Numerical Simulation of Electrostatic Discharge with Energy Distributions Distorted by Electric Field

Electron energies drive many processes in electrostatic discharges: ionization rates, collisional relaxation rates, secondary emission, etc. Especially in the initial phases, the energy delivered to electrons by direct acceleration from the electric field can be just as important as the thermal energies. In these cases, the velocity distribution for the electrons is not a Maxwell-Boltzmann distribution, but skewed along the axis of the electric field. Ideally, one would use the Boltzmann equation to solve for these dynamics, but this is often not practical when modeling realistic problems.

We treat the ballistic velocity distribution (due to field acceleration) and the thermal velocity distribution as uncorrelated, and add their energies in quadrature, to get an average electron kinetic energy. This allows us to define an “effective temperature” as the kinetic energy per degree of freedom and use that to track energy conservation. This is different from normal temperature as the associated energy is not totally random since the velocities are skewed by the electric field. We present results from a drift-diffusion and kinetic energy conservation based numerical model in cylindrical symmetry, which demonstrates the correct threshold behavior.

LA-UR-21-25746