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 (Egamma < Ec where Ec 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 dNgamma emitted by Ne electrons per bunch crossing in the energy interval dEgamma is dNgamma = alpha g Ne dEgamma/Egamma, 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 Ec = 83 keV and g=5.5 at a vanishing beam axis displacement, and g=0.88, Ec=0.24 keV for KEKB. We also calculate the specific dependence of dNgamma on the impact parameter between the two beam axes. In principle, the latter aspect allows for online monitoring of the beam axis displacement.