Dynamic modeling of magnetically insulated transmission line systems

Negative conductors in vacuum transmission lines used in multiterrawatt applications emit electrons freely. These lines are efficient only because the self-magnetic field of the power flow forces the electrons to flow parallel to the electrodes. Excepting numerical simulations, dynamic modeling of systems of these transmission lines has generally either ignored electron flow, or has included only those electrons that cross immediately to the anode at the front of the forward wave. In this paper we describe an analytic model that includes flowing electrons and the effects of these flows on line voltage and on the reduction of magnetic flux. Axial electron currents are modeled using simple, measurable, and calculable parameters. Transverse electron currents are modeled using general patterns found empirically from simulation data. These currents are in turn related by an expanded set of Telegrapher equations. An example of the use of the model is compared to two-dimensional, time-dependent particle-in-cell simulations.