Optimizing Laser Wakefield Acceleration in the Nonlinear Self-Guided Regime for Fixed Laser Energy

The scaling laws for laser wakefield acceleration in the nonlinear, self-guided regime [Lu et al. Phys. Rev. Spec. Top. Accel. Beams 10, 061301 (2007)] are examined in detail using the quasi-3D version of the particle-in-cell code OSIRIS. We find that the scaling laws continue to work well as the plasma density is reduced while the normalized laser amplitude is kept fixed. For fixed laser energy, the energy gain of an isolated bunch of electrons can be improved with some loss in the bunch charge by shortening the normalized pulse length until self-guiding no longer occurs, and through the use of asymmetric longitudinal profiles with rapid rise times. For example, without any external guiding a 15 J,.8\mu m laser with a pulse length of 46 fs (39 fs) is found to generate a quasi-mono-energetic bunch of 355pC (227pC) with a max energy of 3.25 (4.04) GeV with an acceleration distance of 2.43 cm (3.08cm). Furthermore, a bunch with 39.4pC and a maximum energy 4.6 GeV is produced for an asymmetric laser with a rapid rise time. Studies for 30 J and 100 J lasers are also presented.