The authors present a time dependent analysis of current drive due to the nonlinear Hall effect in spherical plasmas and apply this to the rotamak. In the rotamak experiments a rotating magnetic field is applied to a roughly spherical plasma and a combination of toroidal and poloidal currents are driven due to the nonlinear interaction of the oscillating currents and magnetic fields, giving a compact toroidal equilibrium. This study verifies that the currents can be established within a reasonable time and indicates the scaling of this characteristic time with respect to the parameters of the plasma, e.g. resistivity and density. The technique developed can be used efficiently to investigate the current driven by an oscillating field; and, indeed, has predicted the existence of 2 omega and higher temporal harmonics in the driven current, an observation which was subsequently confirmed experimentally. By integrating the equations for a sufficiently long time an alternative method is provided to determine the steady-state current driven by a rotating field and the consequent magnetohydrodynamic equilibrium configuration.
Axisymmetric two-fluid plasma equilibria with momentum sources and sinks