Beam Blow Up due to Beamstrahlung in Circular $e^+e^-$ Colliders

TL;DR

This paper analyzes how beamstrahlung impacts beam parameters in future circular $e^+e^-$ colliders, deriving formulas to predict equilibrium bunch length and energy spread, and emphasizing the importance of controlling dispersion at the collision point.

Contribution

It provides analytical formulas for equilibrium beam parameters considering beamstrahlung effects in circular Higgs factories, accounting for electromagnetic field variations during collision.

Findings

Beamstrahlung significantly increases bunch length and energy spread.

Classical description of beamstrahlung is sufficient for these colliders.

Dispersion control at the collision point is crucial to mitigate beamstrahlung effects.

Abstract

After the discovery of the Higgs boson at the Large Hadron Collider in 2012, several possible future circular colliders -- Higgs factories are proposed, such as FCC-ee and CEPC. At these highest-energy $e^+e^-$ colliders, beamstrahlung, namely the synchrotron radiation emitted in the field of the opposing beam, can greatly affect the equilibrium bunch length and energy spread. If the dispersion function at the collision point is not zero, beamstrahlung will also increase the transverse emittances. In this letter, we first show that, for circular Higgs factories, a classical description of the beamstrahlung is adequate. We then derive analytical formulae describing the equilibrium beam parameters, taking into account the variation of the electromagnetic field during the collision. We illustrate the importance of beamstrahlung, including the increase of bunch length and the implied tolerance on the spurious dispersion function at the collision point, by considering a few examples.