Description of photon scattering with relativistic Maxwellian electrons is numerically complex, and computationally time consuming for the final photon energy and angle distribution. A Monte Carlo method is used to simulate photon scattering with relativistic Maxwellian electrons. The main idea of this method is to transform the interaction of photonmoving electrons in the laboratory coordinate system into that in a new coordinate system in which the electrons are at rest, then to use the exact Klein-Nishina formula to describe this interaction and obtain the outgoing photon energy and angle, finally, to transform it into the primary laboratory coordinate system. In sum, there are eight steps, i.e.two two-dimensional (2D) transforms and two three-dimensional (3D) transforms and two Lorentz transforms, and two sampling. Repeating this process, summarizing and averaging all computed energy values and angles, the distribution of scattered energy and angle can be obtained.
A Monte Carlo processor is developed to simulate a photon of any energy interacting with electrons at any temperature. Some typical cases are simulated. The computed results indicate that the photon spectrum is different from that of the photon scattering with rest electrons remarkably, especially for a low energy photon scattering with the high temperature electrons. The main phenomena are Doppler broading and blue shifting. The moving electron can extend the distribution of the outgoing photon energy, and for a low energy photon scattering with the high temperature electrons, the photon maybe obtains the energy from electrons with significant probability. The angle distribution is very complicated, and it is determined by the incident photon energy, the outgoing photon energy, and the electron temperature. This processor can calculate the energy scattering differential cross-sections or energy-angle scattering double differential cross-sections, and provide the data in a tabulated form for other transport methods.