Influence of variable impedance terminations and input voltages on the operating conditions of an under-matched magnetically-insulated transmission line

Termination of a magnetically-insulated transmission line (MITL) with an impedance that is less than the matched MITL operating impedance launches a re-trapping wave back up the MITL toward the source. A previous investigation [1] obtained the relationship for the MITL operating conditions (voltage and current) after the passage of the re-trapping wave that depended on the input voltage, the termination impedance, and the MITL operating conditions based on parapotential flow at minimum current [2]. The relationship was in agreement with detailed particle-in-cell (PIC) simulations and experiments investigating the re-trapping wave process for large area diodes. The scaling law and simulations however were only applied to a constant input (forward going) voltage and termination impedance. This paper extends those PIC simulations and wave analyses to MITL operating conditions for termination impedances and input voltages that are functions of time. The objective is to determine the constitutive relationships for the propagation of insulation waves that propagate from the voltage source to the load and re-trapping waves that propagate from the under-matched load to the source. Wave propagation questions of hysteresis, superposition, transmission, and reflection coefficients are addressed. Particle-in-Cell simulations based on the RITS-6 [3] dustbin geometry are used extensively in the analyses and compared with linear and non-linear wave propagation. The possibility of treating the MITL as a series of transmission lines is addressed.