Astron stability against poloidal perturbations

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Abstract
An energy principle and stability requirements are derived for low‐frequency poloidal perturbations of an astron ion ring embedded in a dense, low‐temperature plasma. The particle ring equilibrium has a general distribution function f (H, Pϑ), with H the Hamiltonian and Pϑ the canonical momentum in the toroidal direction. The axisymmetric perturbations are treated rigorously using the Vlasov equation for the ring and the equations of ideal magnetohydrodynamics for the plasma. An explicit integration of the Vlasov equation is obtained for conditions where the particle motion is ergodic in the poloidal plane. For finite axial‐length rings, a new term in the perturbation energy is found to arise from the betatron effect of the toroidal electric field perturbation. This has an explicitly stabilizing effect if (∂/∂H) f⩽0. The stabilizing effect of this term is required for, but does not guarantee, the existence of stable equilibria with conducting walls removed to large distances.

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