  The plasma wakefield amplitudes which could be achieved via the modulation of
a long proton bunch are investigated. We find that in the limit of long bunches
compared to the plasma wavelength, the strength of the accelerating fields is
directly proportional to the number of particles in the drive bunch and
inversely proportional to the square of the transverse bunch size. The scaling
laws were tested and verified in detailed simulations using parameters of
existing proton accelerators, and large electric fields were achieved, reaching
1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found
in this case.
