Effect of equilibrium flow on the resistive tearing mode
Abstract
The resistive tearing instability of an incompressible plasma is investigated for the plane sheet pinch in which the equilibrium magnetic field, x̂B_{x0}+ẑB_{z0}, depends only on y. The usual assumption is to take v_{0}=0, but here the effect of a nonzero v_{0} is studied. A linear, timedependent model is used in which perturbations take the form f_{1}(y,t)exp [i (k_{x}x+k_{z}z)]. A new initialvalue code has been developed to solve the resulting higherorder system of equations. For a symmetric magnetic equilibrium and modes α<1, where α=a (k_{x}^{2}+k_{y}^{2})^{1/2}, an exponential growth develops. The growth rate, p=ωτ_{r}, is computed as a function of α and S=τ_{r}/τ_{h}, for several values of v_{0}. The effect is to reduce p for all α, and to reduce the marginal α for instability for values of v_{0} of the order of the resistive diffusion velocity. Results for larger values of v_{0} are briefly discussed. For asymmetric tearing, the effect of the diffusion velocity depends on its sign. The velocity may have either a stabilizing or destabilizing influence on both the growth rates and the critical α for instability.
 Publication:

Physics of Fluids
 Pub Date:
 October 1978
 DOI:
 10.1063/1.862090
 Bibcode:
 1978PhFl...21.1746K
 Keywords:

 Equilibrium Flow;
 Incompressible Fluids;
 Magnetohydrodynamic Stability;
 Plasma Oscillations;
 Boundary Value Problems;
 Electrical Resistance;
 Plasma Waves;
 Plasma Physics