A simple variational procedure is employed to obtain an analytic expression for the collisional particle end-loss rate in a mirror for the electrostatically confined species. The technique circumvents the need for an accurate solution for the distribution function, and is valid when both mirror ratio and barrier height are large, in which case it reproduces the previous results for the loss rate. The analytic result is also in reasonably good agreement with a numerical solution of the full linearized Fokker–Planck equation.
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Catto et al. (1981) studied this question.
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