Test cases for grid-based direct kinetic modeling of plasma flows

Abstract

Grid-based kinetic models are promising in that the numerical noise inherent in particle-based methods is essentially eliminated. Here, we call such grid-based techniques a direct kinetic (DK) model. Velocity distribution functions are directly obtained by solving kinetic equations, such as the Vlasov equation, in discretized phase space, i.e., both physical and velocity space. In solving the kinetic equations that are hyperbolic partial differential equations, we employ a conservative, positivity-preserving numerical scheme, which is necessary for robust calculations of problems particularly including ionization. Test cases described in this paper include plasma sheaths with electron emission and injection and expansion of neutral atom flow in a two-dimensional configuration. A unifying kinetic theory of space charge limited sheaths for both floating and conducting surfaces is presented. The improved theory is verified using the collisionless DK simulation, particularly for small sheath potentials that particle-based kinetic simulations may struggle due to statistical noise. For benchmarking of the grid-based and particle-based kinetic simulations, hybrid simulations of Hall thruster discharge plasma are performed. While numerical diffusion occurs in the phase space in the DK simulation, ionization oscillations are well resolved since ionization events can be taken into account deterministically at every time step.

Interaction of biased electrodes and plasmas: sheaths, double layers, and fireballs

“…Experiments using LIF to measure the ion velocity distribution function also validated the ion flow speed profiles in the presheath and that the Bohm criterion was met at its minimum value (V i = c s ) at the sheath edge [76]. Similar tests of these analytic predictions have also been made using PIC and other kinetic simulations [78,79,80,81,82,83,84,85]. In addition to confirming aspects of the above model, its limitations have also been explored.…”

Plasma Assisted Cooling of Hot Surfaces on Hypersonic Vehicles

“…This theory has been compared to a 1-D Direct-Kinetic simulation and a good agreement is shown [19]. Past work on ETC [9] showed that the effectiveness of ETC in cooling the surface is directly correlated to the amount of emission from the surface as expected given (Equation 5).…”

“…Hara and Hanquist [19] derived an expression from Poisson's equation for space-charge limited emission for a biased surface that is similar to the work of Takamura et al [20] but also accounts for kinetic effects and is written in a form that is more suitable for CFD implementation:…”

Evaluation of Computational Models for Electron Transpiration Cooling

“…Following the previous section, the model of Hobbs and Wesson [38] provides the normalized potential for a space-charge limited, floating surface which is −1.02. Thus, the total normalized potential can be rewritten as Φ w = eφ app T e − 1.02 (26) This theory has shown good agreement when compared to a 1-D Direct Kinetic simulation [39]. Like the model for the floating surface, it is helpful to use the biased surface model to estimate the extent of space-charge limits on the electron emission.…”