Luminosity geometric reduction factor from colliding bunches with different lengths

Abstract

In the interaction point of the future electron-Ion collider eRHIC, the electron beam bunches are at least one order of magnitude shorter than the proton beam bunches. With the introduction of a crossing angle, the actual number of collisions resulting from the bunch collision gets reduced. Here we derive the expression for the luminosity geometric reduction factor when the bunches of the two incoming beams are not equal.