An ongoing experiment is described to demonstrate the principle of multi-pulse laser wakefield acceleration, in which a plasma wakefield is resonantly excited by a train of laser pulses, spaced by the plasma wavelength. Particle-in-cell simulations of the initial single-pulse experimental setup are presented, in order to calculate the expected signal. Preliminary results are presented and future plans, based on work done so far, are discussed. Part of this work involves the implementation of a single-shot wakefield diagnostic - frequency-domain holography, which records the phase shift caused by passage of a probe pulse through the plasma. This implementation is described in detail, along with the associated analysis procedure. Practical difficulties encountered while implementing the diagnostic are discussed, along with possible ways of mitigating them in the future. A method is presented by which the noise level in the resulting phase measurements can be predicted, much more accurately than any previously published method for this technique. Methods of generating pulse trains for use in future multi-pulse laser wakefield acceleration experiments are presented. These include techniques proposed for use in this demonstration experiment, as well as one intended for use in a dedicated high-efficiency, high repetition-rate, multi-pulse driver laser. This last method, based on programmable pulse shaping using a spatial light modulator, requires a suitable mask to be computed based on the parameters of the required pulse train; an algorithm is described to perform this computation.

Accurate single-shot visualization of laser wakefield structures can improve our fundamental understanding of plasma-based accelerators. Previously, frequency domain holography (FDH) was used to visualize weakly nonlinear sinusoidal wakes in plasmas of density n[subscript e] < 0.6 × 10¹⁹/cm³ that produced few or no relativistic electrons. Here, I address the more challenging task of visualizing highly nonlinear wakes in plasmas of density n[subscript e] ~ 1 to 3× 10¹⁹/cm³ that can produce high-quality relativistic electron beams. Nonlinear wakes were driven by 30 TW, 30 fs, 800 nm pump pulses. When bubbles formed, part of a 400 nm, co-propagating, overlapping probe pulse became trapped inside them, creating a light packet of plasma wavelength dimensions--that is, an optical "bullet"--that I reconstruct by FDH methods. As ne increased, the bullets first appeared at 0.8 × 10¹⁹/cm³, the first observation of bubble formation below the electron capture threshold. WAKE simulations confirmed bubble formation without electron capture and the trapping of optical bullets at this density. At n[subscript] >1× 10¹⁹/cm³, bullets appeared with high shot-to-shot stability together with quasi-monoenergetic relativistic electrons. I also directly observed the temporal walk-off of the optical bullet from the beam-loaded plasma bubble revealed by FDH phase shift data, providing unprecedented visualization of the electron injection and beam loading processes. There are five chapters in this thesis. Chapter 1 introduces general laser plasma- based accelerators (LPA). Chapter 2 discusses the FDH imaging technique, including the setup and reconstruction process. In 2006, Dr. N. H. Matlis used FDH to image a linear plasma wakefield. His work is also presented in Chapter 2 but with new analyses. Chapter 3, the main part of the thesis, discusses the visualization of LPAs in the bubble regime. Chapter 4 presents the concept of frequency domain tomography. Chapter 5 suggests future directions for research in FDH. / text