  We present a microscopic derivation of the space charge limited current for
the motion of non-relativistic charged particles inside a parallel vacuum tube
diode taking into account the radiation reaction force. We study the space
charged limited current for two different limiting cases. Our results reveal
that in the low field regime the space charge current does not follow the
Child-Langmuir law, while in the high field regime the space charge current
follows the Child-Langmuir law with and effective electrostatic field, i.e. the
so called modified Child-Langmuir law.
