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A theory of the hollow cathode glow discharge based on the two-temperature electron model is developed. The following two interdependent mechanisms are consistently taken into account: the creation of ions and excited atoms due to electron collisions in the discharge and the emission of secondary electrons on the cathode surface due to ions and ultraviolet photons. Trapped electrons in the hollow are also considered. Numerical calculations are made for helium gas in a cylindrical hollow cathode whose inner diameter and length are 10 and 32 mm, respectively, on the basis of a onedimensional steady state model. Voltage-current relations are obtained at gas pressures of 0.13, 0.27 and 0.40 kPa. Population densities of 64 excited atomic levels are determined as a function of the radial distance r as well as the densities of the ions and electrons.

The energy distribution of high-energy electrons was calculated from the plane-parallel hollow-cathode glow discharge of helium gas. Calculations showed an energy distribution function similar to that of a cylindrical cathode whose function had already been obtained by the authors. However, few electrons whose energy equalled the cathode fall potential existed in the central region, contrary to the many electrons in that region in the cylindrical cathode.

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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.