Tolerances to driver-witness misalignment in a quasilinear plasma wakefield accelerator

Abstract

Plasma-based accelerators offer high accelerating gradients and scalability through staging or long plasma sources, which makes them good candidates for future accelerator and collider concepts. Proton-driven accelerators in particular have the potential to bring particles to high energy in a single stage. In the quasilinear regime - where the plasma wake is only partially evacuated - a witness bunch of electrons drives a cavitated wake, which acts to preserve the emittance of the portion of the witness inside this self-blowout. In the case of a misalignment between the driver and witness, this behaviour can persist, but its effectiveness is reduced. In this paper, we study transverse witness dynamics in this regime, and develop analytical models to describe the witness motion, and develop a metric to estimate emittance preservation based on a single parameter which estimates the density of the witness after phase mixing. Particle in cell simulations using the AWAKE Run 2c baseline parameters show excellent agreement with the predictive models developed. This work allows alignment constraints to be set both for the AWAKE experiment and other wakefield acceleration schemes operating in the quasilinear regime.

Figures (5)

• Figure 1: Schematic view of the simulation setup. For an aligned driver-witness setup we have (a) the plasma (grey), with driver (purple) and witness (red) moving left-to-right in series. (b) The longitudinal fields, showing the beamloading due to the witness, and (c) the transverse force seen by a relativistic particle. We see that the witness blowout creates a region of focusing fields within the larger wake. Fields are normalised to the wavebreaking field $E_0 = m_ee\omega_p/e$. Here $\xi$ is the longitudinal coordinate relative to the driver centroid.
• Figure 2: Snapshots of the 400pC, 2µm emittance bunch for (a) no offset and (c) 20µm offset after 10m, and comparative slice emittances for all charge cases 100 -- 400pC, again for (b) no offset and (d) a 20µm offset. The initial charge density profile of all beams is illustrated by the blue dotted line in (d). Here $\xi$ is the longitudinal coordinate relative to the witness centroid.
• Figure 3: (a) Waterfall plot of the bunch transverse centroid position over its length $\xi$ and the propagation coordinate $z$ and, (b) short-time Fourier transform, showing the propagation distance-resolved oscillation frequency at the point $\xi = -0.5k_p$ in the witness, indicated by the dotted line in (a). The dotted white line shows the blowout betatron frequency $\omega_p/\sqrt{2\gamma}$, and the solid white line shows the numerically calculated quasilinear betatron frequency.
• Figure 4: Projected emittance after 10 metres. The geometric average of the $x$ and $y$-plane emittance is taken as the representative quantity while varying the initial emittance $\varepsilon_n$ and the offset $\Delta x$. Subplots (a) - (d) show increasing charge from 100 - 400 pC. The isobars for a 30µm projected emittance are shown as white dotted lines.
• Figure 5: Fraction of the bunch charge for which emittance is preserved (final emittance $<1.1$ times initial emittance). The effective peak density of the bunch is taken as $n_{b,\mathrm{eff.}} = Q/[e(2\pi)^{3/2}\sigma_z\sigma_y\sqrt{\sigma_x^2+\Delta x^2}]$. The point colour reflects the bunch parameters; charge (redness), offset (blueness) and initial emittance (alpha).