Modeling chromatic emittance growth in staged plasma wakefield acceleration to 1 TeV using nonlinear transfer matrices

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[⟨δγ^{2}⟩] 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 nonlinear wake structures and include other degrees of freedom such as lepton spin.