One-dimensional flow of charged particles in a bounded system is investigated. In particular, the well-known overlap of steady-state solutions in the zero-temperature flow approximation is examined in detail. A stability analysis is performed, and it is proved that not only the overlapping steady-state solutions are unstable to infinitely small perturbations, but that all steady-state flows in which partial reflection of charged particles from a virtual cathode is assumed, are also unstable.
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Y. Winograd (1967) studied this question.
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