Luminosity of a collider with asymmetric beams

TL;DR

This paper derives a general formula for collider luminosity involving asymmetric beams, applicable to various collision scenarios including identical, coasting, and merging beams, enhancing understanding of collider performance.

Contribution

It introduces a comprehensive luminosity formula for asymmetric beam collisions, covering multiple collision configurations and beam types.

Findings

Derived a universal luminosity formula for asymmetric colliding beams.

Presented specific cases including identical, coasting, and merging beam collisions.

Applicable to both counter-propagating and co-propagating beam scenarios.

Abstract

A formula for the collider luminosity is derived for a head-on collision of two beams with different parameters. Three particular cases are presented: the collision of two identical axially symmetric bunches, the collision of a bunch with a coasting beam, and the collision of two coasting beams. The colliding beams have coinciding longitudinal axes. The formula is valid for colliding both counter propagating and co-propagating ("merging") beams.