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

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.

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

Analysis of transverse beam stabilization with radio frequency quadrupoles

Alexej Grudiev, Michael Schenk

A radio frequency (rf) quadrupole has been considered as a potential alternative device for Landau damping in circular hadron colliders. The objective of this study is to benchmark and confirm its stabilizing effect predicted by stability diagram theory by means of numerical tracking simulations. To that end, two complementary models of the device are implemented in PyHEADTAIL, a 6D macroparticle tracking code designed to study the formation and mitigation of collective instabilities. The rf quadrupole model is applied to a slow head-tail instability observed experimentally in the Large Hadron Collider to show that such a device can in principle provide beam stability similarly to magnetic octupoles. Thereafter, alternative usage schemes of rf quadrupoles also in combination with magnetic octupoles are proposed, discussed, and benchmarked with simulations.

2017

Transverse Noise, Decoherence, and Landau Damping in High-Energy Hadron Colliders

Sondre Vik Furuseth

High-energy hadron colliders are designed to generate particle collisions within specialized detectors. A higher number of collisions is achieved with high-quality beams of low transverse emittances, meaning a small transverse cross-section, and high intensity, meaning many particles per bunch. This thesis studies how noise negatively impacts the beam quality in high-energy hadron colliders, both in terms of beam instabilities and emittance growth. The impact is analyzed through the derivation of new theories, multi-particle tracking simulations, the numerical solving of partial differential equations, and dedicated experiments in CERN's Large Hadron Collider (LHC). The impact of noise on beam stability cannot be treated with the first-order, linear Vlasov equation, which is commonly used to study the thresholds of collective instabilities. Therefore, the Vlasov equation has in this thesis been expanded to second order in the perturbation of the beam distribution, finding a diffusion mechanism driven by the interplay between noise, decoherence, and wakefields. The diffusion leads to a local flattening of the distribution, which can cause a loss of Landau damping after a time delay referred to as the latency. An analytical formula for the latency and a specialized numerical diffusion solver were successfully benchmarked against the latency measurements in a dedicated experiment conducted in the LHC. Precaution in the machine operation has to be taken to account for this new mechanism. In particular, it is found that the machine must be operated with a margin to the linear stability threshold. For the case of the LHC, it has previously been found empirically that the octupole current during operation must be increased by about a factor 2, and this thesis provides the explanation as to why that is. Alternative operational settings are suggested to reduce the required octupole current in the LHC. In addition, the new theory allows for extrapolations to future machines, such as the High-Luminosity LHC, as well as the estimation of the impact of new devices, such as crab cavities. External noise and noise from the transverse beam feedback system cause an emittance growth rate due to decoherence of the noise kicks. Analytical theories for the suppression of the emittance growth rate with a bunch-by-bunch feedback have here been extended to a multi-bunch feedback. The numerical study of suppression during collision was conducted by means of a newly developed parallel multi-beam multi-bunch algorithm. For the typical case of low-frequency external noise and non-negligible feedback noise, a multi-bunch feedback has both analytically and numerically been found superior to a bunch-by-bunch feedback, as it can suppress the impact of the external noise equally well, while simultaneously reducing the noise generated by the feedback itself. Suggestions for a more optimal operation of the LHC are discussed, including a reduction of the upper cutoff frequency of the feedback system.