Self-consistent Monte Carlo simulation of the cathode fall including treatment of negative-glow electrons

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Abstract
We present results from a self-consistent Monte Carlo simulation of the cathode fall (CF) of a dc glow. The simulation consists of following electron and ion trajectories under the influence of the electric field which is calculated from Poisson’s equation using the ion and electron densities. The collision cross sections are greatly simplified in order to facilitate understanding of the physical mechanisms which dominate the CF. With this aim, we explicitly sample the electron distribution function and discuss its properties. We also show that it is feasible to simulate the CF in isolation from the negative glow (NG) as long as backscattering from the NG is accounted for. Finally, we take into account the plasma (trapped) electrons in the NG, and formulate a model of the CF-NG boundary region through use of the plasma-sheath equation. We find that the length of the boundary region grows with the NG density, and that there is a corresponding increase in the fraction of the ion flux which enters the CF as opposed to being created in it. For reasonable values of the NG density, we find this fraction to be as high as 25%.