Effect of Initial Velocity on One-Dimensional, Bipolar, Space-Charge Currents

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Abstract
Oppositely directed flows of positive and negative charges constitute a bipolar current. A general case is analyzed in which the charges traverse the evacuated space between plane‐parallel boundaries and all particles of a given charge species are monoenergetic. Moreover, it is assumed that the charges may possess nonvanishing initial kinetic energy. This represents an extension of analyses by Langmuir and Müller‐Lübeck for vanishing initial kinetic energy. Sample calculations of dimensionless current densities, electric and potential fields, and charge‐density distributions are exhibited for cases where the electric field is assumed to vanish at one boundary but the species initial velocities may not. It is shown that resulting ion currents may be several times the Child's law limit if initial kinetic energies are of the order of the potential energy.