#### Abstract

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 $30\text{\hspace{0.28em}}\mathrm{fs}$, 200 TW laser interacting with a 0.75 cm long plasma with density $1.5\times {10}^{18}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{cm}}^{-3}$ to produce an ultrashort (10 fs) monoenergetic bunch of self-injected electrons at 1.5 GeV with 0.3 nC of charge. For future higher-energy accelerator applications, we propose a parameter space, which is distinct from that described by Gordienko and Pukhov [Phys. Plasmas **12**, 043109 (2005)] in that it involves lower plasma 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.

- Received 19 December 2006

DOI:https://doi.org/10.1103/PhysRevSTAB.10.061301

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