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Nonlinear Gyroviscous Force in a Collisionless Plasma

Description: Nonlinear gyroviscous forces in a collisionless plasma with temperature variations are calculated from the gyrofluid moments of the gyrokinetic Vlasov equation. The low-frequency gyrokinetic ordering and electrostatic perturbations are assumed, and an additional finite Larmor radius (FLR) expansion is performed. This approach leads naturally to an expression for the gyroviscous force in terms of the gyrocenter distribution function, thus including all resonant effects, and represents a systematic FLR expansion in a general form (no assumption of any closure is made). The expression for the gyroviscous force is also calculated in terms of the particle-fluid moments by making the transformation from the gyrocenter to particle coordinates. The calculated expression represents a modification of the Braginskii gyroviscosity for a collisionless plasma with nonuniform temperature. It is compared with previous calculations based on the traditional fluid approach. As a byproduct of the gyroviscosity calculations, we derive a set of nonlinear reduced gyrofluid (and a corresponding set of particle-fluid) moment equations with FLR corrections, which exhibit a generalized form of the ''gyroviscous cancellation.''
Date: May 23, 2001
Creator: Belova, E.V.
Partner: UNT Libraries Government Documents Department

Nonlinear and Non-ideal Effects on FRC Stability

Description: New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). We present results of hybrid and two-fluid (Hall-MHD) simulations of prolate FRCs in strongly kinetic and small-gyroradius, MHD-like regimes. The n = 1 tilt instability mechanism and stabilizing factors are investigated in detail including nonlinear and resonant particle effects, particle losses along the open field lines, and Hall stabilization. It is shown that the Hall effect determines the mode rotation and change in the linear mode structure in the kinetic regime; however, the reduction in the growth rate is mostly due to the finite Larmor radius effects. Resonant particle effects are important in the large gyroradius regime regardless of the separatrix shape, and even in cases when a large fraction of the particle orbits are stochastic. Particle loss along the open field lines has a destabilizing effect on the tilt mode and contributes to the ion spin up in toroidal direction. The nonlinear evolution of unstable modes in both kinetic and small-gyroradius FRCs is shown to be considerably slower than that in MHD simulations. Our simulation results demonstrate that a combination of kinetic and nonlinear effects is a key for understanding the experimentally observed FRC stability properties.
Date: October 21, 2002
Creator: Belova, E.V.; Davidson, R.C.; Ji, H. & Yamada, M.
Partner: UNT Libraries Government Documents Department

Plasma simulation studies using multilevel physics models

Description: The question of how to proceed toward ever more realistic plasma simulation studies using ever increasing computing power is addressed. The answer presented here is the M3D (Multilevel 3D) project, which has developed a code package with a hierarchy of physics levels that resolve increasingly complete subsets of phase-spaces and are thus increasingly more realistic. The rationale for the multilevel physics models is given. Each physics level is described and examples of its application are given. The existing physics levels are fluid models (3D configuration space), namely magnetohydrodynamic (MHD) and two-fluids; and hybrid models, namely gyrokinetic-energetic-particle/MHD (5D energetic particle phase-space), gyrokinetic-particle-ion/fluid-electron (5D ion phase-space), and full-kinetic-particle-ion/fluid-electron level (6D ion phase-space). Resolving electron phase-space (5D or 6D) remains a future project. Phase-space-fluid models are not used in favor of delta f particle models. A practical and accurate nonlinear fluid closure for noncollisional plasmas seems not likely in the near future.
Date: January 19, 2000
Creator: Park, W.; Belova, E.V. & Fu, G.Y.
Partner: UNT Libraries Government Documents Department

Kinetic Stability of the Field Reversed Configuration

Description: New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). The FRC is an innovative confinement approach that offers a unique fusion reactor potential because of its compact and simple geometry, translation properties, and high plasma beta. One of the most important issues is FRC stability with respect to low-n (toroidal mode number) MHD modes. There is a clear discrepancy between the predictions of standard MHD theory that many modes should be unstable on the MHD time scale, and the observed macroscopic resilience of FRCs in experiments.
Date: July 9, 2002
Creator: Belova, E.V.; Davidson, R.C.; Ji, H. & Yamada, and M.
Partner: UNT Libraries Government Documents Department

Numerical Study of Global Stability of Oblate Field-Reversed Configurations

Description: Global stability of the oblate (small elongation, E < 1) Field-Reversed Configuration (FRC) has been investigated numerically using both three-dimensional magnetohydrodynamic (MHD) and hybrid (fluid electrons and kinetic ions) simulations. For every non-zero value of the toroidal mode number n, there are three MHD modes that must be stabilized. For n = 1, these are the interchange, the tilt and the radial shift; while for n > 1 these are the interchange and two co-interchange modes with different polarization. It is shown that the n = 1 tilt mode becomes an external mode when E < 1, and it can be effectively stabilized by close-fitting conducting shells, even in the small Larmor radii (MHD) regime. The tilt mode stability improves with increasing oblateness, however at suffciently small elongations the radial shift mode becomes more unstable than the tilt mode. The interchange mode stability is strongly profile dependent, and all n * 1 interchange modes can be stabilized for a class of pressure profile with separatrix beta larger than 0.035. Our results show that all three n = 1 modes can be stabilized in the MHD regime, but the stabilization of the n > 1 co-interchange modes still remains an open question.
Date: October 27, 2000
Creator: Belova, E.V.; Jardin, S.C.; Ji, H.; Yamada, M. & Kulsrud, R.
Partner: UNT Libraries Government Documents Department

Numerical study of tilt stability of prolate field-reversed configurations

Description: Global stability of the Field-Reversed Configuration (FRC) has been investigated numerically using both 3D MHD and hybrid (fluid electron and delta f particle ion) simulations. The stabilizing effects of velocity shear and large ion orbits on the n = 1 internal tilt mode in the prolate FRCs have been studied. Sheared rotation is found to reduce the growth rate, however a large rotation rate with Mach number of M greater than or approximately equal to 1 is required in order for significant reduction in the instability growth rate to occur. Kinetic effects associated with large thermal ion orbits have been studied for different kinetic equilibria. These simulations show that there is a reduction in the tilt mode growth rate due to finite ion Larmor radius (FLR) effects, but complete linear stability has not been found, even when the thermal ion gyroradius is comparable to the distance between the field null and the separatrix. The instability existing beyond the FLR theory threshold could be due to the resonant interaction of the wave with ions whose Doppler shifted frequency matches the betatron frequency.
Date: June 21, 2000
Creator: Belova, E. V.; Jardin, S. C.; H. Ji, M. Yamada & Kulsrud, R.
Partner: UNT Libraries Government Documents Department

Numerical Study of Instabilities Driven by Energetic Neutral Beam Ions in NSTX

Description: Recent experimental observations from NSTX [National Spherical Torus Experiment] suggest that many modes in a subcyclotron frequency range are excited during neutral-beam injection (NBI). These modes have been identified as Compressional Alfven Eigenmodes (CAEs) and Global Alfven Eigenmodes (GAEs), which are driven unstable through the Doppler-shifted cyclotron resonance with the beam ions. The injection velocities of the NBI ions in NSTX are large compared to Alfven velocity, V(sub)0 > 3V(sub)A, and a strong anisotropy in the fast-ion pitch-angle distribution provides the energy source for the instabilities. Recent interest in the excitation of Alfven Eigenmodes in the frequency range omega less than or approximately equal to omega(sub)ci, where omega(sub)ci is the ion cyclotron frequency, is related to the possibility that these modes can provide a mechanism for direct energy transfer from super-Alfvenic beam ions to thermal ions. Numerical simulations are required in order to find a self-consistent mode structure, and to include the effects of finite-Larmor radius (FLR), the nonlinear effects, and the thermal plasma kinetic effects.
Date: July 7, 2003
Creator: Belova, E. V.; Gorelenkov, N. N.; Cheng, C. Z. & Fredrickson, E. D.
Partner: UNT Libraries Government Documents Department

Global Stability of the Field Reversed Configuration

Description: New computational results are presented which provide a theoretical basis for the stability of the Field Reversed Configuration (FRC). The FRC is a compact toroid with negligible toroidal field in which the plasma is confined by a poloidal magnetic field associated with toroidal diamagnetic current. Although many MHD modes are predicted to be unstable, FRCs have been produced successfully by several formation techniques and show surprising macroscopic resilience. In order to understand this discrepancy, we have developed a new 3D nonlinear hybrid code (kinetic ions and fluid electrons), M3D-B, which is used to study the role of kinetic effects on the n = 1 tilt and higher n modes in the FRC. Our simulations show that there is a reduction in the tilt mode growth rate in the kinetic regime, but no absolute stabilization has been found for s bar less than or approximately equal to 1, where s bar is the approximate number of ion gyroradii between the field null and the separatrix. However, at low values of s bar, the instabilities saturate nonlinearly through a combination of a lengthening of the initial equilibrium and a modification of the ion distribution function. These saturated states persist for many Alfven times, maintaining field reversal.
Date: November 15, 2000
Creator: Belova, E.V.; Jardin, S.C.; Ji, H.; Kulsrud, R.M.; Park, W. & Yamada, M.
Partner: UNT Libraries Government Documents Department

Numerical Study of the Formation, Ion Spin-up and Nonlinear Stability Properties of Field-reversed Configurations

Description: Results of three-dimensional numerical simulations of field-reversed configurations (FRCs) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs and the new FRC formation method by the counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n = 1 tilt mode, where n is the toroidal mode number. The n = 2 and n = 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux, and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good agreement with results from the SSX-FRC experiment. Simulations show formation of an FRC in about 30 Alfven times for typical experimental parameters. The growth rate of the n = 1 tilt mode is shown to be significantly reduced compared to the MHD growth rate due to the large plasma viscosity and field-line-tying effects.
Date: November 12, 2004
Creator: Belova, E.V.; Davidson, R.C.; Ji, H.; Yamada, M.; Cothran, C.D.; Brown, M.R. et al.
Partner: UNT Libraries Government Documents Department

Numerical Study of Field-reversed Configurations: The Formation and Ion Spin-up

Description: Results of three-dimensional numerical simulations of field-reversed configurations (FRCs) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs, and the new FRC formation method by counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n = 1 tilt mode, where n is the toroidal mode number. The n = 2 and n = 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux, and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good qualitative agreement with results from the SSX-FRC experiment. The simulations show formation of an FRC in about 20-30 Alfven times for typical experimental parameters. The growth rate of the n = 1 tilt mode is shown to be significantly reduced compared to the MHD growth rate due to the large plasma viscosity and field-line-tying effects.
Date: June 6, 2005
Creator: Belova, E. V.; Davidson, R. C.; Ji, H.; Yamada, M.; Cothran, C. D.; Brown, M. R. et al.
Partner: UNT Libraries Government Documents Department