In plasma-based acceleration a particle bunch surfs a plasma wave, driven by a laser or a particle beam, in order to achieve high energy in a very short distance. Powerful modern drivers create strongly nonlinear wavefields in which the plasma electrons are radially expelled. These wakefields can generate well-defined particle beams in what is referred to as the "blowout" regime. In this dissertation we study with theory and simulations some key physics of the blowout regime and offer methods for designing plasma-based accelerators which are stable, efficient and generate particle beams with good quality.

Starting from a phenomenological theory, originally presented in Ref. [51], which includes the concepts of nonlinear multi-dimensional wake excitation, local pump depletion, dephasing and laser guiding, we design laser wakefield accelerators which accelerate electron beams efficiently in a single stage. Simulations carried out using the Particle-In-Cell (PIC) code QuickPIC confirm much of the theoretical predictions. They show that in this nonlinear blowout regime, the laser excites a stable wake over distances hundreds of Rayleigh lengths long, as long as its spot size and duration are properly matched, k_pw0 = ω_pτ_L = [special characters omitted] In the simulations a₀ is held fixed at 2 and the plasma density is decreased while the spot size is kept matched. Stages that provide an average gradient 3.6GV/m (7.2 GV/m) with a final energy of 100GeV (25 GeV) were demonstrated. We discuss the optimal laser profile of an ultraintense pulse used for plasma-based acceleration and develop a method for describing how such a laser evolves.

The first beam loading theory for electrons in nonlinear wakes is developed starting from the work in Ref. [48, 49]. By assuming that the blowout radius is large, analytical solutions for the shape of the bubble and the loaded wakefield are derived. It is found analytically and confirmed in PIC simulations with OSIRIS, that beam-loading efficiencies exceeding 90% can be achieved while the energy spread of the accelerating electron bunch is essentially conserved for trapezoidally-shaped trailing beams. Analytical solutions for flat-top current profiles are also calculated and it is found through simulations that the results are similar to those for Gaussian-shaped beams. Based on these solutions the amount of loaded charge is calculated for a given acceleration gradient.