Variational theory of electrical conductivity and kinetic tearing modes

Abstract

A variational theory for Ohm’s law, valid for arbitrary collision frequency, is presented for a slab geometry using a pitch angle scattering collision operator. Shear and temperature gradient effects are included but toroidicity is neglected. The variational conductivity is used to examine the effects of shear and electron temperature gradients on tearing mode instabilities. It is shown that shear has a strong stabilizing effect on the so-called ’’collisional’’ and ’’semicollisional’’ electron temperature gradient tearing mode instabilities. In addition, the stabilizing effect of shear on the classical resistive and inertial tearing modes is discussed.