eigenmode resonances were found. As the density was increased, the amplitude maximum along the resonance cone angle became less distinct as the wave became more electromagnetic (helicon -like).

[CP1.47] Stability properties of drift-Alfvén fluctuations associated with a narrow pressure striation

This analytical and numerical study investigates the linear stability properties of low frequency electromagnetic eigenmodes driven by field-aligned pressure striations whose scale transverse to the confining magnetic field is on the order of the electron skin-depth. A full electromagnetic formulation is given in terms of the coupling of the fluctuating axial fields (\tilde E_z, \tilde B_z) and incorporates shear and compressional Alfvén waves, drift waves, and ion acoustic waves. The kinetic response of the electrons includes pitch-angle scattering (Lorentz model) and the ions are treated as a magnetized, cold fluid. Detailed quantitative comparisons of the theoretical predictions are made with laboratory observations of fluctuations generated in controlled pressure depletions [J.E. Maggs and G.J. Morales, Phys. Plasmas 4,

290 (1997)] and in narrow temperature plumes [A.T. Burke, J.E. Maggs, and G.J. Morales, Phys. Rev. Lett. 81, 3659 (1998)].

[CP1.48] Particle and Heat Transport by Drift Waves in Narrow Striations

This analytical and computational study examines the perpendicular transport resulting from drift waves generated by a spatial inhomogeneity (``striation'') embedded in a uniform plasma. Thus the eigenfunctions/eigenvalues obtained properly account for transport away from the source region, in contrast to studies involving the local approximation where mode coupling within the source region dominates. Particle-in-cell simulations indicate a saturated nonlinear state with little relaxation of the perpendicular inhomogeneity. Drift waves in a narrow striation, whose perpendicular scale length is on the order of the electron skin depth or ion sound radius, can couple to LH waves capable of generating fast ions localized in the region of the nonuniformity. This is a situation that may occur in a wide variety of plasmas, including heating experiments, reconnection, z-pinches, and the auroral ionosphere.

[CP1.49] Spontaneous growth of fluctuations in a narrow temperature filament

We report on the properties of fluctuations spontaneously growing in narrow temperature filaments produced in the LAPD at UCLA by injecting a narrow (3 mm) low voltage (15-20 V) beam into the afterglow phase of a large cylindrical He plasma. Drift Alfvén waves with density and magnetic fluctuations are observed to grow first in the steep gradient region of the filament. The measured radial density and magnetic field profiles compare favorably to the predictions of a full electromagnetic theory that includes the effects of Coulomb collisions. These drift Alfvén modes are observed to evolve in azimuthal mode number from m=1 to m >4. Low frequency, m=0, fluctuations are observed to grow later in the center of the filament. These fluctuations are temperature changes and are possibly due to modulations in the strength of the heat source. The spectra of the fluctuations evolves from initially narrow and coherent to broadband turbulence. This transition is coincident with a change in radial heat transport from classical to much faster than classical.

[CP1.50] Shear Alfvén Wave Propagation in Parallel øverline\beta Gradient

Shear Alfvén wave propagation depends on the value of øverline\beta_e \propto \fracv_T_e^2v_A^2. It has been proposed that Alfvén resonance in a dispersive medium such as the Aurora occurs by virtue of the change in perpendicular group velocity between the Kinetic (øverline\beta_e \gg 1) and Inertial ( øverline\beta_e \ll 1) regimes. The behavior of a Shear Alfvén wave propagating from a Kinetic region to an Inertial region is investigated in the Large Plasma Device (LAPD) at UCLA. The wave is launched by two concentric field-aligned current sources, each driven harmonically 180^\circ out of phase. The current source is driven in this way to yield a larger k_\perp, thereby increasing v_g\perp, and clearly discriminating between the Inertial and Kinetic behaviors of the wave. In this experiment, the axial magnetic field and plasma density were varied along the 10 meter column length to give a range of \beta of order 10^3. The magnetic field of the wave was measured as a function of space and time.

[CP1.51] New High Power Alfvén Wave Antenna

Several researchers studying the FAST and Feja satellite data have reported that shear Alfvén waves of short cross-field scale length appear in conjunction with magnetic field-aligned accelerated electrons. They have proposed that these dispersive Alfvén waves which have a parallel electric field could cause the acceleration. A new current loop antenna which is one half wave length long in the field-aligned direction and azimuthally symmetric has been designed to launch high amplitude (\delta B/B_0 \approx 0.01) shear Alfvén waves in the LArge Plasma Device (LAPD) at UCLA. The purpose is to look for non-linear effects such as electron acceleration which is measured with a Langmuir probe. Preliminary results are reported.

[CP1.52] Propagation of the Shear Alfvén Wave from a Skin-Depth-Scale Source into a Magnetic Beach

Experiments are performed in the LArge Plasma Device (LAPD) at UCLA to study the propagation of the shear Alfvén wave into a parallel gradient in the background magnetic field. The waves are excited by modulating an electron current drawn to a disk antenna with a radius on the order of the electron skin-depth, \delta=c/ømega_pe.

The wave is launched with frequency ømega equal to one-half the local ion-cyclotron frequency, ømega_ci and propagates along a slowly decreasing background field to where ømega=ømega_ci. The measured wavelength decreases in accord with WKB solutions of the dispersion relation including finite ion temperature. Wave damping is also observed, and the best agreement with theory requires the inclusion of electron dissipation. Using this best-fit model, theory is used to identify the damping contributions of both species: within one wavelength of the antenna ømega equals 0.94ømega_ci and 51% of the launched energy is dissipated by the electrons (equally by Landau damping and Coulomb collisions). Above 0.94ømega_ci, ion-cyclotron damping dominates. Within the next wavelength, ømega equals ømega_ci by which point the ions have absorbed 45% of the initial energy, and the electrons an additional 3%, for a total of 99% dissipated.

The wave is also observed to develop an axial component, with the maximum ratio: B_\parallel / B_\perp\approx 0.5 at ømega\approx 0.85ømega_ci. The axial component is also studied with experiment and theory in a uniform magnetic field.

[CP1.53] Experimental Measurements of the Propagation of Large Amplitude Shear Alfvén Waves

Shear Alfvén waves have been studied in the Large Plasma Device (LAPD) at UCLA. (He \lambda_\parallel \approx 2 m , Ar \lambda_\parallel \approx 10 m, B = 1.5 kG, 40 cm diameter, 2- 4.0\times 10^12 cm^-3, fully ionized). In this work we have launched waves with the use of a helical antenna ( B_wave/ B_0 \approx 5\times 10^-3). The wave field slowly spreads across the background magnetic field and the current associated with it forms a rotating spiral. The higher power wave causes a localized density perturbation when B_wave/B_0 exceeds 10^-3. We will present data of the wave propagation in a uniform plasma in which vector magnetic field data was acquired at 20,000 spatial locations and 2048 time steps at each location. The data is used to calculate 3D wave currents, wave phase fronts and energy propagation. In Helium the wave pattern is more complex than in Argon. There are up to five braided current channel! s associated with the wave. The geometry of the magnetic field pattern in a linear case is compared to the intense wave. The wave currents are complex as well, and close across the background field via the ion polarization drift. They, as well as the field patterns are displayed in movies.

[CP1.54] Laser-Induced Fluorescence Measurements of Ion Temperatures and Drifts Associated with Shear Alfvén Waves in Argon

Laser-induced fluorescence (LIF) has been used in conjunction with Langmuir probe techniques to make preliminary measurements of the ion temperatures and ion drifts associated with shear Alfvén waves in an argon plasma at the Large Plasma Device at UCLA. The waves are lauched with a helical antenna into a relatively-uniform 40 cm diameter cylindrical plasma column with n_e=1.1\times10^12 cm^-3, T_e=5 eV, T_i=1.1 eV, and B_0=1500 G. A narrow-bandwidth tunable dye laser with output around 611.492 nm is used to excite 3d ^2G_9/2 metastable ions to 4p ^2F_7/2, which then spontaneously decay to 4s ^2D_5/2 by emitting light at 460.957 nm. At the center of the wave pattern where the wave fields and currents are most intense (B_wave/B_0 \sim 10^-3), a local density perturbation and electron heating are observed, along with ion drifts perpendicular to the background magnetic field. From these measured drifts the perpendicular (to B_0) component of the wave electric field is computed. Then, using the wave dispersion relation, the parallel component of the wave electric field is estimated. Both LIF and Langmuir probe data are presented.

[CP1.55] Interaction between shear Alfvén waves of large and small transverse scale.

This analytic study examines the wave-particle interaction that results when a shear Alfvén wave having small scale transverse to the confining magnetic field (and hence having finite parallel electric field) is embedded within another shear Alfvén wave of large transverse scale. Such situations may occur when there is a large-scale shear wave incident on a small-scale source (e.g., a field-aligned density filament) or, in general, in environments in which Alfvénic turbulence develops. The perpendicular drifts caused by the large-scale wave modify the field patterns and affect the wave-particle interaction in both the parallel and perpendicular directions. The structure of the resulting fields is investigated, and electron and ion acceleration is assessed.

[CP1.56] Generalized action invariants for drift waves-zonal flow systems

Generalized action invariants are identified for various models of drift wave turbulence in the presence of the mean shear flow. It is shown that the wave kinetic equation describing the interaction of the small scale turbulence and large scale shear flow can be naturally writen in terms of these invariants. Unlike the wave energy, which is conserved as a sum of small- and large- scale components, the generalized action invariant is shown to correspond to a quantity which is conserved for the small scale component alone. This invariant can be used to construct canonical variables leading to a different definition of the wave action ( as compared to the case without shear flow). It is suggested that these new canonical action variables form a natural basis for the description of the drift wave turbulence with a mean shear flow.

[CP1.57] The wave field of iterative conversion in the tokamak poloidal plane.

We consider the global response of a tokamak plasma to magnetosonic (MS) driving, focusing on conversion at the ion-hybrid (IH) resonance layer. In previous work(\small E.R. Tracy and A.N. Kaufman, 13th Topical Conf. RF Power in Plasmas. (http://www.physics.wm.edu/~tracy/)), we used a simplified model for the poloidal plane of a circular tokamak, with k_\| = 0. An antenna launches a family of MS rays, whose amplitude and phase are WKB-propagated except at the resonance layer. The crossing of the layer is treated in modular fashion using an S-matrix. The transmitted and reflected MS waves propagate away from the resonance, reflect at the plasma edge, and reenter the resonance region. This process repeats ad infinitum, with MS energy lost to IH at each cycle. The resulting field configuration in the cavity is a superposition of the ray families. Fine structure in the IH field is due to the formation of caustics. Here, we consider the following fundamental issues to improve the physical validity of the model: Airy smoothing of caustics; more realistic density profile, magnetic geometry, and wall/antenna modeling; finite k_\|; diffraction effects; edge effects.

[CP1.58] Plasma Profile Behavior in DIII-D Discharges with Counter NBI

Internal transport barriers, ITBs, have been observed in electron and ion temperature profiles and in electron density profiles with counter neutral beam injection into 1.6~MA discharges limited on the inside wall of the vacuum vessel. The profiles exhibited peak values a factor of 2 or more above values outside the barrier. A neutral beam power scan was performed to search for a threshold for the formation of an ITB. No clear threshold was found, however, it was found that for the lower power levels applied, 7--9~MW, a barrier region transiently formed near \rho\sim0.4 and then collapsed to the plasma center. The cause of the collapse is under investigation. At the larger powers, up to 15~MW, the barrier region formed near \rho\sim0.5 and was usually terminated by the onset of a locked mode during the current ramp phase of the discharge. At the larger powers a transient \hboxH--mode phase or dithering occurred which inhibited or destroyed profile peaking and ITB formation. ITB formation resumed following return to an \hboxL--mode phase.

[CP1.59] Thermal Transport in NCS Plasmas with Counter Neutral Beam Injection

Recent experiments in \hboxDIII--D have investigated internal transport barrier (ITB) formation with neutral beams injected in the counter-current direction, assisted by early ECH during current ramp up. For counter injection the v_torB_T term for radial force balance adds to the \nabla p term to determine E\times B flow shear. Compared to ITB plasmas with co-current injection, characteristics with counter injection at similar beam power are: (a) broader profiles of T_I, T_e, n_e, and ømega_tor within a larger barrier radius, (b) reduced profile gradients in the barrier region, and (c) about a factor of 2 higher Z_eff (\sim4) from the carbon impurity. In this paper profile evolution and results of transport analysis will be compared with co-injection plasmas.

[CP1.60] Differences in Dynamics of Enhanced Core Confinement States in Various Experimental Configurations and the Role of Driven Rotation

Aspects of transport barrier dynamics that can differ between experiments include the heating power required for formation, and rates of formation and collapse. The theory of E\timesB flow shear effects on turbulence suggests that some differences may be traced to the interplay between terms of the radial force balance equation and changes that result as rotation is modified in magnitude and sign. On \hboxDIII--D, studies with counter neutral beam injection complement previous work performed with co-injection, as well as that performed on TFTR with co- and counter-NBI. The role of the interplay between pressure and rotation drive in governing barrier dynamics will be examined using data from these studies. Dynamics are also addressed using a 1-dimensional envelope model that self-consistently evolves E\timesB shear, turbulence, transport, and plasma profiles.

[CP1.61] Edge Gradients as Components of the H-mode Trigger

Although the formation of the \hboxH-mode transport barrier can be understood in the context of ExB shear suppression, the physics which provides the trigger for the \hboxL--H transition is still not understood. Edge profiles of electron temperature, density and pressure, obtained from the \hboxDIII--D tokamak, are being examined for evidence of an H-mode trigger. Studies of these parameters with an inductive classification algorithm have shown that knowledge of the values of edge pressure and temperature gradients can be reliably used to determine if the plasma is in the \hboxL--mode or \hboxH--mode states, at least for discharges with a fixed magnetic equilibrium.(R.D. Deranian et al.), ``Inductive Classification of L-mode and H-mode Edge Parameters,'' submitted to Phys.\ Plasmas. This information is insufficient to prove that there is a causal link between these gradients and the transition. However, studies of the time histories of these parameters show a consistent pattern of the edge electron pressure gradient gradually increasing during the \hboxL--mode phase prior to the \hboxL--H transition. These results suggest that the edge pressure gradient may be a component of the trigger for the \hboxL--H transition.

[CP1.62] Plasma Edge Conditions During Pellet Induced H-mode Transitions in DIII-D

\hboxH--mode transitions have been produced as a direct result of pellet injection in \hboxDIII--D. Significant changes to the plasma edge conditions occur during these pellet induced \hboxH--mode transitions. Analysis of these changes can result in a greater understanding of the key quantities responsible for the formation of the edge transport barrier at the \hboxL--H transition. \hboxH--mode transitions were produced by pellets injected from the inner wall into the high toroidal field side (HFS) of the plasma and also by pellets injected from the outer wall into the low field side (LFS) of the plasma. Both the HFS and LFS pellets produced substantial increases in the edge electron density with a simultaneous decrease in the edge temperature at the \hboxL--H transition. This was followed by the establishment of clear \hboxH--mode electron density and temperature pedestals at the plasma edge. Pellet injection was able to produce \hboxH--mode transitions at lower NBI powers of 4.9~MW, compared to non-pellet discharges which remained in \hboxL--mode at NBI powers of 7.3~MW, hence, resulting in an effective reduction of the \hboxH--mode power threshold by 2.4~MW.

[CP1.63] Interpretation of Fast ECE and Soft X-ray Measurements During High Field Launch Pellet Fueling on DIII-D

Similar to observations on ASDEX-Upgrade,(P.T. Lang et al.), Phys.\ Rev.\ Lett.\ (1997) 1487-1490.\ high field launch pellet fuelling experiments on \hboxDIII--D have produced a particle source function shifted inward in minor radius toward the plasma core when compared to the local pellet ablation source. High time resolution measurements of electron cyclotron emission (ECE) and soft \hboxX-ray emission have been obtained during the initial phase of the ablation process. These measurements reflect changes in the flux surface averaged electron temperature during pellet ablation and provide insight into details of the mass redistribution. Measurements are evaluated using the PPPL Tokamak Simulation Code (TSC) assuming several possible mass redistribution models. The ECE and \hboxX-ray measurements are also compared with measurements of ablation light and density for beam heated \hboxDIII--D plasmas with weak shear and high edge q.

[CP1.64] Tests of H-Mode Marginal Stability Using Pellet Perturbations on DIII-D and Transport Physics of PEP Mode Initiation and Sustainment

We have used deuterium and neon-doped pellets to perturb L-- and \hboxH--mode plasmas on \hboxDIII--D. The perturbations result in a stiff response of the temperature profile to edge cooling in \hboxH--Mode plasmas, followed by a slow reheat, comprising a temperature scan lasting \sim800~ms at nearly constant density [D.R. Ernst, to appear in Phys.\ Plasmas (1999); Phys.\ Rev.\ Lett.\ 81 (1998) 2454]. Separately, with early counter-NBI, we obtained PEP modes lasting 1200~ms. Using the GS2 gyrokinetic and TRV neoclassical [D.R. Ernst et al., Phys.\ Plasmas 5 (1998) 665] codes, we examine the role of E_r shear in PEP formation. We simulate PEP modes and the response to pellet perturbations by self-consistently combining the GLF23 model [R.E. Waltz et al., Phys.\ Plasmas 4 (1997) 2482] with a full numerical neoclassical calculation of E_r. The criterion (shearing rate) \sim~(growth rate) is tested in \hboxDIII--D \hboxH--modes.

[CP1.65] Comparison of Deuterium Pellet Injection from Different Locations on DIII-D

During the past year the high field side pellet injection guide tubes have been installed on \hboxDIII--D. As reported by ASDEX,(P.T. Lang et al.), Phys.\ Rev.\ Lett.\ 79, 1487 (1997).\ significantly deeper density penetration for a given pellet velocity is achieved by inside launch as compared to low field side launch. In addition a pellet ``breaker'' guide tube was installed in the outside launch system to further minimize the pellet penetration. These new tools have been used to study the effects of varying penetration depths. These include pellet enhanced performance (PEP) modes(JET TEAM, in Plasma Physics and Controlled Nuclear Fusion Research 1988 (Proc.\ 12th Int.\ Conf.\ Nice, 1988), Vol.~1, IAEA, Vienna (1989).)\ from deep density deposition during the plasma current rise. \hboxH--mode threshold studies and extension of advanced tokamak scenarios by induced ELMs in VH-mode by both deep and shallow deposition.

[CP1.66] Impurity Behavior in DIII-D Discharges with Counter Beam Injection

Accumulation and axial peaking of intrinsic and injected impurities has been studied in \hboxDIII--D discharges with neutral beams injected counter to the direction of I_p. Evolution of the Z_eff profiles has been deduced by cross comparison of data from the Visible Bremsstrahlung (VB) diagnostic, from profile measurements of carbon and neon impurity densities with the Charge Exchange Recombination diagnostic, and from near axial measurements with the Core SPRED diagnostic of XUV charge exchange lines. A recent upgrade in the \hboxDIII--D Thomson Scattering System has extended radial coverage in measured n_e and T_e profiles to the magnetic axis, allowing straightforward analysis of the VB data. Systematic errors in the VB diagnostic have been identified and corrrected in software; hardware changes to eliminate these errors are planned.

[CP1.67] Impurity Analysis and Modeling of DIII-D Radiating Mantle Discharges

Predictive simulations of recent radiating mantle \hboxDIII--D discharges with non-intrinsic seeded impurities such as Ne, Ar and Kr, have been carried out. These \hboxL--mode and ELMing H-mode discharges often exhibit confinement improvement following the impurity injection. The simulations are performed with the \hbox1-1/2D transport code GTWHIST, which has the capability to calculate the transport of all the charge states of several impurity species along with the main plasma particle and energy transport. The importance of neoclassical effects on the impurity transport, as well as the effect of the enhanced edge radiation on the edge pedestal pressure, the edge pressure gradient, and bootstrap current are also discussed.

[CP1.68] Particle Transport in DIII-D Internal Transport Barriers

Analysis of particle transport in a tokamak is complicated by the fact that the central particle source is often small and the off diagonal terms in the equation for the particle flux can be larger than the source term in the plasma core. Understanding particle transport then requires the correct calculation of the off diagonal terms. This is especially true for anomalous transporting discharges where the off diagonal terms can be large. In discharges with an Internal Transport Barrier (ITB) the transport coefficients are small and for neutral beams heated plasmas the central source can become important. A particle transport analysis of \hboxDIII--D ITB plasmas shows the relative size of the source term, the diagonal term and the off diagonal term in the flux equation and under what situations the off diagonal terms can be neglected.

[CP1.69] Complex Dynamics of Turbulent Edge Transport in DIII-D

It is increasingly clear that in order to make progress on understanding plasma turbulent transport that the plasma-turbulence-transport must be treated as an interacting complex dynamical system. Examples include recent work on self-organized systems, long time/spatial correlations, etc. \hboxDIII--D edge data indicate that the plasma is a complex system of turbulence drives, E_r shear reduction, phase decorrelation, and avalanche-like (long time\slash space scale) transport events. We find that \nabla T and\slash or \nabla P are more important drives than \nabla n; that E_r shear reduces turbulent transport by altering fluctuation amplitudes and cross-phases; and that 1/f transport events dominate the total edge transport. These results can improve our understanding of the tokamak as a complex, driven-dissipative system.

[CP1.70] Turbulent Radial Correlation Lengths in the DIII-D Tokamak

Measurements of radial correlation length \Delta r of density fluctuations have been made on the \hboxDIII--D tokamak in Ohmic and \hboxL--mode discharges. These measurements span the radii \rho\approx0.5-1.0 and are found to scale approximately as \rho_\theta,s or 8\times\rho_s. Here \rho_\theta,s is the ion Larmor radius calculated using the local T_e and B_\theta while \rho_s is the same except calculated using the total magnetic field, B_tot. Currently, these scalings are not distinguishable over the radii involved due to uncertainties. The measured values of \Delta r are similar to what is expected from drift wave like fluctuations, including ion temperature gradient driven turbulence. The data were obtained primarily from a heterodyne reflectometer system, however, data from other diagnostics are also presented. Comparison to analytical and numerical models will be made. Such comparisons can be important as they serve to benchmark theory and codes as well as to help identify the type(s) of turbulence involved.

[CP1.71] Comparison of Microturbulence Characteristics in Ohmic and ITB Discharges with Predictions of ITG Models

Fluctuation characteristics measured in \hboxDIII--D discharges are compared with features predicted from gyro-fluid and kinetic codes using measured experimental profiles and geometry. In Ohmic discharges, the dominant instability is predicted to be the dissipative trapped electron mode or the ion temperature gradient mode, depending on specific conditions. Measurements of turbulence, spatial and temporal coherence, and propagation characteristics have been obtained through a density scan in neo-Alcator and saturated confinement regimes and allow comparison of measured turbulence characteristics with code predictions when the dominant mode changes. Additionally, dynamic evolution of turbulence is compared with predictions of empirical dynamical and gyro-fluid stability codes.

[CP1.72] Large Spatial Scale Avalanche Processes in DIII-D

One possible mechanism for transport of heat and particles in plasmas is the avalanche process associated with self-organized criticality. We have found evidence for avalanches in edge and core measurements.(T L. Rhodes et al.), Phys.\ Lett.\ A 253, 181 (1999).^,(P.A. Politzer, Bull.\ Amer.\ Phys.\ Soc.\ 43), 1760 (1998). Recent experiments with low power, essentially stationary \hboxL--mode plasmas have allowed collection of simultaneous core plasma data on electron temperature and density fluctuations using the ECE, BES, and reflectometer diagnostics, and edge data using Langmuir probes. These measurements are examined for evidence of SOC-like behavior. The anticipated characteristics include Fourier spectra (1/f), power-law PDF for events, and extended space-time cross-correlations with power-law tails. Cross-correlations between temperature and density fluctuations should give some indication of the energy transport.

[CP1.73] Transitions to Improved Core Transport in DIII-D L-mode NCS Discharges

Spontaneous increases in core electron and ion temperature and ion rotation velocity have been observed in \hboxDIII--D \hboxL--mode discharges with low density and early neutral beam injection. A reduction in turbulent fluctuation level is usually seen coincident with the changes. Many times these improvements in core confinement correlate with a low order rational q value coming into the plasma, but at other times they do not. We explore the possibility of a threshold for this transition by comparing integer q and non-integer q cases. We also investigate in this class of discharges the case with q_min near 1, just before the onset of sawteeth. These discharges exhibit a state that lacks a well-defined layer of reduced thermal diffusivity as seen in higher q transitions but instead exhibits a broad overall improvement in confinement.

[CP1.74] A Model for the Energy Confinement Scaling of H-mode Plasmas in Tokamaks

ITER96L and ITER98Hy are two examples of deducing from experimental data the scaling of energy confinement time for the \hboxL--mode and \hboxH--mode plasmas. Even though they represent different plasma operation regimes, the scaling laws show similar characteristics. These may be taken to imply strong connections between the heat transport of H and L regimes. For instance, the regimes may share the same thermal diffusivity in the plasma interior. A model is being developed based on the idea that an \hboxH--mode plasma is simply a much larger \hboxL--mode plasma with its boundary truncated in order to fit the machine physical size. In other words, an \hboxH--mode plasma is an L-mode with some unusual boundary conditions, and its confinement scaling ought to be the \hboxL--mode scaling modified by the effects from the new boundary conditions. The model estimates the boundary conditions, taking hints from the differences between ITER96L and ITER98Hy. As a result of these trials, the model creates a number of \hboxH--mode confinement scaling expressions in functional forms different from that of ITER98Hy.

[CP1.75] Stabilization of Resistive Wall Modes by Plasma Rotation

Slowly rotating resistive wall modes (RWMs) are often observed in \hboxDIII--D plasmas which exceed the ideal MHD beta limit calculated without a wall. Theory predicts that sufficiently large plasma rotation in the presence of a resistive wall should stabilize the RWM. Improved stability is found with the broader roation profile obtained by reducing the beam voltage at constant power. Recent counter-injection experiments should help determine which velocity is relevant for stabilization, by separating the diamagnetic and E\times B contributions to the fluid rotation. Slowing of plasma rotation is often observed above the no-wall stability limit, and could be consistent with magnetic braking by field errors or small-amplitude RWMs. If the slowing cannot be avoided, active feedback stabilization will be required.

[CP1.76] Internal Structure of Resistive Wall Modes in DIII-D

Resistive wall modes limit the performance of \hboxDIII--D discharges when beta exceeds the ideal stability limit calculated in the absence of a wall. Theory predicts that the modes should be characterized by slow rotation, on the resistive time scale of the wall, and a kink-like internal structure. The very slow mode rotation prevents use of the usual techniques of Fourier analysis at a single toroidal location to study internal mode structure, but comparison of soft \hboxx--ray and ECE measurements at multiple locations can provide information on the mode structure. Preliminary analysis indicates an ideal mode structure, consistent with expectations. Behavior in the presence of active feedback stabilization will be discussed.

[CP1.77] Beta-Collapse Events in AT Regime on DIII-D

Beta-collapse and rollover events have been observed in negative central shear AT regimes on \hboxDIII--D. These events are associated with a growth of a slow rotating resistive wall mode (RWM), which can stop the plasma rotation and cause fast \beta-collapse after the mode amplitude reaches critical value. The duration of the mode growth and the critical amplitude increase with the \beta_N value at the RWM onset. This increase is correlated with the increase in the toroidal rotation in the high velocity shear region between q_min and q=2. Increase in the heating power and application of an active feedback compensation of the n=1 field at the wall help to sustain rotation and can prevent \beta-collapse, which suggests a strong influence of the velocity shear on the RWM evolution.

[CP1.78] The Effect of Error Fields on Resistive Wall Modes

Experiments on the \hboxDIII--D tokamak have shown that the onset of the resistive wall mode (RWM) instability is correlated with an increase in normalized beta above the ideal resistive wall stability limit and a reduction in the rotation speed below a threshold value. The high beta RWM is also seen to become less stable as the fractional amount of error field correction is reduced. A reduction in the beta limit is observed in the presence of an error field and the RWM typically appears locked in phase to the error field. The intrinsic error field of the tokamak (typically about 10~G) may destabilize the RWM by reducing plasma rotation, by providing a seed perturbation, or by inhibiting the rotation of the RWM. Recently, the error field correction system on \hboxDIII--D was modified to also allow closed loop feedback control of the resistive wall mode. This joint role of the new RWM feedback control system and the relationship of error fields to the stability of the resistive wall mode will be discussed.

[CP1.79] Feedback Stabilization of the Resistive Wall Mode (RWM) in DIII-D

Initial experiments studying feedback stabilization of the RWM in \hboxDIII--D were carried out in plasmas above the no-wall \beta-limit for ideal n=1 kink modes, where the RWM has been observed. The feedback system consists of six driven saddle coils on the midplane, each covering 60^o in toroidal angle, and powered as three independent n=1 pairs. Under each driver coil is a saddle coil sensor to monitor the radial magnetic flux through the vacuum vessel. Application of ``smart shell'' and ``fake rotating shell'' feedback algorithms have demonstrated that the radial field soaking through the vacuum vessel can be controlled, the RWM amplitude can be reduced, and the plasma duration at high \beta extended in agreement with the 3D feedback simulation VALEN.

[CP1.80] Active Feedback on Locked Modes in DIII-D

Experiments to control low density locked modes have been carried out on \hboxDIII--D, using switching power amplifiers (SPAs) to drive external coils in a closed loop configuration. There are six external ``picture frame'' coils mounted around the midplane and each coil spans 60 degrees in the toroidal direction and about 50 degrees in the poloidal direction. The SPAs are designed with less than 0.1~msec internal time delay, adequate for feedback experiments at frequencies comparable to the wall time constant. The maximum radial field which the coils can drive is about 40~G at the vacuum vessel wall. Feedback was tried with the ``smart shell'' algorithm and with direct feedback on the mode amplitude. In this first experiment, the locked modes were not stabilized.

[CP1.81] Optimization of Feedback Control Coils for Resistive Wall Mode Stabilization in DIII-D

Recent experiments in \hboxDIII--D on Resistive Wall Mode (RWM) stabilization with active feedback have been very promising. We investigated extensions to the sensor and control coil set that would further improve RWM stabilization. The VALEN computer code models the RWM as an equivalent current distribution on the unperturbed plasma boundary which duplicates the plasma external magnetic field of the mode, as calculated by GATO. This surface current determines the plasma interaction with all conducting structures. In three dimensions the VALEN code models the unstable plasma, passive structure, proposed sensors, and proposed control coils together with the control logic. The problem may be examined as a transient simulation, or for a linear power supply model, as an eigenvalue calculation. A summary of the configurations examined and their predicted effectiveness will be presented.

[CP1.82] The Relationship of Locked Modes to Edge Current in DIII-D

Locked modes are a familiar problem in low density discharges [\bar n_e(R_0/B_t)q\approx8] for elongated plasmas. In a series of limiter discharges we found the following phenomenology for a particular series. Discharges which were maintained at approximately constant shape during the I_p ramp encountered a locked mode at q_\ell\approx3 leading to a disruptive termination with a probability of approximately 80%. Discharges for which \kappa was initially increased to a larger value than the desired value of 1.6 and later reduced follow a different trajectory in that q_\ell=3 is not reached in the I_p ramp, but in the flattop where \kappa is reduced to its final value. These discharges avoided the locked mode with 100% reliability. The current density is measured with a motional Stark effect diagnostic. At the time q=3 is reached, the edge current density is somewhat higher in the former cases. Experimental results and resistive stability analysis will be presented.

[CP1.83] Measurement of Current in Scrape-off Layer (SOL) Plasma in the DIII-D Tokamak

This work is motivated by a hypothesis based on experimental observations in the TFTR tokamak (H. Takahashi et~al., APS DPP, 1998, K6Q.07) that a SOL current exists that magnetically mimics MHD phenomena, e.g., Stationary Magnetic Perturbations (SMPs) or locked modes. ``Base'' SOL current can be several times as large as previously reported, increases during Resistive Wall Modes, and is often not axisymmetric, contrary to a common assumption. ``Spiky'' current, coincidental with Edge Localized Modes (ELMs), is also often not axisymmetric. Current that oscillates like MHD modes has also been observed. Spiky or oscillating SOL current can be bi-polar, quickly reversing its flow direction. The lack of axisymmetry and bi-polar nature of observed current challenge theoretical explanations of the origin of SOL current. The SOL current, which is measured in \hboxDIII--D using its tile current monitor diagnostic, will be examined as ``edge current'' in equilibrium and stability, and as a provider of ``field errors'' for slowing down and locking of MHD modes.

[CP1.84] Stability Modeling of DIII-D Discharges with Transport Barriers

The stability of \hboxDIII--D discharges with transport barriers is systematically studied by modeling the pressure profiles using a hyperbolic tangent representation with various radii, widths, and amplitudes. The q profiles are modeled using a spline representation with varying q(0), q_min, and \rho_q_min. The equilibria are computed using the EFIT and the TOQ codes based on the parameters from a strongly shaped high triangurality \hboxDIII--D long pulse high performance discharge. Stability against the ideal low n=1 and 2 modes is evaluated using the GATO code with a conducting wall at 1.5~a. The results show that the stability improves with increasing transport barrier width and radius but varies weakly with q(0). When the transport barriers are \hboxL--mode like and have narrow widths in the plasma core, the stability is limited by the n=1 mode. When they are \hboxH--mode like and have large widths extending toward the edge, the stability is limited by the n=2 mode.

[CP1.85] Comparison of Ideal MHD Stability Predictions with MHD Behavior in DIII-D

New diagnostics in \hboxDIII--D have greatly improved equilibrium reconstructions over the past decade. This, coupled to a corresponding improvement in ideal MHD stability code accuracy and capabilities has resulted in a convergence between the predicted MHD stability limits and the observed limits. The comparisons have evolved beyond global scalings to detailed comparisons of the stability predictions of unstable mode structures and growth rates for individual discharges. These demonstrate that ideal MHD predictions are remarkably accurate --- to within a few percent --- for a wide range of discharges. Several prominent examples include infernal modes, resistive wall modes, and intermediate n ideal edge modes in \hboxH--Mode discharges, VH--Mode and NCS \hboxH--Mode discharges, and n=1 ideal modes in \hboxL--Mode NCS discharges.

[CP1.86] Evolution of Flux Surfaces During a Slowly-Driven MHD Precursor

The growth of an ideal magnetohydrodynamic (MHD) instability is modeled in a high temperature plasma in the case where the plasma \beta is driven slowly through its instability threshold. The instability is modeled by evolving experimental equilibrium flux surfaces, using a model for the growth of slowly-driven disruption precursors in the linear regime (J.D. Callen, \itet al.), Report GA-A22845, to be published in \itPhysics of Plasmas.. This precursor model yields time-dependent ideal MHD perturbations of the flux surfaces, which are then added to the equilibrium positions of the flux surfaces. The flux surface evolutions, performed for some appropriate shots from D-IIID, show agreement with experimental ECE fluctuation data.

[CP1.87] L-Mode NCS Discharges with Expanded Radius

Negative Central Shear (NCS) discharges with an \hboxL--mode edge achieve neoclassical ion thermal confinement in the core and, in some cases, neoclassical particle confinement as well. This regime can lead to an attractive AT scenario with good core confinement while maintaining low p' and bootstrap current on the edge. The viability of this approach depends on whether the region of good confinement in the core can be expanded to larger radius. Increased \rho(q_min) has been obtained by injecting \sim5~MW of neutral beam power into the early phase of a current ramp. \hboxL--mode edge NCS discharges with \beta_N = 2.7, q_min = 2.7, and \rho(q_min) =0.65 have been achieved. The duration is limited by the onset of strong MHD activity. Stability analysis shows that n = 1 modes are unstable without a wall for low m numbers. However, when a conducting wall is added, these modes are all marginally stable. In contrast to typical \hboxL--mode discharges, these NCS discharges demonstrate a somewhat broader and flatter pressure profile, consistent with the observed stability.

[CP1.88] Database Analsyis of Disruption Frequency in DIII-D

The disruptivity of a tokamak fusion reactor is a major design and cost factor as design complexity increases with the total number of disruptions allowed. Historically, studies have measured disruption probabilities by binning discharges according to parameters such as normalized beta, density, and safety factor measured at some point during the discharge and calculating the fraction in each bin which disrupt. However, global statistics ignore the fact that most disruptions have identifiable causes which are often unrelated to the discharge's inherent reliability in steady-state operation. These can include details of the discharge evolution, unusual operational practices required for a particular experiment, and equipment failures. We address this question by analyzing a database of several hundred discharges with controls for operational practices, external hardware related disruptions and experimental probing of stability limits. Disruption rates per discharge and per unit time will be presented.

[CP1.89] Simulation of Neoclassical Tearing Mode Stability of DIII-D NCS Discharges by the 3D Nonlinear Code NFTC

The resistive MHD stability of negative central shear (NCS) discharges in \hboxDIII--D is investigated using the nonlinear three-dimensional magnetohydrodynamic code NFTC. The effect of negative central shear profiles on the excitation of neoclassical tearing modes is determined. Both the transport and the polarization current thresholds are now implemented in the NFTC code. Stability calculations for several different reconstructed \hboxDIII--D equilibria were done and the relative importance of conventional tearing modes, neoclassical tearing modes, double tearing modes, and resistive interchange modes was determined in each case. The dependence of the nonlinear threshold amplitude for neoclassical tearing mode excitation on the values of q_min and q_0 is invesigated. The numerical self-consistent simulations for the selected NCS discharges (including transport evolution) are compared with experimental observations and the stability conditions for the important linear resistive modes are determined.

[CP1.90] Toroidal equilibria with poloidal flow

Low beta tokamak equilibria are investigated by solving the MHD equations in the presence of poloidal and toroidal flow. In the presence of poloidal flow, tokamak equilibria develop radially discontinuous density, pressure and velocity profiles. Such profiles are the results of the evolution of a set of shocks distributed along a spiral curve near the poloidal Mach number resonant flux surface. The latter is the flux surface where the poloidal velocity equals the poloidal sound speed. Because of their irreversible nature and poloidal periodicity, such shocks cannot exist in steady state. Instead, they move poloidally and vanish while approaching the inward mid plane. Though shockless, the resulting steady state equilibrium features a radial contact discontinuity. These results may be related to the profile pedestal and large velocity shear observed during H-mode operations.

[CP1.91] Compressible Modes and Toroidal Motion

A compressible ideal MHD mode in a torus, the m=1, n=1 internal kink mode, is shown to have different behavior from the corresponding incompressible mode (i.e., with the ratio of specific heats \Gamma\rightarrow \infty). The compressible mode cannot be described by extremizing the perturbed potential energy \delta W, but requires consideration of the full MHD functional \delta W/K, where K is the perturbed kinetic energy. Compressibility allows the toroidal plasma motion \tildev_\phi to become asymptotically large relative to the radial kink motion \tildev_\phi=O(\epsilon^-1\tildev_\psi) in the limit as the plasma inverse aspect ratio \epsilon=a/R goes to zero, for the typical case of moderate magnetic shear within the q=1 surface, \delta q\equiv (1-q)_ave>\epsilon. The linear mode growth rate scaling (L.E. Sugiyama, \emphPhys. Plasmas), to appear. and the threshold \beta_p required for instability are different from those of the incompressible mode, which has finite \tildev_\phi=O(\tildev_\psi) and is described by \delta W(M.N. Bussac, R. Pellat, D. Edery, J.L. Soule, \emphPhys.Rev. Lett) \textbf35 1638 (1975)..

[CP1.92] Solving for MHD Equilibrium on Unstructured Grids

The present work describes a method for determining the MHD equilibrium in an axi-symmetric torus using two-dimensional finite elements on an unstructured triangular grid. This work is motivated by the proposed development of an adaptive mesh stability code that will solve the ideal linearized stability problem with a resistive wall. In order to create an automatically adapting grid, an unstructured triangular grid is initially generated for the equilibrium evaluation. The Grad-Shafronov equation is modified to accommodate a static toroidal flow velocity. The resulting equation is then solved on the generated grid in the natural cylindrical (R, \phi, Z) coordinate system. By working in the natural coordinate system, there are no singular points to be dealt with in the system. However, there are several numerical problems associated with solving the system of equations that are presented. Benchmark results against the Solov’ev equilibrium as well as the PEST and HELENA codes are also presented.

[CP1.93] Construction of local 3-D MHD equilibria and localized modes

An important element in studying localized instabilities is the effect of the MHD equilibrium. In tokamak applications, procedures have been developed to generate a series of MHD equilibrium, localized to a magnetic surface, that are solutions to the Grad-Shafarnov equation. In particular, Greene and Chance [Nucl. Fusion 21, 453 (1981)] developed a generalized s-/alpha model which allows for variations in the pressure gradient and magnetic shear on a flux surface without the necessity of recalculating the equilibrium. This method has been generalized to 3-D applications by imposing small amplitude variations of the profile parameters, constrained to be consistent with MHD equilibrium conditions, on an arbitrary initial 3-D equilibrium. Two free profile variations describe the set of local equilibria in an analogous manner to the Greene-Chance method [C. C. Hegna and N. Nakajima, Phys. Plasmas 5, 1336 (1997)]. We expand these studies by allowing for variations in the shape of the magnetic surface. The intention of this work is to develop an analytic tool to study 3-D shaping effects on localized instabilities in stellarator configurations.

[CP1.94] Physics Optimization of the ARIES-RS Fusion Power Plant

The 1996 ARIES-RS physics design is being revisited with the goal of further optimization in the following areas: (1) A fully-aligned bootstrap current at the plasma edge to eliminate the need for edge non-inductive current drive, (2) Refinement of the beta-limit calculation to include intermediate n ideal modes, resistive wall and non-ideal effects, (3) Use of physics-based transport model for internal transport barrier (ITB) formation, (4) Comparison of current drive and rotational flow drive using fast wave, electron cyclotron waves and negative ion beam, and (5) Further improvements in heat and particle control. Integrated modeling of the optimized scenario will be performed to study the robustness of the bootstrap alignment, ITB sustainment, and stable ramp-up path to high beta and high bootstrap fraction current operation.

[CP1.95] Stability of Finite-n Global Magnetohydrodynamic Modes Using the GATO Stability Code

This work extends the capability of the GATO stability code(L.C.Bernard et al.), Comput.\ Phys.\ Commun.\ 24, 377 (1981).\ to analyze realistic numerical tokamak equilibria for their stability to higher n (\sim5--10) MHD modes. This is motivated by the experimental evidence of these modes being relevant for both plasma termination and the behavior of ELMs. The ballooning angle transformation(R. Gruber et al.), Comput.\ Phys.\ Commun.\ 24, 363 (1981).\ is applied to the displacement variables in the GATO representation. The potential energy matrix is constructed with the inclusion of extra mapping quantities. The vacuum energy computed from the Green's function is also modified to couple to the transformed displacement at the plasma boundary. The resultant eigenvalue problem is solved with the modified boundary condition in the poloidal direction suitable for these transformed variables. The dependence of the plasma stability as a function of toroidal mode number and plasma equilibrium properties will be presented.

[CP1.96] A Multi-Grid Solver for Up-Down Asymmetric Tokamak Equilibrium

The computer code TOQ produces tokamak equilibria in a coordinate system which uses the poloidal flux surfaces as coodinate surfaces. It is well-suited for providing accurate equilibria to stability analyses. It has been extremely used for beta-optimization in modeling Advanced Tokamak scenarios and the study of bootstrap current driven Spherical Torus. To solve the Grad-Shafranov equation, TOQ uses a multi-grid (MG) package,(P.M. De Zeeuw, Matrix-dependent prolongations and restrictions in a black box multigrid solver), J. Comp.\ and Appl.\ Math.\ 33 (1990) \hbox1-27.\ which has been shown to be very robust in solving elliptic problems. The MG algorithm as implemented has to be modified in order to deal with up-down asymmetric equilibria. In this work we discuss an implementation of the new MG algorithm and give examples of up-down asymmetric high-beta equilibria using the \hboxDIII--D geometry and the ITER geometry. We also explore the stability of such equilibria vis à vis the up-down symmetric ones.

[CP1.97] Delta Prime and Matching Conditions in Linear Resistive MHD Problems

Recently we developed a new technique to solve a system of differential equations with singular points. On this basis a new version of the 2D \hboxTWIST-R code has been developed to solve outer region problem with resonance surfaces, and a new linear resistive MHD stability criterion in a toroidal plasma was proposed. We also applied the same technique to solve the resistive inner layer problem. The results show excellent agreement with earlier published results for a wide range of parameters and growth rates.\par

Different methods of computing \Delta' and matching conditions are compared. The traditional definitions of \Delta' through logarithmic derivatives or the ratio of the asymptotic small and large solutions coefficients suffer from the necessity to subtract infinities from the left and right sides of resonance surfaces to obtain a finite answer and from ambiguity in the definition of the small solution, respectively. We examine instead the possibility of direct matching of inner and outer layer solutions using the transformed solutions obtained with the new numerical technique, and constructing the resistive MHD stability criterion without extracting many terms of Frobenius expansion.

[CP1.98] Algorithms for Finding 2D MHD Equilibria with Given ``Almost Ideal'' MHD Constraints

Under the constraints of ideal MHD, the flux surface topology cannot change. This not true under the constaints of almost ideal MHD (AIMHD). Equilibrium algorithms observing AIMHD constraints can therefore be used for the study of nonlinear properties of tearing modes.(C. Ren, T.H. Jensen, and J.D. Callen, Phys.\ Plasmas 5), 2574 (1998). Only the simplest cases are considered for which (i) \partial/\partial z=0; (ii) \bar\nabla p=0; (iii) (\bar B\times\hat z)^2\slash (\bar B\cdot\hat z)^2\ll1. It is the aim of this work to find algorithms which can deal with cases for which the current density may be different functions of the flux function on the two sides of a singular surface so that a finite gradient of the current density at the singular surface may exist. For such cases, island formation may result in irreversible, quantifiable changes of the AIMHD constraints and a nonlinear instability of tearing modes may exist.(T.H. Jensen and W.B. Thompson, Phys.\ Fluids 30), 3052 (1987). Several approaches to making suitable algorithms for this purpose will be discussed.

[CP1.99] Spatial Singularities of the Ideal MHD Continuum Modes

The spatial singularities that characterize the ideal MHD continuum modes of a nonaxisymmetric toroidal plasma with closed nested magnetic surfaces \psi(r) = const are explored. It was recently reported that in axisymmetric toroidal geometry, the component of the plasma velocity normal to the magnetic surfaces v_\psi generally has an essential singularity (\psi-\psi_0)^i\mu, where \mu is a real number, about the resonant surface \psi = \psi_0 rather than a logarithm.^1 The logarithmic singularity appears only if certain spatial symmetries exist in the plasma equilibrium or wave modes. In the present study, the analysis of Ref.~1 is extended to a nonaxisymmetric toroidal plasma with zero pressure. The continuum frequencies in this case are governed by a second order magnetic differential equation with quasiperiodic coefficients along the magnetic lines. The number of linearly independent quasiperiodic solutions of this equation influences the singularity. It is found that an essential singularity v_\psi \sim (\psi-\psi_0)^i\mu generally characterizes the continuum modes provided that the toroidal asymmetry of the equilibrium is not too strong. [1pt] \small Supported in part by the U.S. DOE under grant No. DE-FG02-97ER54398. [1pt] \small 1.~A.~Salat and J.A.~Tataronis, Phys.~Plasmas, to appear (1999).

[CP1.100] Effect of toroidicity, finite plasma beta, and compressibility on the linear stability of double tearing modes

Double tearing modes are deemed to be of importance for the resistive magnetohydrodynamics (MHD) stability of discharges with deeply reversed magnetic shear in tokamaks. We have been studying the linear MHD stability of double tearing modes in such discharges with the FAR suite of linear and nonlinear, toroidal, reduced and full MHD suite of computer codes. Model equilibria with closely spaced, as well as more widely separated rational surfaces, which are doubly resonant at the same values of the safety factor q, have been constructed. In the cylindrical limit and for zero plasma beta, reduced and full linear MHD stability calculations recover the growth rates and eigenfunctions obtained in cylindrical geometry for double tearing modes. In particular, the linear growth rates asymtotically scale as the one-third power of the resistivity. Linear toroidal calculations further show that, as for single tearing modes, increasing plasma pressure first stabilizes then destabilizes the double tearing modes. Additional results from systematic studies will also be presented.

[CP1.101] Comparison of shear flow formation between resonant and non-resonant resistive interchange modes

It is known that the poloidal shear flow is produced from the nonlinear resistive interchange modes(A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 59) 1581 (1987)(B.A. Carreras and V. E. Lynch, Phys. Fluids B 5) 1795 (1993). Since the non-resonant resistive modes also become unstable(K. Ichiguchi, Y. Nakamura and M. Wakatani, Nucl. Fusion 31) 2073 (1991), the nonlinear behavior is compared between the resonant and non-resonant modes from the point of view of poloidal flow formation. For understanding the difference, we studied single helicity (m,n)=(3,2) mode in a cylindrical geometry.Rotational transform profile, \iota(r), was changed. First, we assumed \iota(r)=0.51+0.39r^2, and increased \iota(0). This change represents a finite beta effect in currentless stellarators. When the resonant surface exists with \iota(r_s)=2/3, the poloidal flow are created near the resonant surface. And, in the case when no resonant surface exists but \iota_min\sim 2/3, the non-resonant (3,2) mode grows and poloidal shear flow is also generated; however, the magnitude decreases sharply with the increase of \iota_min.

[CP1.102] Non-ideal effects on ballooning modes in tokamak plasmas

We examine the effect of finite electron inertia, electron and ion diamagnetic effects on the stability of ballooning modes in tokamak plasmas. In the core where the resistivity is extremely small the electron mass effects can provide the necessary non-ideal effect to break the frozen-in contraint.This mode may be responsible for core transport as well as high-beta disruption. Using a 1D ballooning code we will present results on the modification of growth rates as well as the ballooning threshold compared to the ideal case.

[CP1.103] Simulation Study of Disruption and Halo Currents in the KSTAR Model Structure

A detailed simulation study has been performed for the disruption load analysis in the Korea Superconducting Tokamak Advanced Research (KSTAR) device using the Tokamak Simulation Code. Two different types of disruptions (radial and vertical) are simulated for various initial equilibria and halo region models. Special emphasis is put on the behavior of halo currents in the KSTAR model structure, in which a highly conductive passive plate is located near the plasma. It is found that the path and magnitude of the poloidal halo current depend quite sensitively on the detailed structure model of the KSTAR plasma facing component (PFC). In particular, a local circulation of a very large poloidal halo current is observed to occur near the connector of the up-down passive plates when it is not electrically insulated. An explanation is presented for the physical origin of this rather unusual feature of the halo current in the KSTAR PFC environment. The large poloidal halo current can give a severe electromagnetic load to the KSTAR PFC structure, and an optimized PFC model structure is proposed which can substantially reduce the undesirable halo current.

[CP1.104] Sawtooth Stability in Tokamaks

Tokamak plasmas are often observed to be stable to the n=1 Sawtooth instability even when the central safety factor q_0 < 1. We have conducted a series of numerical simulations of the nonlinear evolution of the n=1 mode using our nonlinear toroidal MHD code, for plasmas with various q_0 and \beta , where \beta is the ratio of the plasma pressure to the nagnetic field pressure. When q_0 is sufficiently below unity (q_0 = 0.7), the n=1 mode grows and reconnects magnetic field lines raising q above unity everywhere. However, for q_0 closer to unity but still smaller (q_0=0.9), the growth of the n=1 mode is halted by toroidal effects and parallel thermal conduction and q_0 remains below unity. Our simulations demonstrate that tokamak plasmas with q_0 < 1 can be stable in the MHD approximation.

[CP1.105] Ubiquitous MHD Flows

Despite its shortcomings, steady-state MHD remains the framework from which plasma confinement theory begins. The allowed MHD time-independent states change drastically when subjected to three requirements, two of which lie outside standard textbook (Grad-Shafranov) theory: (i) small but finite transport coefficients; (ii) resistive and viscous boundary conditions; and (iii) toroidal geometry. There seem to be no force-balanced steady-state profiles without flow [1]. We do not refer to "diffusive" losses needing to be compensated by Pfirsch-Schlueter "sources" of mass, but rather to the inherent non-vanishing local torque density that is implied by a current density and electric field that obey both Ohm's and Faraday's laws in toroidal (but not cylindrical) geometry. There may of course be still other reasons for flows, such as non-zero charge densities. But the most needed ingredient for understanding confinement devices may now be reliable "weather maps" characterizing the flows.

[1] Phys. Plasmas 5, 2649 (1998); Plasma Phys. Control. Fusion 41, A507 (1999).

[CP1.106] Linear Analysis of Resistive drift-Alfvén Instability in a Cylindrical Plasma

The drift-Alfvén wave is an electromagnetic wave appearing in finite \beta (\beta > m_e/m_i) plasmas when the Alfvén wave couples to the drift wave. This wave becomes unstable due to resistivity. Linearized eigenmode equations governing resistive drift-Alfvén modes are derived by using two-fluid model for a cylindrical plasma with a uniform longitudinal magnetic field. The eigenfunction of the resistive drift-Alfvén instability is more localized at the edge region for the larger poloidal mode number m. The growth rate of the most unstable mode is almost independent of the plasma density. It decreases with the increase of electron pressure (or temperature) for m\geq 9, although the electron pressure effect is weak for the low m modes. Details will be shown in the poster.

[CP1.107] Nonlinear Destabilization of Double Tearing Mode

The new features of double tearing mode are presented through the re-examination of linear and nonlinear studies in a cylindrical tokamak. In JT-60 negative shear plasmas, the fast collapse are observed even in a plasma with lower \beta value than the ideal stability[1]. One of the possible explanations of this low \beta collapse is the double tearing mode. The linear stability analysis shows that the exponent index \alpha of the growth rate \gamma on the resistivity \eta, \gamma\sim\eta^\alpha, depends on the radial distance of two rational surfaces, \delta r. When \delta r is small, the mode shows the strong interaction between two rational surfaces and \alpha tends to 1/3. With increasing \delta r, \alpha becomes 3/5, that means the weak interaction between resonance surfaces and the mode behaves as the tearing mode with two magnetic islands. When \delta r is intermediate, \alpha changes from 1/3 to 3/5. The nonlinear study shows that, after the exponential growth, the growth rate reduces with time and the magnetic islands grows as in the Rutherford regime. However, when two magnetic islands contact with each other, we have observed the nonlinear destabilization of the mode. [1] Y.Ishii et al, Plasma Physics and Controlled Fusion, vol.40,1998, p1607

[CP1.108] Nonlinear MHD Alfven Wave Computations in Cylindrical Geometry

Current profile control in the RFP has been shown to reduce significantly MHD fluctuations and restore good flux surfaces. We are investigating Alfven wave current drive, employing the dynamo effect of the Alfvén wave, as a means to control the current profile. We employ the nonlinear, resistive MHD code DEBS to study the RFP application, as well as basic Alfvén wave physics. The issues we are addressing are the effect on wave propagation and current drive of (1) the spectrum of the launched wave, (2) the shear Alfven resonance, (3) the nonlinearity arising from finite wave amplitude, and (4) the background magnetic fluctuations and stochasticity of the RFP plasma. Initial results will be presented.

[CP1.109] Axisymmetric Flowing Equilibria of a Two-Fluid Plasma

The formalism for axisymmetric flowing equilibria of a multi-fluid has been developed.[1] The standard reduced case is a quasi-neutral two-fluid with ideal equations of state and massless electrons. This simplifies to a pair of second order equations for the magnetic and ion flow stream functions plus a Bernoulli equation for the density. This system has no less than six arbitrary surface functions compared with two for a nonflowing "one-fluid" (MHD), i.e. the Grad-Shafranov equation. The resulting wide range of possibilities is greatly narrowed in the case of minimum energy states[2] for which only three arbitrary parameters remain. A solution method in cylindrical (r,z) goemetry is developed using the successive over-relaxation method. Cases of minimum (and near minimum) energy states are solved for compact configurations like spheromaks and FRCs. [1] L.C. Steinhauer, Phys. Plasmas 6, 2734 (1999). [2] L.C. Steinhauer and A. Ishida, Phys. Plasmas 5, 2609 (1998).

[CP1.110] Computational MHD on 3D Unstructured Lagrangian Meshes

Lagrangian computational meshes are typically employed to model multi-material problems because they do not require costly interface tracking methods. Our algorithms, for ideal and non-ideal 3D MHD, are designed for use on such meshes composed of polyhedral cells with an arbitrary number of faces. This allows for mesh refinement during a calculation to prevent the well known problem of mesh tangling. The action of the magnetic vector potential, A \cdot \delta l, is centered on edges. For ideal and non-ideal flow, this maintains \nabla \cdot B = 0 to round-off error. Vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = - \partial W_B / \partial r. This assures symmetry as well as magnetic flux, momentum, and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. The resistive diffusion part is calculated using the support operator method, to obtain energy conservation, symmetry. Implicit time difference equations are solved by preconditioned, conjugate gradient methods. Results of convergence tests are presented. Boundary conditions at plasma vaccuum interfaces have been incorporated. Initial results of an annular Z-pinch implosion problem are shown.

[CP1.111] MH4D: A New Algorithm for Three-dimensional MHD on an Unstructured Tetrahedral Grid

We describe a new algorithm for the solution of the time-dependent, resistive MHD equations in three-dimensional spatial domains of arbitrary shape and connectivity. Applications are thus not limited to geometry having axial symmetry. The algorithm uses a finite-volume approach based on a primary grid of tetrahedral cells, and a secondary dual median grid. The resulting discrete operators preserve the annihilation properties of the divergence and curl, and lead to a compact, self-adjoint formulation. The discrete operators also minimize the same functionals as the original differential operators. The semi-implicit method of time advancement is used. The capability of mesh refinement and coarsening is also considered. The algorithm is being implemented in F90 and MPI, and can be used on either single processor or massively parallel computers. Preliminary results will be presented.

[CP1.112] An Improved Levenberg-Marquardt Solver for Multiple-Target Optimization Multiple-Target Optimization

The Levenberg-Marquardt optimization algorithm as usually developed requires that the user provide an algorithm for calculating the derivatives of the residuals (target functions) with respect to the parameters. In the case optimization of complex systems, such as stellarators, these derivatives are usually calculated by numerical differentiation. This causes the computational effort to increase by a factor of (N+1), where N is the number of parameters. In this poster we discuss the coupling of the Broyden update method for calculation of derivatives in multiple dimensions along with the Levenberg-Marquardt minimization algorithm. Tests of implementations of this algorithm in C++ will be presented. For use with Fortran codes, this requires that such codes be converted to libraries and wrapped in C. This process will also be discussed.

[CP1.113] semidefinite programming approach to electronic structure

The ground state variational problem for a many-electron system may be formulated in terms of reduced density matrices instead of the complete wavefunction [A.~J.~Coleman, ``Structure of fermion density matrices", Rev.\ Mod.\ Phys., 35:668--689, (1963)]. The calculation of ground-state properties then reduces to a linear optimization problem subject to the representability constraints, which are incompletely known but of which the simplest ones are a finite set of linear equalities and bounds on eigenvalues, as in semidefinite programming. We have found new representability conditions through numerical solution of certain dual semidefinite programs. We are exploring numerically the strength of the known representability conditions by calculations on model systems, in which we compare the ground state energy found by the optimization approach with the ground state energy found using full configuration interaction.

[CP1.114] Proper Orthogonal Decomposition and Galerkin projection for a 3D plasma dynamical system

A general method to investigate non-linear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. The technique is applied to a 3D resistive ballooning dynamical system in a tokamak. This system belongs to a large familiy of convective fluid systems including Rayleigh--Bénard convection. A proper orthogonal decomposition of the fluctuating signal obtained by a numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low dimensional system which allows the study of shear flow generation, its subsequent fluctuation reduction and the saturation in oscillating states.

[CP1.115] Recent Algorithmic and Computational Efficiency Improvements in the NIMROD Code

Extreme anisotropy and temporal stiffness impose severe challenges to simulating low frequency, nonlinear behavior in magnetized fusion plasmas. To address these challenges in computations of realistic experiment configurations, NIMROD(Glasser, et al., Plasma Phys. Control. Fusion 41) (1999) A747. uses a time-split, semi-implicit advance of the two-fluid equations for magnetized plasmas with a finite element/Fourier series spatial representation. The stiffness and anisotropy lead to ill-conditioned linear systems of equations, and they emphasize any truncation errors that may couple different modes of the continuous system. Recent work significantly improves NIMROD's performance in these areas. Implementing a parallel global preconditioning scheme in structured-grid regions permits scaling to large problems and large time steps, which are critical for achieving realistic S-values. In addition, coupling to the AZTEC parallel linear solver package now permits efficient computation with regions of unstructured grid. Changes in the time-splitting scheme improve numerical behavior in simulations with strong flow, and quadratic basis elements are being explored for accuracy. Different numerical forms of anisotropic thermal conduction, critical for slow island evolution, are compared. Algorithms for including gyrokinetic ions in the finite element computations are discussed.

[CP1.116] Simulation of neoclassical tearing modes with NIMROD.

The two-fluid NIMROD code has matured to a level that numerical simulations of Neoclassical Tearing Modes (NTM) are now possible. Simulations of NTM's require equilibration of pressure on perturbed flux surfaces which then generates a perturbed bootstrap current through some appropriate neoclassical closure in the viscous stress-tensor. The NIMROD code models pressure equilibration processes with an anisotropic thermal diffusion operator in the pressure evolution equation and models the neoclassical viscous-stress tensor in one of three ways: 1) Island width determination and estimation of the magnitude and direction of the pertubed bootstrap current; 2) pressure equilibration on the perturbed flux surfaces and bootstrap current determination from the pressure gradient(T.A.\ Gianakon, C.C.\ Hegna, J.D.\ Callen. Phys. Plasmas 5) (1996), 4637.; or 3) pressure equilibration on the perturbed flux surfaces and use of a more consistent field/flow formalism for the bootstrap current(F.L.\ Hi nton, H.L.\ Hazeltine, Rev. Mod. Phys. 48) (1976), 239.. Simulations of NTM's with these models will be presented which illustrate the nonlinear threshold, growth, and saturation of the mode in equilibria taken from EFIT reconstructions of select DIIID shots during which a neoclassical tearing mode is observed.

[CP1.118] Implementation of Vacuum Region in NIMROD

MHD stability limits in experiments depend on the presence of a vacuum region and on the location of a (geometrically-complicated) conducting wall. Unlike linear codes where one can use Green's functions to predict the response of a fixed plasma-vacuum boundary, the implementation of a vacuum region in a nonlinear initial-value code with a moving plasma-vacuum boundary presents many challenges. We review these challenges and present a practical model for the vaccum region for initial-value codes. We discuss the implementation of this model in the NIMROD code, which was programmed using a finite-element method in order to handle the complicated geometry of modern experiments, and the benchmarking of the NIMROD code to linear analytic results [1] and to the GATO [2] code. Plans to extend this work to nonlinear regimes and to compare with previous nonlinear results [3] will be discussed. ------- [1] V.D. Shafranov, Soviet Physics Technical Physics 15 (1970) 175 [2] L.C. Bernard et.al, Comp. Phys. Comm. 24 (1981) 377 [3] A. Y Aydemir, et al., Bull. Am. Phys. Soc., 43, 1747 (1998).

[CP1.119] Preliminary Results of the NIMROD High-S Campaign

The NIMROD code[1] has been successfully validated against a number of standard linear and nonlinear test cases. During this validation campaign, resistive MHD calculations have generally been carried out at low to moderate values of the Lundquist number (10**3 < S < 5X10**5). A central aspect of the original design of the NIMROD algorithm is the capability to extend nonlinear calculations to higher values of S (> 10**6). We have recently begun a systematic campaign to extend NIMROD calculations to higher values of S, and to determine the practical limits placed on this parameter. In this paper we report the initial results of this campaign based on previous calculations[2] carried out in simple linear cylindrical geometry. The realism of these calculations will be improved as the campaign prodeeds. While these initial results are based on the linearized MHD equations, we emphasize that the ultimate goal is to extend the values of S that can be used in fully nonlinear simulations.

References: [1] A. H. Glasser, et al., Plasma Phys. Cont. Fus. 41, A747 (1999). [2] J. A. Holmes, et al., Phys. Fluids 26, 2569 (1083).

[CP1.120] MHD Simulations of Spherical Tori and Compact Stellarators Using M3D

The M3D++ unstructured mesh version of the M3D code is being applied to low aspect ratio spherical torus disruption simulations. In addition to spherical tokamaks (ST), similar to NSTX, we also study spherical pinches (SP). It is possible to produce SP equilibria with 1 > q > 1/2, and toroidal current decreasing to zero at the wall. These SP equilibria have reverse magnetic shear except in a narrow layer near the wall. The equilibria are free of the global m=1 modes that plague low q pinches such as RFPs. However there can be unstable (m,n) = (2,3) modes. \par The M3D++ code has been extended to have the capability of using a 3D mesh in configuration space, suitable for stellarator equilibrium, stability, and nonlinear studies, including resistive effects. Equilibria can be initialized with VMEC output or generated from initial data. Applications to compact stellarator configurations such as the PPPL quasi axisymmetric design will be presented.

[CP1.121] Nonlinear resistive MHD simulation on massively parallel computers

We report the development of a nonlinear resistive MHD code for massively parallel computers. The physics kernel is from MH3D, which represents the magnetic field and the plasma flow velocity by scalar potentials. The finite element discretization is inherited from MH3D++. The mesh for a general toroidal geometry consists of a set of equally spaced poloidal planes, each of which is covered by unstructured triangle elements. A three dimensional domain decomposition is implemented for good scalability with problem sizes. The elliptic equations in MH3D give rise to large sparse matrices. These are approximately inverted by iterative methods with Krylov acceleration. Overlapped Schwarz method achieves strong preconditioning with acceptable communication overheads. The parallel data layout are implemented in the framework of PETSc, which also provides highly scalable linear solvers and preconditioners. The design characteristics of our code, and the benchmarks of PETSc, imply potential scalability up to 10^5 processors. The first application of this code will be a check of the VMEC equilibrium profile for toroidal confinements.

[CP1.122] Small-Action Resonance in Hamiltonian Systems and Redistribution of Energetic Ions in Tokamaks

It has been found that an arbitrary small perturbation in an integrable Hamiltonian system typically leads to driven resonance in the regions of the phase space where at least one of the action variables is sufficiently small. In particular, such a small-action resonance is shown to play a dominant role in the sawtooth-crash-induced disappearance of a strongly localized \gamma-ray and neutron emitting region in a tokamak plasma, which was observed experimentally.

[CP1.123] The effect of rotation on ripple loss in Tore Supra

Significant toroidal rotation velocities are routinely measured in Tore Supra. These measurements were done in ohmic plasmas for both heavy impurities and deuterium. These velocities increase with ICRF heating power and can reach 40km/s or more. This behavior poses the question of the role of toroidal rotation and its associated radial electric field on ripple losses. This problem has been investigated by computing the ripple losses versus rotation with a Monte-Carlo code ORBIT (R. B. White and M. S. Chance, Phys. Fluids 27, 2455, (1984)), which computes the particle trajectories in exact equilibria including the ripple perturbation. For a Maxwellian distribution function with a 1keV temperature, losses are dominated by ripple trapped particles. It is found in this case that the loss decreases with rotation, as expected from analytic estimates (P. N. Yushmanov, Nuc. Fus. 22, 315, (1982)). Results will also be shown for a non Maxwellian distribution function, when stochastic ripple losses are also important.

[CP1.124] Nonlinear Evolution and Chaotic Behavior of Alfven Eigenmodes in the Joint European Torus: Observation and Interpretation

Alfven Eigenmodes (AEs) at the Joint European Torus (JET) are studied using a 4-second, 8-channel, 1-MHz magnetic fluctuation probe array. The modes are driven by H-minority ICRH tail ions in Optimised Shear (Advanced Tokamak) D-D and D-T plasmas. The nonlinear mode amplitude evolution reveals for the first time various chaotic and explosive nonlinear AE phenomena. The experimental signatures include spectral broadening, phase flips, frequency sweeping (chirping), and amplitude increases of 1-2 orders of magnitude (to \delta B / B_edge \approx 10^-4 relative to typical steady-state saturated amplitudes. These phenomena are interpreted quantitatively by comparison with a model derived from the general Berk-Breizman-Pekker nonlinear theory of kinetic instabilities [Breizman et al., Phys. Plas. v.4, 1997, p. 1559], and are consistent with several predictions of the theory. These results extend previous results on AE amplitude modulation (pitchfork splitting) [Fasoli et al., PRL v.81, 1998, p. 5564] into a more strongly nonlinear regime. The chaotic and explosive regimes reported here may be associated with a redistribution of fast ions in JET.

[CP1.125] On the excitation and suppression of the Alfvén modes during ICRF heating

We have carried out extensive magnetohydrodynamic - gyrokinetic hybrid simulations to investigate both the toroidal Alfvén eigenmode (TAE) and energetic particle mode (EPM) excited by trapped energetic ions produced during the ICRF heating. Employing the phase diagrams of the nonadiabatical perturbed distribution functions, we have identified that the energetic - particle precessional - drift resonance is the dominant mechanism for wave - particle interactions. It, thus, suggests that reversing the precessional drifts of the energetic ions via either heating at the inner side of the torus and/or negative magnetic shear could suppress the Alfvén instabilities. This conjecture is tested and verified by the simulations.

[CP1.126] Destabilization of Energetic Particle Modes by Localized Particle Sources

In the present work, the issue will be discussed of whether Energetic Particle Modes (EPM)~\footnote[1]L. Chen, Phys. Plasmas 1, 1519, (1994). may be destabilized by the free energy source associated with fast minority ion tails produced during ICRF heating on TFTR~\footnote[2] S. Bernabei et al., Phys. Plasmas 6, 1880, (1999).. Peculiar features of these experiments is the observation of two different types of fluctuations: one group, with ``fixed'' characteristic frequencies, and another one whose frequencies ``chirp'' (downward) in time. Furthermore, fluctuations of different types are known to be located in different regions of the plasma column: the ``fixed frequency'' modes are localized close to the plasma edge, whereas the ``chirping'' modes appear to be excited deep in the plasma core~\footnotemark[2].

A previously developed analytic theory~\footnote[3]F. Zonca and L. Chen, Phys. Plasmas 3, 323 (1996)., with appropriate modifications where necessary, will be applied to demonstrate that the high power densities, achieved via ICRF heating, are sufficient to exceed the excitation threshold of EPM's close to the ICRF deposition region. For the same reason, it will be argued that usual Toroidal Alfvén Eigenmodes (TAE) cannot be excited at the same radial location.

Excitation of TAE's, meanwhile, appears to be the most reasonable explanation for the ``fixed frequency modes'' observed near the plasma edge, where the fast ion free energy density is smaller than the threshold value for EPM excitation.

We will also attempt to present a nonlinear phenomenological model.

Part C of program listing