Kinetic theory of high-voltage low-pressure gas discharge with electron initiation on a cathode in a planar gap

We report one-dimensional kinetic simulation of electron and ion transport and multiplication (based on the Boltzmann kinetic equations) in a self-consistent electric field after electron injection from the cathode. The 1D1V Boltzmann equations take into account the electron impact ionization, elastic electron scattering, and resonant ion recharging. The spatio-temporal evolution of the gas breakdown in a planar diode with a gap of 5 mm filled with nitrogen at pressure of 1 Pa, with applied voltage of 2.5 kV, was demonstrated in detail. In the vicinity of these parameters, an intermediate gap breakdown mode is realized when the discharge exists in the form of relaxation current oscillations. The simulation showed that, during plasma generation, the electric potential acquires non-monotonic spatial distribution in the gap. Under the non-monotonic potential distribution, anode-directed ion flow is formed inside the gap. An extended hump of potential may appear, forming ion fluxes with kinetic energy nominally exceeding the voltage drop (in the calculated spectrum the mean ion energy was at the level of 6-7 keV at an applied voltage of 2.5 kV).