Abstract
ABSTRACT Introduction of time-dependent Poisson equation admits a form of solution which leads to interesting relations for transit time and the current-voltage dependence for both zero and finite initial electron velocities. The analysis is expedited by employment of a reduced spatial variable and the development of inverse power series. The general correspondence with Langmuir's classic solution is demonstrated and, in particular, in the limit of vanishing cathode radius, a simple, non-series description corresponds to the case,β=1.
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