GPU-Powered Modelling of Nonlinear Effects due to Head-On Beam-Beam Interactions in High-Energy Hadron Colliders.

The performance of high-energy circular hadron colliders, as the Large Hadron Collider, is limited by beam-beam interactions. The strongly nonlinear force between the two opposing beams causes diverging Hamiltonians and resonances, which can lead to a reduction of the lifetime of the beams. The nonlinearity makes the effect of the force difficult to study analytically, even at first order. Numerical models are therefore needed to evaluate the overall effect of different configurations of the machines. This report discusses results from an implementation of the weak-strong model, studying the effects of head-on beam-beam interactions. The assumptions has been shown to be valid for configurations where the growth and losses of the beam are small. The tracking has been done using an original code which applies graphic cards to reduce the computation time. The bunches in the beams have been modelled cylindrically symmetrical, based on a Gaussian distribution in three dimensions. This choice fits well with bunches in the Large Hadron Collider, and allows for certain consequences to be derived analytically. There has been good agreement between analytically expected effects and results from simulations. The effect that resonances have on the beam quality has been studied carefully. Resonances have been shown both analytically and numerically to be stronger at lower order and further from the design orbit of the beam. The strength of the beam-beam interaction will be higher after the upgrade from the Large Hadron Collider to the High-Luminosity Large Hadron Collider, and also in the next generation of machines, as the ultimate Future Circular Collider for hadron collisions. An equivalent increase has been shown to greatly limit the possible favourable working points. A scheme to try to cancel the resonances has been applied with noticeable effect.