The FM modeling is based on introduction of total electron energy which is the sum of kinetic energy w and potential energy . When energy relaxation length exceeds typical spatial scale , the total electron energy is practically conserved during an electron displacement over the available region between the turning points. In other words, the EDF, which depends solely on a total electron energy , proves to be suitable for an adequately accurate description of the electron kinetics. The function is to be calculated from the spatially and temporally averaged kinetic equation, which is 1D ordinary differential equation in contrast to 2D initial partial differential equation. The full system of equations consists in ion continuity equation , where ionization sources is given via EDF , ion velocity is determined by plasma potential and mobility.
Plasma potential is to be found from quasineutrality condition .
The RF field in the plasma is to be found from Maxwell equations where conductivity also depends on EDF . In the sheath we solve Poisson eq. and find averaged ion velocity of rf cycle. As one can see ion density, plasma potential, EDF are coupled by system of nonlinear links. The typical output of FM is shown in the Fig. We were able to calculate EDF s for a wide range of discharge currents, as well as other parameters.