Mechanism for the streamer propagation toward the anode and cathode due to background electron multiplication

A simple mechanism for the propagation of an ionization wave in a dense gas due to the multiplication of background electrons in a nonuniform electric field is proposed. The mechanism does not depend on the sign of the field projection onto the streamer propagation direction. The streamer propagation is caused by the enhancement of the electric field at the streamer head. It is shown that, in a prebreakdown field, the intense multiplication of electrons takes place in both electropositive and electronegative gases. The prebreakdown multiplication can provide a fairly high density of background electrons; this allows one to treat the background as a continuous medium when considering streamer propagation as a multiplication wave. The initial ionization is enabled by the natural background of ionizing radiation and cosmic rays. An analytical expression for the velocity of the ionization front is obtained based on a simple equation for the multiplication of background electrons. This expression is in good agreement with numerical simulations performed within both a simple model of background electron multiplication and a more comprehensive drift-diffusion model. In particular, the drift-diffusion model predicts the propagation of the ionization front from a small-radius anode to the cathode due to the multiplication of background electrons. The velocity of the ionization wave front is calculated as a function of the electric field at the streamer head for helium, xenon, nitrogen, and sulfur hexafluoride. It is shown that some features of streamer propagation (e.g., its jerky motion) can be related to the recently found nonmonotonic dependence of ionization frequency on the electric field.