Studies of global stability of field-reversed configuration plasmas using a rigid body model

Global stability of field-reversed configuration (FRC) plasmas has been studied using a simple rigid body model in the parameter space of s (the ratio of the separatrix radius to the average ion gyro-radius) and plasma elongation E (the ratio of the separatrix length to the separatrix diameter). Tilt stability is predicted, independent of s, for FRC's with low E (oblate), while the tilt stability of FRC's with large E (prolate) depends on s/E. It is found that plasma rotation due to ion diamagnetic drift can stabilize the tilt mode when s/E≲1.7. The so-called collisioniess ion gyro-viscosity also is identified to stabilize tilt when s/E≲2.2. Combining these two effects, the stability regime broadens to s/E≲2.8, consistent with previously developed theories. A small additional rotation (e.g., a Mach number of 0.2) can improve tilt stability significantly at large E. A similar approach is taken to study the physics of the shift stability. It is found that radial shift is unstable when E < 1 while axial shift is unstable when E>1. However, unlike tilt stability, gyro-viscosity has little effect on shift stability.