Validity of the Two-Term Boltzmann Approximation Employed in Fluid Models

Abstract

Summary form only given. Typical fluid models in gas discharges use results (such as transport and rate coefficients) of a Boltzmann equation solver as input data. Many Boltzmann equation solvers like BOLSIG and ELENDIF solve the Boltzmann equation, using spherical harmonics expansion of the electron energy distribution function (EEDF) with the so-called two-term approximation. In a constant electric field, the solution for the EEDF can be expressed as a function of the reduced electric field E/n (the ratio of the electric field strength to the gas density). The solution also depends on the energy sharing model for ionization, in which the remaining energy after ionization is partitioned between the incident and secondary electrons. It is widely known that the two-term approximation fails at high values of the reduced electric field since the EEDF becomes highly anisotropic. In this study, from the comparison of electron energy distribution functions in particle-in-cell (PIC) and Boltzmann codes for a wide range of the reduced electric field in argon, the validity of two-term approximation in the Boltzmann equation solver is examined. The effect of three different energy sharing models (Opal's model1, equal energy sharing model, and the model that all remaining energy is taken by incident electrons) for ionization on the solution for the EEDF in PIC and Boltzmann codes are also investigated.