Analytical solutions for the current driven by a rotating magnetic field in a cylindrical plasma with azimuthal field

The generation of steady currents by a rotating magnetic field (RMF) in a cylindrical plasma permeated by a steady azimuthal (or toroidal) magnetic field is studied analytically. Solutions are presented for the following limiting cases: (1) high resistivity, when the penetration of the RMF and current drive are confined to a skin depth layer; (2) low resistivity and weak toroidal field (small compared with the RMF), when the RMF fully penetrates the plasma and the toroidal current is that due to nearly synchronous rotation of the electron fluid with the RMF; (3) low resistivity and intermediate toroidal field (comparable to the axial field associated with synchronous current), when the toroidal current is a significant fraction of its synchronous value, but large oscillating fields are generated; and (4) strong toroidal field, when the RMF fully penetrates the plasma but current is only driven in a boundary layer at the plasma edge. The applicability of these solutions is governed by the relative sizes of three dimensionless parameters.