Abstract. Rotating Magnetic Fields (RMF) have been demonstrated to drive currents in many rotamak experiments, but use with an FRC confined in a flux conserver imposes special constraints. The strong current drive force results in a near zero density at the separatrix, and the high average beta condition requires the current to be carried in an edge layer near the separatrix. The RMF can only penetrate into this layer by driving the azimuthal electron velocity synchronous with the RMF frequency. Build-up or maintenance of the flux throughout the FRC occurs due to the torque imposed on the electrons in this layer exceeding the total resistive torque due to electron-ion friction. Current is maintained on the inner flux surfaces by an inward radial flow. Particle balance is maintained by a swirling axial flow from inner to outer field lines. This process is seen using a new numerical code, and the resultant flux build-up and calculated profiles are demonstrated on the STX and TCS RMF FRC formation experiments.