Effect of the electron drift in a transverse electric field on the width of spark channels in a multichannel sliding discharge

The effect of electron drift on the transverse size of the spark channels in a multichannel sliding discharge on a dielectric surface is considered in a semianalytic approximation. The strength of an electric field transverse to the channel axis is estimated by the mirror image method. The estimate obtained is used to analyze the differential equation for the density of electrons with allowance for their drift from the channel into the surrounding layers. It is shown that the channel expands to a certain steady-state radius at which an increase in the local electron density due to the ionization of atoms is balanced by its decrease due to the electron drift from the surface channel layer into the surrounding layers. Numerical estimates are carried out for the conditions of earlier experiments with discharges in He, Ne, Ar, and Xe. The analysis applies to the initial nanosecond stage of the spark development, when the hydrodynamic expansion of the channels is still insignificant.