Abstract
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 high field regime, the space charge current does not follow the Child-Langmuir law, while in the low field regime, the space charge current follows the Child-Langmuir law with an effective electrostatic field, i.e., the so-called modified Child-Langmuir law.
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