Non-local, diamagnetic electromagnetic effects in magnetically insulated transmission lines

Abstract

We identify the time-dependent physics responsible for the critical reduction of current losses in magnetically insulated transmission lines (MITLs) due to uninsulated space charge limited (SCL) currents of electrons emitted by field stress. A drive current of sufficiently short pulse length introduces a strong enough time dependence that steady state results alone become inadequate for the complete understanding of current losses. The time-dependent physics can be described as a non-local, diamagnetic electromagnetic response of space charge limited currents. As the pulse length is increased or equivalently, the MITL length reduced, these time-dependent effects diminish and current losses converge to those predicted by the well-known Child-Langmuir law in the external (vacuum) fields. We present a simple one-dimensional (1D) model that encapsulates the essence of this physics. We find excellent agreement with 2D particle-in-cell (PIC) simulations for two MITL geometries, Cartesian parallel plate and azimuthally symmetric straight coaxial. Based on the 1D model, we explore various scaling dependencies of MITL losses with relevant parameters, e.g., peak current, pulse length, geometrical dimensions, etc. We propose an improved physics model of magnetic insulation in the form of a Hull curve, which could also help improve predictions of current losses by common circuit element codes, such as BERTHA. Lastly, we describe how to calculate temperature rise due to electron impact within the 1D model.