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. Aside from limiting the maximum electric field, this trapping can lead to accelerated electron bunches with large energy spreads. Here, we introduce a novel regime of plasma wave excitation and wakefield acceleration that allows for arbitrarily high electric fields while avoiding the deleterious effects of unwanted trapping. 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.

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