Characterization of the Point Spread Function for the x-ray pinhole cameras at ALBA Synchrotron

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2020, Tutors: Antoni García-Santiago, Ubaldo Iriso ÁrizThe ALBA facility is a Synchrotron Light Source that accelerates electrons up to 3 GeV to produce synchrotron radiation for scienti c experiments. Transverse size measurements of the electron beam are carried out by imaging with an x-ray pinhole camera, whose spatial resolution is described by the Point Spread Function (PSF). The PSF changes slightly the beam image and determines the minimum beam size measurable, therefore its value is required for precise beam size measurements. This report calculates and compares the PSF analytically, experimentally and by numerical simulations, showing that the results obtained by the three methods are consistent. ALBA is equipped with a pinhole since 2011, and a new one is under design with a better resolution. Finally, this report also calculates the heat load received at the main pinhole elements to evaluate the need of cooling systems

Brownian motion

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Josep Vives i Santa Eulàlia[en] The aim of this work is to study the Brownian motion from a theoretical approach. Brownian motion (also named Wiener process) is one of the best known stochastic processes and plays an important role in both pure and applied Mathematics. In the first chapter, we present the basic concepts of the theory of stochastic processes such as filtrations, stopping times and martingales which are needed to develop further sections of the project. In the second chapter, we define the Brownian motion itself. Furthermore, two different constructions of Brownian motion are provided. The first one presents theorems of existence and continuity of stochastic processes from which we end up building the Brownian motion. The second construction provides another proof for the existence of Brownian motion based on the idea of the weak limit of a sequence of random walks. In the third chapter, we present a discussion of some properties of Brownian motion paths, also called sample path properties. These include characterizations of bad behaviour such as the nondifferentiability, as well as characterizations of good behaviour like the law of the iterated logarithm. Moreover, we study the zero sets, the quadratic variation and the lack of monotonicity of the Brownian paths. Finally, we show some Python simulations of one dimensional Brownian paths

PSF Characterization of the ALBA X-Ray Pinholes

ALBA is currently equipped with two X-ray pinhole cameras for continuous beam size monitoring using the synchrotron radiation from two different bending magnets. The first pinhole was installed on day-1 and it is working properly since 2011 as the work-horse for the ALBA emittance measurements. The second one has been commissioned in early 2021 for redundancy purposes. This paper summarizes the exercises to characterize the Point Spread Function (PSF) of both pinhole cameras using analytical calculations, SRW simulations, and experimental measurements

Bunch-by-bunch Tune Shift Studies for LHC-type Beams in the CERN SPS

After the implementation of major upgrades as part of the LHC Injector Upgrade Project (LIU), the Super Proton Synchrotron (SPS) delivers high intensity bunch trains with 25 ns bunch spacing to the Large Hadron Collider (LHC). These beams are exposed to several collective effects in the SPS, such as beam coupling impedance, space charge and electron cloud, leading to relatively large bunch-by-bunch coherent and incoherent tune shifts. Tune correction to the nominal values at injection is crucial to ensure beam stability and good beam transmission. Measurements of the bunch-by-bunch coherent tune shifts have been performed under different beam conditions. In this paper, we present the measurements of the bunch-by-bunch tune shift as function of bunch intensity for trains of 72 bunches. The experimental data are compared to multiparticle tracking simulations (including other beam variants such as 8b4e beam and hybrid beams) using the SPS impedance model

Probing Transverse Impedances in the High Frequency Range at the CERN SPS

The SPS transverse impedance model, which includes the major impedance contributions in the machine, can be benchmarked through measurements of the Head-Tail mode zero instability. Since the SPS works above transition energy, the head tail mode zero is unstable for negative values of chromaticity. The measured instability growth rate is proportional to the real part of the transverse impedance. Studies performed after the LHC Injectors Upgrade (LIU) showed a relevant impedance around 2 GHz with high-gamma transition optics (Q26). This paper presents the follow-up studies to probe the behavior of this beam coupling impedance contribution

Characterisation of Bunch-by-Bunch Tune Shift Effects in the CERN SPS

After the implementation of major upgrades as part of the LHC Injector Upgrade Project (LIU), the Super Proton Synchrotron (SPS) delivers high intensity bunch trains with 25 ns bunch spacing to the Large Hadron Collider (LHC) at CERN. These beams are exposed to several collective effects in the SPS, such as beam coupling impedance, space charge and electron cloud, leading to relatively large bunch-by-bunch coherent and incoherent tune shifts. Tune correction to the nominal values at injection is crucial to ensure beam stability and good beam transmission. During the beam commissioning of the SPS, measurements of the bunch-by-bunch coherent tune shifts have been conducted under different beam conditions, together with appropriate corrections of the average tunes at each injection. In this paper, we describe the methodology that has been developed to acquire bunch-by-bunch position data and to perform online computations of the coherent tune spectra of each bunch using refined Fourier transform analysis. The experimental data are compared to multiparticle tracking simulations using the SPS impedance model, in view of developing an accurate model for tune correction in the SPS

Electron Cloud Effects in the CERN Accelerators in Run 3

Several of the machines in the CERN accelerator complex, in particular the Large Hadron Collider (LHC) and the Super Proton Synchrotron (SPS), are prone to the build-up of electron clouds. Electron cloud effects are observed especially when the machines are operated with a 25 ns bunch spacing, which has routinely been used in the LHC since the start of its second operational run in 2015. After the completion of the LHC Injectors Upgrade program during the latest long shutdown period, the machines are currently operated with unprecedented bunch intensity and beam brightness. With the increase in bunch intensity, electron cloud effects have become one of the main performance limitations, as predicted by simulation studies. In this contribution we present the experimental observations of electron cloud effects since 2021 and discuss their implications for the future operation of the complex

Beam Performance with the LHC Injectors Upgrade

The LHC Injectors Upgrade (LIU) project was put in place between 2010 and 2021 to increase the intensity and brightness in the LHC injectors to match the challenging requirements of the High-Luminosity LHC (HL-LHC) project, while ensuring reliable operation of the injectors complex up to the end of the HL-LHC era (ca. 2040). During the 2019-2020 CERN accelerators shutdown, extensive hardware modifications were implemented in the entire LHC proton and ion injection chains, involving the new Linac4, the Proton Synchrotron Booster (PSB), the Proton Synchrotron (PS), the Super Proton Synchrotron (SPS) and the ion PS injectors, i.e. the Linac3 and the Low Energy Ion Ring (LEIR). Since 2021, beams have been recommissioned throughout the injectors’ chain and the beam parameters are being gradually ramped up to meet the LIU specifications using new beam dynamics solutions adapted to the upgraded accelerators. This paper focuses on the proton beams and describes the current state of the art