Linear gyroviscous stability of field-reversed configurations with static equilibrium

Abstract

A discrepancy persists between field-reversed configuration experiments, which are generally stable, and theoretical predictions of instability. The common consensus has been that the stability is the result of finite Larmor radius (FLR) effects. An FLR analysis is presented that finds the self-consistent displacement functions and complex frequency. This is done using the linear gyroviscous model, a fluid-based representation of FLR that allows a wide range of equilibria and modes to be examined with modest computations. The conclusion is that FLR in static FRC fails to explain the observed stability. The cause of stability must lie elsewhere.

Inductive Sustainment of Oblate FRCs with the Assistance of Magnetic Diffusion, Shaping and Finite-Lamor Radius Stabilization

“…The n = 1 axially polarized co-interchange mode is more commonly known as the "tilt" instability, 31,32 while the n = 1 radially polarized mode is known as the "radial shift" mode. These modes are predicted to have a growth time comparable to the Alfven time, 33,38,40 and have been predicted to terminate the plasma configuration. 35,38,39 Further discussion regarding the co-interchange mode can be found in Ref.…”

“…Simulations using both the gyroviscous formulation 40 and with a hybrid code 41 have predicted that FLR effects cannot reduce the tilt mode linear growth rate to zero in a prolate FRC. However, the nonlinear saturation of the tilt instability was observed in hybrid simulations, 42 as the plasma nonlinearly evolved to a new rotating equilibrium from a stationary initial condition.…”

“…This phase shift introduces a reactive effect, which results in a finite real frequency and reduced mode growth rates. 40 The reactive effect manifests itself by modifying the typical MHD dispersion relationship…”

Kinetic Effects on the Stability Properties of Field-reversed Configurations: I. Linear Stability

“…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.…”

Full-Particle Simulation of Electromagnetic Waves Induced by Electron Motion in a Field-Reversed Configuration

“…Additionally, because the plasma core region contains a field-null circle, the plasma size and ion radius are comparable. As a result, the finite Larmor radius effect contributes to the stability of FRC, and so far the deviation between MHD prediction and experimental observation has been considered as the research subject [3][4][5]. Although FRC plasma is a promising candidate that can be used as nuclear-fusion core plasma, the FRC generated by field-reversed theta-pinch method depicts a short lifetime of the order of 100 µs [1], and an improvement of the transport characteristics is essential for future applications.…”