In the pursuit of discovering the fundamental laws and particles of nature, physicists have been colliding particles at ever increasing energy for almost a century. Lepton (electrons and positrons) colliders rely on linear accelerators (LINACS) because leptons radiate copious amounts of energy when accelerated in a circular machine. The size and cost of a linear collider is mainly determined by the acceleration gradient. Modern linear accelerators have gradients limited to 20-100 MeV/m because of the breakdown of the walls of the accelerator. Plasma based acceleration is receiving much attention because a plasma wave with a phase velocity near the speed of light can support acceleration gradients at least three orders of magnitude larger than those in modern accelerators. There is no breakdown limit in a plasma since it is already ionized. Such a plasma wave can be excited by the radiation pressure of an intense short pulse laser. This is called laser wakefield acceleration (LWFA). Much progress has been made in LWFA research in the past 30 years. Particle-in-cell (PIC) simulations have played a major part in this progress. The physics inherent in LWFA is nonlinear and three-dimensional in nature. Three-dimensional PIC simulations are computationally intensive.
In this dissertation, we present and describe in detail a new algorithm that was introduced into the Particle-In-Cell Simulation Framework. We subsequently use this new quasi three-dimensional algorithm to efficiently explore the parameter regimes of LWFA that are accessible for existing and near term lasers. This regimes cannot be explored using full three-dimensional simulations even on leadership class computing facilities. The simulations presented in this dissertation show that the nonlinear, self-guided regime of LWFA described through phenomenological scaling laws by Lu et al., in 2007 is still useful for accelerating electrons to energies greater than 10 GeV.
Fortunately, in many situations the physics of LWFA is nearly azimuthally symmetric and the most salient three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed by Lifschitz et al. [J. Comp. Phys. 228 (5) 2009] to model LWFA by expanding the fields and currents in azimuthal harmonics and truncating the expansion. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r-z grid and a procedure for calculating the complex current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this dissertation, we describe in detail the implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r-z and a gridless description in phi (which we have subsequently coined the ‘quasi-3D' method). We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented.
In almost all of the recent experiments progress on LWFA the plasma wave wake has been excited in the nonlinear blowout regime. A phenomenological description of this regime was given by Lu et al. [PRSTAB, 10 (061301) 2007]. This included matching conditions for the laser spot size and pulse length so that the laser evolution and wake excitation would be stable and the laser would self-guide. Scaling laws for the electron electron energy (self or externally injected) in terms of the laser and plasma parameters was also given. The parameters for the supporting simulations were limited due to the computational demands for such simulations particularly for higher electron energy.
The recent implementation of the quasi-3D algorithm into OSIRIS including the charge conserving current deposit, now make it possible to study these scaling laws and examine how well they still hold for higher laser intensities and laser energies. We have studied in detail how well the nonlinear, self-guided regime works for existing and near term 15-100 Joule lasers. We demonstrate that the scaling laws do capture the key phenomenological characteristics LWFAs under a wide range of different laser and plasma parameters, but are not meant to give exact predictions for a choice of parameters. The simulations indicate that the self-injected particles reach slightly higher energies than estimated by the scaling laws, although the evolution of the maximum energy looks similar when scaled to the dephasing time. We also find that shape of the evolution of the energy, spot size, and wake amplitude scales if the normalized vector potential, and transverse and axial profile shapes remain fixed. If the normalized vector potential is changed then the scaling laws are still useful but the shape of energy evolution curve changes. We also used the scaling laws to optimize the energy gain for a fixed laser energy. We then use the quasi-3D OSIRIS code to study study in detail how to optimize the energy gain for fixed laser energy including how to optimize the axial laser profile. We find that shortening the pulse length and reducing the plasma density is effective in producing a higher energy beam with a low energy spread, given a fixed laser energy.
