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The characteristics of a monopolar space‐charge region under the effect of charge injection with a uniform initial velocity are studied. Poisson’s equation has been solved as a Dirichlet boundary‐value problem, other than by conventional serial integrations, to yield exact analytical expressions for the potential, field, charge density, and current. The structure of the space‐charge region is characterized by a potential well and an effective diode gap, and can be explained in terms of the initial kinetic energy of the charge. The Child–Langmuir limit, when calculated by using the effective diode gap, is a firm limit. © 1995 American Institute of Physics.