Abstract: Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence of a constant velocity region, near the baryonic matter distribution, followed by a quick decay at large distances. In this work, we consider the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained within the framework of the recently proposed hybrid metric-Palatini gravitational theory. The latter is constructed by modifying the metric Einstein-Hilbert action with an f(R) term in the Palatini formalism. It was shown that the theory unifies local constraints and the late-time cosmic acceleration, even if the scalar field is very light. In the intermediate galactic scale, we show explicitly that in the hybrid metric-Palatini model the tangential velocity can be explicitly obtained as a function of the scalar field of the equivalent scalar-tensor description. The model predictions are compared model with a small sample of rotation curves of low surface brightness galaxies, respectively, and a good agreement between the theoretical rotation Curves and the observational data is found. The possibility of constraining the form of the scalar field and the parameters of the model by using the stellar velocity dispersions is also analyzed. Furthermore, the Doppler velocity shifts are also obtained in terms of the scalar field. All the physical and geometrical quantities and the numerical parameters in the hybrid metric-Palatini model can be expressed in terms of observable/measurable parameters, such as the tangential velocity, the baryonic mass of the galaxy, the Doppler frequency shifts, and the stellar dispersion velocity, respectively. Therefore, the obtained results open the possibility of testing the hybrid metric-Palatini gravitational models at the galactic or extra-galactic scale by using direct astronomical and astrophysical observations.

Abstract: The post-linac energy collimation system of future e(+)e(-) multi-TeV linear colliders is designed to fulfil an essential function of protection of the Beam Delivery System (BDS) against miss-steered or errant beams likely generated by failure modes in the main linac. For the case of the Compact Linear Collider (CLIC), the energy collimators are required to withstand the impact of a full bunch train in case of failure. This condition makes the design of the energy collimation system especially challenging, if we take into account the need to dispose of an unprecedented transverse beam energy density per beam of the order of GJ/mm(2), when assuming the nominal CLIC beam parameters at 3 TeV centre-of-mass energy, which translates into an extremely high damage potential of uncontrolled beams. This leads to research activities involving new collimator materials and novel collimation techniques. The increase of the transverse spot size at the collimators using nonlinear magnets is a potential solution to guarantee the survival of the collimators. In this paper we present an alternative nonlinear optics based on a multipole magnet pair for energy collimation. In order to preserve an acceptable luminosity performance, we carefully study the general conditions for self-cancellation of optical aberrations between two multipoles. This nonlinear optics scheme is adapted to the requirements of the post-linac energy collimation system for the CLIC BDS, and its performance is investigated by means of beam tracking simulations. Although applied to the CLIC case, this nonlinear protection system could be adapted to other future colliders.