Theoretical Model for Time Evolution of an Electron Population under Synchrotron Loss

Many astrophysical sources radiate via synchrotron emission from relativistic electrons. The electrons give off their kinetic energy as radiation and this radiative loss modifies the electron energy distribution. An analytical treatment of this problem is possible in asymptotic limits by employing the continuity equation. In this article, we are using a probabilistic approach to obtain the analytical results. The basic logic behind this approach is that any particle distribution can be viewed as a probability distribution after normalizing it (as is done frequently in statistical mechanics withi ensembles containing very large number of particles). We are able to reproduce the established results from our novel approach. Same approach can be applied to other physics problems involving spatial or temporal evolution of distribution functions.