Electron multiplication in the glow-discharge cathode fall

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Abstract
A one-dimensional model is formulated for electron multiplication in the cathode fall of a glow discharge. The associated Boltzmann equation in z and v is converted to an integrodifferential equation in new variables that can be solved numerically using standard methods for ordinary differential equations in a single variable. The resulting distribution function in the (z,v) phase space is also the energy distribution of electron flux, which is used to find the current multiplication factor and the energy transport per unit electron current. Even in low-voltage discharges with large current multiplication, the nonionizing collisions play a small role in determining the electron-energy distribution and swarm behavior. Comparison with highly complex simulation, and with experiment, is very favorable.

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