A novel approach to the Child-Langmuir law

G. González, F.J. González

Abstract


We analyze the motion of charged particles in a vacuum tube diode using a new set of variables. We obtain the space charge limited current for a charged particle moving non-relativistically in one dimension for the case of zero and non zero initial velocity without solving a nonlinear differential equation. We introduce what we call the microscopic Child-Langmuir law which is valid for the classical and relativistic cases that allows to determine the space charge limited current without solving a nonlinear differential equation.

Keywords


Child-Langmuir law; Mott-Gurney Law; space charge current

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Revista Mexicana de Física E

e-ISSN: In Process

Semiannual publication of Sociedad Mexicana de Física, A.C.
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