Predominant Contribution of Direct Laser Acceleration to High-Energy Electron Spectra in a Low-Density Self-Modulated Laser Wakefield Accelerator

The two-temperature relativistic electron spectrum from a low-density (\(3\times10^{17}\)~cm\(^{-3}\)) self-modulated laser wakefield accelerator (SM-LWFA) is observed to transition between temperatures of \(19\pm0.65\) and \(46\pm2.45\) MeV at an electron energy of about 100 MeV. When the electrons are dispersed orthogonally to the laser polarization, their spectrum above 60 MeV shows a forking structure characteristic of direct laser acceleration (DLA). Both the two-temperature distribution and the forking structure are reproduced in a quasi-3D \textsc{Osiris} simulation of the interaction of the 1-ps, moderate-amplitude (\(a_{0}=2.7\)) laser pulse with the low-density plasma. Particle tracking shows that while the SM-LWFA mechanism dominates below 40 MeV, the highest-energy (\(>60\) MeV) electrons gain most of their energy through DLA. By separating the simulated electric fields into modes, the DLA-dominated electrons are shown to lose significant energy to the longitudinal laser field from the tight focusing geometry, resulting in a more accurate measure of net DLA energy gain than previously possible.