  Laser wakefield accelerators rely on the extremely high electric fields of
nonlinear plasma waves to trap and accelerate electrons to relativistic
energies over short distances. When driven strongly enough, plasma waves break,
trapping a large population of the background electrons that support their
motion. This limits the maximum electric field. Here we introduce a novel
regime of plasma wave excitation and wakefield acceleration that removes this
limit, allowing for arbitrarily high electric fields. The regime, enabled by
spatiotemporal shaping of laser pulses, exploits the property that nonlinear
plasma waves with superluminal phase velocities cannot trap charged particles
and are therefore immune to wave breaking. A laser wakefield accelerator
operating in this regime provides energy tunability independent of the plasma
density and can accommodate the large laser amplitudes delivered by modern and
planned high-power, short pulse laser systems.
