  The excitation and breaking of relativistically intense electron-ion modes in
a cold plasma is studied using 1D-fluid simulation techniques. To excite the
mode, we have used a relativistic rigid homogeneous electron beam propagating
inside a plasma with a velocity close to the speed of light. It is observed
that the wake wave excited by the electron beam is identical to the
corresponding Khachatryan mode, a relativistic electron-ion mode in a cold
plasma. It is also seen in the simulation that the numerical profile of the
excited electron-ion mode gradually modifies with time and eventually breaks
after several plasma periods exhibiting explosive behavior in the density
profile. This is an well known phenomena, known as wave breaking. It is found
that the numerical wave breaking limit of these modes lies much below than
their analytical breaking limit. The discrepancy between the numerical and
analytical wave breaking limit has been understood in terms of phase-mixing
process of the mode. The phase mixing time (or wave breaking time) obtained
from the simulations has also been scaled as a function of beam parameters and
found to follow the analytical scaling.
