Heating a plasma by means of magnetic pumping

We present two models for the heating of a cylindrical plasma by an oscillating magnetic field. The model for collisional heating, applicable at low temperatures and high densities, is extended to include dissipative effects. Both linear and nonlinear numerical calculations yield heating times which agree for moderate values of the modulation index. A model for collisionless transit-time heating, applicable at high temperatures, is extended to include the self-consistent electric fields; the ions are treated by means of a Vlasov equation and the electrons are treated as a fluid in equilibrium. Inclusion of the electric fields enhances the heating rate by as much as a factor of four. Heating rates calculated from the two theories are in essential agreement when the mean free path of the ions is comparable to the length of the pumping section.