Evaluation of the Ambipolar Diffusion Approximation Using an Eulerian Boltzmann-Poisson-BGK Solver

Abstract Because first principles modeling of a weakly ionized gas is computationally expensive, the ambipolar diffusion approximation is often invoked. This approximation assumes the ionized gas undergoes ideal ambipolar diffusion, and is conventionally considered valid if the electron Debye length is orders of magnitude smaller than the neutral mean free path. However, this criterion is not intrinsic to ambipolar diffusion theory. An improved set of criteria for evaluating the validity of the ambipolar diffusion approximation is proposed, then verified with theory and simulation. An Eulerian Boltzmann-Poisson-BGK solver, which circumvents consideration of statistical noise present in particle methods, is used to simulate an unsteady expanding weakly ionized gas undergoing ideal ambipolar diffusion. Potential consequences of incorrectly applying the ambipolar diffusion approximation are demonstrated and discussed.