The stability of space-charge limited flow in planar diodes is investigated. It is found that the flow is unstable whenever the electron transit time is approximately n+ (1)/(4) , cycles where n is an integer, of the high-frequency modes supported by the diode structure. Analytical and numerical solutions are found for the resulting dispersion relation in the nonrelativistic limit. The analytical results lead to a simple physical explanation of the instability and provide accurate solutions over a wide range of parameters. Numerical solutions are also obtained for the relativistic case.
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Antonsen et al. (1984) studied this question.
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