A hybrid hydrodynamic-like model for pseudospark discharge

A hybrid hydrodynamic-like formalism is presented for the study of the inception of breakdown and development of plasma bubble in the hollow cathode phase of a pseudospark switch discharge. It allows one to obtain the spatio-temporal evolution of the electronic and ionic densities, velocities, and energies in fast transient situations in low pressure discharges. This hybrid formalism allows the study of situations where the mean free path is not low compared to the spatial variations of the macroscopic parameters, and/or situations for which the transport energy (respectively, the transport velocity) is of the same order of magnitude as the thermal energy (respectively, the thermal velocity), as in the case of pseudospark discharge. The model is self-consistent and its formalism stands on a particular representation of the anisotropic nonlocal distribution function for electrons as having a beam component. The nonlocal electronic velocity is computed as a moment of the distribution function. The transport equations for mass and energy for electrons and ions are solved by the flux-corrected transport (FCT) method where the source terms are calculated from the nonlocal distribution function. The electric field is calculated by the Poisson's equation. The discharge physics is modeled in both main gap and hollow cathode simultaneously to permit a correct coupling of the charged particles, photons, and field between the two zones. Results show that the transport velocity and ionization growth for the case of highly anisotropic nonlocal distribution function is largely higher than that based on a pure hydrodynamic nearly Maxwellian distribution function. The energetic and high density positive ions impacting the inner walls and the back of the cathode hole participate in a composite effect yielding a cathode surface phenomena of super dense secondary emission of electrons which enhances the plasma bubble inception inside the cathode hole. We propose a criterion for switch operation in the pseudospark mechanism based on the formation of the plasma bubble, inside the cathode hole, known as the hollow cathode phase, as a transition phase between the breakdown phase and the conduction phase.