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

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.