Modelling Chromatic Emittance Growth in Staged Plasma Wakefield Acceleration to 1 TeV using Nonlinear Transfer Matrices

TL;DR

This paper develops a nonlinear transfer matrix framework integrated with particle-in-cell simulations to model and analyze chromatic emittance growth in staged plasma wakefield accelerators reaching 1 TeV, aiding collider design.

Contribution

It introduces a novel nonlinear transfer matrix method up to ninth order for modeling emittance growth in plasma accelerators, enabling detailed multi-stage energy scaling analysis.

Findings

Minimal emittance growth for initial energy spreads below 10^{-3}

Energy-spread growth below 10^{-5} per stage under certain conditions

Framework applicable for plasma collider design and extension to complex wake structures

Abstract

A framework for integrating transfer matrices with particle-in-cell simulations is developed for TeV staging of plasma wakefield accelerators. Using nonlinear transfer matrices in terms up to ninth order in normalized energy spread $\sqrt{\langle\delta\gamma^2\rangle}$ and deriving a compact expression for the chromatic emittance growth in terms of the nonlinear matrix, plasma wakefield accelerating stages simulated using the three-dimensional particle-in-cell framework OSIRIS 4.0 were combined to model acceleration of an electron beam from 10 GeV to 1 TeV in 85 plasma stages of meter scale-length with long density ramps and connected by simple focusing lenses. In this calculation, we find that for initial relative energy spreads below $10^{-3}$, energy-spread growth below $10^{-5}$ of the energy gain per stage and normalized emittance below mm-mrad, the chromatic emittance growth can be minimal. The technique developed here may be useful for plasma collider design, and potentially could be expanded to encompass non-linear wake structures and include other degrees of freedom such as lepton spin.