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A theoretical model is developed to describe the behavior of an ion‐injection electrostatic confinement device. It is assumed that there is a shallow potential well in the center. Distribution functions, which are consistent with atomic processes occurring and with mechanisms leading to particle angular momentum, are obtained for ions and electrons. Using these distribution functions, Poisson's equation is solved to obtain potential and density profiles. By varying the experimental parameters, the conditions needed to go from a shallow potential well to a deep potential well are studied. The most important problems are found to be nonspherical focusing through grid construction asymmetry, and neutralization by electrons. Deeper wells are produced by increasing ion perveance, improving spherical symmetry, and reducing pressure.