Quantifying the relaxation rate of the electron-energy distribution function to determine the fidelity of tabulated rates for fluid plasma models

Rate coefficients for fluid models of low-temperature plasmas (LTP) are often calculated with an equilibrium Boltzmann solver, and then tabulated as a function of the reduced electric field (E/N, where E is the electric field and N is the density of the neutral background gas). This approach produces excellent results for LTP simulations, as long as the equilibration time is short compared to the intrinsic time scales in the problem (the adiabatic approximation). In some cases, the problem time scale is shorter than the time it takes for the electron energy distribution function (EEDF) to reach equilibrium, and in this case the adiabatic approximation is not valid. In this work we attempt to quantify the EEDF relaxation time by using a time-dependent Boltzmann solver to measure how long it takes for the EEDF to respond to a change in the applied electric field. We illustrate our method by applying it to a toy model of molecular nitrogen chemistry, which includes elastic scattering and three representative inelastic processes. In this case we find relaxation times can reach 100's of nanoseconds, which is much longer than the time scale of some pulsed electron-beam driven problems of interest. This indicates that using equilibrium rates may not be appropriate for modeling these fast pulsed problems.