Dependence of space-charge-limited flow on conducting current

A generalized equation, which governs the dependence of space charge current flow on conducting current in three relativistic configurations, is deduced from Poisson's equation with assumption of space-charge-limited flow and electrons' canonical momentum conservation. A method for solution to the equation is introduced and the characteristic of the solution for the three configurations is discussed. It is concluded that for these configurations the effect of conducting current on magnetic insulation is much significant with increase of anode voltage, and that for the same anode voltage their SCL flows will behave differently when their geometrical factors become small, with the SCL flow of the two non-plane conductors smaller than that of the plane conductor for negative polarity and larg