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

Abstract

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

Formation and sustainment of field reversed configuration (FRC) plasmas by spheromak merging and neutral beam injection

“…This generic idea has been verified in C-2 experiment carried out recently at Tri Alpha Energy Company [30]. Although promising FRC reactor concepts have been developed in the past [4], a reactor design is outside the scope of the present paper, The physics basis for the SPIRIT concept has been verified in numerical calculations [6][7][8][9][10][11][12][13], as well as oblate FRC experiments. Some numerical studies have found an operation regime in an oblate FRC which is stable against all global modes.…”

“…In these studies, (a) the role of ion FLR effects in affecting FRC stability properties has been clarified showing stability of FRC for finite gyro-radius effects; (b) resonant particle effects have been demonstrated to be responsible for the instability drive in cases where FLR effects and the Hall term stabilize the MHD-unstable modes [10]; (c) modern relaxation theory and the properties of two-fluid flowing equilibria have been studied; (d) and the nonlinear saturation of the n=1 tilt instability has been discovered in low-S* configurations [11]. The recent simulations demonstrate for variety of equilibria that the normalized tilt mode growth rate is a function only of the parameter S*/E [8]. This supports the empirical stability scaling obtained earlier with the parameter S*/E [5] shown in Eq.…”

“…S* is also approximately equal to s, the ratio of the separatrix radius to the ion gyroradius ρi in the external magnetic field (since ρi~λi for β~1). Since S* is a key factor for stabilizing effects of finite ion Larmor radius effects (FLR effects), several recent theoretical studies have considered the stabilizing effects of finite ion FLR effects together with the effects of the Hall term and those of sheared ion flow on the n=1 tilt mode in prolate FRC configurations [6][7][8][9][10][11]. These studies have resulted in significant advances in the basic understanding of FRC stability properties in comparison with simpler rigid rotation models.…”

“…Effects of energetic beam ions: Thermal ion kinetic effects play a major role in stabilization of global MHD modes in low-S* prolate FRC experiments [6][7][8][9][10][11]. Injection of energetic beam ions can provide an additional stabilizing mechanism in both prolate and oblate FRCs, provided that the beam ions carry a significant fraction of the total plasma current [12][13][14].…”

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

“…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.…”