Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.

Exploiting spectrally resolved satellite observations to assess the performance of climate models

The accurate representation of the Earth Radiation Budget by General Circulation Models (GCMs) is a fundamental requirement to provide reliable historical and future climate simulations. In this study, we found reasonable agreement between the integrated energy fluxes at the top of the atmosphere simulated by 34 state-of-the-art climate models and the observations provided by the Cloud and Earth Radiant Energy System (CERES) mission on a global scale, but large regional biases have been detected throughout the globe. Furthermore, we highlighted that a good agreement between simulated and observed integrated Outgoing Longwave Radiation (OLR) fluxes may be obtained from the cancellation of opposite-in-sign systematic errors, localized in different spectral ranges. To avoid this and to understand the causes of these biases, we compared the observed Earth emission spectra, measured by the Infrared Atmospheric Sounding Interferometer (IASI) in the period 2008-2016, with the synthetic radiances computed on the basis of the atmospheric fields provided by the EC-Earth GCM. To this purpose, the fast σ-IASI radiative transfer model was used, after its validation and implementation in EC-Earth. From the comparison between observed and simulated spectral radiances, a positive temperature bias in the stratosphere and a negative temperature bias in the middle troposphere, as well as a dry bias of the water vapor concentration in the upper troposphere, have been identified in the EC-Earth climate model. The analysis has been performed in clear-sky conditions, but the feasibility of its extension in the presence of clouds, whose impact on the radiation represents the greatest source of uncertainty in climate models, has also been proven. Finally, the analysis of simulated and observed OLR trends indicated good agreement and provided detailed information on the spectral fingerprints of the evolution of the main climate variables.

Decoding complex flow phenomena via Dynamic Mode Decomposition

In this thesis, the viability of the Dynamic Mode Decomposition (DMD) as a technique to analyze and model complex dynamic real-world systems is presented. This method derives, directly from data, computationally efficient reduced-order models (ROMs) which can replace too onerous or unavailable high-fidelity physics-based models. Optimizations and extensions to the standard implementation of the methodology are proposed, investigating diverse case studies related to the decoding of complex flow phenomena. The flexibility of this data-driven technique allows its application to high-fidelity fluid dynamics simulations, as well as time series of real systems observations. The resulting ROMs are tested against two tasks: (i) reduction of the storage requirements of high-fidelity simulations or observations; (ii) interpolation and extrapolation of missing data. The capabilities of DMD can also be exploited to alleviate the cost of onerous studies that require many simulations, such as uncertainty quantification analysis, especially when dealing with complex high-dimensional systems. In this context, a novel approach to address parameter variability issues when modeling systems with space and time-variant response is proposed. Specifically, DMD is merged with another model-reduction technique, namely the Polynomial Chaos Expansion, for uncertainty quantification purposes. Useful guidelines for DMD deployment result from the study, together with the demonstration of its potential to ease diagnosis and scenario analysis when complex flow processes are involved.