Abstract: Short duration, large bandwidth laser pulses may be manipulated to produce space-time coupled beams whose focal volume structure fundamentally differs from a traditional Gaussian beam. Such beams present opportunities to drive matter in unique ways. Laser-foil interactions with various focused spatially chirped beams reveal the formation of proton beam jets with enhanced and tunable energy spectra. A 1D spatially chirped beam can be created from the output of a single-pass grating pair and results in a pulse front tilt (PFT) when focused. The PFT fundamentally changes the interaction of the laser pulse with a target. The orientation of the pulse front can be modified through changing the f-number of the focusing system and through axisymmetric extensions of spatial chirp. We present a simulation technique that enables the modeling of these pulses with particle-in-cell codes and show the effect on laser-accelerated protons.