Nonlinear magnetohydrodynamic studies of the tilt mode in field-reversed configurations

Milroy, R. D.; Barnes, D. C.; Bishop, Robert C.; Webster, Robert B.

doi:10.1063/1.858998

Cited by 41 publications

(22 citation statements)

References 19 publications

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“…In MHD calculations including the effect of gyro-viscosity 5 , up to a factor of 3 reduction in growth rate has been found, but not complete stability. It has also been found that there is no nonlinear saturation of the n = 1 tilt instability in the MHD description 2,7 .…”

Section: Introductionmentioning

confidence: 97%

“…A substantial literature exists of FRC stability studies in both the MHD (ie, fluid) and kinetic (ie, particle ion) descriptions [2][3][4][5][6][7][8][9] . The n = 1 tilt instability is thought to be the most dangerous MHD instability because it is both strongly growing and a global mode that is not readily stabilized when kinetic effects are included.…”

Section: Introductionmentioning

confidence: 99%

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Numerical study of tilt stability of prolate field-reversed configurations

Белова¹,

Jardin²,

Ji³

et al. 2000

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Global stability of the Field-Reversed Configuration (FRC) has been investigated numerically using both 3D MHD and hybrid (fluid electron and δf 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 ∼ > 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. Our 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.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Numerical study of tilt stability of prolate field-reversed configurations

Белова¹,

Jardin²,

Ji³

et al. 2000

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“…The simulations in Ref. 9 were performed for FRCs with a racetrack separatrix shape, which could possibly account for the disagreement with the variational studies 4,6 . We were motivated to 5 study the Hall-MHD stability for a class of elliptic configurations, which have been suggested to have favorable stability properties 14 .…”

Section: Effects Of the Hall Termmentioning

confidence: 99%

“…The discrepancy is even stronger for configurations with large E and racetrack-like separatrix shapes 7 . Moreover, several self-consistent numerical calculations [8][9][10][11] , including FLR or Hall effects, as well as a fully kinetic ion description, find that the n = 1 tilt mode remains linearly unstable even in the highly kinetic regime: S * /E ∼ 1.…”

Section: Introductionmentioning

confidence: 99%

Kinetic effects on the stability properties of field-reversed configurations. I. Linear stability

Белова

Davidson

2003

Physics of Plasmas

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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. The n = 1 tilt instability mechanism and growth rate reduction mechanisms are investigated in detail including resonant particle effects, finite Larmor radius and Hall stabilization, and profile effects. It is shown that the Hall effect determines the mode rotation and the change in the linear mode structure in the kinetic regime; however, the reduction in the growth rate is mostly due to finite Larmor radius effects. Resonant wave-particle interactions are studied as a function of (a) elongation, (b) the kinetic parameter S * , which is proportional to the ratio of the separatrix radius to the thermal ion Larmor radius, and (c) the separatrix shape. It is demonstrated that, contrary to the usually assumed stochasticity of the ion orbits in the FRC, a large fraction of the orbits are regular in long configurations when S * is small. A stochasticity condition is found, and a scaling with the S * parameter is presented. Resonant particle effects are shown to maintain the instability in the large gyroradius regime regardless of the separatrix shape.1

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“…Velocity-space diffusion is computed using the Rosenbluth form of the Fokker-Planck oper-ator [ll], with the potentials found by first using the Green's function to get the potentials on a numerical boundary in velocity space and then finding the interior solution by Poisson solves using an iterative method [12]. To accomplish the bounce averaging, the unknown distribution function is first represented as a function of the constants of the motion for a spherically symmetric system, that is, the total energy and the total angular momentum.…”

Section: Theoretical Analysismentioning

confidence: 99%

Beyond the Brillouin limit with the Penning Fusion Experiment

1997

Self Cite

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FFR 3 4 1997ST ----Several years ago, it was proposed that a dense nonneutral plasma could be produced in a Penning trap. Nonneutral plasmas have excellent codnement.Thus, such a dense plasma might produce simultaneously high density and good confinement (as needed for fusion). Recently, this theoretical conjecture has been demonstrated in a small (3 mm radius) electron experiment (PFX).Densities up to 35 times the Brillouin density (limiting number density in a static trap) have been inferred from the observed strong (1OO:l) spherical focussing. Electrons are injected at low energy from a single pole of the sphere. A surprising observation is the self-organization of the system into a spherical state, which occurs precisely when the trap parameters are adjusted tc produce a spherical well. This organization is observed by a bootstrapping which produces a hysteresis. Additional observations which co&m the dense spherical focus are energy-scattered electrons and deflections of an electron probe beam by the space charge of the central focus.

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Nonlinear magnetohydrodynamic studies of the tilt mode in field-reversed configurations

Cited by 41 publications

References 19 publications

Numerical study of tilt stability of prolate field-reversed configurations

Numerical study of tilt stability of prolate field-reversed configurations

Kinetic effects on the stability properties of field-reversed configurations. I. Linear stability

Beyond the Brillouin limit with the Penning Fusion Experiment

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