Linac Envelope Optics

TL;DR

This paper introduces a formalism for calculating beam envelopes in linear accelerators using on-axis electric fields, incorporating space charge effects and addressing the challenge of unknown reference particle coordinates.

Contribution

It develops a new formalism and algorithm for simultaneous calculation of beam envelopes, reference particle coordinates, and transfer matrices in linacs.

Findings

Implemented in the TRANSOPTR code for general elements with known transfer matrices.

Successfully incorporated space charge effects into envelope calculations.

Demonstrated examples of the formalism's application to linac beam dynamics.

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.