A Continuum Kinetic Investigation into the Role of Transport Physics in the Bohm Speed formulation.

Non-oscillatory solutions to the Bohm criterion require the ion exit flow speed at the sheath entrance to be greater than or equal to the Bohm speed, which is generally equal to the sound speed in collisionless plasmas. This formulation, however, is only applicable when the sheath entrance is well defined, a condition that is not satisfied in many numerical and experimental cases of interest. Instead, a sheath transition region is found to exist. To resolve this and provide a Bohm speed formulation for the intermediate plasma regime, a new fluid sheath model that considers the effects of transport terms such as the electron heat flux, thermal force, and temperature isotropization has been proposed by [Y. Li et al., Physical Review Letters (2022)]. This work studies this model and numerically solves the Vlasov-Maxwell equations using a continuum kinetic formulation in the Gkeyll code to capture the sheath physics, which is inherently kinetic in nature, without tracking individual particles. Multiple cases ranging from a Knudsen number of 20 to 5000 have been considered in a 1X3V domain using the Lenard-Bernstein collisional operator. The results of the simulations offer insights into the formation of the sheath transition region, the Bohm speed in this region, and the role of the transport terms in the formulation of the Bohm speed. The noise-free continuum-kinetic approach is benchmarked to the particle-in-cell results.