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The long proton beams present at CERN have the potential to evolve into a train of microbunches through the self-modulation instability process. The resonant wakefield generated by a periodic train of proton microbunches can establish a high acceleration field within the plasma, facilitating electron acceleration. This paper investigates the impact of plasma density on resonant wakefield excitation, thus influencing acceleration of a witness electron bunch and its corresponding betatron radiation within the wakefield. Various scenarios involving different plasma densities are explored through particle-in-cell simulations. The peak wakefield in each scenario is calculated by considering a long pre-modulated proton driver with a fixed peak current. Subsequently, the study delves into the witness beam acceleration in the wakefield and its radiation emission. Elevated plasma density increases both the number of microbunches and the accelerating gradient of each microbunch, consequently resulting in heightened resonant wakefield. Nevertheless, the scaling is disrupted by the saturation of the resonant wakefield due to the nonlinearities. The simulation results reveal that at high plasma densities an intense and broadband radiation spectrum extending into the domain of the hard X-rays and gamma rays is generated. Furthermore, in such instances, the energy gain of the witness beam is significantly enhanced. The impact of wakefield on the witness energy gain and the corresponding radiation spectrum is clearly evident at extremely elevated densities.

Beam-driven plasma wakefield accelerators typically use the external injection scheme to ensure controllable beam quality at injection. However, the externally injected witness bunch may exhibit a non-Gaussian transverse density distribution. Using particle-in-cell simulations, we show that the common beam quality factors, such as the normalized RMS emittance and beam radius, do not strongly depend on the initial transverse shapes of the witness beam. Nonetheless, a beam with a highly-peaked transverse spatial profile can achieve a higher fraction of the total beam charge in the core. The same effect can be seen when the witness beam's transverse momentum profile has a peaked non-Gaussian distribution. In addition, we find that an initially non-axisymmetric beam becomes symmetric due to the interaction with the plasma wakefield, and so it does not cause a detrimental effect for the beam acceleration.

Plasma wakefield acceleration is a promising technology to reduce the size of particle accelerators. Use of high energy protons to drive wakefields in plasma has been demonstrated during Run 1 of the AWAKE programme at CERN. Protons of energy 400 GeV drove wakefields that accelerated electrons to 2 GeV in under 10 m of plasma. The AWAKE collaboration is now embarking on Run 2 with the main aims to demonstrate stable accelerating gradients of 0.5-1 GV/m, preserve emittance of the electron bunches during acceleration and develop plasma sources scalable to 100s of metres and beyond. By the end of Run 2, the AWAKE scheme should be able to provide electron beams for particle physics experiments and several possible experiments have already been evaluated. This article summarises the programme of AWAKE Run 2 and how it will be achieved as well as the possible application of the AWAKE scheme to novel particle physics experiments., Comment: 21 pages, 8 figures. Submitted to Symmetry journal

The spectroscopy of betatron radiation from the focusing plasma column can work as a powerful non-invasive beam diagnostic method for plasma wakefield acceleration experiments such as the AWAKE. In this paper, the effects of radial size mismatch and off-axis injection on the beam dynamics, as well as the spectral features of the betatron radiation emitted by the witness electron bunch in the quasi-linear proton-driven plasma wakefield are studied. It is shown that the evolution of the critical betatron photon energy and the overall photon angular distribution can effectively reveal the initial injection conditions of the witness electron bunch. The possibility of using this method for the diagnostics of the seed electron bunch in the proton self-modulation stage of AWAKE Run 2 is also discussed.

Particle acceleration in a quasilinear plasma wake provides access to high acceleration gradients while avoiding self-trapping of the background electrons. However, the plasma response to the externally injected witness bunch leads to a variation of the focussing fields along the bunch length, which can lead to a emittance growth. In order to investigate the impact of this emittance growth on the overall beam quality, we develop a single figure of merit based on a potential high-energy application for the AWAKE experiment at CERN. We show that the development of such a figure of merit naturally gives rise to constraints on both the tunability and stability of the initial witness bunch parameters. It is further shown that the unique physics of the quasilinear wake gives rise to broad tolerances for the witness bunch radius at the injection point, as the plasma wakefields self-match to the witness bunch., Comment: 10 pages, 12 figures