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