Quasi-static modeling of beam-plasma and laser-plasma interactions

Plasma wave wakefields excited by either laser or particle beams can sustain acceleration gradients three orders of magnitude larger than conventional RF accelerators. They are promising for accelerating particles in short distances for applications such as future high-energy colliders, and medical and industrial accelerators. In a Plasma Wakefield Accelerator (PWFA) or a Laser Wakefield Accelerator (LWFA), an intense particle or laser beam drives a plasma wave and generates a strong wakefield which has a phase velocity equal to the velocity of the driver. This wakefield can then be used to accelerate part of the drive beam or a separate trailing beam. The interaction between the plasma and the driver is highly nonlinear and therefore a particle description is required for computer modeling. A highly efficient, fully parallelized, fully relativistic, three-dimensional particle-in-cell code called QuickPIC for simulating plasma and laser wakefield acceleration has been developed. The model is based on the quasi-static or frozen field approximation, which assumes that the drive beam and/or the laser does not evolve during the time it takes for it to pass a plasma particle. The electromagnetic fields of the plasma wake and its associated index of refraction are then used to evolve the driver using very large time steps. This algorithm reduces the computational time by at least 2 to 3 orders of magnitude. Comparison between the new algorithm and a fully explicit model (OSIRIS) are presented. The agreement is excellent for problems of interest. Direction for future work is also discussed. QuickPIC has been used to study the "afterburner" concept. In this concept a fraction of an existing high-energy beam is separated out and used as a trailing beam with the goal that the trailing beam acquires at least twice the energy of the drive beam. Several critical issues such as the efficient transfer of energy and the stable propagation of both the drive and trailing beams in the plasma are investigated. We have simulated a 100 GeV and a 1 TeV plasma "afterburner" stages for electron beams and the results are presented. QuickPIC also has enabled us to develop a new theory for understanding the hosing instability of the drive and trailing beams. The new theory is based on a perturbation to the ion column boundary which includes relativistic effects, axial motion and the full electromagnetic character of the wake. The new theory is verified by comparing it to the simulation results. In the adiabatic long beam limit it recovers the result of previous work from fluid models.