Variational quadratic form for low-frequency electromagnetic perturbations. II. Application to tandem mirrors

Abstract

In this paper the low-frequency quadratic form governing the linear response of electromagnetic trapped particle modes is applied to a tandem mirror geometry and several problems are treated. It is shown that the long-wavelength magnetohydrodynamic (MHD) wall stabilization mechanism persists even when the line bending energy is suppressed by allowing an electrostatic response. In another problem, the amount of charge uncovering needed to suppress electrostatic trapped particle modes is determined as the beta of the plasma rises to its critical MHD beta value βcr and the required charge uncovering is shown to increase substantially as beta approaches βcr. A third problem treats trapped particle instabilities driven by rotation and field line curvature in diffuse and steep boundary models. The steep boundary model offers the possibility of an enhanced ‘‘robust’’ finite Larmor radius (FLR) stabilization due to an amplification of the finite Larmor radius magnetic compressional term when steep pressure gradients are present. Otherwise, one finds relatively small regions of stability in parameter space when electric field drifts are comparable to diamagnetic drifts. Detailed stability plots are presented for parameters applicable to the Tara experiment [Nucl. Fusion 22, 549 (1982)].