Abstract

GONZALEZ, G.  and  GONZALEZ, F.J.. A novel approach to the Child-Langmuir law. Rev. mex. fís. E [online]. 2017, vol.63, n.2, pp.83-86. ISSN 1870-3542.

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.