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

We consider the 1-D motion of an electron under a periodic force and take into account the effect of radiation reaction dissipation force on its motion, using the formulation of novel radiation reaction force as a function of the external force expression. Two cases are considered: A simple sinusoidal time depending force and sinusoidal electromagnetic force with position and time dependence. The purpose of the study of these cases is to bring about a way to find an experimental study to determine the validity of this novel approach for the radiation reaction force. We found that the difference of the normalized (with respect the speed of light) velocities, with and without radiation reaction, is 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.