Ionization waves in low-current dc discharges in noble gases obtained with a hybrid kinetic-fluid model

A hybrid kinetic-fluid model is used to study ionization waves (striations) in a low-current plasma column of dc discharges in noble gases. Coupled solutions of a kinetic equation for electrons, a drift-diffusion equation for ions, and a Poisson equation for the electric field are obtained to clarify the nature of plasma stratification in the positive column. A simplified two-level excitation-ionization model is used for the conditions when the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons are negligible. It is confirmed that the nonlocal effects are responsible for the formation of moving striations in dc discharges at low plasma densities and low values of pR (the product of gas pressure and tube radius). The calculated properties of self-excited waves of S-, P-, and R types in neon and S type in argon agree with available experimental data. The reason for helium plasma stability to stratification is clarified. It is shown that sustaining stratified plasma is more efficient than striation-free plasma when the ionization rate is a nonlinear function of the electric field. However, the nonlinear dependence of the ionization rate on the electric field is not required for plasma stratification. Striations of S-, P-, and R types in neon exist with minimal or no ionization enhancement. Effects of the column length and plasma density on the wave properties are demonstrated.