Influence of an inductive impedance of the time evolution of the distribution function

Abstract

The evolution of the distribution function in analytic form contains much more than a good visual agreement between the analytically-derived and the tracked distribution in phase space. 1. Transverse matching of transport lines: A parameter composed of the [beta] functions of the beam and the [beta] functions of the lattice may be identified as a driving term of the filamentation process. Assuming an octupole-like perturbation in a storage ring (or a chromatic perturbation in a linac), this parameter is the well-known [beta][sub mag] factor. 2. First and second moments may be derived from the relatively simple analytic expression of the distribution function. A comparison between actual measurements of the center of mass and beam size and these analytic expressions may allow the injection to be optimized. The expression of the first moment contains the information of the incoming beam emittance and may be used to extract the beam emittance out of turn-by-turn BPM data. In this paper we want to treat the influence of an inductive wakefield on the time evolution of the distribution function. To be specific, we work in the longitudinal phase space and assume the transport line to be a storage ring.