Emission of low-energy photons by electrons at electron-positron and electron-ion colliders with dense bunches

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_{γ}<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_{γ} emitted by N_{e} electrons per bunch crossing in the energy interval dE_{γ} is dN_{γ}=αgN_{e}dE_{γ}/E_{γ}, where α 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 International Linear Collider, 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_{γ} on the impact parameter between the two beam axes. In principle, the latter aspect allows for online monitoring of the beam axis displacement.