Kinetics of relativistic electrons undergoing small recoils in periodic structures and matter

TL;DR

This paper presents a general method to evaluate the energy spectrum evolution of relativistic electrons experiencing small quantum losses in matter and periodic fields, accounting for recoil spectra and scattering events.

Contribution

It introduces a novel approach to analyze energy spectrum changes of relativistic electrons with small recoils, including derivation of detector and straggling functions.

Findings

Derived the detector function for arbitrary recoil spectra.

Estimated the minimum average number of recoils for spectrum dependence on mean recoil energy.

Provided moments for the straggling and detector functions.

Abstract

We developed a general method for evaluating the energy spectrum evolution of relativistic charged particles that have undergone small quantum losses, such as the ionization losses when the electrons pass through matter and the radiation losses in the periodic fields. These processes are characterized by a small magnitude of the recoil quantum as compared with the particle's initial energy. The `detector' function for arbitrary recoil spectrum is derived in addition to the straggling function. These functions are determined by the average number of scattering events undergone by the particle over the length of the detector (ionization losses) or the periodic field and the specific spectrum of the recoil. Moments for both the straggling function and the detector function are derived. The minimum average number of recoils, above which both functions depend only upon the mean energy of recoil quantum, is estimated. The average of this number is about 10 recoil events.