Short-range longitudinal and transverse wakefield effects in FERMI@Elettra FEL project

Abstract

The FERMI@Elettra Free Electron Laser (FEL) project is a soft X-ray fourth generation light source under development at the ELETTRA Laboratory of Sincrotrone Trieste. It is one of the FEL based European projects, designed to become the international user facility in Italy for scientific investigations, with ultra high brilliance X-ray pulses, of ultra-fast and ultra-high resolution processes in material science and physical biosciences. When ultra-relativistic charged particles pass through cross section variations of the vacuum chamber wall or experience the finite conductivity of the wall, they generate electromagnetic fields, which are named wakefields since they remain behind the exciting particles. These electromagnetic fields usually influence the energy and the transverse motion of trailing particles leading to beam instabilities, such as single bunch energy spread variations and emittance growth. Since FEL operation requires a beam with a short bunch and high quality in terms of bunch energy spread and emittance, a good knowledge of these wakefields is needed to predict the beam quality. This thesis deals with analytical and numerical studies of the short-range longitudinal and transverse wake?elds and their effects along the linac and undulator chain. In Ch. 2 we have estimated the short-range wake?elds in the backward traveling wave (BTW) accelerating structure. Each section is a backward traveling (BTW) structure composed of 162 nose cone cavities coupled magnetically. To calculate the effect of the longitudinal and transverse wake?elds we have used the time domain numerical approach with a new implicit scheme for calculation of wake potential of short bunches in long structures. The wake potentials of the BTW structure are calculated numerically for very short bunches and analytical approximations for wake functions in short and long ranges are obtained by fitting procedures based on analytical estimations. Finally the single bunch energy spread induced by short-range longitudinal wake?elds is analyzed. In Ch. 3 we have studied these electron beam dynamics in the presence of the linac transverse wake?eld. Trajectory manipulation is used to gain control of the transverse wake?eld induced instability and this technique is also validated in the presence of shot-to-shot trajectory jitter. A specific script working with Courant-Snyder variables has been written to evaluate the residual banana shape after instability suppression in the presence of shot-to-shot trajectory jitter. In Ch. 4 we have analytically derived expressions for the high-frequency longitudinal and transverse resistive-wall coupling impedance of an elliptical cross-section vacuum chamber. Then, the corresponding longitudinal and transverse wake functions have been obtained by calculating numerically the inverse Fourier transforms of the impedances. In Ch. 5 we report a novel concept to passively linearize the bunch compression process in electron linacs for the next generation X-ray free electron lasers. This can be done by using the monopole wake?elds in a dielectric-lined waveguide. The optimum longitudinal voltage loss over the length of the bunch is calculated in order to compensate both the second-order RF time-curvature and the second-order momentum compaction terms. Thus, the longitudinal phase space after the compression process is linearized up to a fourth-order term introduced by the convolution between the bunch and the monopole wake function.