Lower limit of the transverse emittance growth in deflecting rf fields

The Panofsky-Wenzel theorem connects the transverse deflecting force in an rf structure with the existence of a longitudinal electric field component. In this paper it is shown that a transverse deflecting force is accompanied by an additional longitudinal magnetic field component which leads to an emittance growth in the direction perpendicular to the transverse force. The general description of transverse deflecting waves requires a linear combination of basis modes to cope with the boundary conditions and to support the simultaneous existence of electric and magnetic longitudinal field components. The mode description is preferably performed in the hybrid HM-HE basis to avoid convergence problems, which are fundamental for the transverse TM-TE basis.