Formalism for Local Correction of Vertical Crabbing in Hadron Storage Ring
The Electron-Ion Collider (EIC) incorporates crab cavities in both the Electron Storage Ring (ESR) and the Hadron Storage Ring (HSR) to achieve unprecedented luminosity goals. This technical note presents a formalism for the local correction of vertical crabbing in the HSR, addressing the complexities introduced by the integration of crab cavities and the interplay between betatron coupling and crabbing dispersion. Various strategies, including the use of skew quadrupoles and adjustments of Twiss functions, are explored to compensate vertical crabbing to achieve optimal beam-beam performance. The derived theoretical formulas offer practical guidance for minimizing the required vertical crabbing corrections, and will be implemented in the HSR lattice design.