High-order moment models for low pressure discharges

We introduce a novel electron fluid model based on the resolution of higher-moment equations that aims at extending the validity of the fluid equations for transitional collisional regimes between the continuum and the kinetic descriptions. In addition to mass, momentum, and energy conservation equations, the model explicitly solves for the evolution of the heat flux vector and the contracted fourth moment to capture perturbations in the skewness and the kurtosis of the electron distribution function. We use the model to study an argon inductively coupled discharge in the low-pressure range (p < 100 mTorr). We will discuss the closure of the system of equations with Grad’s method and considering a full Boltzmann collisional operator, as opposed to the commonly used Krook operator simplification. The new equations show new effects in the mass and energy transport that are consequence of the dependency of the transport coefficients on the kurtosis of the electron distribution function. Numerical simulations of the new system of equations will be compared to particle in cell simulations as well as to experimental measurements of the electron quantities in low-pressure ICP discharges.