Laser-driven electron plasma waves with relativistic phase velocities have applications in plasma acceleration of charged particles or as relativistic plasma mirrors for radiation generation. The phase velocity of the plasma wave is a critical parameter that can, for example, determine the energy gain in a laser-plasma accelerator or the frequency up-shift after reflection of laser light. In the linear regime of laser-driven plasma wave excitation, the phase velocity of the plasma wave is equal to the laser group velocity. In the quasi-linear and nonlinear regimes, the laser phase velocity is significantly less than the laser group velocity and is determined by the drive laser evolution. In this talk, we describe the phase velocity of the laser-driven plasma wave in the quasi-linear and nonlinear regimes, and we determine the plasma density variation, i.e., taper, that allows for phase velocities at the speed of light. Density tapering may also be used to generate large amplitude plasma waves with accelerating wave fronts for radiation generation applications.
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