Multipole-field stabilization of the rotational instability in a theta pinch. I

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Abstract
A theoretical analysis based on the magnetohydrodynamic approximation is carried out on the effect of multipole‐field suppression of the rotational instabilities excited in a high‐β plasma column. The multipole field is assumed not to penetrate into the plasma column but to exert magnetic pressure on its boundary surface in order to suppress the distortion of the plasma column. Analytical theory, which takes into account only the effects of the fundamental wave, gives the stability criterion for the n=2 mode as B s ≥B s,c = 1/2 (m−1)− 1 / 2 r s ‖Ω‖(μ0 ρ0)1 / 2, where r s , ρ0, and Ω are the radius, mass density, and rotational angular velocity of the plasma column, respectively, 2m the order of the multipole field, B s the field strength at radius r s in the vacuum state, and μ0 the permeability of vacuum. Numerical calculations including the effects of the waves parasitic to the fundamental wave support the stability criterion for hexapole (m=3) and octopole (m=4) fields. For quadrupole (m=2) fields, it is shown that the stable range of B s is limited between 0.841 B s,c and 0.856 B s,c , where B s,c is the analytical threshold for m=2.