A general formalism of two-dimensional lattice potential on beam transverse plane for studying channeling radiation

TL;DR

This paper introduces a comprehensive formalism for calculating the two-dimensional lattice potential in crystal channeling, enabling precise modeling of ultra-relativistic electron beam interactions for studying channeling radiation.

Contribution

A new general formalism for the 2D lattice potential that accounts for Lorentz contraction, applicable to any crystal direction and interaction model.

Findings

Allows exact calculation of lattice potential without approximation.

Applicable to any crystal orientation and electron-ion interaction model.

Provides a standard method for studying channeling radiation.

Abstract

To study channeling radiation produced by an ultra-relativistic electron beam channeling through a single crystal, a lattice potential of the crystal is required for solving the transverse motion of beam electrons under the influence of the crystal lattice. In this paper, we present a general formalism for this two-dimensional lattice potential of a crystal with a Lorentz contraction in the beam channeling direction. With this formalism, the lattice potential can be calculated without approximation from any given model of electron-ion interaction for an ultra-relativistic beam channeling in any crystal direction. The formalism presented should be the standard recipe of the lattice potential for studying the channeling radiation.