Fundamental characteristics of transverse deflecting field

TL;DR

This paper explores the fundamental electromagnetic characteristics of transverse deflecting fields, revealing the necessity of combined mode descriptions and their impact on beam emittance in rf structures.

Contribution

It demonstrates that transverse deflecting fields inherently include a longitudinal magnetic component and require a mixed mode basis for accurate representation.

Findings

Transverse deflecting forces are accompanied by longitudinal magnetic fields.

Pure TM or TE mode descriptions are insufficient for transverse deflecting waves.

Using the HM--HE basis improves convergence in mode analysis.

Abstract

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 always accompanied by an additional longitudinal magnetic field component which leads to an emittance growth in the direction perpendicular to the transverse force. Transverse deflecting waves can thus not be described by pure TM or TE modes, but require a linear combination of basis modes for their representation. The mode description is preferably performed in the HM--HE basis to avoid converge problems, which are fundamental for the TM--TE basis.