Rescaling of equilibrium magnetically insulated flow theory based on results from particle-in-cell simulations

Abstract

By relaxing an assumption on the electron density in the flow layer used in magnetically insulated transmission line (MITL) theory, the theory is rescaled to match particle-in-cell (PIC) simulation results, providing a more accurate determination of the line voltage from the measurement of anode and cathode currents over a broad range of parameters. Results from the PIC simulations also show that self-limited flow is not determined by either a minimum-current or a minimum-energy condition, but rather is closer to saturated flow. In addition, analytic expressions are obtained for the first time for the self-limited flow impedance ZfSL(V)∕Z0 and the self-limited anode and cathode currents Z0IaSL(V) and Z0IcSL(V), where Z0 is the vacuum impedance of the line and V is the voltage. Similar expressions for both minimum-current flow and minimum-energy flow are also obtained. Results are compared with other models for MITL flow and show that this rescaled MITL flow model is most consistent with the PIC simulation results. Finally, it is shown that a matched load condition can never be satisfied for self-limited (or line-limited) flow.