  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.
