Two-dimensional, time-dependent theory of magnetically insulated electron flow

Magnetic insulation has provided a means of exceeding the limitations on power flow density imposed by material insulator breakdown. Particle beam fusion is just one of many possible applications of this important phenomenon. In this paper, an earlier 1-D theory for magnetically insulated electron flow has been extended to treat problems with gradual variations in time and a second spatial dimension. The flow is self-consistently specified by a distribution function of electron energy and canonical momentum which varies in space and time. The electron Hamiltonian and a phase space continuity equation are presented. An example is given which provides useful insights into the physics of insulated flow