Electron-electron scattering in a quasi-neutral particle simulation code for ECR plasma processing devices

Summary form only given. We have recently developed an axisymmetric quasi-neutral particle simulation code to study heating and transport of plasma in an ECR reactor configuration in which the electrons are always strongly magnetized, but the degree of magnetization of the ions varies spatially. For this system with pressures on the order of a few milliTorr, the plasma is considered to be weakly collisional with mean free paths on the order of a few centimeters. Electrons may collide with the neutral gas in various states, and with each other. Electron-electron (e-e) collisions are especially important since these collisions are responsible for forming the tail of the electron distribution function and for redistributing the energy toward a Maxwellian. The energy distribution is determined by a competition between e-e collisions, which tend to Maxwellianize the distribution, and inelastic electron-atom collisions, which deplete the high energy tail. Therefore it is important to use the right rate coefficients to represent e-e collisions. For particle simulations, Fokker-Planck collisions may be cast in the form of a "grid" based force in the form of the Langevin equation. A method for this has been outlined by Jones et al (1996). We have implemented a more exact Langevin equation based on diffusion and drag coefficients appropriate for electrons in a plasma. These coefficients depend on the test particle velocity and are calculated self-consistently during each time step from the plasma electrons using grid laydown methods. The procedure is implemented in such a way as to conserve the local electron energy and momentum.