# Dynamics of 1-D Electron Motion under a Periodic Electric Field with Radiation Reaction Effect

## TL;DR

This paper investigates the impact of radiation reaction forces on the one-dimensional motion of an electron under periodic electric fields, finding that the differences in velocities are extremely small, posing challenges for experimental detection.

## Contribution

It introduces a formulation of radiation reaction force as a function of external force and analyzes its effects on electron dynamics under different periodic forces.

## Key findings

- Velocity differences due to radiation reaction are extremely small, from 10^{-31} to 10^{-14}.
- The study considers both sinusoidal and electromagnetic forces with position dependence.
- Results suggest experimental measurement of radiation reaction effects is challenging.

## Abstract

We consider the 1-D motion of an electron under a periodic force and taking into account the effect of radiation reaction dissipation force on its motion, using the formulation of the radiation reaction force as a function of the external force. Two cases are considered: a simple sinusoidal time depending force, and sinusoidal electromagnetic force with position and time dependence. We found that the difference of the normalized (with respect the speed of light) velocities, with and without radiation reaction, are quite small between $10^{-31}$ to $10^{-14}$ for intensities on the electric field of $10^{-8}$ to 1 $Dynes/ues$, which may represent some concern to measure experimentally.