Intensity-dependent effects in the Accelerator Test Facility 2 and extrapolation to future electron-positron linear colliders

The high energy physics community considers electron-positron linear colliders in order to complement the results obtained at the Large Hadron Collider. In order to achieve the design luminosity above 10$^{34}$ cm$^{-2}$s$^{-1}$, these linear colliders require a nanometer beam size at the Interaction Point (IP). The electron and positron beams are transported inside the Beam Delivery Systems (BDS) from the linear accelerators (LINACS) to the IP. The beam is focused by two strong quadrupoles in the Final Focus System (FFS) where chromatic effects and aberrations are corrected thanks to a local chromaticity correction scheme. Two projects are being studied now, the International Linear Collider (ILC) and the Compact Linear Collider (CLIC). Their FFS and the local chromaticity correction are being tested at the Accelerator Test Facility 2 (ATF2) at KEK in Japan. This test facility has been studying this matter for more than 20 years, achieving two of its main goals: obtaining a stable beam size around 37 nm at the IP and an orbit stabilisation with a nanometer precision at the IP. However, these goals were achieved at 10% of the nominal beam intensity. Indeed, when increasing the beam intensity, the beam becomes more unstable and its size grows. This is mainly due to wakefields in the ATF2 extraction line. Ultra-relativistic electrons going through the beam pipe interact with the surrounding structure and create an electromagnetic field, the wakefield. This field interacts with electrons inside the same bunch (short-range wakefield) but also with electrons in the following bunches (long-range wakefield). In ATF2, one considers that bellows, flanges and cavity BPMs are the main sources of wakefield. This effect results in increasing significantly the beam size at the IP. This thesis will show the impact of these intensity-dependent effects inside ATF2 and how to mitigate them. It will also show the impact of the same intensity-dependent effects in future electron-positron linear colliders, the ILC and CLIC.