Stability of long field-reversed configurations

The stability of very elongated field-reversed configurations is solved by an expansion in the small parameter epsilon (inverse elongation). It is first shown that all possible unstable modes have small growth rates (gamma similar toepsilon). The internal tilt mode is considered in detail. An explicit form for deltaW in leading order is derived, and leads to a quadratic form including Hall terms. A sufficient condition for stability is obtained by minimizing deltaW, leading to a field-line ordinary differential equation. Sufficient stability conditions are obtained from this formulation, and indicate stability for S-*/E<2 (where S-* is the ratio of separatrix radius to collisionless ion skin depth and E the elongation of the separatrix), if the local criterion is used. It is argued that a volume-averaged condition is more appropriate when finite ion orbit effects are included. This leads to S-*/E<3.5-4 for stability, independent of separatrix shape or x(s) (separatrix radius to wall radius at the midplane). This condition for stability compares favorably with experimental observations. (C) 2002 American Institute of Physics.