ON THE COMPUTATION OF PHASE AND ENERGY GAIN FOR A THIN-LENS RF GAP USING A GENERAL FIELD PROFILE

Abstract

The thin-lens representation for an RF accelerating gap has been well developed and is documented by Lapostolle [5], Weiss [6], Wangler [14], and others [9], [10]. These models assume that the axial electric field is both centered and symmetric so it has a cosine expansion. Presented here is a model that considers general axial fields. Both the cosine and sine transit time factors are required plus their Hilbert transforms. The combination yields a complex Hamiltonian rotating in the complex plane with the synchronous phase. The phase and energy gains are computed in the pre-gap and post-gap regions then aligned with asymptotic values of wave number. Derivations are outlined, examples are shown, and simulations presented.