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 simulation of ECR discharges using the Monte Carlo technique for the EDF calculation is very computer time expensive, since the electron and ion time scales are 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-pressure ECR discharges. An analytical solution for the EDF in a loss cone was derived. To check the validity of the FM, one-dimensional (in coordinate) and two-dimensional (in velocity) Monte Carlo simulation codes were developed. The validity of the fast modeling method is proved by comparison with the Monte Carlo simulations. The complete system of equations for FM is presented and ready for use in a comprehensive study of ECR discharges. The variations of plasma density and of wall and sheath potentials are analyzed by solving a self-consistent set of equations for the EDF.

The principles of fast modelling (FM) of a low-pressure radio-frequency capacitively coupled discharge are presented. They are based on averaging over fast electron and ion motions and on eliminating a small spatial scale, the Debye radius. As a result, the solution of a self-consistent system of the electron kinetic equation, Poisson and ion continuity equations takes approximately 10 min on a 486 PC. The calculation of discharge parameters has been performed for a wide range of current and pressure. The comparison with full-scale Monte Carlo calculations and experimental data has been performed. The performed comparisons demonstrate that the developed method of fast modelling has a good accuracy for calculating the global parameters such as central plasma density, applied voltage, sheath thickness, ionization rate, etc, and the profiles of plasma density and the electric fields. The accuracy of the electron distribution function (EDF) calculation is high when the EDF form is not enriched by slow electrons, and seems satisfactory in the case of a strongly peaked EDF. The results are in qualitatively good agreement with the experiment. The quantitative agreement is mainly within a factor of two. This discrepancy can be attributed to the fact that the EDF form is very sensitive to the details of plasma description, e.g. small variation of cross-sections results in considerable changes in the EDF. The mechanism of non-Maxwellian EDF formation due to non-locality effects has been analysed. The evolution of the low-pressure radio-frequency collisional capacitively coupled discharge with current and pressure variation has been investigated.

The results of modeling a low-pressure capacitively coupled radio-frequency (rf) discharge based on the nonlocal approach are reported. The approximation employed enables fast modeling (FM) of the electron distribution function. The solution of the full problem, which consists of calculation of the electron distribution, rf, and stationary electric fields, and of the plasma density profile, for simple atomic gas takes ∼10 min on the IBM PC 486DX2/66. To check the validity of the FM the full scale Monte Carlo modeling was performed. The results of the fast and the full scale modeling are in agreement.

The transport of charged species in collisional currentless plasmas is traditionally thought of as a diffusion-like process. In this paper, it is demonstrated that, in contrast to two-component plasma, containing electrons and positive ions, the transport of additional ions in multi-species plasmas is not governed by diffusion, rather described by nonlinear convection. As a particular example, plasmas with the presence of negative ions have been studied. The velocity of a small perturbation of negative ions was found analytically and validated by numerical simulation. As a result of nonlinear convection, initially smooth ion density profiles break and form strongly inhomogeneous shock-like fronts. These fronts are different from collisionless shocks and shocks in fully ionized plasma. The structure of the fronts has been found analytically and numerically.

Abstract-Index Terms-Nonlocal ionization by secondary electrons, radio frequency capacitively coupled discharge.