Transverse Impedance of Ferrite Elements

A specific feature of ferrites is that these materials behave either as metals or magneto-dielectrics, depending on the frequency range. Their magnetic permeability is a function of frequency as well. In this paper, the transverse impedance of a ferrite kicker is calculated. The method suggested in Ref. [1] is generalized here for ferrites. Namely, in [1] it is assumed that the electric field of the beam charge dipole is always perfectly shielded. In fact, this assumption requires the conductivity being high compared with the frequency. This is not necessarily true for the high frequencies of a proton single-bunch spectrum. That is why the dynamics of the electric shielding has to be taken into account for ferrite kickers. The generalized analytic result is applied for the ferrite MKE kickers at the CERN SPS, and a fairly good agreement with observations [2] is found.