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Passing a beam from one stage to the next without losing particles or blurring it has not been demonstrated.","posed_since":"","precise":"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.","problem_ref":null,"references":"","settled_by":"A two-stage experiment with independent drivers meeting the stated charge, emittance and energy-spread metrics.","status_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.","title":"Multistage plasma acceleration with preserved beam 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