By simultaneously and self-consistently solving Maxwell's equations, the Am
mosov-Delone-Krainov (ADK) field ionization equation, and the relativistic
cold plasma equations, we have investigated the propagation of intense, ult
rashort laser pulses through spatially inhomogeneous longitudinal gas gradi
ents, Along with highly accurate calculations of the spatial and temporal b
eam profiles of the pulse at the end of various gradients, we have also det
ermined simple scaling rules for the location of the vacuum-gas interfere i
n 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.