Rotating magnetic field current drive of FRCs subject to equilibrium constraints

The standard analysis for rotating magnetic field (RMF) current production in simple fixed density plasma columns is extended to include the critical interaction between the RMF drive and an elongated field reversed configuration (FRC) equilibrium inside a flux conserver. The standard analysis involves penetration of the RMF into a highly conducting plasma through production of synchronous rotation of the electron fluid due to Hall terms in Ohm's law. In the present article the RMF analysis is combined with two dimensional equilibrium constraints, which have a defining role in governing the RMF penetration. Very simple analytic models are developed, based on instantaneous RMF penetration into an edge layer, that illuminate the basic parameters necessary for current drive and flux buildup or sustainment to be successful. The model does not account for time dependent RMF penetration or transport consistent density profiles, but it clearly points out the basic conditions that must be satisfied, and how they scale, for RMF sustainment of FRCs to be effective.