Luminosity of a collider with asymmetric beams
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.
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