Nonlinear plasma wavelength scalings in a laser wakefield accelerator

Laser wakefield acceleration relies on the excitation of a plasma wave due to the ponderomotive force of an intense laser pulse. However, plasma wave trains in the wake of the laser have scarcely been studied directly in experiments. Here we use few-cycle shadowgraphy in conjunction with interferometry to quantify plasma waves excited by the laser within the density range of GeV-scale accelerators, i.e., a few 10^{18}cm^{-3}. While analytical models suggest a clear dependency between the nonlinear plasma wavelength and the peak potential a_{0}, our study shows that the analytical models are only accurate for driver strength a_{0}≲1. Experimental data and systematic particle-in-cell simulations reveal that nonlinear lengthening of the plasma wave train depends not solely on the laser peak intensity but also on the waist of the focal spot.