New Challenges in Plasma Accelerators: Final Focusing for Wakefield Colliders

TL;DR

This work analyzes final-focus challenges for TeV-scale plasma wakefield collider designs, focusing on chromaticity, the Oide effect, and beamstrahlung as key bottlenecks to achieving nanometer-scale IP spot sizes and high luminosity. It adopts a 10 TeV flat-beam design by scaling the CLIC 7 TeV lattice, and evaluates performance with a multi-code workflow (MAD-X, MAPCLASS2, PLACET, GuineaPIG), finding substantial luminosity loss due to SR, with the 10 TeV design reaching $\mathcal{L}_{GP} \approx 1.08\times10^{35}\ \mathrm{cm}^{-2}\ \mathrm{s}^{-1}$ versus a Snowmass target of $3.41\times10^{35}\ \mathrm{cm}^{-2}\ \mathrm{s}^{-1}$. The study also highlights the potential of plasma lenses to reduce FFS length and mitigate Oide effects, while acknowledging practical challenges in plasma shaping and stability. The paper outlines future work on round-beam configurations, plasma-lens-based focusing, and redesigned collimation to improve viability of PWFA-based linear colliders at multi-TeV energies. Overall, it provides a concrete design path, performance benchmarks, and clear directions for advancing the FFS in high-gradient plasma-based collider concepts.

Abstract

The focusing of particle beams for collider experiments is crucial for maximizing the luminosity and thus the discovery potential of these machines. In recent years, plasma wakefield acceleration has emerged as a leading candidate for achieving higher energy collisions with smaller facility footprints due to the large accelerating gradients in the plasma. This higher beam energy poses significant challenges for the final focusing system of the collider. Here, we discuss the various challenges of final focusing for TeV-scale plasma accelerators and propose possible solutions. Finally, we present the first design of a final focusing system for a 10 TeV linear wakefield collider, evaluate its performance, and discuss its shortcomings as well as improvements for future designs.

Figures (6)

• Figure 1: Diagram illustrating the focal points for particles with momentum deviations with respect to the nominal reference energy $p_{0}$. Figure adapted from Ref. Wiedemann.
• Figure 2: Horizontal and vertical $\beta$ functions and dispersion for the 7 TeV (top) and 10 TeV (bottom) FFS. Surveys of the FFS designs are shown above each plot using the same horizontal scale. The 7 TeV design is 767 meters long and the 10 TeV design is 865 meters long. Dipoles shown in green, quadrupoles in blue, sextupoles in red, and higher-order multipoles shown in brown.
• Figure 3: Vertical beam size at the IP as a function of the normalized vertical emittance. Green and red curves show beam size for different values of the normalized horizontal emittance, while the blue and purple lines shown the expected beam size scaling with (Eq. \ref{['eq:oide_limit']}) and without (Eq. \ref{['eq:spotsize']}) the Oide effect, respectively. Beam sizes are calculated using PLACET.
• Figure 4: Vertical beam size (purple) and luminosity (red) at the IP as a function of the vertical beta function at the IP. The vertical line shows the nominal beam size for the 10 TeV FFS design. Values for $\beta_{y}^{*}$ obtained from MAD-X, while spot sizes and luminosity obtained via PLACET simulations and GuineaPIG, respectively.
• Figure 5: Horizontal (blue) and vertical (red) beam sizes at 10 TeV calculated to different orders in the map. Values calculated using MAPCLASS2.