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Abstract

In this thesis we report on the first direct experimental observation of the non-axi-symmetric Hosing Instability of a long relativistic proton bunch propagating through a m-scale plasma with density $n_{pe} \sim 0.5\cdot10^{14}$\,cm$^{-3}$ in the AWAKE experiment at CERN.\\ Analyzing streak camera images, we observe a periodic oscillation of the proton bunch centroid with growing amplitude along the bunch. We calculate by means of a Fast Fourier Transform that the frequency of the oscillation is equal to the cold electron plasma frequency. Moreover, by capturing time-integrated radial proton bunch profiles, we show that the Hosing Instability develops along a characteristic plane in the bunch.\\ We discuss the results of three-dimensional particle-in-cell simulations of the Hosing Instability performed in the OSIRIS code at similar parameters compared to our experiment in different propagation distances along the plasma and in different planes across the bunch.\\ By performing fits to the bunch centroid position in simulation and experiment, we show good agreement to the theoretical model of the Hosing Instability and give evidence for Coupled Beam Hosing, i.e. the coupling of the bunch centroid oscillation to the modulation of the bunch density due to the process of Seeded Self-Modulation via the plasma wakefields.\\ Furthermore, we show that in the case that the Self-Modulation process is not seeded, the occurrence of the Hosing Instability depends on the delay between the high-power laser pulse ionizing the Rubidium vapour and the arrival of the proton bunch. In this configuration, both events where the Self-Modulation Instability or the Hosing Instability (with and without coupling to the Self-Modulation process) develops can be observed. Eventually, we infer that the Hosing Instability can also be induced by a deliberate misalignment of the plasma channel with respect to the proton bunch trajectory.