  Effect of ion motion on the spatio-temporal evolution of a relativistically
strong space charge wave, is studied using a 1-D fluid simulation code. In our
simulation, these waves are excited in the wake of a rigid electron beam
propagating through a cold homogeneous plasma with a speed close to the speed
of light. It is observed that the excited wave is a mode as described by
Khachatryan [Phys. Rev. E 58, 7799 (1998)] whose profile gradually sharpens and
the wave eventually breaks after several plasma periods exhibiting explosive
behaviour. It is found that breaking occurs at amplitudes, which is far below
the breaking limit analytically derived by Khachatryan [Phys. Rev. E 58, 7799
(1998)]. This phenomenon of wave breaking, at amplitudes well below the
breaking limit, is understood in terms of phase mixing of the excited wave. It
is further found that the phase mixing time (wave breaking time) scales
inversely with the energy density of the wave.
