Simulation of a Radio-Frequency Quadrupole with the Method of Moments

The Myrrha project aims at developing a sub-critical reactor driven by a LINear ACcelerator (LINAC). A Radio-Frequency Quadrupole (RFQ) is a RF cavity placed at the beginning of the accelerator. Its goal is focusing the beam, bunching it and giving it its first acceleration. The quality of the beam inside further sections of the LINAC is very sensitive to the quality of the output beam of the RFQ. For a high-current beam LINAC, the undesired effects due to repulsive forces between charges may be very strong. The goal of this thesis is to develop a fast and accurate solver for RFQ simulations. The Method of Moments (MoM) is a boundary element solver widely used to solve the harmonic Maxwell’s equations for radiation and scattering problems. The MoM is used for the first time in this thesis to obtain the electromagnetic fields produced inside the accelerator by the RF source. In order to reduce the computation time, innovative fast methods for low-frequency problems with the MoM have been developed: they are based on an appropriate pre-conditioner and some SVD compressions on top of a local approximation of the Green function for radiation. Besides, a beam dynamics solver based on an efficient particle-to-particle interaction has been developed. It relies on several smart physical approximations allowing a good complexity and on an efficient implementation on Graphics Processor Unit (GPU) with OpenCL, while preserving in their concept a good platform independence