Nonlinear plasma wakefield theory and optimum scaling for laser wakefield acceleration in the blowout regime

In this dissertation, we analyze through theory and simulation many important aspects of a highly nonlinear regime for plasma based acceleration, namely the blowout regime. In chapter 2, a nonlinear non-fluid theory for plasma wake field excitation in the blowout regime by either electron beams or laser pulses is presented. This theory can be used to predict the Wakefield amplitudes and blowout radius in terms of the electron beam or laser beam parameters, as well as predict the nonlinear modifications to the wakes wavelength and waveform. The theory is used to show when linear fluid theory breaks down and how this leads to a saturation of the logarithmic divergence in the linear Green's function. The requirements for forming a spherical waveform are also discussed. In chapter 3, we apply the theoretical framework presented in chapter 2 to four different unsolved problems for the blowout regime. These problems include the optimum plasma density for maximum Wakefield amplitude for given beam parameters, beam loading in the blowout regime, the transformer ratio for a linearly ramped electron beam driver, and the electron hosing instability in the blowout regime. In chapter 4 we give an extensive analysis of electron trapping in arbitrary electromagnetic fields with translational symmetry. The general trapping condition and limits on energy gain are derived. We then discuss the differences between particle trapping in 1D and 3D driven wakes and show that the acceleration gradient that causing trapping can be lower in 3D driven wakes. In chapter 5, we discuss possible parameter regimes for LNVFA to be usable as a real accelerator technology. We start with a discussion of the necessary conditions for an accelerator and show that the assumption of a weakly nonlinear wake is inconsistent with these requirements and that the blowout regime is the natural result. We then discuss many physical aspects in the blowout regime and develop a phenomenological theory to extrapolate this regime to higher energy (GeV and beyond). This theory is verified by 3D PIC simulations. Finally in chapter 6, we summarize the results and provide directions for further research.