Abstract
A linear stability analysis of the planar one dimensional space charge limited flow shows that the classical Child’s solution is stable in time. Small perturbations of the flow are accompanied by high frequency oscillations that decay exponentially. These oscillations should appear when the flow regime changes rapidly, and they might be detectable experimentally by their electromagnetic radiation. We also study the stationary state of more general space charge limited flow and obtain a relation between the current density and the electric field at the emitter surface for arbitrary emission laws and a fixed non-zero initial speed of electrons. In such a case there is the possibility of creation of electrostatic barriers for the emission and stationary flow regimes in this simple model.
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