The non-linear beam dynamics of a circular accelerator, such as the Large Hadron Collider, can have a significant impact on its operation. In order to avoid limitations on the performance reach of the accelerator, and ensure machine protection, it is vital that the beam dynamics are well understood and controlled. This thesis presents the results of studies of non-linear beam dynamics undertaken on the Large Hadron Collider at CERN, during the 2010 to 2013 period. It sets out to quantify the understanding of the non-linear beam dynamics through the comparison of beam-based measurements to simulation, and where able and appropriate seeks to explain deviations of measurement from the model, and define corrections for relevant aspects of the dynamics. The analyses presented in this thesis represent considerable advances in the understanding of the LHC beam dynamics which should allow for an improved operation of the machine in the coming years.

In the Large Hadron Collider (LHC), particle physics events are created by colliding high energy proton beams at a number of interaction points around the ring. One of the main performance indicating parameters of the LHC is the luminosity. The luminosity is limited by, amongst other things, the strength of the beam-beam interaction. In this thesis, the effect of the beam-beam interaction on the luminosity performance of the LHC and the proposed High Luminosity Large Hadron Collider (HL-LHC) is investigated. Results from a number of dedicated, long-range beam-beam machine studies are presented and analysed. In these studies, the minimum beam-beam separation for two different beta star— optics are identified. This separation defines the minimum operational crossing angle in the LHC. The data from these studies are then compared to simulation of the dynamic aperture and the results are discussed. In addition to studies of the LHC, an analytical approach is derived in order to describe the hourglass effect, which may become a contributing factor in limiting the luminosity performance of the HL-LHC.

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The thermodynamics inside the helium liquefier in the FREIA laboratory still contains many unknowns. The purpose of this project is to develop a theoretical model and implement it in MATLAB, with the help of the CoolProp library. This theoretical model of the FREIA liquefaction cycle aims at finding the unknown parameters not specified in the manual of the manufacturer, starting from the principle of enthalpy conservation. Inspiration was taken from the classical liquefaction cycles of Linde-Hampson, Claude and Collins. We developed a linear mathematical model for cycle components such as turboexpanders and heat exchangers, and a non-linear model for the liquefaction in the phase separator. Liquefaction yields of 10% and 6% were obtained in our model simulations, with and without liquid nitrogen pre-cooling respectively - similar to those in the FREIA liqueuefier within one percentage point. The sensors placed in FREIA showed similar pressure and temperature values, even though not every point could be verified due to the lack of sensors. We observed an increase of more than 50% in yield after adjustments of the heat exchanger design in the model, especially the first one. This constitutes a guideline for possible future improvements of the liquefier. / Termodynamiken bakom heliumförvätskaren i FREIA-laboratoriet innehåller fortfarande många okända aspekter. Detta kandidatarbete syftar till att utveckla en teoretisk modell och implementera den i MATLAB med hjälp av biblioteket CoolProp. Denna modell av FREIA:s förvätskningscykel syftar till att hitta de okända parametrar som inte specificerats av tillverkaren, och baserar sig på principen om entalpins bevarande. Inspiration togs från de klassiska förvätskningscyklerna Linde-Hampson, Claude och Collins. Vi utvecklade en linjär matematisk modell för cykelkomponenter såsom expansionsturbiner och värmeväxlare, och en icke-linjär modell för själva förvätskningen i fasseparatorn. En förvätskningsverkningsgrad på 10% och 6% uppnåddes i våra modellsimuleringar, med respektive utan förkylning med flytande kväve - liknande verkningsgraderna i FREIA- förvätskaren inom en procentenhet. Sensorerna placerade i FREIA visade på liknande tryck och temperaturer, även om bristen på sensorer gjorde att vi inte kunde bekräfta varje punkt. Vi observerade en ökning på mer än 50% i verkningsgrad efter att ha justerat värmeväxlardesignen något, speciellt för den första. Detta kan utgöra riktlinjer för var man framöver kan förbättra den faktiska förvätskaren. / <p>Subject reader/Ämnesgranskare: Roger Ruber</p>

Fourier filtering is a powerful technique to improve the contrast when imaging through turbid media. However, the trade-off between contrast and spatial resolution is a long-standing issue that limits the Fourier filtering technique to low spatial resolution requirements. This report circumvents this trade-off by combining several high contrast but low spatial resolution images into one high spatial resolution, high contrast image using a phase retrieval algorithm. The high contrast, low resolution images were obtained in two methods; rotating an asymmetric Fourier filter and translating a symmetric pinhole filter across the Fourier domain. The former approach, when combined with the phase retrieval algorithm, successfully constructed a high spatial resolution, high contrast image through an optical density of OD = 13.7. The problem with this technique is its temporal sluggishness as several images need to be captured and then processed to form one high resolution image making it difficult to use for fast moving object e.g. Combustion sprays. Here, I propose a new technique called Phase Retrieval Algorithm for Multiple Exposures (PhRAME) which is an instantaneous method to capture all the required images for the phase retrieval algorithm by utilising an ultra-fast imaging technique called Frequency Recognition Algorithm for Multiple Exposures (FRAME). FRAME captures several images in one exposure allowing different spatial frequencies to be captured with the same high contrast in each image. These images are then combined via the phase retrieval algorithm into one high contrast, high spatial resolution image. While this report doesn't demonstrate the working of PhRAME, it demonstrates an intermediately step, that FRAME and the phase retrieval algorithm work in tandem.

The initial goal of the project as given to us was a fully automatic control system for the beam align-ment of an ion microprobe in order to improve efficiency building on previous automation efforts.We have worked in python to develop code for reading two 4-channel picoammeters connected toadjustable rods along the beam line and translating those electrical readings into a calculated beamposition with no visual input. We then use this to recommend current adjustments to the steeringdipole electromagnets. Development was started on a standalone GUI to ease this process for newbeam compositions but was not feature complete in time.

This thesis describes the design a novel type of particle accelerator for charged particle therapy. The accelerator is called a non-scaling, Fixed Field Alternating Gradient (ns-FFAG) accelerator, and will accelerate both protons and carbon ions to energies required for clinical use. The work is undertaken as part of the PAMELA project. An existing design for a ns-FFAG is taken as a starting point and analysed in terms of its ability to suit the charged particle therapy application. It is found that this design is particularly sensitive to alignment errors and would be unable to accelerate protons and carbon ions at the proposed acceleration rate due to betatron resonance crossing phenomena. To overcome this issue, a new type of non-linear ns-FFAG is developed which avoids resonance crossing and meets the requirements provided by clinical considerations. Two accelerating rings are required, one for protons up to 250 MeV and fully stripped carbon ions to 68 MeV/u, the other to accelerate the carbon ions up to 400-430 MeV/u. Detailed studies are undertaken to show that this new type of accelerator is suitable for the application. An alignment accuracy of 50 micrometers will not have a detrimental effect on the beam and the dynamic aperture for most lattice configurations is found to be greater than 50 pi.mm.mrad normalised in both the horizontal and vertical plane. Verification of the simulation code used in the PAMELA lattice design is carried out using experimental results from EMMA, the world's first ns-FFAG for 10-20 MeV electrons built at Daresbury Laboratory, UK. Finally, it is shown that the described lattice can translate into realistic designs for the individual components of the accelerator. The integration of these components into the PAMELA facility is discussed.

This thesis describes an investigation into the performance of different schemes for generating short x-rays pulses via synchrotron radiation emission. A review is given of the methods that have been previously proposed for this task. From this review, three leading schemes are selected for in-depth investigations, each of which explores the boundary of what is presently achievable in accelerator-based light sources. The first scheme generates short x-ray pulses by operating an electron storage ring in a quasi-isochronous state using a ‘low-alpha’ lattice. High and low emittance lattices are developed, studied through simulation and then implemented on the Diamond storage ring. Beam dynamics and bunch length measurements are presented for a variety of machine conditions, and an assessment is made of the minimum practically achievable bunch length for stable user operation. Radiation pulses of 1 ps r.m.s. are demonstrated using this scheme. The second and third schemes investigate performance limits for a linac-based light source through numerical simulations. The first of these generates ultra-short pulses by passing a highly compressed electron bunch through a long undulator to radiate in the ‘single-spike’ regime. A comparison is made with theoretical predictions for the required electron bunch length to operate in this way, which highlights the need for accurate start-to-end simulations. The final scheme generates ultra-short x-ray pulses through laser manipulation of the electron bunches. The modulated electrons pass through a long undulator with tapered gap, such that only the centre of the modulated portion experiences high free-electron laser (FEL) gain. A method to enhance the FEL output from this scheme using a wavelength filter and grating-compressor is investigated. The sensitivity of the two schemes to jitter sources is determined, and it is demonstrated both schemes are capable of generating GW-level, fully coherent sub-fs soft x-ray pulses. Such pulses would open up the development of time-resolved science to new regimes.

Neste trabalho apresentamos o projeto do microtron principal do IFUSP. Inicialmente são apresentados os fundamentos teóricos relativos à estabilidade do feixe em um microtron, bem como discussões sobre a ótica do feixe. No trabalho são feitas basicamente 3 tipos de simulações distintas: simulação da dinâmica longitudinal e transversal da etapa síncrona, simulação da dinâmica transversal das linhas de transferência (inserção e extração) e a simulação relativa à otimização do projeto dos eletroímãs principais. As simulações longitudinais mostraram que é possível reduzir a energia de entrada do microtron principal de 4,9 para 2,5 MeV, o que permitira a eliminação do primeiro estágio síncrono (microtron booster). A energia final do microtron principal passa a ser 38 MeV. Foram realizados os projetos de duas linhas de inserção no principal para essas as duas energias (2,5 e 4,9 MeV) e foi feita uma análise comparativa desses dois projetos. O projeto da linha de extração também foi analisado levando em consideração duas energias de extração (5,8 e 38 MeV) para se mostrar a viabilidade dessa etapa. / In this work we present the design of the IFUSP main microtron. Initially, the theoretical foundations for the beam stability in the microton are presented as well as the beam optics is discussed. Three different kinds of simulations were done: Longitudinal and transversal beam dynamics in the synchronous part of the machine, transversal beam dynamics concerning the transfer lines and simulations related to the design of the main magnets. The longitudinal simulations sugested that it is possible to reduce the initial energy of the main microtron from 4.9 to 2.5 MeV, this would permit the elimination of the first synchronous stage (booster microtron). The final energy of the main microtron will be 38 MeV. The design of two insertion lines in the main microtron for the two different energies (2.5 and 4.9 MeV) was done and a comparative analysis between these two designes is presented. The design of the extraction line also takes into account two different extraction energies (5.8 and 38 MeV) in order to show de viability of this part.

Neste trabalho apresentamos o projeto, construção e testes de eletroímãs dipolares usados na linha de transporte do feixe do Microtron do IFUSP. Inicialmente são feitos estudos da contribuição do campo de borda dos eletroímãs na curvatura total do feixe e posteriormente esses valores foram usados para a definição de parâmetros de projeto. Foram construídos e caracterizados dois dipolos (30 e 45o) e ainda um eletroímã seletor (+/- 90o) com simetria azimutal. Os resultados obtidos nos testes realizados com os dipolos mostraram um desempenho adequado à operação do acelerador. Também é descrito um método para a simulação da trajetória de elétrons na presença de um campo magnético. / In this work we present the design, construction and testing of dipole magnets used on the beam line of IFUSP-Microtron. Initially we studied the fringe field of the magnets on the total beam bending, these values had been used for the definition of design parameters. It has been constructed two dipoles (30 and 45o) as well as a switch magnet (+/- 90o) with azimuthal symmetry. The tests results of the dipoles had shown an adequate performance to the accelerators operation. A method for the simulation of the electron path in the presence of a magnetic field is also described.