Linac Envelope Optics

Abstract

I develop the formalism that allows calculation of beam envelopes through a linear accelerator given its on-axis electric field. Space charge can naturally be added using Sacherer formalism. A complicating feature is that the reference particle's energy-time coordinates are not known a priori. Since first order matrix formalism applies to deviations from the reference particle, this means the reference particle's time and energy must be calculated simultaneously with the beam envelope and transfer matrix. The code TRANSOPTR is used to track envelopes for general elements whose infinitesimal transfer matrices are known, and in the presence of space charge. Incorporation of the linac algorithm into TRANSOPTR is described, and some examples given.