In this dissertation, a new method for producing ultra-bright electron beams in nonlinear plasma wave wakes driven by an electron beam driver is explored using particle-in-cell simulations and analytic theory. In order to understand this process an accurate description of a nonlinear wakefield is required. These nonlinear wakefields are excited by intense particle beams or lasers pushing plasma electrons radially outward, creating an ion bubble surrounded by a sheath of electrons characterized by the source term $S \equiv -\frac{1}{en_p}(\rho-J_z/c)$, where $e$ is the electron charge, $n_p$ is the plasma number density, $\rho$ is the charge density, and $J_z$ is the axial current density. Previously, the sheath source term was described phenomenologically with a positive-definite function thereby resulting in a positive definite wake potential. In reality, the wake potential is negative at the rear of the ion column, which is important for self-injection and accurate beam loading models.
To account for this, in the first part of this dissertation a multi-sheath model in which the source term, $S$, of the plasma wake can be negative in regions outside the ion bubble is introduced. Using this model, a new expression for the wake potential and a modified differential equation for the bubble radius is obtained. Numerical results obtained from these equations are validated against particle-in-cell simulations for unloaded and loaded wakes. The new model provides accurate predictions of the shape and duration of trailing bunch current profiles that flatten plasma wakefields. It is also used to design a trailing bunch for a desired longitudinally varying loaded wakefield. The multi-sheath model is also applied to beam loading in laser wakefields. Areas where the multi-sheath model can be improved for laser drivers in future work are discussed.
In the second part of this dissertation, a new method of controllable injection to generate high quality electron bunches in the nonlinear blowout regime driven by electron beams is proposed and demonstrated using particle-in-cell simulations. Injection is facilitated by decreasing the wake phase velocity through focusing the drive beam spot size. Two regimes are examined. In the first, the spot size is focused according to the vacuum Courant-Snyder (CS) beta function while, in the second, it is self-focused by the plasma ion column. The effects of the driver intensity and vacuum CS parameters on the wake velocity and injected beam parameters are examined via theory and simulations. For plasma densities of $\sim 10^{19} ~\centi\meter^{-3}$, particle-in-cell (PIC) simulations demonstrate that peak normalized brightnesses $\gtrsim 10^{20}~\ampere/\meter^2/\rad^2$ can be obtained with projected energy spreads of $\lesssim 1\%$ within the middle section of the injected beam and with normalized slice emittances as low as $\sim 10 ~\nano\meter$.
In the last part of the dissertation, a predictive model for injection using the self-evolving driver method in the plasma focusing regime is developed. The model is used to characterize how the wake evolution and final injected beam parameters scale with the driver parameters. Parameter scans of PIC simulations using different drivers are performed and compared with the model predictions. In particular, the dependence of the injected beam parameters with the diffraction length, energy, intensity, spot size, and duration of the driver is examined. It is found that injection and optimal beam loading can be simultaneously achieved. The multi-sheath model is also used to study the beam loading effects from the injected bunch in this case. PIC simulation results indicate that the injected beam can be efficiently accelerated to $18.27$ GeV with a projected energy spread of $ 0.49\%$ and peak normalized brightess of $B_n \sim 10^{20}~\ampere/\meter^2/\rad^2$ for a plasma density of $\sim 10^{19} ~\centi\meter^{-3}$.
