Simulation of electron kinetics in gas discharges

We review the state-of-the-art for the simulation of electron kinetics in gas discharges based on the numerical solution of the Boltzmann equation. The reduction of the six-dimensional Boltzmann equation to a four-dimensional Fokker-Planck equation using two-term spherical harmonics expansion enables efficient and accurate simulation of the electron distribution function in collisional gas discharge plasmas. We illustrate this approach in application to inductively coupled plasmas, capacitively coupled plasmas, and direct current glow discharges. The incorporation of the magnetic field effect into this model is outlined. We also describe recent efforts towards simulating collisionless effect in gas discharge plasma based on Vlasov solvers and outline our views on future development of the numerical models for gas discharge simulations