Radial current density effects on rotating magnetic field current drive in field-reversed configurations

Abstract

Steady state solutions, suitable for field-reversed configurations (FRCs) sustained by rotating magnetic fields (RMFs) are obtained by properly including three-dimensional effects, in the limit of large FRC elongation, and the radial component of Ohm’s law. The steady electrostatic potential, necessary to satisfy Ohm’s law, is considered to be a surface function. The problem is analyzed at the midplane of the configuration and it is reduced to the solution of two coupled nonlinear differential equations for the real and imaginary parts of the phasor associated to the longitudinal component of the vector potential. Additional constraints are obtained by requesting that the steady radial current density and poloidal magnetic flux vanish at the plasma boundary which is set at the time-averaged separatrix. The results are presented in terms of the degree of synchronism of the electrons with the RMF and compared with those obtained when radial current effects are neglected. Three important differences are observed when compared with the case without radial current density. First, at low penetration of the RMF into the plasma there is a significant increase in the driven azimuthal current. Second, the RMF amplitude necessary to access the high synchronism regime, starting from low synchronism, is larger and the difference appears to increase as the separatrix to classical skin depth ratio increases. Third, the minimum RMF amplitude necessary to sustain almost full synchronism is reduced.