Field harmonic analysis of short, current-dominated, beam transport magnets

Abstract

The theory of long, current-dominated, beam transport magnets is generalised to include the case of short magnets for which end effects are important. It is shown that the effect of a current-dominated beam transport magnet on a high momentum charged particle beam is conveniently characterised by a complex “parallel trajectory field integral” whose real and imaginary parts are the integrals of the transverse components of the magnetic field along a trajectory parallel to the axis of the magnet. This function is an analytic function of the position of the intersection of the parallel trajectory with the complex plane normal to the magnet axis. Furthermore, its relationship to the Fourier components of the longitudinal integral of the longitudinal current density in the magnet is identical to the relationship between the complex field and the Fourier components of the longitudinal current density in an infinitely long magnet.