Effect of radiation damping on the Child-Langmuir law in open diodes

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.