Influence of Inhomogeneous Electric Field Geometry Factors on Runaway Electrons Generation Conditions

In this paper, dynamics of runaway electrons was investigated in nitrogen of 1 atm pressure for the case of a strongly non-uniform electric field. 2D Monte-Carlo technique and 1D Boltzmann's equation were employed. The discharge system under investigation comprised of two confocal parabolic electrodes: a cathode and an anode. For such a discharge system, analytical expressions of potential distribution within the discharge gap are known. A curvature radius of the parabolic cathode was varied in a wide range. The distance between apexes of the electrode parabolas was constant. As a result, the dependences of the critical electric field strength Ecr near the cathode and of the critical voltage Ucr applied to the discharge gap from the cathode curvature radius were obtained. A comparison of the results obtained with analytical ones was carried out. It was found, that, for the Monte-Carlo and kinetic models, both Ecr with an increase in the cathode curvature radius and Ucr with a decrease in the cathode curvature radius tended to some constant values, what was in qualitative agreement with analytical data. It was clearly shown that a sharp-edged cathode required much more field strength near the cathode edge compared with the classical criterion to generate runaway electrons.