Transverse beams stability studies at the Large Hadron Collider

A charged particle beam travelling at the speed of light produces large electromagnetic wake fields which, through interactions with its surroundings, act back on the particles in the beam. This coupled system may become unstable, resulting in a deterioration of the beam quality. Such effects play a major role in most existing storage rings, as they limit the maximum performance achievable. In a collider, the presence of a second beam significantly changes the dynamics, as the electromagnetic interactions of the two beams on each other are usually very strong and may, also, limit the collider performances. This thesis treats the coherent stability of the two beams in a circular collider, including the effects of the electromagnetic wake fields and of the beam-beam interactions, with particular emphasis on CERN's Large Hadron Collider. As opposed to other colliders, this machine features a large number of bunches per beam each experiencing multiple long-range and head-on beam-beam interactions. Existing models describing the beams stability need to be extended accordingly. The beam-beam interactions are very non-linear, as a result, different particles in the beams oscillates with slightly different frequencies, which generates Landau damping of coherent motion. A numerical integrator is developed in order to estimate the effect of Landau damping on potentially unstable coherent modes of oscillation. As the characteristics of the machine and the beams vary along the operational cycle of the Large Hadron Collider, the beam-beam forces and consequently the effect of Landau damping may vary significantly. It is shown that some configurations are particularly critical. Measurements of coherent instabilities during these operational phases, as well as in dedicated experiments, are presented and compared to the model. While most observations are in agreement with the model, some observed instabilities remain unexplained. A mechanism is proposed as an explanation for these instabilities. It is shown that the distribution of particles in the beam can be distorted in the presence of external noise and that non-measurable variations of the distribution functions can lead to significant deterioration of the Landau damping strength. Multiparticle tracking simulations are used to demonstrate this effect in realistic conditions. The coherent modes of oscillation of the coupled system including the two beams and the electromagnetic wake fields is discussed by extending an existing linear model introduced earlier to describe single bunches encountering a single beam-beam interaction in order to describe the beams in the Large Hadron Collider, i.e. involving multiple bunches and multiple beam-beam interactions. It is shown that under certain circumstances, a resonant action of the beam-beam forces and the electromagnetic wake fields may lead to strong instabilities. An experiment was performed to test these effects in the Large Hadron Collider, showing a good agreement with the models. Mitigation techniques against these instabilities are investigated, the effect of Landau damping is discussed by comparing the linear model with multiparticle tracking simulations. An operational solution to relax the limitations due to coherent instabilities, taking advantage of the stabilising effect of the head-on beam-beam interactions, is discussed based on the models developed and tested experimentally.

Beam Transfer Function measurements and transverse beam stability studies for the Large Hadron Collider and its High Luminosity upgrade

Claudia Tambasco

The motion of high energetic particle beams in accelerators is influenced by their interactions with the accelerator environment through electromagnetic fields induced by the particle passages. Traveling with a speed close to the speed of light, the particles induce image charge and currents in the surroundings generating wake-fields that act back on the beams. Destabilizing effects may arise from the coupled motion between the circulating particles and the induced wake fields compromising the accelerator performances. The stability of the beams is ensured by the Landau damping of coherent motions generated by the diversity of oscillation frequencies of the particles in the beams. Under the effect of non linear forces produced by machine non linearities or beam-beam interactions the particles oscillate with slightly different frequencies depending on their amplitudes in the beams (tune spread). At the Large Hadron Collider (LHC) transverse instability thresholds are evaluated via the computation of the dispersion integral that depends on the tune spread in the beams as well as on the particle distribution. A large tune spread is beneficial for the Landau damping as long as no diffusive mechanism is present. In the presence of diffusive mechanisms, caused by resonance excitations or noise, the stability diagram can be deformed due to the modification of the particle distribution inside the beam leading to a possible lack of Landau damping of the impedance coherent modes previously damped by lying within the unperturbed stability area. This work aims to experimentally explore the transverse stability of the beams by means of Beam Transfer Function measurements at the LHC. They provide direct measurements of the stability diagrams and are sensitive to particle distribution changes. First measurements of the Landau stability diagrams at the LHC are presented and compared to model expectations. Experimental studies have been carried out in the presence of different sources of non linear effects such as octupole magnets and beam-beam interactions and compared to the model expectations. Limitations deriving from transverse coherent instabilities in the LHC are analysed and possible explanations for the observed LHC instabilities are discussed. In the perspective of the High-Luminosity LHC upgrade (HL-LHC), transverse stability studies for different beam-beam interactions and machine configurations are presented together with possible solutions to compensate reductions of the Landau damping during the operational phases of the HL-LHC.

EPFL2017

A novel approach to Landau damping of transverse collective instabilities in future hadron colliders

Michael Schenk

Transverse collective instabilities induced by the beam-coupling impedance of the accelerator structure lead to beam quality degradation and pose a major limitation to the machine performance. Landau damping, a powerful stabilising mechanism that can be employed against various types of instabilities, is present in the transverse planes when there is a betatron frequency spread among the beam particles. Traditional approaches use octupole magnets to introduce betatron detuning with the transverse particle oscillation amplitudes. Their damping efficiency depends on the transverse geometric beam emittances which decrease with increasing beam energy and brightness. For the Future Circular Collider (FCC) they may hence no longer be the most suitable instability mitigation tool. Within the framework of this PhD thesis a novel approach to Landau damping is studied from the theoretical, numerical, and experimental points-of-view. The novelty of the method is to introduce the betatron frequency spread through detuning with the longitudinal instead of the transverse amplitudes. This is motivated by the fact that in typical high-energy proton machines the longitudinal emittance is several orders of magnitude larger compared to the transverse ones. Two equivalent detuning schemes are considered: a radio-frequency (rf) quadrupole cavity and nonlinear chromaticity. The first achievement of the project is the development of the Vlasov theory for nonlinear chromaticity to provide the analytical foundation for the novel Landau damping technique. The formalism is validated successfully against the circulant matrix model and the PyHEADTAIL tracking code. Based on the new theory, two beam dynamics effects introduced by detuning with longitudinal amplitude are identified: Landau damping and a change of the effective impedance altering the head-tail instability formation mechanism. Second, the first numerical proof-of-concept of an rf quadrupole for Landau damping is realised in PyHEADTAIL. A two-family scheme for rf quadrupoles is also evaluated for FCC operational scenarios demonstrating an improved overall damping performance of the device. In particular, the required active magnetic length of the rf quadrupole is significantly shorter compared to octupole elements. Third, the numerical models and the theory are validated against measurements in the Large Hadron Collider (LHC) and the Super Proton Synchrotron (SPS) at CERN. In the two machines, the second-order chromaticity is successfully enhanced using a sextupole and an octupole scheme respectively and the measured nonlinear optics parameters are shown to be consistent with MAD-X calculations. The stabilisation of single bunches by means of a betatron frequency spread produced by nonlinear chromaticity is demonstrated in the LHC which marks the first experimental proof of the novel Landau damping method. The measurements are in good agreement with detailed PyHEADTAIL simulations. In particular, the two effects predicted by the theory are consistently observed in both experiments and simulations confirming a thorough understanding of the involved beam dynamics.

EPFL2019

Loss of transverse Landau damping by noise and wakefield driven diffusion

Xavier Buffat, Sondre Vik Furuseth

Landau damping of coherent modes is strongly dependent on the exact shape of the particle bunches. One often assumes that the transverse distributions in high-energy hadron colliders can be approximated by Gaussian distributions, in acceptable agreement with measurements, but known to be only a first approximation. In this paper, it is investigated how a specific change of the transverse distributions can cause a loss of Landau damping. A mechanism is introduced where the coherent modes, which are excited by noise in the machine, act back on the individual particles through wakefields. The impact is modeled as a narrow diffusion in frequency space, and therefore also in action space due to amplitude dependent detuning, which leads to a local flattening of the distribution. This distribution evolution corresponds to the drilling of a borehole in the stability diagram, i.e. a local reduction of the imaginary part of the curve. Hence, initially stable regions are changed into unstable ones at the real frequencies of the coherent modes. To mitigate this instability mechanism, one must operate the machine with a stability margin of magnitude that depends on the noise amplitude and the coherent modes. In this model, the latency is defined as the time from the start of the noise excitation, on an initially Gaussian distributed bunch, to the bunch instability. The proposed model is found to agree with results in dedicated latency experiments performed in the LHC, where bunches eventually went unstable with more than twice the detuning strength required for the stabilization of a Gaussian distribution.