The blowout regime is a limiting case of a nonlinearly excited plasma wave that overcomes problems identified in past linear regime studies of the plasma wake-field accelerator. Here, it is studied with the aid of simulations and by conducting experiments. Fluid model and particle-in-cell simulations have been used to study the propagation of drive pulses short enough to couple to the plasma mode, over distances comparable to the energy depletion length. Evolution of the beam radial dynamics in the simulations, and the associated wake-field phase shifts, outline phenomena important for achieving the maximum energy gain for the accelerated electrons. An experiment to demonstrate long-term drive beam propagation of a short electron pulse in an underdense plasma shows good agreement with simulations, with minor differences thought to originate from the limitation of simulating only a two-dimensional system. An experiment to measure electron acceleration is part of an ongoing effort, and has shown a 2.6 MeV energy gain and a 22 MeV/m acceleration gradient.
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