High-quality positron acceleration in beam-driven plasma accelerators

Acceleration of positron beams in plasma-based accelerators is a highly challenging task. To realize a plasma-based linear collider, acceleration of a positron bunch with high-efficiency is required, while maintaining both a low emittance and a subpercent-level energy spread. Recently, a plasma-based positron acceleration scheme was proposed in which a wake suitable for the acceleration and transport of positrons is produced in a plasma column by means of an electron drive beam [Diederichs et al., Phys. Rev. Accel. Beams 22, 081301 (2019)]. In this article, we present a study of beam loading for a positron beam in this type of wake. We demonstrate via particle-in-cell simulations that acceleration of high-quality positron beams is possible, and we discuss a possible path to achieve collider-relevant parameters.

Figure 1

Two-dimensional ($\zeta$, $x$) map of the accelerating wakefield, $E_z/E_0$. Positrons can be accelerated in the region $-14\lesssim k_p\zeta \lesssim -10$. Inset: transverse dependence of accelerating field in the positron accelerating region at three different longitudinal locations denoted by the dashed ($k_p\zeta =-12.5$), solid ($k_p\zeta =-11.5$), and dotted ($k_p\zeta =-10.5$) lines. The accelerating field falls off for increasing distance from the propagation axis. The gradient of the transverse field decreases further behind the driver.

Figure 2

Two-dimensional ($\zeta$, $x$) map of the focusing wakefield, $(E_x-B_y)/E_0$. Positrons can be focused in the region $-14\lesssim k_p\zeta \lesssim -9$, which widely overlaps with the positron accelerating region. Inset: transverse dependence of focusing field at three different longitudinal locations denoted by the dashed ($k_p\zeta =-12.5$), solid ($k_p\zeta =-11.5$), and dotted ($k_p\zeta =-10.5$) lines. The focusing field decays almost linearly for increasing distances from the propagation axis. The field decreases further behind the driver.

Figure 3

Current profiles for an optimally loaded wake $I_b/I_A$ (red), and corresponding lineouts of the transversally averaged accelerating field, $⟨E_z⟩/E_0$ (blue). The current profiles and their corresponding accelerating gradient is given for four values of the witness bunch head position, $k_p{\zeta }_{\text{head}}=-11.0$ (dotted dashed), $-10.8$ (solid), $-10.6$ (dashed), $-10.4$ (dotted). Their relative averaged accelerating gradients within the beam are (in the same order as the starting position) 0.462,0.438,0.403,0.367 with respect to the maximum averaged accelerating gradient of the unloaded wake $⟨E_{\max }⟩/E_0=0.49$. The same line style marks the current profile and its corresponding field lineout. The presented current profiles optimally load the wake, resulting in a flattened $⟨E_z⟩/E_0$.

Figure 4

Mean energy of each slice vs longitudinal position in the positron bunch after acceleration. The blue line refers to algorithm flattening $⟨E_z⟩$ with a longitudinal uniform ${\sigma }_r$. The red line and the green line refer to additionally applying slice-by-slice matching and averaging of the bunch spot size over the acceleration distance, respectively. That way, the correlated energy spread can be reduced to the noise level.

Figure 5

Relative slice energy spread vs acceleration distance. Advancing test particles in an approximated step function yields similar energy-spread in comparison with the hipace simulation. The results indicate that emittances smaller than $0.1\mu \mathrm{m}$ induce an energy spread below 0.1%.