Linear and non-linear analysis of unstable pinch modes with small Hall parameter
Abstract
We present an analytic form of the linear dispersion relation for m=0, visco-resistive, Hall MHD assuming a Bennett equilibrium. For the ideal (dissipationless) regime, the linear instability growth rates are in agreement with previous numerical studies[1]. Further, the analysis suggests a real frequency component of order the growth rate even for small values of the parameter a ω_pi/c, where a is the pinch radius and c/ω_pi the ion collisionless skin depth. Results from fully 3-D simulation with a Hybrid PIC code demonstrate the presence of high mode number structures during the non-linear development of pinch instability. In the presence of damping via finite viscosity, the linear analysis provides a cut-off for mode growth at high mode number. The saturation of these high mode number structures via viscosity may provide a mechanism for ion heating in Z-pinches. 1. V.I. Sotnikov et al Phys. Plasmas 9, 913 (2002)
- Publication:
-
APS Division of Plasma Physics Meeting Abstracts
- Pub Date:
- November 2004
- Bibcode:
- 2004APS..DPPHP1097O