Bremsstrahlung, Synchrotron Radiation, and Compton Scattering of High-Energy Electrons Traversing Dilute Gases

TLDR

The study derives expressions for the total energy loss and photon‑production spectra of Compton scattering, bremsstrahlung, and synchrotron radiation from highly relativistic electrons. The authors analytically derive the spectra for each process—including Compton scattering in various limits, bremsstrahlung in Coulomb and atomic fields with shielding, and synchrotron radiation for circular and helical orbits—and combine them to obtain the total photon‑production spectrum for a power‑law electron distribution, also examining how these processes influence the electron energy distribution. They find that small, continuous energy losses lead to a continuity equation for the electron distribution, while discrete losses require an integro‑differential equation, and they provide approximate solutions for specific cases.

Abstract

Expressions are derived for the total energy loss and photon-production spectrum by the processes of Compton scattering, bremsstrahlung, and synchrotron radiation from highly relativistic electrons. For Compton scattering, the general case, the Thomson limit, and the extreme Klein-Nishina limit are considered. Bremsstrahlung is treated for the cases where the electron is scattered by a pure Coulomb field and by an atom. For the latter case the effects of shielding are discussed extensively. The synchrotron spectrum is derived for an electron moving in a circular orbit perpendicular to the magnetic field and also for the general case where the electron's motion is helical. The total photon-production spectrum is derived for each process when there is a power-law distribution of electron energies. The problems of the effects of the three processes on the electron distribution itself are considered. It is shown that if the electron loses a small fraction of its energy in a single occurrence of a process, the electron distribution function satisfies a continuity equation which is a differential equation in energy space. For the more general case where the electron can lose energy in discrete amounts (as in bremsstrahlung and extreme Klein-Nishina Compton losses), the electron distribution function satisfies an integro-differential equation. Some approximate solutions to this equation are derived for certain special cases.