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Many astrophysical sources radiate via synchrotron emission from relativisticelectrons. The electrons give off their kinetic energy as radiation and thisradiative loss modifies the electron energy distribution. An analyticaltreatment of this problem is possible in asymptotic limits by employing thecontinuity equation. In this article, we are using a probabilistic approach toobtain the analytical results. The basic logic behind this approach is that anyparticle distribution can be viewed as a probability distribution afternormalizing it (as is done frequently in statistical mechanics withi ensemblescontaining very large number of particles). We are able to reproduce theestablished results from our novel approach. Same approach can be applied toother physics problems involving spatial or temporal evolution of distributionfunctions.

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