Generating multi-GeV electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime

The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for Laser WakeField Acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample Particle-In-Cell (PIC) simulation of a 30f sec, 200T W laser interacting with a 0.75cm long plasma with density 1.5*10^18 cm^-3 to produce an ultra-short (10f s) mono-energetic bunch of self-injected electrons at 1.5 GeV with 0.3nC of charge. For future higher-energy accelerator applications we propose a parameter space, that is distinct from that described by Gordienko and Pukhov [Physics of Plasmas 12, 043109 (2005)] in that it involves lower densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.