Cathode boundary conditions for fluid model discharges on the right-hand branch of the Paschen curve

It is shown that a fluid description of discharges on the right-hand branch of the Paschen curve must take into account a change in the effective secondary emission coefficient γ eff of the cathode, which is related to the electron backscattering effect. Simple kinetic expressions for γ eff are obtained which indicate that the effective secondary emission is determined by the initial energy of emitted electrons and by the applied field amplitude.