Emission of Low-Energy Photons by Electrons at Electron-Positron and Electron-Ion Colliders with Dense Bunches

TL;DR

This paper investigates low-energy photon emission during electron bunch collisions at colliders, especially when classical beamstrahlung approximations fail, providing new calculations based on classical currents for dense bunch scenarios.

Contribution

It introduces a novel calculation method for low-energy photon emission in dense bunch collisions, extending beyond traditional beamstrahlung approximations.

Findings

Calculated the critical photon energy E_c for ILC and KEKB.

Derived the photon emission dependence on impact parameter.

Provided potential for online beam axis displacement monitoring.

Abstract

Usually, the emission of low-energy photons in electron-positron (or electron-ion) bunch collisions is calculated with the same approach as for synchrotron radiation (beamstrahlung). However, for soft photons (E_gamma < E_c where E_c is a critical photon energy), when the coherence length of the radiation becomes comparable to the bunch length, the beamstrahlung approximation becomes invalid. In this paper, we present results of our calculation for this region based on approximation of classical currents. We consider several colliders with dense bunches. The number of low-energy photons dN_gamma emitted by N_e electrons per bunch crossing in the energy interval dE_gamma is dN_gamma = alpha g N_e dE_gamma/E_gamma, where alpha is the fine-structure constant, and the function g, which depends on the bunch parameters, typically is of order unity for modern colliders. In particular, for the ILC, we find that E_c = 83 keV and g=5.5 at a vanishing beam axis displacement, and g=0.88, E_c=0.24 keV for KEKB. We also calculate the specific dependence of dN_gamma on the impact parameter between the two beam axes. In principle, the latter aspect allows for online monitoring of the beam axis displacement.