A New Approach to Magnetohydrodynamic Stability Ii Sigma Stable Diffuse Pinch C

P Sakanaka

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2. Procedure .
We investigate numerically the a-stability of diffuse linear pinch configurations. The equilibria are described by the three profiles p(r), B (r), and B (r), which are connected through the equilibrium equation (p + ^ B^)'+ B^/r = 0. (1) Fixing the value of B, where B = E(0), (2) p{0) + B^(0)/2 this leaves two of the three profiles to be chosen arbitrarily, e. G. , p and v = B /rB . In order to reduce the number of possibilities further we restrict the analysis to those equilibri...a for which the pressure is a monotonically decreas- ing function of r (p' ^ °- l^lmax^ ^ 1- |y(0) |, which would spoil the suffi- ciency of criterion (16) .
For our purpose the only useful form of the toroidal periodic condition is the following, completely general but 17 Implicit, condition for the absence of the m=l instabilities. One easily shows that the pinch is stable for fixed m as k -> oo. Consequently, the interval of unstable k-values has to be limited: k^ k, or A

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