Propagation of intense laser pulses through inhomogeneous ionizing gas profiles

By simultaneously and self-consistently solving Maxwell´s equations, the Ammosov-Delone-Krainov (ADK) field ionization equation, and the relativistic cold plasma equations, we have investigated the propagation of intense, ultrashort laser pulses through spatially inhomogeneous longitudinal gas gradients. Along with highly accurate calculations of the spatial and temporal beam profiles of the pulse at the end of various gradients, we have also determined simple scaling rules for the location of the vacuum-gas interface in order to minimize the pulse distortion at the focus. We show the benefits of using either preionized or low-Z gases, and we discuss the implications of this work for plasma-channel laser wakefield acceleration.