On Electric Fields in Stellarator Equilibria

The paper describes the electric field in stellarator equilibria and discusses the methods of how to compute the electric potential. The momentum balance in a given magnetic field including viscous and friction forces is considered in the frame of a multifluid model. A general ambipolar condition on closed pressure surfaces is derived that is still valid if magnetic surfaces do not exist. The need for an extended model originates from the singularities of the plasma current in the ideal magnetohydrodynamic model of stellarator equilibria, where parallel current density becomes singular leading to singular parallel electric fields. Viscosity and friction forces eliminate these singularities. The paper investigates the mathematical implications of the extended plasma model and discusses the existence of solutions using the methods of functional analysis.