Session PW3: Modeling and Simulation: Computational Methods II

Live

We present MCIG, a new computer code for the solution of the Boltzmann equation for electrons or ions in weakly ionized gases, based on an efficient Monte-Carlo algorithm. MCIG will be released as freeware with a user-friendly interface similar to that of BOLSIG+, with very similar inputs and outputs. The purpose of MCIG is to obtain distribution functions, transport coefficients and reaction rate coefficients from cross section data, without invoking the two-term approximation used by BOLSIG+ and many other electron Boltzmann equation solvers. These outputs can then be used to check the validity of two-term Boltzmann results, or directly as input data for fluid models. MCIG can handle electrons as well as ions, and includes options for DC and AC electric and magnetic fields, gas temperature, superelastic collisions, anisotropic scattering and many more. We show various examples to illustrate its use and interest.   

Live

We will present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The implicit treatment of the coupled equations allows using large time steps, and the full-Newton method enables fast non-linear convergence at each time step, offering improved efficiency of fluid plasma simulations. The new solver allows solving several problems we could not solve before with existing software: two- and three-dimensional structures of the entire DC discharges including cathode and anode regions with electric field reversals, normal cathode spot and anode ring, plasma stratification in DC and RF discharges [1]. To address the disparity of the electron and ion time scales, we also implement a modular split of the fast (electron) solvers and slow (ion) transport solvers. This split allows adding kinetic solvers for electrons to our framework. We will also report an initial development of an implicit chemistry module for additional time step increase. A few demo/validation cases will be discussed in our presentation. [1] R Arslanbekov and V Kolobov, Implicit and Coupled Multi-Fluid Solver for Collisional Low-Temperature Plasma, https://arxiv.org/abs/2003.03812   

Live

Low-pressure plasma discharges in presence of crossed electric and magnetic fields often show strong translational non-equilibrium. This limits the validity of fluid and hybrid fluid-kinetic descriptions and leads to the incorrect prediction of transport processes. Extended fluid-like descriptions based on higher-order moments promise to offer enhanced physical accuracy over commonly employed 5-moments formulations. We investigate a 14 moments maximum entropy formulation for the description of electrons colliding with a neutrals background. The proposed description embeds pressure anisotropy, characteristic of magnetized plasmas, and includes additional non-equilibrium features such as the possibility to reproduce Druyvensteyn and ring-like velocity distributions. We compare the solution of the 14 moments system to Particle-In-Cell simulations for operating conditions characteristic of Hall thruster discharges. A solution of a 5-moments system is provided as a baseline comparison. The 14 moments system shows able to accurately predict electrons transport both in steady and unsteady conditions, reproducing accurately the non-Maxwellian distribution function. The solution is more computationally expensive than the 5 moments system, but much cheaper than a kinetic solution.   

Live

Multi-temperature distributions are a convenient way to describe nonequilibrium gases close to equilibrium. However, they can require an arbitrary energy partitioning. We present a general method to determine the uncertainties of multi-temperature models. The contribution of each energy mode is calculated in the diagonal basis of the molecular Hamiltonian, and the various possible assignations of the energy terms and groupings of the temperatures are compared. The method is applied to the CO$_{\mathrm{2}}$ molecule: we determine the nonequilibrium temperature ranges where the calculated nonequilibrium partition functions are insensitive to the assignation or grouping scheme. We then compare the results of this advanced model to the partition functions computed with a simple, uncoupled vibrating rotor (UVR) model. We show that the advanced model only slightly increases the domain of validity compared to the UVR model. We also demonstrate that the uncertainty induced by the assignation of the coupling terms cannot be neglected outside this validity domain. The implications for spectral modeling of nonequilibrium plasma discharges is discussed.   

Live

Most fluid plasma simulations employ electrostatic Poisson equation for obtaining the electric field due to charge distribution along with continuity equations for calculating all the species densities and an energy equation for updating absorbed energy by electrons. Single frequency electromagnetic waves have a spatial field variation that can be attributed to two different effects: i) electrostatic effect which is responsible for field variation between electrodes having dissimilar potentials; ii) electromagnetic wave effect which is responsible for field variation over dimensions comparable to wavelength. Plasma simulations that only include the Poisson equation consider the electrostatic effect but ignore the electromagnetic wave effect assuming that the plasma reactor dimensions are much smaller than the radio frequency wavelength. In this paper, we propose a new potential gauge with the same scalar potential as the electrostatic solution of the Poisson equations. The magnetic vector potential obtained using this new potential gauge is a direct indicator of electromagnetic wave effect. This potential gauge is built such that the electrostatic effect and electromagnetic wave effect are effectively divided between the scalar potential and the vector potential respectively. Electromagnetic solvers that employ this gauge can be used to study large area capacitively coupled plasma (CCP) reactors where the radial variation of plasma density within process gap can be significant due to the electromagnetic standing wave effect.   

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The objective of this work is to assess some of the potential advantages and limitations of finite volume method applied to multifluid equations as compared to Particle-In-Cells (PIC) methods. Hydrogen and Argon plasma discharges in 2D are simulated using a two-fluid isothermal Euler-Poisson equations finite volume method. The structure of sheaths in non-magnetized cases, and the appearance of instabilities in magnetized cases are compared with PIC simulations. We also present preliminary result obtained via a second order discretization finite volume methods using Adaptive Mesh Refinement (AMR) method. Finally, we present ongoing work on adapting a recently developed asymptotic preserving method to the 2D framework presented here. We aim at showing that, and evaluating to what extent, fluid models associated with tailored numerical methods have a lot of potential for plasmas of interest in electric propulsion applications.   

Live

Global modeling can often provide initial insight into the physics of complex chemically reacting plasmas (e.g. gas discharges, ion sources). From global species continuity and electron energy equations, global models provide quick estimates of volume-averaged plasma properties such as species number densities and temperatures. However, such models cannot provide spatial profiles of these properties. Interpretation of global modeling results can thus be difficult; simulations may differ from experimental measurements due to limitations of the global model assumptions, uncertainties in chemical reaction data, etc. In this talk, we present an overview of conventional global models and their limitations. We also present a more general new framework, Pade Approximation Residuals Norm Minimization Algorithm (PARNMA), for solving 1D steady-state plasma fluid equations. The model uses a rational function representation of various plasma properties. These profiles are substituted into the fluid equations. We then solve a multi-objective minimization problem to find optimal coefficients for the rational function representation. The framework allows sheaths to be resolved without imposing any artificial boundary conditions. We demonstrate its use in simulations of various gas discharges.   

Live

A full-fluid moment model is developed to study low-temperature magnetized plasmas. The governing equations are derived by taking moments of the Boltzmann equation, and flux boundary conditions are calculated by taking moments of a shifted Maxwellian distribution. An initially quasineutral plasma is modeled between two non-emitting walls to assess the performance of the model in capturing plasma-wall interaction. Sensitivities of the boundary conditions and other physical phenomena, including ion drag and electromagnetic fields, are evaluated. Inclusion of momentum transfer collisions displayed variations in plasma sheath properties in close agreement with analytical trends. It was also observed that an inverse sheath is formed using an applied transverse magnetic field. Finally, the full-fluid moment model is employed to simulate the low-temperature plasma discharge in Hall-effect thrusters. The results are compared against a nonneutral drift-diffusion model and a quasineutral drift-diffusion model to investigate the effects of the quasineutral assumption and electron inertial terms on cross-field electron transport. Fluid shear is found to affect the cross-field electron transport.