Energy Loss by Radiation in Many-Particle Numerical Simulation With Lorentz-Dirac Equation

Abstract

We studied the possibilities for numerical integration of Lorentz‐Dirac equation that is the equation describing the motion of a charged point particle when radiation reaction is taken into account. In numerical modelling based on particle models usually the equations of motion without radiation force are used and the corrections for radiation are used consequently, expressed by laws given by averaged particle parameters as the temperature or particle density. If the complete equation of motion concluding the radiation would be used, the corrections for radiation reaction force could be used for every charged particle individually from more fundamental laws. Thus the model could be able to describe more physical phenomena. However from theory of Lorentz‐Dirac equation there are known various problems with non‐physical solutions and nonuniqueness that are often solved and tested by various methods. One way to eliminate the non‐physical solutions is to use integro‐differential equation, which is used here. The leap‐frog method is used for numerical integrating and accuracy is verified for electron in magnetic field. This approach is proposed to be used for PIC (particle‐in‐cell) integration method, which is often used as an effective method of simulation in plasma physics for many charged particles interactinge with electromagnetic field.