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Abstract-Beam instabilities cover a wide range of effects in particle accelerators and they have been the subject of intense research for several decades. As the machines performance was pushed new mechanisms were revealed and nowadays the challenge consists in studying the interplays between all this intricate phenomena, as it is very often not possible to treat the different effects separately. The aim of this paper is to review the main mechanisms, discussing in particular the recent developments of beam instability theories and simulations.

We discuss the possibility of creating novel research tools by producing and storing highly relativistic beams of highly ionised atoms in the CERN accelerator complex, and by exciting their atomic degrees of freedom with lasers to produce high-energy photon beams. Intensity of such photon beams would be by several orders of magnitude higher than offered by the presently operating light sources, in the particularly interesting γ-ray energy domain of 0.1-400 MeV. In this energy range, the high-intensity photon beams can be used to produce secondary beams of polarised electrons, polarised positrons, polarised muons, neutrinos, neutrons and radioactive ions. New research opportunities in a wide domain of fundamental and applied physics can be opened by the Gamma Factory scientific programme based on the above primary and secondary beams.

In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green's function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and the indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be differentiated and integrated, it can be used to fully describe the radiation process of a particle beam travelling inside a waveguide of elliptical cross section, and it is valid for any elliptic geometry. The equations are used to evaluate the coupling impedance due to indirect space charge in case of elliptical geometry. In addition, they are useful as preliminary studies for the determination of the coupling impedance in different cases involving elliptic vacuum chambers, as, for example, the effect of the finite conductivity of the beam pipe wall or the geometrical variation of the vacuum chamber due to elliptic step transitions existing in some accelerators.

The High-Luminosity Large Hadron Collider (HL-LHC) project aims at extending the operability of the LHC by another decade and increasing by more than a factor of ten the integrated luminosity that the LHC will have collected by the end of Run 3. This will require doubling the beam intensity and reducing the transverse beam size compared to those of the LHC design. The higher beam brightness poses new challenges for machine safety, due to the large energy of 700 MJ stored in the beams, and for beam stability, mainly due to the collimator contribution to the total LHC beam coupling impedance. A rich research program was therefore started to identify suitable materials and collimator designs, not only fulfilling impedance reduction requirements but also granting adequate beam-cleaning and robustness against failures. The use of thin molybdenum coatings on a molybdenum–graphite substrate has been identified as the most promising solution to meet both collimation and impedance requirements, and it is now the baseline choice of the HL-LHC project. In this work we present the main results of the coating characterization, in particular addressing the impact of coating microstructure on the electrical resistivity with different techniques, from Direct Current (DC) to GHz frequency range.

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The beam coupling impedance is one of the main sources of beam instabilities and emittance blow up in circular accelerators. A refined machine impedance evaluation is therefore required in order to understand and model intensity dependent effects and instabilities that may limit the machine performance. For this reason, many impedance source localization techniques have been developed. In this work we present the impedance localization technique based on the observation of phase advance versus intensity at the beam position monitors using ac dipoles to force betatron oscillations. We present analytical formulas for the interpretation of measurements together with simulations to benchmark and illustrate the equations. Studies on the method accuracy for different Fourier transform algorithms are presented as well as first exploratory measurements performed in the LHC.

The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will undergo a major upgrade in the 2020s. This will increase its rate of collisions by a factor of five beyond the original design value and the integrated luminosity by a factor ten. The new configuration, known as High Luminosity LHC (HL-LHC), will rely on a number of key innovations that push accelerator technology beyond its present limits. Among these are cutting-edge 11 − 12 T superconducting magnets, including Nb 3 Sn-based magnets never used in accelerators before, compact superconducting cavities for longitudinal beam rotation, new technology and physical processes for beam collimation. The dynamics of the HL-LHC beams will be also particularly challenging and this aspect is the main focus of this paper.