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A new regime of proton-driven plasma wakefield acceleration is discovered, inwhich the plasma nonlinearity increases the phase velocity of the excited wavecompared to that of the protons. If the beam charge is much larger thanminimally necessary to excite a nonlinear wave, there is sufficient freedom inchoosing the longitudinal plasma density profile to make the wave speed closeto the speed of light. This allows electrons or positrons to be accelerated toabout 200 GeV with a 400 GeV proton driver.

Ultimate plasma wakefield acceleration with 400 GeV proton driver