Multistage plasma acceleration with preserved beam quality
In plain words
Each plasma stage can only add a limited energy, so a collider needs many stages in a row. Passing a beam from one stage to the next without losing particles or blurring it has not been demonstrated.
Precise statement
Between stages the strongly focused beam diverges and must be refocused, producing chromatic emittance growth $(\Delta \epsilon/\epsilon)^2 \sim (W \sigma_{\delta})^2$ with chromatic amplitude $W \sim \beta_{\mathrm{lens}}/f$. Demonstrate acceleration through at least two independently driven stages with charge coupling above 90 percent, normalized emittance growth below 10 percent and rms energy spread below 1 percent, or show it is impossible with known optics. An answer is an experiment or a proof of a fundamental limit.
What would settle it
A two-stage experiment with independent drivers meeting the stated charge, emittance and energy-spread metrics.
Status in the literature
Unverified note
As of 2025 no staging of beam-driven plasma accelerators had been demonstrated; the only two-stage laser-driven test (2016) coupled about 3.5 percent of the charge.