The effect of anomalous resistivity on fast electrothermal instability

This manuscript presents a new theoretical contribution toward the growth rate of the "fast" form of electrothermal instability (ETI) in the presence of anomalous resistivity (AR). Current-driven ETI is present in all pulsed-power platforms, and has been shown to seed the disruptive magneto Rayleigh-Taylor instability. Fluid simulations of low-density, current-carrying plasmas are often subject to nonphysical runaway Ohmic heating due to an under predicted resistivity when using purely collisional resistivity models. AR models provide mechanisms to increase the resistivity as the drift speed increases through increased current density. The derivation of a new, generalized growth rate is presented for the ETI, which includes a resistivity that is dependent on current density, and marks the key contributions of this work. This new growth rate is then compared to the growth rate without AR. Although the striation form of the ETI growth rate is unaffected by the inclusion of AR, the filamentation form of the ETI growth rate depends on the AR. Hence, the new growth rate is verified through 1D simulations of the filamentation form of ETI. The impact of AR can be significant: up to twelve orders of magnitude on the temporally varying local growth rate for a certain choice of parameters. For experimentally relevant conditions based on kinetic simulations, the growth rate can be increased by up to four orders of magnitude if the AR is dominated by the lower-hybrid drift instability. Published under an exclusive license by AIP Publishing