Wakefield Analysis of Superconducting RF-Dipole Cavities

RF-dipole crabbing cavities are being considered for a variety of crabbing applications. Some of the applications are the crabbing cavity systems for LHC High Luminosity Upgrade and the proposed Electron-Ion Collider for Jefferson Lab. The design requirements in the current applications require the cavities to incorporate complex damping schemes to suppress the higher order modes that may be excited by the high intensity proton or electron beams traversing through the cavities. The number of cavities required to achieve the desired high transverse voltage, and the complexity in the cavity geometries also contributes to the wakefields generated by beams. This paper characterizes the wakefield analysis for single cell and multi-cell rf-dipole cavities. INTRODUCTION In rf cavities electromagnetic fields are excited by the charged particle beam traversing through the cavity, which then may affect the dynamics of the beam itself. A bunch on-axis can generate longitudinal wakes and a bunch at an offset may generate transverse wakefields [1]. Longitudinal wakefields can cause power losses in the cavity and increase in energy spread in the beam. Similarly transverse effects can amplify the effects leading to beam instabilities. The wakefield effects can be characterised into wake potentials and wake impedances. These excited wakefields then can be related to the higher order modes (HOMs) present in the cavity. Wake potential is defined as the change of momentum in a charge particle following a bunch with charge Qb at a distance s. The longitudinal wake potential is calculated by integrating the longitudinal electric fields as 1 ( , , ) , , , d , z z b s z W x y s E x y z t z Q v(1) and the transverse wake potential is given by