Combined effects of Crab Dispersion and Momentum Dispersion in Colliders with Local Crab Crossing Scheme

TL;DR

This paper analyzes how linear transverse-longitudinal coupling, including crab and momentum dispersion effects, impacts beam size at the interaction point in colliders with local crab crossing, combining analytic formulas and simulations.

Contribution

It derives analytic formulas for crab and momentum dispersion effects and compares linear predictions with nonlinear beam-beam simulations.

Findings

Non-zero momentum dispersion at crab cavities affects beam size.

Phase errors from crab cavities influence beam size distortion.

Analytic formulas agree with simulation results.

Abstract

In this paper, we present the effects of linear transverse-longitudinal coupling on beam size at Interaction Point (IP) of a collider with local crab crossing scheme, when time dependent transverse deflection (crab kicks) and dispersive orbit intertwine near IP. The analytic propagation formula and the closed orbit form of the crab dispersion and momentum dispersion are derived. The non-zero momentum dispersion at crab cavities and the non-ideal phase from crab cavities to IP are detailed with the derived propagation formula to predict the beam size distortion at IP with or without the beam-beam interaction. The linear results are compared with nonlinear simulation using the weak-strong beam-beam code.