Plasma-based accelerators have the ability to sustain extremely large accelerating gradients, with possible high-energy physics applicaitons. This disertation further develops the theory of plasma-based accelerators byaddressing three topics: the performance of a hollow plasma channel as an accelerating structure, the generation of ultrashort electron bunches, and the propagation of laser pulses is underdense plasmas.

A warm, relativistic fluid theory of a nonequilibrium, collisionless plasma is developed to analyze nonlinear plasma waves excited byintense drive beams. The maximum amplitude and wavelength are calculated for nonrelativistic plasma temperatures and arbitrary plasma wave phase velocities. The maximum amplitude is shown to increase in the presence of a laser field. These results set a limit to the achievable gradient in plasma-based accelerators.

A method is proposed for conditioning electron beams via Thomson scattering. The conditioning provides a quadratic correlation between the electron energy deviation and the betatron amplitude of the electrons, which results in enhanced gain in free-electron lasers. Quantum effects imply conditioning must occur at high laser fluence and moderate electron energy. Conditioning of x-ray free-electron lasers should be achievable with present laser technology, leading to significant size and cost reductions of these large-scale facilities.

The electric field in the temporal and spectral domain of coherent diffraction-limited transition radiation is studied. An electron bunch, with arbitrary longitudinal momentum distribution, propagating at normal incidence to a sharp metal-vacuum boundary with finite transverse dimension is considered. A general expression for the spatiotemporal electric field of the transition radiation is derived, and closed-form solutions for several special cases are given. The influence of parameters such as radial boundary size, electron momentum distribution, and angle of observation on the waveform (e.g., radiation pulse length and amplitude) are discussed. For a Gaussian electron bunch, the coherent radiation waveform is shown to have a single-cycle profile. Application to a novel THz source based on a laser-driven accelerator is discussed.

Raman forward scattering of a high-intensity, short-duration, frequency-chirped laser pulse propagating in an underdense plasma is examined. The growth of the direct forward scattered light is calculated for a laser pulse with a linear frequency chirp in various spatio-temporal regimes. This includes a previously undescribed regime of strongly-coupled four-wave nonresonant interaction, which is important for relativistic laser intensities. In all regimes of forward scattering, it is shown that the growth rate increases (decreases) for positive (negative) frequency chirp. The effect of chirp on the growth rate is relatively minor, i.e., a few percent chirp yields few percent changes in the growth rates. Relation of these results to recent experiments is discussed.

Using higher-order transverse laser modes as drivers for plasma wave excitation, and, in particular, using a ring laser beam with maximum intensity off-axis, results in reversal of the focusing anddefocusing phase regions in a laser wakefield accelerator. This results in improved performance of self-trapping and laser injection schemes. Specifically, the trapping threshold required for opticalinjection is decreased and the maximum energy gain of the trapped electrons is increased. This scheme could also be of interest for the generation of ring electron beams or for beam conditioning.