14-moment maximum-entropy modeling of collisionless ions for Hall thruster discharges

Abstract

Ions in Hall effect thrusters are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 partial differential equations (PDEs) for the density, momentum, pressure tensor components, heat flux vector, and fourth-order moment associated with the particle velocity distribution function. The model is applied to the study of collisionless ion dynamics in a Hall thruster-like configuration, and its accuracy is assessed against different models, including the Vlasov kinetic equation. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping, and finally the evolution of ions in the axial-azimuthal plane. Most of this work considers ions only, and the coupling with electrons is removed by prescribing reasonable values of the electric field. This allows us to obtain a direct comparison among different ion models. However, the possibility to run self-consistent plasma simulations is also briefly discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy system appears to be a robust and accurate option for the considered test cases. The accuracy is improved over the simpler pressureless gas model (cold ions) and the Euler equations for gas dynamics, while the computational cost shows to remain much lower than direct kinetic simulations.

Inertial and anisotropic pressure effects on cross-field electron transport in low-temperature magnetized plasmas

“…The five-moment model does not account for such off-diagonal pressure contribution. The present results obtained from the PIC-MCC model suggest the need of a higher-order moment fluid model to capture such asymmetric non-Maxwellian effects [29,59].…”

“…various collisional transport, plasma-wall interactions, and plasma-wave interactions), it is unclear how many moments need to be captured and what type of closure is needed for the fluid model to be predictive. While recent fluid moment approaches include fivemoment using gyroviscous tensor [26], nine-moment [27], ten-moment [28], and fourteen-moment [29]), results obtained from a kinetic (e.g. PIC-Monte Carlo collision (MCC)) simulation are required to benchmark the hierarchy of fluid moment models and understand the necessary closure model.…”

Numerical simulation of rarefied supersonic flows using a fourth-order maximum-entropy moment method with interpolative closure

“…These approximations are relevant to a number of collisionless situations, including the simulation of (low-density) plasmas. 28 Two-dimensional simulations are accelerated on Graphics Processing Units (GPUs), with CUDA. Our simple CUDA implementation of the maximum-entropy system, not implementing any advanced memory management strategy, resulted in a speed-up of roughly 340 times, when run on an NVIDIA A100 GPU, with respect to single-core computations.…”

“…In such conditions, the wake is often characterized by an extremely low density, and the gas that fills the wake from the sides of the blunt body crosses at the center-line, resulting in a ring-like VDF. 3,38 Finally, we remark that, whereas a direct knowledge of the VDF is not needed in the present work, there are cases where a full computation of the coefficients vector, α, might be required. For instance, an accurate modelling of chemical reactions, as well as non-equilibrium collision frequencies, may require this, unless non-equilibrium formulas and approximations are developed.…”

Electron cyclotron drift instability and anomalous transport: two-fluid moment theory and modeling

“…Finally, it should be noted that, the focus of this work is on the fundamental properties and scaling of the dispersion relation and the development of anomalous transport without additional collisions. The work performed here may be extended in the future to use the ten-moment model, and possibly even higherorder moment fluid models, with improved plasma closure relations based on physical constraints [2,4,5,25,42,44,58] or data-driven approaches [12,59,60].…”