Analytical Approximations for Beamstrahlung at Very High Energy Electron-Positron Colliders

TL;DR

This paper derives simplified analytical formulas for beamstrahlung spectra at very high energies, especially relevant for 10 TeV electron-positron colliders, aiding future collider design and analysis.

Contribution

It introduces universal functions and approximations for beamstrahlung spectra in the large quantum parameter regime, simplifying calculations at TeV energies.

Findings

Beamstrahlung spectra expressed via universal functions.

Approximations provided for these functions.

Simplified description applicable to 10 TeV collider designs.

Abstract

Among the many effects that occur in beam-beam electron-positron collisions at TeV energies, emission of hard synchrotron radiation, or beamstrahlung, has special importance. Beamstrahlung determines the energy spectrum of the most energetic electrons, positrons, and photons and supplies the initial condition for the calculation of all other QED processes. In this paper, we show that the description of beamstrahlung simplifies in the limit of large quantum parameter $\Upsilon$, which is realized in 10 TeV collider designs. The beamstrahlung spectra for electrons and photons are given in terms of universal functions. We supply approximations to these functions that will be useful for more general studies of the beam-beam interaction at very high energies.