ENERGY PRINCIPLE WITH INDUCED SURFACE CURRENTS

An extended analysis is presented of the earlier investigated induced surface current effects which arise in a magnetized plasma when the confining field has an imposed inhomogeneous part generated by currents in external conductors. The electromagnetic induction law requires a corresponding contribution from these effects to be added to the formulation of the energy principle for plasma MHD stability. For a plasma with a free boundary, conventional theory therefore holds in a strict sense only when there is a homogeneous external magnetic field. When the characteristic spatial derivative of the imposed field is comparable to or larger than that of the field generated by the plasma currents, the induced surface current effects on electromagnetic free-boundary modes become at least as important as any other effect due to the plasma forces. This holds both in the case of small (linear) and of large (non-linear) plasma displacements. Any non-uniform displacement which includes a translatory component of the plasma motion across the imposed magnetic field then leads to a restoring partial force and a positive contribution to the change in potential energy. An illustration is given by two-dimensional straight Extrap geometry with a peaked current distribution. subject to a combined translational and ballooning-like displacement. In this case there are strong restoring forces, leading to stable oscillations around the plasma equilibrium position.