  There has been much interest in the blowout regime of plasma wakefield
acceleration (PWFA), which features ultra-high fields and nonlinear plasma
motion. Using an exact analysis, we examine here a fundamental limit of
nonlinear PWFA excitation, by an infinitesimally short, relativistic electron
beam. The beam energy loss in this case is shown to be linear in charge even
for nonlinear plasma response, where a normalized, unitless charge exceeds
unity. The physical basis for this effect is discussed, as are deviations from
linear behavior observed in simulations with finite length beams.
