Coherent bremsstrahlung in a bent crystal

TL;DR

This paper analyzes the radiation spectrum of high-energy electrons and positrons in bent crystals, deriving a closed-form expression for uniformly bent crystals and discussing key spectral features and coherence effects.

Contribution

It provides a new analytical expression for the radiation spectrum in uniformly bent crystals and explores the dependence of coherence length on crystal geometry.

Findings

Spectrum features include sharp end and volume reflection turnover.

Coherence length depends only on crystal geometry, not particle energies.

Dipole approximation is valid for bending angles around 10^{-4} radians.

Abstract

Radiation spectrum from high energy $e^\pm$ in a bent crystal with arbitrary curvature distribution along the longitudinal coordinate is evaluated, based on the stationary phase approximation. For a uniformly bent crystal a closed-form expression for the spectrum is derived. Features such as sharp end of spectrum and volume reflection turnover at beginning of the spectrum are discussed. The coherence length in a bent crystal appears to depend only on the crystal geometry and not on the electron or photon energies, which is essential for interpretation of the results. Estimates of non-dipole radiation and multiple scattering effects are given. The value for the crystal bending angle at which the dipole coherent bremsstrahlung theory holds best appears to be $\sim 10^{-4}\mathrm{rad}$.