ELECTRONS in a plasma undergo collective wave-like oscillations near t
he plasma frequency, These plasma waves can have a range of wavelength
s and hence a range of phase velocities(1). Of particular note are rel
ativistic plasma waves(2,3), for which the phase velocity approaches t
he speed of light; the longitudinal electric field associated with suc
h waves can be extremely large, and can be used to accelerate electron
s (either injected externally or supplied by the plasma) to high energ
ies over very short distances(2-4). The maximum electric field, and he
nce maximum acceleration rate, that can be obtained in this way is det
ermined by the maximum amplitude of oscillation that can be supported
by the plasma(5-8). When this limit is reached, the plasma wave is sai
d to 'break'. Here we report observations of relativistic plasma waves
driven to breaking point by the Raman forward-scattering instability(
9,10) induced by short, high-intensity laser pulses, The onset of wave
-breaking is indicated by a sudden increase in both the number and max
imum energy (up to 44 MeV) of accelerated plasma electrons, as well as
by the loss of coherence of laser light scattered from the plasma wav
e.