Radiation Reaction and Thomson Scattering

In recent years high power high irradiance lasers of peta-watt order have been or are under construction. In addition, in the next 10 years lasers of unprecedented powers, exa-watt, could be built If lasers such as these are focused to very small spot sizes, extremely high laser irradiances will be achieved. When electrons interact with such a laser, they become highly relativistic over very short time and spatial scales. Usually the motion of an electron under the influence of electromagnetic fields is influenced to a small extent by radiation emission from acceleration. However, under such violent acceleration the amount of radiation emitted by electrons can become so large that significant damping of the electron motion by the emission of this radiation can occur. In this lecture note we will study this problem of radiation reaction by first showing how the equations of motion are obtained. Then, we will examine the problems with such equations and what approximations are made. We will specifically examine the effects of radiation reaction on the Thomson scattering of radiation from counter-streaming laser pulses and high energy electrons through the numerical integration of the equations of motion. We will briefly address the fundamental physics, which can be addressed by using such high irradiance lasers interacting with high energy electrons