Equilibrium and stability of high-β toroidal multipoles

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Abstract
The equilibrium and stability of finite‐β toroidal plasmas confined by multipole fields (with no toroidal component) is studied within the framework of ideal magnetohydrodynamics. Equilibria are obtained by the numerical solution of the Grad–Shafranov equation, including the effect of rigid current‐carrying rings within the plasma. Stability to pressure‐driven modes (interchange and ballooning) is examined for these equilibria using standard methods. The spatial variation of the critical pressure gradient and the nature of the marginally stable eigenfunctions are discussed. Results are presented for three configurations (quadrupole, octopole, and dodecapole) with parameters similar to those for the Surmac experiment.