Luminosity of Asymmetric e+e- Collider with Coupling Lattices

TL;DR

This paper derives a formula for the luminosity of asymmetric e+e- colliders with coupled lattices, analyzing how beam tilt and aspect ratio influence luminosity and applying the results to measure and correct coupling effects.

Contribution

It provides an explicit luminosity formula for asymmetric colliders with coupled lattices and demonstrates its practical application in measuring and correcting beam coupling.

Findings

Derived explicit luminosity formula considering beam tilt and aspect ratio.

Measured the tilted angle of the luminous region in PEP-II.

Proposed a method for coupling correction at the collision point.

Abstract

A formula of luminosity of asymmetric e+e- collider with coupled lattices is derived explicitly. The calculation shows how the tilted angle and aspect ratio of the beams affect the luminosity. Knowing the result of the calculation, we measure the tilted angle of the luminous region of the collision for PEP-II using two dimensional transverse scan of the luminosity. The method could be applied to correct the coupling at the collision point.