Efficient Modeling of Plasma Wake Field Acceleration Experiments Using Particle-In-Cell Methods

There is no clear path for building a particle accelerator at the energy frontier beyond the Large Hadron Collider (LHC). One option that is receiving attention is to use plasma wave wakefields driven by intense particle beams. Recent experiments conducted at the Stanford Linear Accelerator Center (SLAC) show that accelerating gradients in such wakefields in excess of 50 GeV/m can be sustained over meter scales. Based on this, a linear collider concept of staging one-meter long plasma cells together has been proposed. A facility at SLAC has been built to study the physics in one stage. In this dissertation we describe improvements and enhancements to a highly efficient simulation model for simulating current experiments at SLAC as well as parameters beyond the reach of current experiments. The model is the quasi-static particle-in-cell (PIC) code QuickPIC. A modified set of quasi-static field equations were developed, which reduced the number of predictor corrector iteration loops and an improved source deposit scheme was developed to reduce the parallel communication. These improvements led to a factor of 5 to 8 (depending on the simulation parameters) speedup compared with the previous set of field equations and deposition scheme. Several new modules were also added to QuickPIC, including the multiple field ionization and improved beam and plasma particle diagnostics. We also used QuickPIC to study the optimum plasma density for maximizing the acceleration field for fixed electron beam parameters. QuickPIC simulations were also used to study and design two-bunch PWFA experiments at SLAC including methods for mitigating the ionization-induced beam head erosion. The mitigation methods can enhance the energy gain in two-bunch PWFA experiments at SLAC by a factor of 10 for the same beam parameters. For beam parameters beyond SLAC but perhaps necessary for a future collider, QuickPIC was used to study how the ultra high electric fields of a tightly focused second electron bunch could lead to ion motion, which disrupts the focusing fields on the second bunch. The resulting nonlinearity in the transverse focusing force of the plasma wake will lead to emittance growth. We used QuickPIC to carry out the first fully self-consistent high resolution simulation on the effects of ion motion for PWFA linear collider problems. Preliminary results showed that the plasma-ion-motion-induced emittance growth was limited to less than a factor of 2. In addition to the electron beam driven PWFA, we also study how a short proton beam can excite a large plasma wake. Such short proton beams are currently not experimentally available. We therefore also study how long proton beams such as those at Fermi National Laboratory and CERN may drive a large plasma wake through a self-modulation instability. A linear theory for the self-modulation instability is presented under the wide beam limit. QuickPIC simulations show that the self-modulation of a long proton beam in a plasma may lead to the micro-bunching of the beam and excite a large plasma wake.