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

TL;DR

This paper introduces a novel probabilistic method to analytically model the time evolution of relativistic electron populations under synchrotron losses, providing an alternative to traditional asymptotic analysis.

Contribution

It presents a new probabilistic framework for deriving analytical solutions to electron energy distribution evolution under synchrotron radiation.

Findings

Reproduces established results using the probabilistic approach

Demonstrates applicability to other physics problems involving distribution evolution

Provides a novel analytical method for astrophysical electron populations

Abstract

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.