The equilibrium and stability of rotating plasmas

TLDR

In rotating equilibrium, velocity and magnetic fields share the same flux surfaces. The study derives a second‑order PDE that determines axisymmetric equilibrium states. The authors formulate coordinate‑free flux‑surface equations that determine the Alfvén and cusp spectra and provide a sufficient condition for global stability when flow is parallel to the magnetic field up to rigid rotation. The derived stability condition is also necessary for mirror configurations lacking toroidal field under pure rigid rotation.

Abstract

In a rotating equilibrium state, the velocity and magnetic fields are shown to share the same flux surfaces. A simplified derivation is given of a second-order (not necessarily elliptic) partial differential equation which determines axisymmetric equilibrium states. For general configurations, equations on flux surfaces which determine the Alfvén and cusp continuous spectrum are derived and the stability investigated. These equations are written without the use of any particular coordinate system. Similar equations yield a sufficient condition for global stability of axisymmetric equilibria if the flow is parallel to the magnetic field up to a rigid rotation of the plasma. This condition is also necessary for stability in a mirror configuration with no toroidal field and a pure rigid rotation.