This thesis is concerned with investigating the effects of ellipticity on the seeded self-modulation process of long particle beams in plasma accelerators, and the implications for accelerated beams, using theoretical and computational models.
Proton-driven plasma wakefield acceleration is a novel approach to plasma-based particle acceleration pioneered by the AWAKE experiment at CERN. The use of high-energy-content proton beams allows sustained high gradient (gigavolts per meter) plasma wakefields, allowing in principle, acceleration of witness beams over 10s or even 100s of meters. The scheme used at AWAKE relies on the seeded self-modulation (SSM) of long particle bunches, where the stability of the microbunch trains produced by SSM over tens or hundreds of meters is crucial for extrapolating this scheme as proposed for use in several high energy plasma-based linear colliders. Further, the uniformity and reproducibility of the resultant wakefields is essential for determining injection parameters and preservation of phase-space quality for witness beams during acceleration.
Transverse asymmetry is often characteristic of synchrotron-generated beams. However, aside from the competing hosing instability, few works have examined other effects of transverse asymmetry in this process. In this thesis, analytical modelling and 3D particle-in-cell (PIC) simulations are used to characterise the impact on the SSM growth process and resultant wakefields due to elliptical transverse asymmetry in the beam.
Metrics are constructed for quantifying the asymmetry of the evolving transverse beam profile in PIC simulations. Using these it is found that while beam asymmetry undergoes an order-of-magnitude increase during saturation of the SSM, the initial azimuthal complexity remains low and increases only slightly during the SSM growth stage. This allows the construction of a new analytical model for asymmetric SSM growth, from which a scaling for the reduction of the SSM growth rate with aspect ratio of the initial beam profile is obtained. A new method for estimating the SSM growth rate from simulations is developed, which allows these to be quantitatively verified. Finally, using heuristic knowledge of witness beam behaviour, the impact of azimuthal asymmetry of the longitudinal component of the wakefield on the final energy spread of an accelerated witness beam is estimated and found to be at most a few percent of the energy spread due to variation in a symmetric wakefield
