A chirped laser pulse focused by a chromatic lens exhibits a dynamic, or flying, focus in which the trajectory of the peak intensity decouples from the group velocity. In a medium, the flying focus can trigger an ionization front that follows this trajectory. By adjusting the chirp, the ionization front can be made to travel at an arbitrary velocity along the optical axis. We present analytical calculations and simulations describing the propagation of the flying focus pulse, the self-similar form of its intensity profile, and ionization wave formation. The ability to control the speed of the ionization wave and, in conjunction, mitigate plasma refraction has the potential to advance several laser-based applications, including Raman amplification, photon acceleration, high harmonic generation, and THz generation.
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