Abstract
In this study, the Boltzmann equation with electric acceleration term is discretized and solved by the unified gas-kinetic scheme (UGKS). The charged particle transport driven by electric field is included in the electric acceleration term. To capture non-equilibrium distribution function, the probability distribution functions of gas is discretized in a discrete velocity space. After discretization, the numerical flux for distribution function is computed to update the microscopic and macroscopic states. The flux is decided by an integral solution of Boltzmann equation based on characteristic problem. An electron-ion collision model is introduced in the Boltzmann Bhatnagar-Gross-Krook (BGK) equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. For simplicity, the electric field induced by charged particles is controlled by the Poisson’s equation, which is solved using the Green’s function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical cases, linear Landau damping and Gaussian beam, are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Comparison results show good accuracy and higher efficiency than particle based methods. Difference between Poisson’s equation and complete electromagnetic Maxwell equation is presented by numerical results based on the two models. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily. The UGKS-Poisson model is proved to be promising in plasma flow simulation.
Highlights
The Boltzmann equation describes time evolution of physical state under external field using gas-distribution function [1]
We solve the Boltzmann equation to simulate the plasma flow based on the unified gas-kinetic scheme (UGKS)
The time step is restricted according to dissipative length scale determined by the physical transport
Summary
The Boltzmann equation describes time evolution of physical state under external field using gas-distribution function [1]. In description of plasma with long-range Coulomb interaction, Vlasov showed the difficulties when kinetic theory based on standard transport-collision is applied: (1) Theory of pair collisions disagrees with the discovery by Rayleigh, I. Tonks that vibrations exist in electron plasma; (2) Theory of pair collisions without Coulomb interaction will lead to divergence of kinetic term; (3) Theory of pair collisions cannot explain results of experiments by. Webb that electrons scatter anomalously in gaseous plasma [2]. Binary interaction is taken as the rule. In plasma, waves, or organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces
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