Shear-ballooning stability analysis of low-. beta. plasmas

A model of magnetic configurations that has both shear and variation of the field curvature along the magnetic field is constructed. The stability analysis of this system is performed by expanding the perturbation functions to phi/sub 0/ which is constant along the field and phi/sub 1/ which is sinusoidally varied along the field line. The shear term is retained in the form of differntial operations in zeta, the coordinate parallel to the pressure gradient. After several simplifications, the equation reduces itself to the fourth order differential equation. The eigenvalue of this equation is numerically obtained. The calculated critical ..beta.. plotted versus the well depth parameter, h, makes a smooth transition between h < 0 (maximum average B) and h > 0 (minimum average B). Using the same technique, the nondivergent solution to the localized shear mode (Suydam mode) is also obtained by retaining the inertia term