Theory and simulation of the electrothermal instability in pulsed power electrode plasmas

Linear theory of the electrothermal instability is rederived and applied to conditions expected in pulsed power electrode surface plasmas comprised of either hydrogen or carbon. The analysis includes losses due to Coulomb collisions, inelastic processes derived from a collisional radiative model, and thermal conduction. The predicted growth rates are relevant for pulse durations typical of pulsed power devices. Linear theory reveals that the growth rate peaks at a characteristic wavenumber kmax, which is dependent on electron current density Je, number density ne, and temperature Te. Analysis of nonlinear simulations finds that saturation occurs as a result of Coulomb collisions, which limit the electron temperature to go no lower than the ion temperature such that Te≳Ti. When the instability is driven by a perturbation with broadband sinusoidal content, the peak in the energy spectrum nonlinearly shifts away from kmax toward smaller wavenumbers (or longer wavelengths) during saturation. The ETI is shown to be capable of driving plasma filaments with perturbed current densities and electron temperatures that exceed the initial, steady-state values.