Beam loading assisted matching working point for PWFA beam driven experiment at SPARC_LAB

This thesis concerns the investigation of the methods to improve the quality of beams accelerated via beam-driven plasma wakefield acceleration (PWFA) schemes in therms of emittance and energy spread. In the I chapter the motivation that led to the use of plasma wakefields in order to accelerate beams instead of conventional RF-based accelerating structures is reviewed, reporting also the state of the art of beam driven PWFA experiments. Investigating the differences between linear and non linear plasma wake, a proposal for a new scheme is elaborated. This scheme is based on the combination of a low quality high charge driver that generates an accelerating wakefield in linear regime and an high quality low charge witness that is injected in a region close to the crest of the accelerating wakefield. Since most of the focusing field is guaranteed by the beam loading effect, this scheme was called Beam Loading ASsisted maTching (BLAST) scheme. The theoretical tools to develope the study of this kind of working point are also discussed. The II chapter introduces the models used to describe the fields inside plasma. The very well-estabilished plasma linear theory will be developed in electrostatic approximation in order to derive a complete solution of the fields in the entire space. This solution will be used to obtain scaling laws that describe the main features of plasma acceleration i.e. maximum attainable energy, expected energy spread growth and optimal injection phase of witness for beam loading compensation of energy spread. The solution for the transverse field will be used in order to find the matching conditions via the envelope equation. Finally a procedure for the design of BLAST working points will be presented. The III chapter will introduce the SPARC\_LAB facility, pointing out the features of the injector and the experimental setup for the plasma acceleration experiments. In chapter IV the scaling laws derived in chapter II will be verified through the simulation of a working point for an experiment of high quality plasma acceleration to be performed at SPARC\_LAB. The robustness of this working point will be also investigated through a tolerance analysis.