An analytical backtracking method for electron beam longitudinal phase space shaping

TL;DR

This paper introduces an analytical backtracking method to optimize the longitudinal phase space of high-brightness electron beams in accelerators, enabling faster and more accurate system configuration without extensive simulations.

Contribution

The paper presents a novel analytical approach for backward tracking of phase space, including collective effects, to optimize accelerator configurations efficiently.

Findings

Successfully applied to LCLS-II to increase peak current

Achieved good agreement with Elegant simulations

Enabled rapid optimization of phase space configurations

Abstract

Many applications of high brightness, highly relativistic electron beams carry strict requirements on longitudinal phase space quality. To meet these requirements, accelerator systems typically utilize dispersive elements to manipulate the correlated energy spread acquired during acceleration or via collective effects. The many free variables in these systems make finding an optimal configuration difficult. We present here an analytical method for tracking a desired final longitudinal phase space backwards through an accelerator section composed of an acceleration or drift section followed by a dispersive section, including analytical models of pertinent collective effects. This backtracking can serve as a fast and accurate tool for optimization and study of the longitudinal phase space dynamics of an accelerator system. Here, we consider the LCLS-II accelerator as an example case, using this method to find an accelerator configuration and longitudinal phase space at the injector exit that lead to a significant increase in peak current while maintaining a narrow energy spread at the accelerator exit. The validity of this method is tested by comparison with Elegant simulations, showing good agreement.