Plasma stratification in ac discharges in noble gases at low currents

A hybrid kinetic-fluid model is used to study plasma stratification in alternating current (ac) discharges in noble gases at low plasma densities. Self-consistent coupled solutions of a nonlocal kinetic equation for electrons, a drift-diffusion equation of ions, and a Poisson equation for the electric field are obtained for a positive column and the entire discharge with near-electrode sheaths. Standing striations are obtained for the reduced values of electric fields, E/p, corresponding to the inelastic energy balance of electrons in a range of driving frequencies. An analog of Novak's law, Λ≈ɛ_{1}/(e〈E〉) (striation length Λ proportional to the excitation threshold of atoms ɛ_{1} and inversely proportional to the mean square root of the electric field 〈E〉, where e is the electron charge), is observed in simulations, indicating the nonlocal nature of standing striations in ac discharges at low plasma densities. Stratified plasma operates in a dynamic regime for various driving frequencies. In this regime, ions respond to the time-averaged electric field, whereas electrons react to the instantaneous electric field. The disparity of time scales between ambipolar diffusion, which occurs at the ion time scale, and electron kinetics in the coordinate-energy phase space, which occurs at the free electron diffusion time scale, produces complicated fluxes in the phase space (due to electron heating, energy loss in collisions, and ionization processes) that are responsible for the stratification. Our paper emphasizes the need for the kinetic approach to analyze stratification phenomena in ac discharge of noble gases. It promotes an efficient method for the kinetic treatment of electrons that is an alternative to the commonly used particle-in-cell method.