Electron Boltzmann kinetic equation averaged over fast electron bouncing and pitch-angle scattering for fast modeling of electron cyclotron resonancedischarge

The electron distribution function (EDF) in an electron cyclotron resonance (ECR) discharge is far from Maxwellian. The self-consistent simulation of ECR discharges requires a calculation of the EDF on every magnetic line for various ion density profiles. The straightforward self-consistent simulati on of ECR discharges using the Monte Carlo technique for the EDF calculatio n is very computer time expensive, since the electron and ion time scales a re very different. An electron Boltzmann kinetic equation averaged over the fast electron bouncing and pitch-angle scattering was derived in order to develop an effective and operative tool for the fast modeling (FM) of low-p ressure ECR discharges. An analytical solution for the EDF in a loss cone w as derived. To check the validity of the FM, one-dimensional (in coordinate ) and two-dimensional (in velocity) Monte Carlo simulation codes were devel oped. The validity of the fast modeling method is proved by comparison with the Monte Carlo simulations. The complete system of equations for FM is pr esented and ready for use in a comprehensive study of ECR discharges. The v ariations of plasma density and of wall and sheath potentials are analyzed by solving a self-consistent set of equations for the EDF.