Solvable Self-Similar Model of the Sausage Instability in a Resistive Z-Pinch.

摘要

A solvable model is developed for the linearized sausage mode within the contest of resistive MHD. The model is based on the assumption that the fluid motion of the plasma is self-similar, as well as several assumptions pertinent to the long-wavelength limit. The perturbations to the magnetic field are not assumed to be self-similar, but rather are calculated. Effects arising from time dependences of the equilibrium, e.g., current rising as T, alpha ohmic heating, and time variation of the pinch radius, are included in the analysis. The formalism appears to provide a good representation of those modes that involve coherent sausage distortion of the entire cross section of the pinch, but excludes modes that are localized radially, and higher radial eigenmodes. for this and other reasons, it is expected that the model underestimates the maximum instability growth rates, but is reasonable for global sausage modes. The net effect of resistivity and time variation of the equilibrium is to decrease the growth rate if alpha somewhat< 1, but never by more than a fact of about two. The effect is to increase the growth rate if alpha somewhat>1. Keywords: Sausage instability; Magnetohydrodynamic Instability. (JHD)