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

## TL;DR

This paper derives how radiation damping affects the Child-Langmuir law in open diodes, showing deviations at low fields and modifications at high fields due to radiation reaction forces.

## Contribution

It provides a microscopic derivation of space charge limited current considering radiation reaction, revealing regime-dependent deviations from the classical Child-Langmuir law.

## Key findings

- Low field regime: current deviates from Child-Langmuir law
- High field regime: current follows modified Child-Langmuir law
- Radiation reaction influences space charge limited current

## 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 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.