Electron-distribution-function cutoff mechanism in a low-pressure afterglow plasma

A model is developed for self-consistent simulations of transient phenomena in a low-pressure afterglow plasma. The model is based on the nonlocal approach which allows a kinetic description of the plasma decay under nonquasistationary conditions. Such conditions arise when collisions (mainly electron-electron) are not sufficient for the electron distribution function (EDF) to follow changes in the self-consistent electric fields and the ion density once the power is turned off. As a result, collisions cannot provide the electron and ion particle balance by allowing electrons to flow out of the potential well. A cutoff mechanism is suggested that provides such a balance during the transient period-from the glow, stationary plasma to the quasistationary, afterglow plasma. This mechanism is essential for determining correctly the self-consistent wall potential (and hence the energy of ions impinging upon the wall surface) and other parameters, such as diffusion cooling, which is the most important cooling mechanism at low pressures. These phenomena are modeled using the time-dependent nonlocal electron Boltzmann equation with a nonlinear electron-electron collision operator. A numerical treatment is made by extending Rockwood's method for finite-difference discretization of this operator in the total energy formulation. The model calculates self-consistently the temporal evolution of the nonlocal EDF and the electric potentials in the plasma and the wall sheath. Strongly non-Maxwellian EDF's are predicted and it is observed that, depending on plasma conditions, the transient period maybe rather long, of order of the ambipolar diffusion time, lower pressures resulting in longer transient times. The proposed approach can be applied to model self-consistently pulsed plasmas during both the power-on and power-off periods, including the breakdown period.