The Optimal Beam-loading in Two-bunch Nonlinear Plasma Wakefield Accelerators

TL;DR

This paper develops empirical formulas using advanced optimization and regression techniques to determine optimal beam parameters for minimizing energy spread in nonlinear two-bunch plasma wakefield accelerators, enhancing design efficiency.

Contribution

It introduces two new fitting formulas for calculating beam parameters and the transformer ratio, enabling optimized beam-loading in nonlinear plasma wakefield accelerators.

Findings

Formulas enable optimal charge and transformer ratio calculation.

Scaling law relates drive and trailing beam charges.

Formulas improve accelerator design efficiency.

Abstract

Due to the highly nonlinear nature of the beam-loading, it is at present not possible to analytically determine the beam parameters needed in a two-bunch plasma wakefield accelerator for maintaining a low energy spread. Therefore in this paper, by using the Broyden-Fletcher-Goldfarb-Shanno algorithm for the parameter scanning with the code QuickPIC and the polynomial regression together with k-fold cross-validation method, we obtain two fitting formulas for calculating the parameters of tri-Gaussian electron beams when minimizing the energy spread based on the beam-loading effect in a nonlinear plasma wakefield accelerator. One formula allows the optimization of the normalized charge per unit length of a trailing beam to achieve the minimal energy spread, i.e. the optimal beam-loading. The other one directly gives the transformer ratio when the trailing beam achieves the optimal beam-loading. A simple scaling law for charges of drive beams and trailing beams is obtained from the fitting formula, which indicates that the optimal beam-loading is always achieved for a given charge ratio of the two beams when the length and separation of two beams and the plasma density are fixed. The formulas can also help obtain the optimal plasma densities for the maximum accelerated charge and the maximum acceleration efficiency under the optimal beam-loading respectively. These two fitting formulas will significantly enhance the efficiency for designing and optimizing a two-bunch plasma wakefield acceleration stage.