Analysis of non-local heat flux in capacitively coupled plasmas

Abstract The transport equation of the electron heat flux, i.e. the third-order moment of the Boltzmann equation, in capacitively coupled plasmas consists of non-local (advective), local (diffusive), and collisional terms and is analyzed using a one-dimensional electrostatic particle-in-cell, Monte-Carlo collision (PIC-MCC) model. It is shown that the non-local and local terms are dominant over the collisional terms in the rarefied (low pressure) regime, illustrating the importance of non-local heat flux effects. In the intermediate regime, the non-local, local, and collisional terms are comparable. In the collisional (high pressure) regime, the local and collisional terms are dominant and the non-local terms are negligible. Further analysis of the PIC-MCC results shows that the heat flux tensor is anisotropic, i.e. the contracted heat flux vector that is typically used in conservation of energy, is insufficient in the rarefied regime. In addition, it is shown that the fourth-order tensorial terms and the contracted fifth-order moment derived using the Grad closure theory are valid as long as the fourteen moments, i.e. 1 mass, 3 momentum vector, 6 anisotropic pressure tensor, 3 heat flux vector, and 1 scalar kurtosis, are captured.