Abstract
In this paper, we address the energy spread and slice energy spread of an externally injected electron beam in plasma wakefield accelerators operating in the linear or quasilinear regime. The energy spread is first derived taking into account the phase dependence of the wakefield along the finite-length bunch together with the dephasing during acceleration and found to be strongly dependent on the bunch length. This could be compensated by the beam loading effect, the energy spread from which is then derived and found to be nearly independent of the bunch length. However, the transverse dependence of the beam loading effect also makes the particles at the same longitudinal position experience different accelerating fields, introducing a significant slice energy spread. To estimate the slice energy spread, a theoretical analysis was conducted by taking the transverse betatron motion into account. As a study case, 3D simulations for the 5 GeV laser-plasma acceleration stage of the European Plasma Research Accelerator with eXcellence in Applications project have been performed. Careful optimization of the parameters allows one to obtain an energy spread of $\ensuremath{\le}1%$ and a slice energy spread of $\ensuremath{\le}0.1%$, with good agreement between theories and simulations.
Highlights
Plasma-based accelerators [1,2,3,4] have been considered as promising candidates to drive compact x-ray light sources [5] or future lepton colliders [6] thanks to their ability to provide extremely high accelerating fields
While the energy spread induced by the plasma wakefield is directly dependent on the bunch length, the energy spread induced by the beam loading effect is not, in the limit of kpσz ≪ 1
These assumptions mean that the beam loading effect [determined by np and kpσr as in Eq (16)] will be constant despite the acceleration, or Ez;bðξ; zÞ 1⁄4 Ez;bðξÞ, and its contribution to the slice energy spread will be the same period after period
Summary
Plasma-based accelerators [1,2,3,4] have been considered as promising candidates to drive compact x-ray light sources [5] or future lepton colliders [6] thanks to their ability to provide extremely high accelerating fields The principle of such accelerators is to use a nonflat laser pulse or an electron beam to push the plasma electrons to the sides of its pathway by the ponderomotive force or the space charge force. The EuPRAXIA project [8] for example aims at providing beams at the final energy of 5 GeV, with σE=E ≤ 1% and σEs=E ≤ 0.1%, capable of driving an x-ray free electron laser Reaching such a low energy spread requires careful optimization of the driver (laser or particle beam), the plasma and the input beam parameters, which implies many simulations, each being very time consuming. We search to optimize the acceleration parameters in order to minimize σE=E and σEs=E through simulations of the EuPRAXIA electron beam (30 pC) externally injected by a plasma or rf injector
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