Are local-field and local-energy approximations appropriate for modeling nanosecond discharges?

Abstract A comprehensive solution of the electron kinetics in gas discharges, accounting for dependencies in space, velocity and time, is often unfeasible. Therefore, the electron behavior is frequently coupled to fluid models under one of two assumptions: the local-field approximation (LFA), which equates the electron kinetics to the steady-state calculation with the local and instantaneous value of the reduced electric field; or the local-energy approximation (LEA), in which the rate coefficients and the electron power distribution among different collisional channels depend on the local value of the mean electron energy. In this work, we focus on time-locality to assess the impact of the LFA and LEA assumptions on the calculation of the temporal evolution of the electron kinetics in nanosecond discharges. To do so, we consider an accurate Monte Carlo time-dependent formulation as golden standard. We study electron relaxation in different background gases (air, argon, and mixtures of both) at two pressures (10 and 100 Torr). The LEA generally provides more accurate results than the LFA, with increasing differences at lower pressures, where energy relaxation is slower. The greater accuracy of the LEA comes from the temporal effects introduced by the equation for the mean electron energy, which is absent in the LFA. Opting by the LFA in conditions of slow relaxation can lead to serious degradation of the model results, with errors on the production of excited species up to several tens of percent. Hence, in those scenarios, and when a kinetic approach is not possible, the LEA should be adopted instead of the LFA. The comparison is extended to a two-term time-dependent solver based on a quasi-stationary assumption for the first anisotropy. This method provides a good description of the electron kinetics, except at early times ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>≲</mml:mo> <mml:mn>0.2</mml:mn> </mml:mrow> </mml:math> ns) at 10 Torr, where the quasi-stationary assumption becomes inaccurate.