 Solution

Conventional RF cavities accelerate beams with controlled phase, energy spread and transverse beam emittance. Their material surfaces limit sustainable gradients to order $10$–$100\mathrm{MV}{\mathrm{m}}^{-1}$, depending on technology and operating conditions. Mature RF systems already reached multi-GeV and much higher beam energies in 2015. The 2013 ILC baseline proposed $250\mathrm{GeV}$ electrons colliding with $250\mathrm{GeV}$ positrons, approximately $31.5\mathrm{MV}{\mathrm{m}}^{-1}$ superconducting cavities and a roughly $31\mathrm{km}$ facility. These were design parameters, not an operating collider.^[ref]

In plasma wakefield acceleration, an intense laser displaces plasma electrons and excites a longitudinal charge-density wave. A suitably injected electron bunch gains energy from that wave, with fields of order tens to hundreds of $\mathrm{GV}{\mathrm{m}}^{-1}$. A concrete result available before this examination was $4.2\mathrm{GeV}$ from a $9\mathrm{cm}$ capillary, with $6\%$ rms energy spread, $6\mathrm{pC}$ bunch charge and $0.3\mathrm{mrad}$ rms divergence. These values characterize that experiment, not every laser-plasma beam; divergence alone is not an emittance measurement.^[ref]

A collider concept stages many separately driven plasma modules, with fresh laser pulses, interstage capture and refocusing, controlled injection, and a final collision focus. Dephasing and pump depletion limit a single stage. Although the accelerating sections could be much shorter than ILC linacs, a useful collider also requires high repetition rate and wall-plug efficiency, reproducible low energy spread, preserved normalized emittance, stable timing, high bunch charge and acceptable beam-beam effects. Positron acceleration is an additional challenge because an electron-optimized plasma wake need not focus positrons. Large gradient alone does not demonstrate the luminosity or beam quality of an RF collider.