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.
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