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Person# Sondre Vik Furuseth

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Xavier Buffat, Sondre Vik Furuseth

A transverse feedback system can effectively mitigate the emittance growth caused by injection oscillations and machine noise in hadron beams. However, as its action on the beam depends on beam position measurements of finite accuracy, it introduces additional noise on its own. The machine noise is in general strongest at low frequencies. Hence, the feedback is less needed at high frequencies. In this paper, two theories for the reduction of the machine noise induced emittance growth rate, with a bunch-by-bunch feedback, have been extended to a multibunch feedback. The extended theories show quantitative agreement with sophisticated macroparticle simulations. The emittance growth caused by the beam position measurement noise is numerically found to be only weakly dependent on the feedback's cutoff frequency, while it is strongly dependent on the single-bunch gain. The ultimate goal of this study is to find the optimal transverse feedback bandwidth and gain, determined by the minimization of the total emittance growth rate. The optimum depends on the ratio between the amplitudes of the beam position measurement error and the machine noise, the power spectrum of the machine noise, the response of the feedback filters, and the magnitude and details of the detuning. For the illustrative case of the Large Hadron Collier during collision in run 2, the optimum is found at the currently lowest possible cutoff frequency of 0.5 MHz, with a single-bunch damping time of approximately 270 turns. Using a chromaticity of 15 units, the minimal emittance growth rate at this cutoff frequency is 72% lower than with a bunch-by-bunch feedback. If the beam position measurement error can be reduced relative to the machine noise, the optimum will shift to larger single-bunch gains, or equivalently shorter single-bunch damping times.

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.

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Noise can have severe impacts on particle beams in high-energy synchrotrons. In particular, it has recently been discovered that noise combined with wakefields can cause a diffusion that leads to a loss of Landau damping after a latency. Such instabilities have been observed in the Large Hadron Collider. This paper, therefore, studies the beam response to noise in the presence of wakefields, within the framework of the Vlasov equation. First, a wakefield beam eigenmode transfer function (MTF) is derived, quantifying the amplitude of a wakefield eigenmode when excited by noise. Then, the MTFs of all the wakefield eigenmodes are combined to derive the beam transfer function (BTF) including the impact of wakefields. It is found to agree excellently with multi-particle tracking simulations. Finally, the MTFs are also used to derive the single-particle diffusion driven by the wakefield eigenmodes. This new Vlasov-based theory for the diffusion driven by noise-excited wakefields is found to be superior to an existing theory by comparing to multi-particle tracking simulations. Through sophisticated simulations that self-consistently model the evolution of the distribution and the stability diagram, the diffusion is found to lead to a loss of Landau damping after a latency. The most important technique to extend the latency and thereby mitigate these instabilities is to operate the synchrotron with a stability margin in detuning strength relative to the amount of detuning required to barely stabilize the beam with its initial distribution.