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 $\sqrt{⟨\ensuremath{\delta}{\ensuremath{\gamma}}^{2}⟩}$ 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 ${10}^{\ensuremath{-}3}$, energy-spread growth below ${10}^{\ensuremath{-}5}$ 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.
Highlights
Laser- and beam-driven plasma wakefield acceleration are promising approaches for accelerating leptons to high energy [1] and plans for a plasma-based accelerator facility are at a mature stage [2]
VI outlines a design for a simple lattice comprising “cells” of a plasma accelerating stage, two drift spaces, and a simple lens accelerating a beam of particles from 10 GeV to 1 TeV—as shown in the schematic in Fig. 1—and calculates the resulting chromatic emittance growth as a function of initial transverse emittance and beam energy spread
The matrix can be expanded to arbitrarily high terms in δγ (Note that we expand in powers of δγ rather than δ 1⁄4 δγ=γ because even though the equations would be more compact, δ is not a constant as the particle is in general accelerated in energy.) For staged plasma accelerators, we may wish to go to a high number of orders because of the relatively large energy spread and acceleration over many betatron periods
Summary
Laser- and beam-driven plasma wakefield acceleration are promising approaches for accelerating leptons to high energy [1] and plans for a plasma-based accelerator facility are at a mature stage [2]. We show how transfer matrices for plasma accelerators can be constructed from the fields calculated in self-consistent particle-in-cell simulations Having such a framework allows integration of plasma elements simulated with particle-in-cell codes with conventional accelerator design codes/techniques. This method is not a replacement for full-scale simulations, as feedback of the beam on the wakefields cannot be included. VI outlines a design for a simple lattice comprising “cells” of a plasma accelerating stage, two drift spaces, and a simple (thin) lens accelerating a beam of particles from 10 GeV to 1 TeV—as shown in the schematic in Fig. 1—and calculates the resulting chromatic emittance growth as a function of initial transverse emittance and beam energy spread
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