Calculations for the Distribution Function of Energetic Electrons in a Helium Hollow Cathode Glow Discharge with the Monte Carlo Method

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Abstract
The distribution function of energetic electrons is calculated by tracing their trajectories with the Monte Carlo method. Electrons were made to have inelastic and elastic collisions with helium atoms in the ground state. Calculations were made for a cylindrical hollow cathode whose inner diameter is 1 cm. The electron density increased rapidly with decreasing energy near the lower limit of its energy. The number density of electrons whose energy equals the cathode-fall potential has a peak at the central axis. Their velocities are found to be directed along a collisionless trajectory. The broad angular distribution of the velocity was found in slower electrons. The peak of the number density at the central axis decreased with increasing pressure. The energetic electrons can hardly penetrate into the central region when the gas pressure is 1.3 kPa.