Analytic model of 3D beam dynamics in a wakefield device

In this paper we suggest an analytic model, and derive simple formulas, for the beam dynamics in a wakefield structure of arbitrary cross-section. The results could be applied to estimate an upper limit of the projected beam size in devices such as the dechirper and the wakefield streaking device. The suggested formalism is also applicable to the case when slices of the beam are distributed along an arbitrary line in 3D.