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Unidentified falling objects in the Large Hadron Collider : formation, charging mechanisms and dynamics… Belanger, Philippe 2020

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Unidentified Falling Objects in the Large Hadron Collider:Formation, Charging Mechanisms and Dynamics of Dust Particulates ina High Energy Proton AcceleratorbyPhilippe BelangerB. Eng., Polytechnique Montre´al, 2018a thesis submitted in partial fulfillmentof the requirements for the degree ofMaster of Scienceinthe faculty of graduate and postdoctoral studies(Physics)The University of British Columbia(Vancouver)September 2020c© Philippe Belanger, 2020The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the thesis entitled:Unidentified Falling Objects in the Large Hadron Collider:Formation, Charging Mechanisms and Dynamics of Dust Particulates in aHigh Energy Proton Acceleratorsubmitted by Philippe Belanger in partial fulfillment of the requirements for the degree ofMaster of Science in Physics.Examining Committee:Rick Baartman, TRIUMFCo-supervisorReiner Kruecken, Department of Physics & AstronomyCo-supervisorDaniel Wollmann, CERNAdditional ExamineriiAbstractMicrometer-sized dust particulates present in the LHC beam pipe are known to be causing alarge number of sporadic beam loss events all around the LHC, some of which are large enoughto provoke protection dumps or induce magnet quenches. These so-called Unidentified FallingObjects (UFOs) remain one of the important unknowns related to LHC operation after severalyears of high intensity beam operation in the LHC. In this thesis, the current understandingof the UFO problem is reviewed. The dynamics of charged dust particulates interacting withthe LHC proton beam is discussed based on observations, theoretical predictions and numericalsimulations. Using a reviewed version of the UFO model, it is found that the time profile ofproton losses from half of the observed events present a time asymmetry which can’t be explainedwith the current understanding of UFO dynamics. Furthermore, loss profiles recorded overmore than 4 years of LHC operation are analyzed. It is shown that UFOs must carry an initialnegative charge to explain the length of proton losses observed experimentally. Theoreticalconsiderations, originally developed for dust-in-plasma, are introduced to support this claim.Plausible release mechanisms of UFOs in the LHC are also discussed, and the energy requiredfor dust particulates to leave the walls of the beam chamber is presented. Finally, the theoreticalpossibility of having negatively charged dust particulates orbiting the proton beam of the LHCis discussed. It is found that stable orbits exist, but that only unstable orbits could result inimportant proton losses.iiiLay SummaryParticle accelerators around the globe provide important contributions to fundamental physicsresearch, medical technologies, aerospace technologies, safety systems and plenty of emergingtechnologies. The largest accelerator in the world, the Large Hadron Collider (LHC), suffersfrom the presence of micrometer-sized dust particulates entering the accelerated proton beam.These so-called Unidentified Falling Objects (UFOs) represent an important limitation for highenergy accelerators, causing particle losses and often bringing experiments to a halt in order toprotect the instruments and the infrastructure of the accelerator. In this thesis, the currentunderstanding of this phenomenon is discussed and experimental observations from several yearsof data collection are reviewed. Novel experimental methods and theoretical explanations forthe UFO problem are presented and discussed.ivPrefaceThis dissertation is an original intellectual work from the author, P. Belanger. Unless specifiedotherwise, all figures were made by the author. Intellectual property of previous authors isidentified throughout the text when needed. However, outside of published work, many ideasare the result of a collaboration from many experts. In particular, all members of CERN’sPerformance Evaluation Section in the Machine Protection and Electrical Integrity Group ofthe Technology Department (TE-MPE-PE) directly or indirectly contributed to this work.Chapter 1 The material is based on the author’s personal notes from introductory AcceleratorPhysics course and on previous authors, cited where applicable. The description of theelectric field is a portion of a note published on arXiv, titled: "Generalizing the Methodof Images for Complex Boundary Conditions: Application on the LHC Beam Screen", ofwhich P. Belanger is also the author [1].Chapter 2 The material is a literature review made by the author. The interpretation and thediscussion is an original work from the author. Material from previous authors is citedwhere applicable.Chapter 3 The material is based on private communications and literature review made by theauthor. Material from previous authors is cited where applicable. The numerical methodsproposed are an original work from the author.Chapter 4 The material is a literature review made by the author. Material from previousauthors is cited where applicable. The study of dust particulates in the Large HadronCollider based on dusty plasma considerations is discussed for the first time and is anoriginal work from the author. The calculation of the activation energy for dust particulatesto leave the beam screen is an original work from the author.Chapter 5 The material is based on one previous work on the subject. Material from previousauthors is cited where applicable. The validation of the model and the discussion is anoriginal work from the author. The study of orbiting dust particulates in the Large HadronCollider is an original work from the author.Chapter 6 The material is based on data collected by a large group of experts over severalyears. The analysis and the interpretation presented are an original work from the author.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1I The UFO Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Particle Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1 Elements of Beam Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Electron Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Beam Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 The UFO Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1 The UFO Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 UFO Observations and UFO Types . . . . . . . . . . . . . . . . . . . . . . . . 152.3 UFO Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4 Dust Sampling in the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Loss Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Proton-Nucleus Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Ionisation Chamber Beam Loss Monitors (ICBLMs) . . . . . . . . . . . . . . . 223.3 Diamond Beam Loss Monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . 24viTable of Contents4 Dust Particulates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1 Dust Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 Charging Mechanisms and Charging Models . . . . . . . . . . . . . . . . . . . 314.3 UFO Release Mechanism in the LHC . . . . . . . . . . . . . . . . . . . . . . . 345 UFO Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1 UFO Dynamics Simulation Tool . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Suggested Future Upgrades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.3 Orbiting UFOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48II UFO Time Profile Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596 Time Profile Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.1 Monte-Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.2 Measurement Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.3 UFO Time Profile: Skewed Gaussian Signal . . . . . . . . . . . . . . . . . . . 636.4 Skewness Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.5 UFO Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72A Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78A.1 Beam Electric Field (sec. 1.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . 78A.2 UFO Release Mechanism in the LHC (sec. 4.3) . . . . . . . . . . . . . . . . . 79viiList of Tables1.1 LHC design parameters and operational values from Run II . . . . . . . . . . . . . 81.2 Beam screen dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1 Naming conventions for ICBLMs in standard arc cells . . . . . . . . . . . . . . . . 244.1 Typical values for charged dust in cosmic and terrestrial plasmas . . . . . . . . . . 325.1 Best UFO Candidate Parameters for the 2018-09-30 22:47:52 UFO event . . . . . . 466.1 Input parameters for Monte-Carlo simulations. . . . . . . . . . . . . . . . . . . . . 61viiiList of Figures1.1 Curvilinear coordinate system used for particles in accelerators . . . . . . . . . . . 51.2 CERN’s accelerator complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 LHC arc cell layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4 LHC layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 Comparison of the free space Bassetti-Erskine E-field with the field from a chargedfilament . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.6 LHC Beam screen cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.7 Electric field of the beam in presence of the beam screen . . . . . . . . . . . . . . . 121.8 Electric field from an off-centered beam . . . . . . . . . . . . . . . . . . . . . . . . 132.1 Example trajectory for a falling dust particulate in the LHC . . . . . . . . . . . . . 152.2 Comparison of the loss signature for three UFO types . . . . . . . . . . . . . . . . 162.3 UFO rate observed in the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Dust samples collected in the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.1 ICBLMs mounting position in the LHC tunnel . . . . . . . . . . . . . . . . . . . . 223.2 ICBLM response in a standard arc cell . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 Schematic representation of the collimators in the LHC . . . . . . . . . . . . . . . 253.4 Bunch-by-bunch losses measured by dBLMs for 10 bunches . . . . . . . . . . . . . 253.5 Proof of principle of the UFO triangulation method using simulated losses . . . . . 274.1 The three stages of dust growth in plasmas . . . . . . . . . . . . . . . . . . . . . . 304.2 Range of the possible number of electrons carried by dust as a function of the dustradius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3 Comparison of the adhesive forces against the releasing forces for different chargingmechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.4 Energy required for a charged dust particulate to leave the beam screen . . . . . . 395.1 Angular distribution of electrons as they leave the UFO . . . . . . . . . . . . . . . 445.2 Comparison of the current model with FLUKA, average number of escaping electronsand energy spectrum of knock-on electrons . . . . . . . . . . . . . . . . . . . . . . 455.3 Comparison of a simulated UFO candidate with the ICBLM measurement for the2018-09-30 22:47:52 UFO event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.4 Comparison of the simulated turn-by-turn bunch losses with the 2018-09-30 22:47:52UFO event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.5 Quasi potential as a function of r . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51ixList of Figures5.6 Examples orbits of charged dust particulates around the LHC beam . . . . . . . . 525.7 Radial period for orbiting UFOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.8 Evolution of the instantaneous orbit parameters during one pass close to the beam 565.9 Example trajectory for a negatively charged dust particulate orbiting the LHC beam 575.10 Example of the evolution of the lifetime of a large dust particulate orbiting theLHC beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.11 Example beam losses for a negatively charged dust particulate orbiting the LHC beam 586.1 Distribution of arc UFOs along both beams for a regular arc cell during Run II . . 626.2 Typical UFO measurement from ICBLMs . . . . . . . . . . . . . . . . . . . . . . . 636.3 Histogram of the fitting parameters for validated UFO events from Run II . . . . . 656.4 Distribution of event lengths from Monte-Carlo simulations . . . . . . . . . . . . . 666.5 Example of measured UFO events with negative skewness and positive skewness . 666.6 Measured skewness and peak loss rate of UFO events . . . . . . . . . . . . . . . . 676.7 Distribution of rise times found in Monte-Carlo simulations and in measurements . 68A.1 Error on the electric potential for a cylindrical beam screen . . . . . . . . . . . . . 78A.2 Maximal error for an off-centered filament in a cylindrical beam screen . . . . . . . 78A.3 Escape velocity for a charged dust particulate to leave the beam screen . . . . . . 79xList of Symbolsα Shape parameterβ Ratio of v to cβx, βy Beta functions` Inelastic collision rate (proton losses)γ Lorentz factorγ1 Skewnessλ Linear charge densityλinel Mean free pathE Complex amplitude of the electric fieldH HamiltonianS Particulate stiffnessφp Surface potentialρ Densityσ Scale parameterσx, σy Beam size in the transverse planeθx, θy, θz Angles from the direction cosinesε EmittanceA Amplitude parametera AccelerationB Magnetic fieldc Speed of light in vacuumxiList of SymbolsDx, Dy Dispersion factorE Energy or Electric fieldh Specific angular momentumJ FluxK Kinetic energyL(T ) Practical rangeM Molar massm Massnd Volumetric density of dust particulatesNe Number of electronsne Volumetric density of electronsNp Number of protonsp MomentumQ UFO Chargeq ChargeQpp Average charge produced per passing protonR UFO Radiusr Positions Longitudinal position along the LHCt TimeTe Electrons temperatureTi ions temperatureTmax Maximum energy transferTmin Minimum energy transferV Electric potentialv VelocityW Work functionx, y, z Real space coordinatesxiiAcknowledgementsFirst and foremost, I wish to express my deepest gratitude to my mentor and CERN supervisor,Daniel Wollmann. I wouldn’t be working in this fascinating field today if it wasn’t for him.From the very first day I met him, his guidance has been the most precious and helpful elementin my professional development. He pushed me into incredibly challenging situations and guidedme along the way to ensure my success and professional growth. His dedication toward thesuccess of his students, regardless of the amount of work he has to put into it, is admirable. Forall of this, I am incredibly grateful.I want to extend my gratitude to Rick Baartman, my TRIUMF supervisor, who welcomed mein his team with the most inspiring curiosity for my project. I learned a lot from his experiencein the field, and his passion for physics, which is contagious. Countless discussions with Rickled me to new ideas and helped identify the hidden truths in a situation or a problem. Hiscontribution to this project is very much appreciated.I also wish to thank Rüdiger Schmidt, who was adamant about sharing his profound knowledgeof the LHC and the UFO problem, and guided me in my debut at CERN. His advice was alwaysthoughtful, enriching and guided me in developing a good collaborative spirit.Next, I wish to express my gratitude to my colleagues from TRIUMF and CERN with whom Ishared the pleasure of research and teamwork, as well as the hardship of it all. The countlessdiscussions were very insightful. Specifically, I want to sincerely thank my colleague and friendBjörn Lindström, who presented me with numerous brilliant ideas, debated every single oneof our unconventional propositions and guided me along the way. His input was vital to thesuccess of this work.In addition, I would like to express my gratitude to Oliver Kester, who brought me intoTRIUMF, taught me about accelerator physics, believed in me and gave me a very uniqueopportunity to accompany him to Fermilab.xiiiAcknowledgementsFurthermore, I would like to thank Reiner Kruecken, who agreed to supervise me and made thisproject possible. I am especially grateful for his trust and support.I would also like to thank Anton Lechner, for his essential contribution to this work from hisexpertise on nuclear physics and for his exceptional FLUKA simulations. The results of thisdissertation were made stronger by his input.Last but not least, I would like to extend my deepest gratitude to my family, who alwaysnourished my curiosity and supported me. They believed in me throughout this project, sharedmy passion for pursuing in this field and were incredibly understanding of all the sacrifices itrequired.xivIntroductionThe European Organization for Nuclear Research (CERN) is the largest particle and acceleratorphysics laboratory in the world. It has been the home of several Nobel Prize laureates alongthe years and led to important contributions to society, including the invention of the WorldWide Web. Between 1998 and 2008, CERN built the Large Hadron Collider (LHC), whichis the result of a worldwide scientific collaboration involving more than 10,000 people frommore than 70 countries. The LHC is a 27 km long hadron collider, where two beams of 1014protons (or sometimes positively ionized heavy ions) are accelerated to almost the speed oflight before being collided, at a nominal center of mass energy of 14 TeV. In 2008, as the firstprotons were circulating in the LHC, a major incident occurred, which required over 14 monthsof repairs and multiple magnet replacements. This event emphasized the importance of machineprotection systems, ensuring the safe extraction of the energy stored in the superconductingmagnet system and the safe extraction of the two beams in case of problems in one of the manysystems vital for the operation of the LHC. The constant monitoring of the LHC beam andof all the equipment around the LHC helps improve the machine and identify novel failurescenarios. Above all, it ensures the continuous operation of the LHC for particle collisions. Thisis essential for the four main experiments included in the LHC, which require collisions to pushthe frontier of high-energy physics.Since the start of its operation, the LHC has suffered from the presence of micrometer-sizeddust particulates entering the proton beam, leading to proton losses which can cause magnetquenches and impact the LHC availability. These so-called Unidentified Falling Objects (UFOs)remain one of the important unknowns related to LHC operation after several years of particlecollisions. Since 2009, falling dust particulates triggered the extraction of the LHC beams intothe beam dumps hundreds of times to limit proton losses in nearby equipment, and causeddozens of quenches in the superconducting magnets around the LHC. Over the years, morethan 30 publications discussed the impact of UFOs on the LHC availability and reported obser-vations of beam losses caused by UFOs in order to improve the understanding of this phenomenon.1IntroductionFor the forthcoming High Luminosity upgrade of the LHC (HL-LHC), in which Canada’sparticle accelerator center, TRIUMF, is involved with several in-kind contributions, the originof UFOs, their release mechanism and their dynamics need to be studied. The approach takenin the context of this dissertation is twofold. First, the theoretical aspects of the problem havebeen reviewed. This part can be divided into three subtopics: a thorough review of the currentunderstanding of the UFO phenomenon based on important observations, a first validation ofcritical sections of the current numerical and physical models used to simulate UFO eventsand the proposition of novel and original formation mechanisms to explain the presence ofdust particulates in the LHC. Second, the experimental observations of protons losses causedby falling dust particulates have been analyzed. For the first time, a systematic study of thetime profile of UFO losses, recorded by beam loss monitors, was done. This experimentalapproach can also be divided into three subtopics: the study of observations collected sincethe start of LHC operation, the development of new methods of analysis to study UFO lossesand the comparison of simulations with measurement to infer important conclusions about UFOs.In Chapter 1, the principles of particle accelerators are presented and the Large HadronCollider is introduced in more details. In addition, a novel numerical method to evaluate theelectric field of the LHC beam in presence of the surrounding beam screen is presented. InChapter 2, the UFO problem is discussed, the current understanding of the UFO phenomenonis stated, and general observations gathered in the past years are reviewed and discussed. InChapter 3, proton losses and the detectors used to measure them along the LHC ring arepresented. Furthermore, novel numerical methods making use of ultra fast (ns resolution)beam loss monitors are introduced. In Chapter 4, the formation, growth and ionization of dustparticulates in the vicinity of the LHC beam are discussed for the first time since the startof UFO studies. Several charging mechanisms are presented based on observations of cosmicdust and electron storage rings. In Chapter 5, the model used to describe UFO dynamics isreviewed and the simulation tool developed is validated against FLUKA [2], a particle transportsimulation tool widely used. In addition, the novel idea of negatively charged dust particulatesorbiting the LHC proton beam is discussed. Finally, in Chapter 6, the measured proton lossesfrom UFO events are analyzed and a comparison with simulations is presented. For the firsttime, the time profile of UFO losses is studied and used to better understand UFO dynamics.2PART IThe UFO Problem3CHAPTER 1Particle AcceleratorsA particle accelerator is a machine which uses electromagnetic fields to accelerate chargedparticles (protons, electrons, ions, etc.) to high energies and contain them in well-defined beams.These machines can be used for several applications. For example, the particles acceleratedby TRIUMF’s 520 MeV cyclotron (Canada’s national particle accelerator) are used to probenuclear structures, study proton irradiation, study proton therapy, produce rare isotope beamsand produce medical isotopes, critical for medical imaging. The largest and most powerfulaccelerator in the world is the result of an international collaboration regrouping more thantwenty countries. It is the Large Hadron Collider (LHC), found at CERN, the world’s largestparticle physics and accelerator physics laboratory. CERN’s accelerator complex regroupsthousands of scientists from around the world working on many different research projects.Its main objective is to push the frontiers of Science by studying the basic constituents ofmatter and answering fundamental questions in physics. In its first 10 years of operation, theLHC led to numerous groundbreaking discoveries in particle physics. Outside of fundamentalphysics, CERN also contributes to the development of emerging technologies, collaborates withindustries, engages with stakeholders brings nations together [3]. In this chapter, we introducesome key elements of beam dynamics, present the Large Hadron Collider in more detail anddiscuss the electric field of a beam of particles.1.1 Elements of Beam DynamicsParticles in modern accelerators are accelerated to relativistic energies, where the velocity isoften given as the ratio of v to c, the speed of light, and noted β = v/c. The Lorentz factorγ = 1√1−β2 appears in many relativistic equations as it describes both the time dilation andthe length contraction of spacetime. At relativistic speeds, the momentum and the energy of aparticle are:E =√p2c2 +m2c4 (Total energy)K = (γ − 1)mc2 (Kinetic energy)~p = γm~v (Relativistic momentum)(1.1)41.1. Elements of Beam Dynamicswherem is the rest mass of the particle. If the particle is charged, its motion in an electromagneticfield ~E, ~B, is governed by the Lorentz force:d~pdt= q(~E + ~v × ~B) (1.2)The Lorentz force is the fundamental tool used to design accelerator components, as it describeshow electromagnetic fields accelerate and guide charged particles. In circular accelerators like theLHC, the main components are the accelerating cavities, dipole magnets (which bend the beamalong a circular trajectory) and quadrupole magnets (which focus the particles to a well-definedbeam). These components are chosen to guide particles along a closed reference orbit describingthe trajectory of a theoretical reference particle. However, for a group of particles travelingtogether, small deviations around the closed orbit are unavoidable. This is taken into account inthe design of an accelerator, and the electromagnetic fields in all components are, furthermore,chosen to control this effect and confine the particles to small deviations about the referenceorbit. Some corrector magnets are also added to compensate for field errors and other highorder perturbations. To study any deviation from the closed orbit, it is useful to work with acurvilinear coordinate system following the reference particle, as shown in Fig. 1.1.Figure 1.1: Curvilinear coordinate system used for particles inaccelerators. ~r0(s) describes the reference orbit and xˆ, yˆ, zˆ formthe basis of the coordinate system following the reference particle. s isthe longitudinal position along the ring.In this so-called Frenet-Serret coordinate system, x and y quantify the deviation of anyparticle from the ideal reference orbit in the transverse plane. One can show that the equationsof motions of charged particles in an accelerator describe harmonic oscillations about the closedorbit. In order to study the dynamics of an ensemble of particles traveling together (a beamof particles), rather than individual particles, it is convenient to look at the region that theyoccupy in phase space. For a simple description of beam dynamics, it is generally assumed thatthe radial and axial motions (x and y) are independent and can be treated separately. Thearea occupied in the phase space by the particles is called the horizontal and vertical beamemittance, x and y. Under the influence of conservative forces, the particle density in phasespace (and therefore the emittance) stays constant. However, in presence of accelerating fields,the emittance varies with the particles’ momentum. This is due to the adiabatic damping, where51.2. The Large Hadron Colliderp11 = p22. For this reason, in systems where the beam energy is changing, it is common touse instead the truly invariant normalized emittance defined by:n = βγ (1.3)In practice, because of dissipating processes (synchrotron radiation, scattering, damping, etc.)even the normalized beam emittance is not exactly constant, which is why accelerators like theLHC constantly monitor the beam emittance.As mentioned previously, particles in the beam follow trajectories described by:xn(s) = σx cos(ψx(s) + δn) and yn(s) = σy cos(ψy(s) + δn) (1.4)where δn is an arbitrary phase constant for particle n, ψ is the betatron phase (ψi(s) =∫ s0dsβi(s))and σ is the beam size. The beam size in both directions σx(s) and σy(s) varies longitudinallyfollowing the betatron function βi(s) (i ∈ {x, y}), which is determined by exterior forces, mostlydue to the quadrupole magnets arrangement forming the accelerator. From there, one can seethat all particles stay within a precise region of space called the beam envelope and delimitedby the beam size. If we also consider the dispersion Di(s) in both directions, the beam size in xor y follows:σi(s) =√βi(s)nβγ+(Di(s) · ∆pp0)2(1.5)where ∆p/p0 is the momentum spread (∼ 10−4 for the LHC) of the particles in the beam. Thebeam size can also be used to describe the transverse charge density in the beam, ρ(x, y). If Npis the number of particles (protons in the case of the LHC) in the beam, we have:ρ(x, y) = Np2piσxσye−(x22σ2x+ y22σ2y)(1.6)1.2 The Large Hadron ColliderThe Large Hadron Collider (LHC) is the largest and most powerful particle accelerator in theworld. It is a 27 km circumference ring designed to accelerate two proton (or ions) beams up to7 TeV before forcing them into head-on collisions. The LHC depends on a chain of accelerators,shown in Fig. 1.2, which pre-accelerate the protons up to an energy of 450 GeV before beinginjected into the LHC. The proton source is a bottle of hydrogen gas, where hydrogen atomsare stripped of their electron. Protons are then successively accelerated by the Linac 2 (upto 50 MeV), followed by the Proton Synchrotron Booster (PSB, up to 1.4 GeV), the ProtonSynchrotron (PS, up to 26 GeV) and the Super Proton Synchrotron (SPS, up to 450 GeV).From there, protons are transferred into the two beam pipes of the LHC and accelerated totheir maximum energy of 7 TeV. Starting in 2021, Linac 4 will replace the first element of this61.2. The Large Hadron Colliderinjector chain. Negative hydrogen ions will be sent to the Proton Synchrotron Booster at anenergy of 160 MeV and the PSB will remove the excess electrons from the hydrogen ions beforeaccelerating the remaining protons and injecting them in the rest of the chain.Figure 1.2: CERN’s accelerator complex. © CERN (2019).The LHC is not a perfect circle, it is made of eight arcs and eight insertions, which consistof straight sections with dispersion suppressors at each end. The insertions are used for specifictasks: beam collisions for the four big experiments (ATLAS, ALICE, CMS and LHCb), beaminjection, beam cleaning, beam acceleration, beam diagnostics and beam dumping. The arcs onthe other hand, mainly guide and focus the beam along its circular trajectory. Each arc contains23 arc cells made of a regular structure shown in Fig. 1.3. The layout of the LHC is shownin Fig. 1.4. It is divided in eight sectors, a sector being defined as the part of the machinebetween two insertion points. The four big experiments, ATLAS (A Toroidal LHC ApparatuS),ALICE (A Large Ion Collider Experiment), CMS (the Compact Muon Solenoid) and LHCb(study of physics in B-meson decays at LHC) are respectively located at the insertion regions(IRs) 1, 2, 5 and 8. The two cleaning IRs, 3 and 7, contain the LHC collimation system, whichprotects the accelerator equipment against beam losses by removing protons from the beam halo.Finally, the beam dumping system (IR 6), is designed to extract the circulating beams fromeach ring and send them to an external dump block, located at the end of a 700 m long beamline. The dump block is a cylinder of graphite composite encased in a steel housing and concreteshielding blocks. It is the only element in the LHC able to withstand the impact of the full beam.71.2. The Large Hadron ColliderFigure 1.3: LHC arc cell comprising dipoles (MBA and MBB) andquadrupoles (MQ) along with some other multipole magnets. One arccell is 106.9 m long. © CERN (1999).Table 1.1: LHC design parameters [4] andoperational values from Run II [5].Parameter Nominal Value Operational ValueCircumference 26,659 m -Dipole operating temperature 1.9 K -Number of dipoles 1232 -Number of quadrupoles 858 -Peak magnetic dipole field 8.33 T 7.73 TNominal energy 7 TeV 6.5 TeVStored beam energy 360 MJ 320 MJDesign Luminosity 1034 cm−2s−1 0.5 - 2.1×1034 cm−2s−1Number of RF buckets 35640 -Number of bunches per beam 2808 2556Bunch spacing 25 ns 25 nsNumber of protons per bunch 1.15× 1011 1.2× 1011Number of turns per second 11245 -Figure 1.4: LHC layout showingthe 8 sectors separating the 8labeled insertion points.Protons in the LHC are bent by strong magnetic fields produced by superconductingelectromagnets. These are made of niobium-titanium coils operated at a temperature of 1.9 K.For this reason, the LHC tunnel houses the cryogenic ring beside the beam pipe, allowing for aconstant flow of liquid helium to cool the magnets. Moreover, the beam pipe also needs to bekept under ultrahigh vacuum to avoid collisions between the protons and gas molecules. Thevacuum system of the LHC is responsible for keeping a pressure of about 10−7 Pa in the beampipe and lower than 10−9 Pa close to the interaction points where the proton-proton collisionstake place.81.3. Electron CloudsProton Bunches in the LHCTo ensure that protons always see an accelerating voltage, the LHC beam is not continuous, butbunched into groups of ∼ 1.15× 1011 protons separated by 25 ns gaps. Each bunch is about1 ns long. In fact, the center of each bunch is a point of minimal energy (a stable point) whereprotons will naturally tend to go because of phase focusing. The RF system of the LHC leadsto the formation of 35,640 potential wells with this kind of stable point, called RF buckets.Each RF bucket is about 2.5 ns long. For LHC operation, protons are injected following agiven filling scheme (an arrangement of filled and unfilled buckets) which always ensure that allfilled buckets (proton bunches) are separated by at least 9 empty buckets, leading to the 25 nsbetween bunches. By design, up to 2808 buckets can be filled with protons.The bunched nature of the beam is important when studying beam losses. As will bediscussed later, some detectors are fast enough to measure the individual contribution of eachbunch, and others are too slow to resolve it. Likewise, some processes are influenced by thebunch-by-bunch interaction with the beam, like the electron cloud formation, whereas otherslow processes behave as if the beam was continuous, like dust particulates interacting with thebeam, also called Unidentified Falling Objects (UFOs).1.3 Electron CloudsIn the LHC and other accelerators, free electrons can be generated by ionization of the residualgas in the beam chamber, photoemission from the chamber’s wall and beam particle lossesimpinging on the chamber’s wall. Those free electrons can move significantly over short timescales (smaller than the bunch spacing) and are highly influenced by the bunched nature of thebeam. The electrons are accelerated toward the center of the beam chamber during the passageof a bunch, and drift freely during the gap between bunches. Electrons are therefore constantlybombarding the chamber’s walls which, depending on the secondary electron emission yield,can lead to an avalanche effect, increasing the number of free electrons in the beam pipe. Thismultiplication effect is called multipacting and is a key element in the formation of electronclouds. Electron cloud formation is an important research subject at CERN because of itsimpact on the beam and because of the heat load deposited on the chamber’s wall around thebeam [6]–[8].1.4 Beam Electric FieldTo study the interaction between a particle beam and any charged particle, an accuratedescription of the electric field is necessary. For a 2D Gaussian charge distribution like the LHCbeam, the electric field in the transverse plane follows the Bassetti-Erskine formula [9]. For an91.4. Beam Electric Fieldasymmetric beam with σx > σy, we have:~E = λ2ε0√2pi(σ2x − σ2y)(Im(E(x, y))xˆ+ Re(E(x, y))yˆ)(1.7)where λ = Npe/C is the linear charge density of the beam, Np is the total number of protons inthe beam, C is the circumference of the LHC and E is the complex amplitude of the field givenby:E = w(z2)− e(z21−z22)w(z1) (1.8)with z1 = (σy/σx)x+i(σx/σy)y√2(σ2x−σ2y) and z2 =x+iy√2(σ2x−σ2y). w(z) is the complex generalization of the errorfunction:w(z) = e−z2(1 + 2i√pi∫ z0ez′2dz′)(1.9)In a case where σx < σy, the coordinate transformation y → x and x→ −y can be used to findthe corresponding field. In presence of a round beam (σx = σy = σ), the field is purely radialand can be expressed following:Er(r) =λ2piε0r(1− e− r22σ2)(1.10)From (1.10), one can see that for r  σ, the field becomes identical to the one of an infinitelylong charged filament. One can also show (Fig. 1.5) that for positions a few sigmas away fromthe center, the beam can be approximated by a round one.(a) (b) (c)Figure 1.5: Comparison of (a) The free space Bassetti-Erskine E-field of a beam withσx = 335 µm, σy = 105 µm; (b) The free space Bassetti-Erskine E-field of a round beam withσx = σy = 335 µm; (c) The free space E-field of an infinite charged filament. (b) and (c)show the magnitude of the relative error vector (component by component) on the color barErr = |( ~Ebeam − ~Eapprox)/ ~Ebeam|. The level curve for an error of 1% is shown. Outside thisregion, the difference between all fields is negligible.101.4. Beam Electric FieldEffect of the Beam ScreenThe LHC beam is surrounded by a conductive beam screen, which changes the electric field dueto surface charges building up. A cross section of the beam screen is shown on Fig. 1.6.Figure 1.6: LHC Beam screen cross section [10]. Thedimensions are given in Table 1.2Table 1.2: Beam screen dimensionsSymbol Valuead 36.9 mmas 46.5 mmα 52.4◦β 37.6◦ri 25.0 mmre 26.5 mmtbs 1.00 mmIn electrostatics, Maxwell’s equations, and more precisely Poisson’s equation, have to besatisfied. The presence of a closed conductive surface around the proton beam of the LHCimposes a boundary condition: the electric potential has to be constant over the beam screen.This implies that the electric field around the beam has to be different than the free-spacefield. Typically, finite element methods are employed to numerically solve this boundary valueproblem and compute the total electric field in presence of the beam screen. In the context ofthis thesis, a novel numerical method was developed to solve this problem using a generalizationof the method of images. The method of images (or method of mirror images) is a mathematicaltool for solving differential equations, in which additional fictional charges are added outside ofthe physical boundaries of the problem to mimic the effect of a conductor. In 3D, adding anynumber of point charges doesn’t change the Laplacian inside the boundary. In 2D, the samecan be said about infinitely long charged filaments. The main advantage of this method comesfrom its simplicity and its computing efficiency. A complete description of the work done on thesubject was published online [1].The general idea is to find the exact solution to the problem of a discretized boundary, whichcan be arbitrarily close to the exact solution of the actual continuous boundary, with smallenough discretization steps. This approach takes advantage of the fact that the potential is asmooth function which does not vary significantly between neighbouring points. Let’s place Nimage charged filaments, distributed evenly along the polar angle θ, and located right outsidethe beam screen at a position k~rB(θ), where ~rB(θ) is the position of the beam screen in polarcoordinates. The constant k is a free parameter, which can be adjusted to ensure that thepotential over the whole beam screen is as uniform as possible depending on the discretization.111.4. Beam Electric FieldFor an infinite number of image filaments, k → 1 and for a few hundred image filaments, k isgenerally between 1.05 and 1.10. The position of the nth filament is ~rn and its linear chargedensity is λn. Because the boundary is far away from the center of the chamber in comparisonwith the beam size, the contribution from the beam is approximated to be the one of an infinitelylong charged filament of linear density λQ, located at ~rQ. Mathematically, the problem can bewritten as N equations, specifying the potential on the boundary directly under a given chargen. The nth equation is:−N∑i=1λi2piε0ln(|~rn/k − ~ri|) = λQ2piε0 ln(|~rn/k − ~rQ|) (1.11)Or, putting everything in matrix form, the N equations are:− 12piε0ln(|~r1/k − ~r1|) ln(|~r1/k − ~r2|) . . .ln(|~r2/k − ~r1|) ln(|~r2/k − ~r2|) . . ....... . . .λ1λ2... = λQ2piε0ln(|~r1/k − ~rQ|)ln(|~r2/k − ~rQ|)... (1.12)To validate this method, the problem of a cylindrical boundary, for which an analytic solutionexists, was considered. With only 200 image filaments, the maximum relative error for thepotential everywhere inside the boundary is below 10−4 for a beam located anywhere inside theboundary (see appendix A.1). Applying the method to the case of the LHC beam screen, theelectric field obtained is shown in Fig. 1.7.(a) (b)Figure 1.7: Comparison of (a) the total electric field around the beam in presence of thebeam screen (b) the free space Bassetti-Erskine E-field. The magnitude of the relative errorvector (free space field compared with the total field) is shown on the color bar of (b). Thelevel curves for errors of 1%, 5% and 10% are shown. Outside of those regions, the free spaceelectric field differs greatly from the total electric field and is no longer a good approximation.121.4. Beam Electric FieldThe method presented above applies equally well to the case of an off-centered beam, even withthe complex geometry of the LHC beam screen. The equipotential lines and the electric fieldfor the case of an off-centered beam are shown in Fig. 1.830 20 10 0 10 20 30x (mm)201001020y (mm)(a) (b)Figure 1.8: The case of an off-centered beam. (a) Equipotential lines, showing that thebeam screen is held at a constant potential. (b) Total electric field around the beam.13CHAPTER 2The UFO ProblemMicrometer-sized dust particulates present in the LHC beam pipe are believed to be the causeof sporadic beam loss events distributed all around the LHC. These so-called UnidentifiedFalling Objects (UFOs) have been present ever since high intensity beam operations began [11].Beam losses from UFO events are intense enough to trigger both beam dumps and magnetquenches [12], which significantly impact the beam availability in the LHC [13]. Historically,beam losses due to dust particulates have been observed in electron and antiproton storagerings, where positively ionized dust was trapped in the beam core due to Lorentz forces [14]–[16].More recently, samples of dust were also collected in the SuperKEKB electron-positron collider[17] to study beam-dust interactions as a hypothetical explanation for sudden pressure burstsobserved during the beam commissioning [18]. A knocker was even installed on the beam pipe ofSuperKEKB to trigger the release of dust particulates. In the LHC, dust-related limitations toregular beam operations were mitigated by appropriate countermeasures, but never completelyeliminated [19]. In this chapter, historical observations about UFOs in the LHC are presentedand the UFO hypothesis is introduced and discussed. Dust sampling experiments in the LHCare also presented.2.1 The UFO HypothesisThe prevailing hypothesis to explain the Gaussian-like beam loss events observed in the LHCis that macroscopic dust particulates with radii between 1 µm and 100 µm enter the beam,producing beam losses due to their interaction with the protons (see Ch. 3). Previous work onthe subject has shown consistency between the theoretical model and observations on severalaspects: comparable beam loss time profiles [20], comparable distribution of the beam loss peaksduring Run I [21] and consistency with dust contamination in the beam pipe [22]. Followingthis hypothesis, the sequence of events goes as follows:• A dust particulate falls from the beam screen toward the beam,• The dust particulate is ionized by elastic collisions with the proton beam,• The now positively charged dust particulate is repelled from the beam by its electric field.142.2. UFO Observations and UFO TypesFigure 2.1: Example trajectory for a falling dust particulate in the LHC.The particulate is ionized by the proton beam and is then repelledbecause of the electric field. The beam is represented by the red ellipsein the center of the beam chamber. The beam screen height is 36.9 mm.A typical UFO trajectory is depicted in Fig. 2.1. Previous studies generally assumed thatUFOs are neutral and fall from the beam screen due to gravity. This assumption will beaddressed multiple times in this thesis (Ch. 4,5,6). During the whole process, inelastic collisionsresult in particle showers recorded by the beam loss monitors of the LHC. Beam losses are themain observable related to UFOs and discussed in more detail in Ch. 3. In the past, somealternative hypotheses were considered to explain the observed beam losses: local impact ofprimary protons on the aperture of the arcs, local increase of the vacuum pressure leading tobeam-gas interactions and local increase of electron-cloud density leading to beam-electroninteractions. These alternative hypotheses were invalidated from simple considerations [23],leaving beam-dust interactions as the only plausible explanation for UFO observations.2.2 UFO Observations and UFO TypesThroughout LHC Run I (2009-2013) and Run II (2015-2018), UFOs were generally observedall around the LHC, with no clear triggering mechanism. However, three specific locationsshowed an increased UFO activity leading to recurrent beam dumps and significant impacton machine availability. Studies were carried out in each case to understand the problem andimplement workaround solutions. The characteristics of those localized and recurrent UFOtypes are discussed below, along with the standard UFO losses. Typical beam losses observedfor each case are shown in Fig. 2.2.152.2. UFO Observations and UFO Types.050100150.MKI.01020304050.ULO.0510152025.16L20.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0.0200400600.UFOTime (ms)Losses (mGy/s)Figure 2.2: Comparison of the loss signature for the three distinctiveUFO types (MKI, ULO, 16L2) observed during Run I and Run II alongwith losses from a regular UFO (bottom).Regular UFOs (UFO Type I)Regular UFOs, sometime called UFO type I, refer to most UFOs observed in the LHC andare the main experimental evidence around which the UFO hypothesis was based. Regularbeam losses (see bottom plot, Fig. 2.2) follow an asymmetric Gaussian profile which is believedto be a result of the convolution of the UFO trajectory with the beam profile, approximatedby a two-dimensional Gaussian. Typical losses span several orders of magnitude in amplitudewith peak values between 10−4 Gy/s and 3 Gy/s. With events lasting between 80 µs and fewms, the integrated dose for most regular UFOs is between 10−7 Gy and 10−3 Gy. The mainmitigation strategy applied to reduce the impact of regular UFOs was to increase the ICBLMthreshold (the tolerated beam losses) toward or above the magnet quench limit and to profitfrom the conditioning effect [24], discussed in the following section. A relocation of the beamloss monitors was also performed and allowed for better monitoring of UFOs, reducing thenumber of unnecessary beam dumps.The release mechanism of regular UFOs is still unknown after several years of operation, butimportant observations have been made. First, UFO losses are not correlated with perturbationsof the beam dynamics and appear sporadically throughout the whole LHC cycle. Once thebeam reaches a stable configuration at top energy, UFOs are often released after a few hours162.2. UFO Observations and UFO Typesof operation. Second, UFO losses have a high probability of lasting for less than 1 LHC turn,and the observation probability decreases for longer events. This could be due to the fact thatUFOs with small radii are more numerous than UFOs with large radii, which is consistentwith dust sampling results (see section 2.4) and observed dose distribution during Run 1 [12].Third, UFOs originate from various positions across standard arc cells. Some UFOs appear tobe located close to the magnet interconnections and some appear to be located inside dipolemagnets [23]. Fourth, the UFO rate appears to be dependent on the bunch spacing (higherfor 25 ns spacing than with 50 ns spacing) [23], but is not correlated with the density of theelectron clouds [12] or the spatial distribution of heat load measured on the cryogenic system[25]. Finally, a correlation of the UFO rate on the beam intensity was observed, both in Run I[24] and Run II [25]. The UFO rate increases as the beam intensity increases.Injection Kicker Magnet (MKI) UFOsUFOs at the injection kicker magnets (MKIs) had an important impact on machine availabilityin 2010, causing 21 beam dumps. Unlike standard UFOs, which tend to happen after a fewhours of stable beam, MKI UFOs typically occurred within 30 minutes after the last injection[23]. The time profile of MKI UFOs is very similar to what is observed all around the LHCfor standard UFOs. They last for 80 µs to 2 ms and follow an asymmetric Gaussian profile,as shown in the first plot of Fig. 2.2. Two dedicated experiments (machine developmentexperiments, or MDs) were carried out in 2011 and 2012 to study the release mechanism ofMKI UFOs [26], [27]. A clear correlation between pulsing the MKIs and the occurrence of MKIUFOs was found. Following this observation, improvement on the UFOs detection system wasimplemented. During normal beam injection, MKI UFOs were shown to occur only 2 ms afterinjection. Since this delay is too short to be explained by gravity alone, it was suggested thatAl2O3 particulates from the ceramic tube of the MKIs were charged by electron clouds andreleased due to vibrations or by the electric field of the MKI pulse [23]. This is consistent withthe dust inspection done on one MKI, removed from IR2 in 2010, where more than 5 millionAl2O3 particulates were found, with radii up to 100 µm.With FLUKA simulations, it was shown that the UFOs had to be located in the MKIs in orderto explain the observed loss pattern in the beam loss monitors surrounding the MKIs [23]. Basedon the measured rate of inelastic collisions, it was also calculated that the Al2O3 particulatesize required to explain MKI UFO events was around 30 µm [28]. To mitigate the problem,new cleaning procedures of the MKI magnets were implemented and screening conductors wereadded to the MKIs to reduce the electric field on the ceramic parts during the MKI pulse [23].The detection threshold was also changed, which reduced the number of UFOs leading to abeam dump.172.3. UFO ConditioningUnidentified Lying Object (ULO)In 2015, a high UFO activity was observed in the half-cell 15R8, leading to 14 beam dumps.Aperture measurements [29] revealed the presence of an object, so-called unidentified lyingobject (ULO), at the bottom of the beam pipe. It became apparent that the interaction of thisobject with the beam triggered UFOs. To mitigate the problem, a local orbit bump (horizontallyand vertically) was implemented to bypass the ULO, which reduced the UFO rate in 15R8 andsolved the problem. In 2019, the ULO was removed and identified as a strip of plastic originatingfrom the beam pipe wrapping and introduced during the installation [30]. As can be seen on thesecond plot of Fig. 2.2, the losses from most ULO events show a clear oscillation with a periodof about 1 LHC turn (each bin is 40 µs long). A Fourier transform on the signal confirmedthe presence of oscillations with a frequency of 11245.75 Hz, which is the LHC frequency. Thisoscillating component is due to the fact that most ULO events were recorded with only a fewbunches circulating in the LHC, leading to high losses at the start of each turn, followed by along gap with no losses.UFO Type II (16L2)In 2017, a new type of UFO-like beam loss located near the 16L2 half-cell quadrupole led to 68beam dumps amongst the 75 beam dumps caused by beam losses at high energy during thatyear [31]. Because of the significant impact on LHC operations, several studies were carried outto better understand these losses. The typical signal for 16L2 events starts with a UFO-likespike followed by a fast loss rise (see third plot of Fig. 2.2). Generally, the beam dumps weretriggered by ICBLMs in the betatron collimation region, where the losses increased continuouslyover several milliseconds. In-depth analysis of the losses revealed that the initial UFO-like spikewas due to all bunches interacting with solid matter, while the following beam losses were causedby transverse beam instabilities [32]. The probable cause for the losses observed in 16L2 was thepresence of solid nitrogen, oxygen and water in the surrounding vacuum chamber, introducedby an accidental air inflow [31]. It is believed that solid particulates of the contaminants weresubject to a phase transition to the gas phase following their interaction with the beam [31]–[33].Since a correlation with electron clouds was observed, the recurring beam dumps in 16L2 weremitigated by installing a solenoid around the 16L2 interconnect to decrease electron multipacting.The frozen gas will be removed from the beam pipe before the start of Run III, during the longshutdown.2.3 UFO ConditioningAs highlighted by several studies [19], [24], [30], the UFO rate in the LHC follows a clearreduction over time during normal operation, referred to as the UFO conditioning. This effect isvisible in Fig. 2.3 (taken from [25]), where the UFO rate in stable beam is plotted over 5 years.The predominant bunch spacing is shown on the top axis. Throughout 2011 and 2012 (Run I),182.3. UFO Conditioninga decrease in the UFO rate by a factor 5 was observed [24]. A similar reduction was observedfor Run II, between 2015 and 2018, where the UFO rate decreased by almost two orders ofmagnitude. However, this effect is compensated by a deconditioning effect observed wheneverthe cold parts of the LHC are warmed up or when the beam vacuum is opened. During thewinter technical stop of 2011-2012, the UFO rate increased by a factor 2.5. Similarly, during thelong shutdown before the start of Run II, the UFO rate increased by a factor 10 and the UFOrate observed at the end of Run 1 was only recovered after 1.5-2 years of conditioning [30].Figure 2.3: UFO rate measured in standard arc cells in stable beambetween 2012 and 2018, from A. Lechner [25]. Only fills with morethan 1 hour in stable beam and more than 100 bunches per beam areconsidered. Only ICBLM common to Run I and Run II are consideredwith different detection thresholds used for different beam energies.The bunch spacing is indicated on the top axis, and the beam intensityfor each fill is shown by the red dots.Moreover, whereas the distribution of UFOs in the eight sectors of the LHC has been almostconstant over the years, local increased UFO rates have been linked to recently exchangedmagnets. In 2015, this was observed for at least 5 magnets. A similar effect was observed in 2017with one specific magnet in sector S12 [25]. In addition to these observations, when one MKIwas exchanged in July 2011 with special cleaning procedures and additional screen conductorsto reduce the electric field during the pulse, the UFO rate observed was significantly decreasedcompared with other MKIs [24]. All together, these observations indicate that the handlingand cleaning procedures of accelerator equipment has an important effect on the local UFOrate. Hence, combined with the observations mentioned above, it is generally believed that dustparticulates are introduced in the beam pipe of the accelerator when warming up, handling oropening parts of the LHC. The conditioning effect is not yet understood, but is self-consistentwith the previous statement if UFOs are assumed to only interact a finite number of times withthe beam, leading to a decrease of the UFO rate over time. As will be shown in Ch. 4, dust192.4. Dust Sampling in the LHCparticulates require a significant amount of energy in order to be picked up from the bottomof the beam screen, but can spontaneously fall from the top of the beam screen. This simpleconsideration could be responsible for the conditioning effect and requires to be further studied.2.4 Dust Sampling in the LHCStudies have been carried out to inspect the dust present in the beam pipe of the LHC [22], [23],[34]. As mentioned above, in 2010, one MKI was removed and the ceramic tube was flushedwith N2 to extract dust particulates with a filter. Al2O3 particulates were found, with radii upto 100 µm [23]. Images of the collected dust are shown in Fig. 2.4. In 2016, a dipole magnetwas removed, allowing for dust samples to be collected [22]. Using X-ray spectroscopy, metallicelements were found (Ca, Ti, Au, In, Al, Si, Ag, Fe) along with oxygen, suggesting the presenceof ceramic compounds. The particulate radii ranged from 1 µm to 200 µm. Small particles werepredominant, with more than 90% of them having a radius smaller than 5 µm. Excluding theseparticles, more than 50% of the dust still had a radius smaller than 30 µm.(a) (b)Figure 2.4: Dust samples collected from the ceramic tube of an MKI,taken from [23]. (b) shows an enlarged view of a Al2O3 particulatewith a radius of about 5 µm.20CHAPTER 3Loss MeasurementsIn particle colliders, particles from the stored beam are unavoidably lost over time. In the LHC,these so-called beam losses can be caused by collisions with residual gas in the vacuum chamber,proton-proton collisions at the interaction points, beam halo cleaning at the collimators andaccidental events like equipment malfunctions or UFO events [28]. If not properly controlled,small beam losses can lead to increased heat load in the cryogenic system, long-term radiationdamage and aging of equipment components. The main problem, however, is equipment damageand magnet quenches from large instantaneous losses. The LHC collimators are intendedto protect the accelerator against such events and clean the tails of the beam which getpopulated by beam disturbances all around the ring, long-range beam-beam effects, electroncloud effects and space charge effects. When studying the UFO problem, beam losses are themain experimental evidence available. Since it is not possible to make direct measurements(optically or electromagnetically) on the dust present in the beam pipe during regular LHCoperation, the beam acts as a probe and the losses coming from beam-dust interactions are usedto infer information about the dynamics and the nature of the dust particulate interacting withthe beam. In this chapter, the beam loss monitors used in the LHC are presented and theirapplication for the study of UFOs is discussed.3.1 Proton-Nucleus InteractionsWhen high energy protons hit a solid dust particulate, they have a certain probability to collidewith nuclei of the atoms forming the particulate. If the interaction is elastic, protons are slightlydeviated from their initial trajectory and populate the tails of the beam [35], participating in theformation of the beam halo. Protons located outside of the aperture restriction formed by theprimary collimators in IR7 remain in the beam halo until colliding with the collimators, whichcan take up to 20 turns. On the other hand, if the interaction is inelastic, new particles areproduced and trigger particle showers which are absorbed in the surrounding vacuum chamberand accelerator equipment [36]. The energy deposited by these particle showers needs to bemonitored, as it can cause significant damage. The probability of a proton-nucleus inelasticcollision is quantified by the microscopic cross section σinel. For a macroscopic particulate, the213.2. Ionisation Chamber Beam Loss Monitors (ICBLMs)macroscopic cross section Σinel has to be considered:Σinel =1λinel= Nσinel (3.1)where N is the atomic density of the particulate (N = NAρM , with the molar mass M) andλinel is the mean free path, which describes the average distance travelled by a proton betweentwo successive collisions. The probability density dp(s) that a proton interacts with a nucleusbetween a penetration s and s+ ds follows:dp(s) = 1λinele−s/λinel ds (3.2)3.2 Ionisation Chamber Beam Loss Monitors (ICBLMs)The Ionisation Chamber Beam Loss Monitors (ICBLMs) of the LHC are the main loss monitoringdevices used all around the ring. About 4000 ICBLMs are installed close to LHC magnets,collimators and other sensitive equipment along the LHC beam pipe. They are made of a 50 cmlong cylindrical chamber with a diameter of 9 cm and filled with N2 gas at a pressure of 1.1 bar[37]. Inside the chamber, 61 circular aluminum electrodes are placed with a potential of 1.5kV applied to every second electrode. When particle showers enter the chamber, the energydeposited ionises the gas and creates electrons and ions, which are collected by the electrodes.The charge collected is measured to get the radiation dose (Gy) deposited in the chamber. Thecollection time takes about 300 ns for the electrons and 80 µs for the ions, which is similar tothe duration of one LHC turn. The position of ICBLMs in the transverse plane is shown inFig. 3.1.Figure 3.1: ICBLMs mounting position in the LHC tunnel. Aroundthe ring, ICBLMs are located on the inner or outer side of quadrupolemagnets or above the interconnect between dipole magnets.223.2. Ionisation Chamber Beam Loss Monitors (ICBLMs)For predictions on the expected losses due to different scenarios and for the design of futureaccelerators, particle shower simulations are commonly used. Apart from Geant4 (used for largedetectors) the main tool used at CERN for accelerator studies is FLUKA, a Monte-Carlo codewhich allows simulating hadron-nucleon, hadron-nucleus, and nucleus-nucleus interactions up tocosmic ray energies [28]. It is based on a combination of microscopic interaction and transportmodels which allow computing the development of particle showers across accelerator equipment.A. Lechner [28] present an extensive validation study of the capabilities of FLUKA and how itcan be used to simulate multiple loss scenarios, including UFO events.UFO BusterThe amount of data generated by the thousands of ICBLMs around the LHC ring is too massiveto be continuously recorded with the highest time resolution. To study UFO losses, a dedicatedtool (the UFO Buster) is used to identify possible UFO events in real time and trigger therecording of ICBLM signals with an 80 µs resolution. The beam parameters at the time of theevent are also recorded, as well as the maximum losses from every ICBLM, integrated over 12different time intervals (between 40 µs and 83.8 s). Sec. 6 presents a study of the data collectedin the UFO Buster database. The spatial distribution of ICBLMs around the LHC is highlyrelevant for UFO studies, as it can be used to estimate the location of the source of particleshowers along an arc cell. This is made possible by the coverage of the whole arc cell by acombination of multiple ICBLMs, as shown in Fig. 3.2. The first vertical BLM (red) covers thefirst dipole magnet and the upstream short section, the second vertical BLM (green) covers thecentral dipole and the lateral BLM (blue) covers the interconnect of the dipole and quadrupolemagnets. The last BLM (orange) after the quadrupole-dipole interconnect is redundant [38].For a given UFO location, particle showers enter the downstream ICBLMs and the uniquecombination of ICBLM responses, i.e. dose per inelastic collision, leads to a unique combinationof peak losses measured on these monitors. By comparing the losses measured on severalICBLMs, it is therefore possible to estimate the position of the UFO event within the arc cell.This method was shown to give accurate estimations with an uncertainty of less than a meter[28], [30]. It can be applied to any UFO Buster event, but every event has to be analyzedseparately and the process is time consuming. Once the position of a UFO event is known, thedose measured by any neighbouring ICBLM can be converted back to a proton-nucleus inelasticcollision rate, which can be compared with simulations from the UFO Dynamics SimulationTool (see Ch. 5) to infer information about the UFO parameters and its dynamics.233.3. Diamond Beam Loss MonitorsTable 3.1: Naming conventions for ICBLMs in standard arc cells [38]. xxyz indicatesthe location of the half-cell around the LHC (e.g.: 15R8, 16L2, etc.)ICBLM Family Beam 1 Beam 2Upstream of MQ BLMQI.xxyz.B1I10_MQ BLMQI.xxyz.B2E10_MQDownstream of MQ BLMQI.xxyz.B1I30_MQ BLMQI.xxyz.B2E30_MQAbove MB-MB interconnect BLMBI.xxyz.B0C10_MBA_MBBBLMBI.xxyz.B0C20_MBA_MBBFigure 3.2: ICBLM dose per inelastic interaction for a solid particulate located at agiven position in an arc cell for Beam 1, computed using FLUKA [38]. The beamdirection is from the left to the right.3.3 Diamond Beam Loss MonitorsTo study the fine time structure of beam losses, faster loss monitoring devices are needed, asICBLMs have a time resolution comparable to the duration of one LHC turn due to the ionscollection time and the electronics. Diamond Beam Loss Monitors (dBLMs) are made of a singleor polycrystalline diamond placed between two electrodes. Particle showers passing through thecrystal create charges which can be rapidly collected by the electrodes. The integrated currentcreated is proportional to the charge collected in the diamonds, which makes this device idealfor measuring beam losses with a fast time resolution. However, due to their size (1 cm× 1 cm),dBLMs offer only a small acceptance angle for the incoming particle showers. In the LHC,dBLMs are installed behind the primary collimators (TCPs) in the betatron collimation regionand monitor secondary particles leaving the collimators, as shown in Fig. 3.3.The FPGA used to sample the signal from dBLMs allows for a time resolution of 1.6 ns,which is fast enough to distinguish losses due to individual bunches of the beam. In Fig. 3.4,the losses from ten different bunches (along the horizontal axis) are shown for several LHCturns (along the vertical axis) to demonstrate that individual bunches can be distinguished indBLM signals. During LHC operation, the recording of dBLMs is triggered either by a beamdump or by a separate real-time UFO detection algorithm, which is independent from the UFO243.3. Diamond Beam Loss MonitorsFigure 3.3: Schematic representation of the collimators in the LHC(adapted from [39]). The dBLM are located behind the primarycollimators and measure secondary particle showers. The beam halo iscleaned by the collimators to protect the accelerator equipment (MBand MQ) downstream.Buster. In 2017, one dBLM per beam was installed around the 16L2 interconnect to monitor16L2 losses and is the only dBLM providing local losses. The dBLMs at the collimators offerthe advantage of being able to monitor every UFO event around the ring, from the elasticallyscattered protons remaining in the halo of the beam. However, the background losses are higherand the tracking of protons between a UFO location and the collimators adds more uncertaintyto the measurements (multiturn effects, phase advance, etc.).Figure 3.4: Bunch-by-bunch losses measured by dBLMs for 10 bunches.The measured signal is shown over 80 ns windows for each bunch(horizontal axis) on a turn-by-turn basis (vertical axis). Bunches inbuckets 4501 and 17851 have a vertically blown-up emittance and startinteracting with the wire scanner (red line) a few turns before the otherbunches.253.3. Diamond Beam Loss MonitorsIn 2017, an experiment was carried out to validate the bunch-by-bunch losses measuredby dBLMs when solid matter interacts with the beam [40]. A 30 µm carbon wire (the LHCwire scanner) was passed through the beam with some bunches having an increased emittance,horizontally or vertically. It was found that the plane of movement of the wire could easily beidentified by looking at the bunches with blown-up emittance. Fig. 3.4 shows an example ofthe time evolution of the losses for 10 individual bunches and shows that the signal is observedseveral turns earlier for the two bunches with a vertically blown-up emittance when the wiretravels through the beam vertically.Numerical Methods for Bunch-by-Bunch Loss AnalysisIn the context of this thesis, new methods making use of the different bunch parameters weredeveloped to analyze dBLM measurements in UFO studies. The fundamental assumption forthese methods to be valid is that the losses `i for a given bunch i interacting with a UFO locatedat (x, y) from the beam center follow:`i =A ·Ni2piσxiσyie−(x22σ2xi+ y22σ2yi)(3.3)where A is an arbitrary calibration constant (in practice, the ICBLM dose per inelastic collision),Ni is the intensity of a given bunch and σxi , σyi are the bunch sizes in both directions. In theLHC, the beam parameters are monitored on a bunch-by-bunch basis, which allows makingestimations of the losses for each bunch based on this equation. The methods mentioned abovewere validated using simulated bunch-by-bunch losses (see Ch. 5), but could not be successfullyused on measurements. This is believed to be due to either noise on the bunch parameters, orbecause of the unavoidable multiturn losses collected by the TCP dBLMs, making the lossesdiffer from Eq. (3.3). To successfully apply those methods on measurements, local dBLMs wouldensure that the uncertainty is minimized and that the losses for every bunch follows Eq. (3.3).UFO TriangulationCombining losses from a pair of bunches, it is possible to get rid of the calibration factor bytaking the ratio `2/`1. Because of the 25 ns bunch spacing, which is much smaller than thetimescale over which UFOs move significantly, it can be assumed that the position of the UFOdoes not change between the interaction with two consecutive bunches. In that case, one cansolve for the position (x, y) by taking the ratio `2/`1. One can write:2 ln[`2`1N1N2σx2σy2σx1σy1]=(σ2x2 − σ2x1σ2x1σ2x2)x2 +(σ2y2 − σ2y1σ2y1σ2y2)y2 (3.4)which either describes an ellipse (if σ2x2 − σ2x1 and σ2y2 − σ2y1 are of the same sign) or a hyperbola(if one of σ2x2 − σ2x1 or σ2y2 − σ2y1 is negative) corresponding to the possible location of the UFO263.3. Diamond Beam Loss Monitorsin real space. If two distinct pairs of bunch losses are considered, which requires a minimum ofthree bunches, the crossing point of the conic curves obtained gives the average UFO positionduring the interaction with the bunches. Since the UFO trajectory in real space has to becontinuous, one can expect all the conic curves from every successive pair of bunches to becontinuously evolving from one to another. Fig. 3.5 shows a 2D histogram obtained from thecollection of all conic curves from a simulated trajectory. The density of points is very highalong the actual UFO trajectory, and can be seen as a position probability density. As one canexpect, the position probability density is symmetric in all quadrants because of the squaredposition coordinates in Eq. (3.4). If some bunches are off-centered, it is possible to lift thatsymmetry and identify in which quadrant the UFO is moving.(a) Probability density in real space. (b) Enlarged first quadrant.Figure 3.5: Proof of principle of the UFO triangulation method usingsimulated losses. This 2D histogram is obtained from the collection ofall the conic curves for successive pairs of bunches, given by Eq. (3.4).The dashed lines show the distance from the center of the beam (redellipse) in multiples of σ. The UFO trajectory is highlighted by its highposition probability density. The gaps in the filling pattern considered(half-full beam) are also visible.UFO Angular Position EstimateOne generally expects to see a correlation between the bunch sizes and the UFO bunch-by-bunchlosses. For a UFO located at a given angular position, the correlation coefficient between thebunch losses and the bunch sizes should be maximal when the bunch sizes are measured alongthe corresponding angle. Mathematically, the general expression for a two-dimensional Gaussiandistribution in a reference frame (xθ, yθ), rotated clockwise by an angle θ compared to the bunch273.3. Diamond Beam Loss Monitorsreference frame, follows exp(− [ax2θ + 2bxθyθ + cy2θ]) with:a = cos2(θ)2σ2x+ sin2(θ)2σ2y, b = sin(2θ)4σ2x− sin(2θ)4σ2y, c = sin2(θ)2σ2x+ cos2(θ)2σ2y(3.5)Hence, for a UFO interacting with a bunch from an angular position θ, one can set xθ = r,yθ = 0 to find that the losses follow:`i(r, θ) =A ·Ni2piσxiσyie−(r22σ2θi)with σθi =σxiσyi√σ2xi sin2(θ) + σ2yi cos2(θ)(3.6)where σθi is the bunch size measured along the angle θ. Assuming that the angular positiondoes not change significantly during the interaction with several consecutive bunches, we findthat the losses should, indeed, be correlated with the bunch size measured along the correctangle. One can write:ln[`i(r, θ)(2piσxiσyi)Ni]= −(r22)1σ2θi+ ln(A) (3.7)The implementation of this method requires two steps. First, the angular position has to beidentified by finding the angle along which the correlation coefficient between Y (the left-handside of Eq. (3.7)) and X = 1/σ2θi is maximized. Then, the radial position of the UFO can beobtained by fitting Eq. (3.7) to the same set of data, Y and X, where the slope corresponds to−r2/2.In this method, the calibration constant appears as a simple nuisance parameter which doesnot influence the result of the fit of Eq. (3.7). Moreover, this method implicitly lessen the impactof systematic uncertainties on the measurements of the bunch parameters, since the angle isestimated by maximizing the correlation coefficient and is not obtained from a direct calculationbased on the bunch parameters. The estimation of the radial position from the fit, however, issensitive to those systematic uncertainties. This method has not been applied to measurementsyet but should be considered for future work.28CHAPTER 4Dust ParticulatesOutside of the LHC, dust particulates made of fine grains of solid matter have been thesubject of numerous research projects in the past years because of their impact on high vacuumenvironments, formation of planet surfaces [41]–[43], cosmic plasmas [44], [45], laboratory plasmasand microelectronic industry. Cosmic dust shares many similarities with dust in the LHC (highvacuum, near-zero temperatures, impinging photons and electrons, etc.) and their propertiescan be enlightening to better understand the UFO problem. When multiple neighbouringcharged dust particulates interact at close range in a plasma, they can form stable structures,called Coulomb crystals [46] and lead to so-called dusty plasmas. On the contrary, when dustparticulates are isolated, the system is referred to as dust-in-plasma [44]. While it is normallypossible to make direct measurement of the composition and the charge of dust in the scenariosmentioned above, the case of the LHC is different since the usual methods employed (i.e., directillumination or electromagnetic trapping) are hardly practicable without disturbing the LHCbeam. In this chapter, the properties of dust particulates in the LHC before their interactionwith the proton beam are discussed. Several hypotheses for the formation, charging and releasemechanisms of dust in the LHC are discussed based on the literature. In particular, the roleof electron clouds in the charging mechanism is discussed and the attractive forces with theconductive beam screen are studied.4.1 Dust FormationBefore addressing dust growth in high vacuum environments, an important statement from Ch. 2has to be restated. Based on the UFO conditionning, dust sampling and other UFO observations,it is generally believed that the dust particulates responsible for UFOs are introduced in thebeam pipe of the accelerator and remain trapped in the LHC until their interaction with thebeam. However, the conditioning effect is not yet understood, as trapped dust particulatescould potentially interact with the beam more than once, without necessarily being destroyedfollowing an interaction. Instead, if dust particulates are grown in the LHC, the conditionningeffect could be explained by a diminution of the available free radicals on the surface of the beamscreen over time. A similar effect is already well known in electron clouds studies concerning the294.1. Dust Formationreduction of the secondary electron yield of the inner surface of the beam screen over time [47].Formation and Growth of Dust in a PlasmaStudies on dusty plasmas [48], [49] have shown that dust can be grown inside plasmas whenatoms or molecules from any surface close to the plasma are sputtered away. The process goesthrough three steps [50], represented on Fig. 4.1.Nucleation consists of a series of chemical reactions where parent species (e.g.: copper atomsejected from the beam screen, alumine molecules from a ceramic part, etc.) are transformedinto small clusters of about 2 nm in size.Coagulation takes place when enough primary clusters are formed. Several of them can collideto form a larger particulate. The resulting arrangement grows rapidly in size to about 50nm.Surface growth is the last step, where plasma radicals begin to stick to the existing particulate,which behaves as a small substrate. This continues until the particulate reaches a fewmicrons in size.Nucleation Coagulation Surface Growth~ 0.2 nm ~ 2 nm ~ 50 nm ~ 1 µmFigure 4.1: The three stages of dust growth in plasmas. Reproducedfrom [50].It is noteworthy that coagulation and surface growth can be accelerated by a bipolar distributionof grain charges, where large grains (radius R ∼ 0.1 µm) are charged negatively and verysmall grains (R ∼ 1 nm) are charged positively, which has been observed in cold plasmas(kBTe of a few eV, like electron clouds in the LHC) [49]. This difference in polarity comesfrom the fact that the secondary electron emission yield increases sharply for grain sizescomparable to the penetration depth of primary electrons [44]. As will be seen in the followingsection, for low-temperature plasmas, the resulting dust (in the micrometer range) generallyacquires a negative charge, as secondary electron emission is negligible for these large particulates.The growing process generally takes place over several minutes in order to reach micrometer-sized dust particulates. With several hours of operation every day during normal operation, it304.2. Charging Mechanisms and Charging Modelsis not impossible that the LHC offers favourable conditions for the growth of dust particulates.With such a phenomenon taking place, the UFO conditioning could be explained by the surfacetreatment of the beam screen over time, reducing the number of radicals available for theformation of dust.4.2 Charging Mechanisms and Charging ModelsEven if direct measurement of the charge carried by dust in the LHC is not possible, otherenvironments with similar conditions have been studied thoroughly in recent years. Mendis[44] gives an overview of typical values found in cosmic and terrestrial plasmas (Table 4.1),where multiple charging mechanisms can be at play simultaneously. This is consistent withother observations, reported by Piel [45], stating that dust grains generally obtain large negativesurface charges of 1,000e-10,000e for particles in the 1-10 µm range. For dust to acquire a netcharge, electrons must be transferred between the dust and its surroundings. This can happenvia several mechanisms:1. Induction from conductive surface2. Triboelectrification3. Electron collection from ambient electron clouds or plasma4. Secondary electron emission5. Photoelectron emission6. Thermoionic emissionAside from thermionic emission (negligible at low temperature), all these charging mechanismscould take place in the LHC. The proximity of dust with the conductive beam screen canlead to a negative induced charge because of the beam’s electric field. The electron cloudsand synchrotron radiation, present all around the ring, could lead to electron collection andphotoelectron emission, respectively, as well as secondary electron emission. Lastly, it is notexcluded that triboelectrification could take place if dust migrates on the beam screen surfacebecause of mechanical vibrations. A more detailed description of these charging mechanism ispresented below.314.2. Charging Mechanisms and Charging ModelsTable 4.1: Typical values for charged dust in cosmic and terrestrialplasmas, taken from Mendis [44]. ne is the plasma charge density, kbT isthe plasma energy, nd is the volumetric density of dust particulates, R istheir radius, Q/e is their charge-to-mass ratio and the last column is anexample of the calculated charge-to-mass ratio for carbon particulates.Environment ne (cm−3) kBT (eV) nd (cm−3) R (µm) Q/e Carbon Q/m (C/kg)Saturn’s E-ring 10 10-100 10−7 1 ∼ 104 ∼ 10−1Saturn’s F-ring 10 10-100 < 10 1 ∼ 10− 102 ∼ 10−3 − 10−4Saturn’s spokes 0.1-102 2 1 1 ∼ 10 ∼ 10−4Zodiacal dust disc 5 10 10−12 10 ∼ 104 ∼ 10−4Lab-plasma (DA-wave) 108 2-4 104 5 > 103 > 10−4Lab-plasma (Dust-Ball) 108 2-4 103 5 ∼ 103 ∼ 10−4Coulomb dust crystal 109 2 104 − 105 5 ∼ 104 ∼ 10−3Electron collection from plasmaThe proton beam circulating in the LHC vacuum chamber ionizes the residual gas releasingelectrons as well as positive ions. The charge Q collected on a dust particulate by a balanceof the electron current, the ion current and secondary electron emission is generally presentedin terms of the surface potential φp = Q/(4piε0R) [45]. The surface potential ends up beingnegative under most conditions, because of the high mobility of electrons and the small secondaryelectron emission yield for micrometer-sized particulates. The electron and ion currents, Ie andIi respectively, are:Ie = −4piR2nee(kBTe2pime)1/2exp(eφpkBTe)and Ii = 4piR2nie(kBTi2pimi)1/2 (1− eφpkBTi)(4.1)where ne and ni are the electron and ion density, Te and Ti are the electron and ion temperatureand R is the particulate radius. As one can see from Table 4.1, the order of magnitude of thecollected charge is mainly dependant on the plasma temperature and does not change with neor nd, which vary by several orders of magnitudes for different environements. Based on thisobservation, Tsintsadze [51] presents a simple model to explain the charge acquired by dust.Because of the high mobility of electrons, they dominate the charging mechanism until thesurface potential φp becomes of the same order of magnitude as the thermal kinetic energy ofelectrons. As a result, the temperature of the electrons alone determines the charge acquired bythe dust, following:Q = −2.5kBTee(4piε0)R (4.2)This is consistent with experimental observations and with the capacitance model discussed byPiel [45]. Using this expression, we can estimate the expected order of magnitude of dust chargein the LHC from this charging mechanism. With electron cloud temperatures between 1-250 eV[6], and dust particulates with radii between 1-100 µm, dust could acquire a negative charge inthe order of 102e− 107e This result is interesting in the context of UFOs, since observations324.2. Charging Mechanisms and Charging Modelshave shown that the UFO rate was not correlate with electron clouds density, but that thebunch spacing (and therefore multipacting effects) played a role in the UFO rate.Photoelectrons and Electron Collection: Patched Charge ModelEven in the case where photoelectron emission becomes important, it seems that Eq. (4.2)remains appropriate. To explain dust lofting measurements where dust particulates were subjectto a plasma and UV radiation, Wang [41], [42] introduces the Patched Charge Model. In thismodel, it is assumed that the particulate of interest lies on a dusty surface where cavities arepresent between neighbouring dust particulates. Each of them is subject to a vacuum-sidepatch, charged from photoelectric emission and impinging electrons, and a cavity-side patch,carrying a high negative charge due to photoelectrons and secondary electrons emitted from theneighbouring particulates. The result is that the equilibrium charge of the dust follows:Q = −η2kBTee(4piε0)R (4.3)where η > 1 is the ratio of the emitted electron energy from neighbouring particulates to thecutoff energy of absorbed electrons. Empirically, η was found to be between 4 and 10 [42]. Asone can see, η = 5 corresponds to Eq. (4.2). An important result from Schan and Wang [41]is that even in the absence of a plasma, dust exposed to UV radiation will end up negativelycharged because of the photoelectron emission from its surroundings. Sickafoose [52] comes to asimilar conclusion, where only perfectly isolated dust grains end up positively charged whenilluminated by UV radiation.TriboelectrificationTriboelectrification, or contact charging, happens when two materials are brought into contactand exchange electrons. When the materials are separated, a charge remains in each of thebodies. Sternovsky [53] investigated this charging mechanism for several materials under vacuum.The charge transferred scales with the difference in the work function of both materials, as wellas the dust radius: Q ∼ (φ1 − φ2)R. It is also reported that for oxidized materials, the effectivework function is close to 5.5 eV, independently of the material’s own work function. The precisecharge acquired is hard to predict, because it depends on the degree of dust migration upon thesurface. In Sternovsky’s work, with forced mechanical vibration of the flat surface supportingthe dust, the acquired charge reached 105e to 106e, which is in the same order of magnitude asthe other charging mechanisms presented above. In the LHC, this effect could become importantin regions with high levels of mechanical vibrations.Beam Screen InductionWhen one or many dust particulates are in contact with a conductive surface in presence of anelectric field, charges can move from the conductive surface to the particulate and vice versa. In334.3. UFO Release Mechanism in the LHCthe LHC, the beam screen acts as the conductive surface, and the beam’s electric field providesthe driving force to move electrons from the beam screen into the dust particulate, makingit negatively charged. Depending on the nature of the contact between the particulate andthe conductive surface (oxide layer, rugosity, contact area, etc.), the charging time can vary.Musinski [54] discusses the time constant of such a system based on the contact resistanceand capacitance. In general, the charging occurs in the order of milliseconds to seconds, forradii in the micrometer range to the millimetre range. In a vacuum environment, dependingon the intensity of the background electric field EBG, the charge buildup eventually reaches asaturation charge [55], given by:Q = −pi218( 3εrεr + 2)ε0(4piR2)EBG (4.4)where 3εrεr+2 is the Pauthenier’s coefficient with εr, the relative permittivity of the dust particulate.For the LHC case, due to the relatively long charging time, the bunched nature of the beam canbe neglected and EBG corresponds to the average electric field. Taking a perfectly conductivedust particulate lying on the beam screen (E-field typically in the order of kV/m) as an example,the expected charge for radii between 1-100 µm is in the order of 100e−104e. However, Eq. (4.4)is derived for the case of a uniform electric field. In the LHC, where surface charges (imagecurrent) build up in the beam screen directly above and below the beam, it is possible that theactual induced charge could reach few orders of magnitude above this estimate. For a perfectlynon conductive dust particulate, the charge transfer would be impossible and no net inducedcharge could be obtained.Combined EffectsIt is important to note that all the charging mechanisms mentioned above are self-limiting.For some critical surface potential, the charging stops because the energy barrier for electrontransfers becomes too important. Hence, if multiple of these charging mechanisms are combined,the acquired charge wouldn’t add up. Instead, the equilibrium charge acquired by the dustwould be slightly shifted, based on a balance of the charging mechanisms at play. In Fig. 4.2,we show the range of possible charges acquired by dust based on a combination of the chargingmechanism discussed previously. The smallest possible charge follows Eq. (4.4) and the highestpossible charge follows Eq. (4.2).4.3 UFO Release Mechanism in the LHCBecause of the sporadic nature of UFO events, it is apparent that dust present in the beampipe of the LHC remains in the surroundings of the beam until it is suddenly released. For anegatively charged dust to remain far away from the beam, it can be trapped in several ways.344.3. UFO Release Mechanism in the LHC0 20 40 60 80 100Dust Radius ( m)101102103104105106107108Number of electrons (|Q/e|)(a)0 20 40 60 80 100Dust Radius ( m)10 710 610 510 410 310 210 1100Charge-to-mass ratio (C/kg)(b)Figure 4.2: Range of the possible number of electrons carried by dustas a function of the dust radius, and correspond charge-to-mass ratiofor Cu dust. The upper limit of |Q/e| is given by (4.2) with a plasmaenergy of kBTe = 250 eV and the lower limit is given by (4.4).The current hypothesis is that it remains attached to the beam screen because of adhesive forces,until it reaches a critical state (critical mass, charge, background electric field, etc.).Adhesive Forces on the Beam ScreenIn a vacuum, capillary forces that might arise from the presence of water on the surfaces canbe neglected. In the literature, particulates are generally considered to be in contact when thesurfaces are separated by a distance d0 ∼ 4 Å. Walton [56] gives an exhaustive overview of theadhesive forces for charged lunar dust:The Cohesive Force is the force required to overcome the surface energy of two surfaces (of thesame material) in contact. This would apply to dust particulates that are formed by separatingthem from a substrate made of the same material. For the case of a rigid sphere of radius R incontact with a planar surface it follows:Fsurface = 4γpiR (4.5)where γ is the surface energy per unit area required to break the molecular bonds. Typicalvalues of γ range from 0.02 to 2 J/m2 [56].The Van der Waals Force is the resulting force between atoms or molecules of two surfacesbarely in contact. It is a very short-range force, which varies by orders of magnitude based onthe rugosity of the planar surface. For a sphere in contact with a planar surface, it follows:FVDW =AR6d2 (4.6)354.3. UFO Release Mechanism in the LHCwhere A is the Hamaker constant of the interaction, which depends on both materials, and dis the distance between the surfaces. The Hamaker constant typically takes values between1× 10−20 J and 10× 10−20 J [57].The Image Charge Force is the force between a charged particulate and a conductive surfacedue to the induced charges in the conductive surface. Assuming that the conductive surface isinfinite, the image charge force on a sphere carrying a charge Q is:Fimage =Q216piε0(R+ d)2(4.7)and is always oriented toward the conductive surface, independently on the charge polarity. It isnoteworthy that the image charge force is the only adhesive force which depends on the chargeof the particulate.To study the conditions under which a dust particulates could be released from the beamscreen surface in the LHC, one has to compare these adhesive forces with gravity and theelectrostatic attraction to the beam. For this, the bunched nature of the beam can be neglected:even in the most optimistic case where no adhesive forces are present and the charge-to-massratio is maximized, the displacement from the peak field from a bunch (roughly ten timeslarger than the average field) is in the order of tenths of picometres. Since bunch spacing is10 times longer than the bunch length itself, this sudden displacement could not pull the dustfar enough from the surface to mitigate short-range forces. Fig. 4.3 shows a comparison of theadhesive forces against the releasing forces for different charging mechanisms. Two cases are tobe considered: dust stuck to the top of the beam screen, where gravity acts as a releasing forcealong with the beam’s electric attraction, and dust stuck to the bottom, where gravity acts asan adhesive force, along with the Van der Waals and image charge forces.Release From the Beam ScreenBefore enlisting plausible release mechanisms, it is important to emphasize the conclusions fromthe last section: the charge carried by dust depends on its radius. Two consequences follow fromthat. First, we can’t randomly pick a charge, or a charge-to-mass ratio, and attribute it to adust particulate of a given radius: the charging mechanism at play determines it unequivocally.Second, because of the fast response of electrons for all charging mechanisms, if the chargestate of a dust particulate is seen to change over several minutes, either the dust is undergoingsurface growth, or the charging mechanism is changing.UFOs in the LHC can happen after few hours of stable beam. The release mechanism behindsuch events remains a mystery. To explain this observation, it is necessary that dust, presentin the vicinity of the beam, goes from being in a stable configuration to being in a critical364.3. UFO Release Mechanism in the LHCconfiguration, where it is released in the beam. The critical condition could be reached becauseof a change in mass, charge, or ambient electromagnetic fields. A sudden impulse could also begiven to the dust, mechanically or electromagnetically. Based on the forces introduced above,one can see that depending on the charging mechanism, the adhesive forces typically dominateover the releasing forces, up to a certain radius, as shown in Fig. 4.3.10 1110 910 7.Top of Beam ScreenAdhesive ForcesReleasing Forces0 20 40 60 80 100Dust Radius ( m)10 1110 910 7.Bottom of Beam ScreenAdhesive ForcesReleasing ForcesForce (N)(a) Q ∝ R. Plasma energy kBTe = 0.5 eV10 1110 1010 910 810 7.Top of Beam ScreenAdhesive ForcesReleasing Forces0 20 40 60 80 100Dust Radius ( m)10 1110 1010 910 810 7.Bottom of Beam ScreenAdhesive ForcesReleasing ForcesForce (N)(b) Q ∝ R. Plasma energy kBTe = 10 eV10 1110 910 7.Top of Beam ScreenAdhesive ForcesReleasing Forces0 20 40 60 80 100Dust Radius ( m)10 1410 1210 1010 810 6.Bottom of Beam ScreenAdhesive ForcesReleasing ForcesForce (N)(c) Q ∝ R2. Surface separation d = 3 nm10 1110 910 7.Top of Beam ScreenAdhesive ForcesReleasing Forces0 20 40 60 80 100Dust Radius ( m)10 1410 1210 1010 8.Bottom of Beam ScreenAdhesive ForcesReleasing ForcesForce (N)(d) Q ∝ R2. Surface separation d = 200 nmFigure 4.3: Comparison of the adhesive forces against the releasingforces for different charging mechanisms. (a) and (b) represent plasmacharging (triboelectrification would be similar) using (4.2) and the mainparameter influencing the crossing point of the forces is the plasmatemperature. (c) and (d) represent beam screen induction (4.4) andthe main parameter influencing the crossing point of the forces is thedistance between the particulate surface and the beam screen. In allfour cases, for a dust particulate lying at the bottom of the beamscreen, the adhesive forces are stronger than the releasing forces.There are several interesting conclusions coming from Fig 4.3. First, depending on theplasma energy and the surface rugosity of the beam screen, both charging mechanisms exhibita critical point between the forces for a dust particulate stuck to the top of the beam screen.374.3. UFO Release Mechanism in the LHCThis implies that dust can be released if its radius changes or if the crossing point of the forceschanges. The latter could happen if there is a change in the electron cloud average energy (Fig.4.3 (a) and (b)), or if the dust is transported (by electromagnetic forces) on a section of thebeam screen with more important rugosity (Fig. 4.3 (c) and (d)). It is noteworthy that if thecontact with the beam screen is ideal (d ∼ 4 Å), the Van der Waals force dominates by ordersof magnitude and the dust remains stuck on the beam screen. In practical cases, this is hardlyachievable, and surface impurities would also mitigate the strength of the adhesive force bysmall patches of surface charge. Moreover, it is clear that for a dust in contact with the bottomof the beam screen (from d ∼ 4 Å to d ∼ 0.1 µm), the adhesive forces are always stronger thanthe releasing forces. Hence, one can conclude that dust cannot be picked up from the bottom ofthe beam screen, unless there is some kind of mechanical agitation. This result is consistentwith the experiment from Saeki [58], where dust could only be picked up from the bottom of abeam chamber when the electric field reached 105 V/m, which is two orders of magnitude abovethe electric field of the LHC beam in regular operation. Note that the instantaneous field at thebeam screen from a single bunch is around 105 V/m, but is only present during 2.5 ns, followedby 25 ns of zeros-field (the image field’s response is almost instantaneous), which would lead tothe same result.The situation is different, however, if the dust is lifted to a few hundreds of micrometresabove the surface by some mechanical agitation, or given an initial velocity by an electrical ormechanical impulse. If the dust acquires a sufficient energy (activation energy) to overcome thepotential well of the close-range adhesive forces, it could be released from the surface and freelyattracted by the proton beam. Fig. 4.4 shows the activation energy for several charge-to-massratios and dust radii, consistent with the charging mechanisms presented earlier. In this space,every point uniquely defines the mass, the charge and the radius of a dust particulates andallows computing the energy required to leave the beam screen. As one can see, the activationenergy is not especially high. The corresponding velocity, or escape velocity, for 1010 eV, is about4 m/s for the smallest dust particulates (see corresponding figure, Appendix A.2). For most ofthe radii under study, dust lying on the bottom of the beam screen requires an escape velocitybetween 0.5 m/s and 1 m/s in order to be picked up by the beam. This is orders of magnitudesabove mechanical vibrations observed in the beam screen during earthquakes (∼ 20 µm/s [59])as well as mechanical vibrations observed during the pulsing of MKI magnets (∼ mm/s [60]).As for dust stuck to the top of the beam screen, the escape velocities are small enough thatmechanical vibrations could be implicated in the release mechanism. It is noteworthy that theboundary between the spontaneously released dust and the ones requiring an activation energyis determined by the initial surface separation between the dust and the beam screen.38(a) Surface separation d = 200 nm (b) Surface separation d = 200 nm(c) Surface separation d = 500 µm (d) Surface separation d = 500 µmFigure 4.4: Energy required for a charged dust particulate to leave thebeam screen. (a) and (b) correspond to an initial surface separation of200 nm whereas (c) and (d) correspond to an initial surface separationof 500 µm. The blue regions have a negative activation energy,which corresponds to a spontaneous release. The charge-to-mass ratioconsidered are the ones allowed from Fig. 4.2. Note that for a perfectcontact (d ∼ 4Å), every dust requires an activation energy of a few eVbefore reaching a surface separation of 200 nm.394.3. UFO Release Mechanism in the LHCProposed Release MechanismsBased on the considerations presented in this chapter, plausible release mechanisms are listedbelow.1. The dust, either stuck to the bottom or the top of the beam screen, is released bymechanical vibrations or electric field pulses, exceeding the activation energy. For a perfectcontact (d ∼ 4Å), all dust require an activation energy of a few eV in order to reach asurface separation of 200 nm (then Fig. 4.4(a) and (b) apply).2. The dust, stuck to the top of the beam screen, is released following a sudden decrease incharge, bringing its activation energy to zero. This decrease in charge could be due to achange of the electron cloud state, or if induction comes to dominate over other chargingmechanisms. Indeed, the charge induced is typically well below the charge acquired fromplasma. Any exceeding charge would be transferred to the conductive beam screen ifinduction becomes the predominant charging mechanism.3. The dust, stuck to top of the beam screen, is released following an increase in mass (dueto surface growth), bringing its activation energy to zero. As shown in Fig. 4.3, for agiven charging mechanism, the releasing forces eventually exceed the adhesive forces asthe radius increases.4. The dust is already not in contact with the beam screen and is released when a criticalstate (mass or charge) is reached. This could happen if the dust is orbiting the beam or ifit is trapped in the electromagnetic fields surrounding the beam. Even if the magneticforce acting on the dust particulate is negligible because of its very small velocity, electronclouds are highly affected by magnetic fields, and could possibly trap the dust by shieldingthe electric field of the beam.In the absence of experimental evidence, it is hard to rule out any of these release mechanisms.However, one might question the plausibility of having the dust being stuck on top of the beamscreen. Indeed, when no beam is circulating in the LHC, most of the charging mechanismsdescribed earlier vanish. In that case, any conductive dust particulate would be neutralized bythe conductive beam screen, and would fall to the bottom. The only way to prevent this wouldbe to have a near-perfect contact between the dust and the beam screen, with d being in theorder of angstroms. In that case, Van der Waals forces dominate all other forces, and the dustcould remain stuck to the top of the beam screen. Then, the only possible release mechanismwould be that the dust is released by mechanical vibrations. If the dust is nonconductive, itwould be possible for a previously acquired charge to keep the dust stuck on the top of thebeam screen via the image charge force.40CHAPTER 5UFO DynamicsTo better understand UFO losses and assess the hazard in the LHC and future accelerators, theUFO Dynamics Simulation Tool was developed starting in 2010 and continuously upgraded [20],[21], [61]. It consists of a set of numerical routines used to integrate the equations of motion andthe time evolution of the charge of a dust particulate, and compute the resulting inelastic collisionrate with the LHC beam. This tool allows to study the effect of UFO properties (mass, material,size), initial conditions (charge, position, velocity) and beam properties (energy, intensity,transverse size) on the resulting proton losses, and compare them with ICBLM measurements.In the context of this thesis, the code was translated in Python and the implementation wasreworked to facilitate Monte-Carlo simulations. In this chapter, the upgrades made to theUFO Dynamics Simulation Tool are discussed, a validation of some key results of the model ispresented and future necessary upgrades are also discussed. Finally, the theoretical descriptionof stable orbits for negatively charged particulates is presented as a new possibility for UFOdynamics.5.1 UFO Dynamics Simulation ToolThe simulation of UFOs interacting with the proton beam of the LHC is based on the UFOHypothesis described in section 2.1. A complete description of the original model is presented ina note from B. Auchmann [62] (see also the work of S. Rowan [21]). The dynamics of chargedUFOs in the LHC can be separated in three main parts:Equations of motion: The driving forces considered are gravity, the electric field from the beamand the UFO image force from the top or bottom of the beam screen. The magneticfield in dipole or quadrupole magnets, as well as the magnetic field from the beam, areneglected in first approximation because of the small velocity of UFOs.Charging rate: In the current model, initially charged UFOs (positively or negatively) getpositively charged following their interaction with the proton beam. As UFOs approachthe immediate vicinity of the beam, the only charging mechanism considered is coming415.1. UFO Dynamics Simulation Toolfrom energetic knock-on electrons (δ rays) leaving the dust particulate following the energydeposited by the beam of protons.Inelastic collision rate: Proton-nucleus interactions lead to both elastically and inelasticallyscattered protons. The elastically scattered protons contribute to the beam halo and arelost at the collimators. Inelastically scattered protons on the other side, contribute tothe energy deposited in nearby magnets, the so-called local losses, which are measuredby local ICBLMs distributed along the LHC. In the model, the inelastic collision rate issimulated based on the proton flux impinging on the dust particulate and the inelasticcross section of the material.When translating the code to Python, small practical changes were implemented to facilitateMonte-Carlo simulations. The physics of the model was reviewed, which led to a more accuratedescription of the electric field from the beam (Sec. 1.4), a validation of the main chargingmechanism at play and a validation of the inelastic collision rate, presented below. Moreover,it led to the idea of having orbiting dust particulates carrying a negative charge, discussed inSec. 5.3.Energetic knock-on electrons (δ rays)When high energy protons pass through matter, knock-on electrons (also called δ rays orsecondary electrons) are produced. According to the Particle Data Group [63], the maximumenergy transfer per collision can be described from first principles as:Tmax =2mec2β2γ21 + 2γmemp +(memp)2 (5.1)where mp is the proton mass, me is the electron mass and β, γ are the relativistic factors forthe proton beam. The distribution of electrons d2NdTds with kinetic energies T (Tmin < T < Tmax)for a penetration ds follows:d2NdTds= 2pir2emec2z2n1β2F (T )T 2(5.2)where re and me are the classical electron radius and mass, z is the charge number of theimpinging particle (z = 1 for protons), n is the electron density in the particulate, β is therelativistic velocity of the protons and F (T ) is a spin-dependent factor which is approximatelyF (T ) ≈ 1 for T  Tmax (which is the case here, since Tmax ∼ TeV in the LHC). To find thecharging rate of the dust particulate Q˙, the secondary electron distribution has to be integratedwith the proton flux J impinging on the particulate between the allowed energies Tmin and Tmax.425.1. UFO Dynamics Simulation ToolThe average charge produced per passing proton, Qpp [62], is:Qpp =∫∫∫J(x, y) d2NdTds dAdT ds∫J(x, y) dA ≈(4R3)[2pir2emec2n1Tmin]e (5.3)Theoretically Tmin is the mean excitation energy of the material, which is in the order of tens ofeV [63]. However, to study the ionization of a dust particulate, Tmin is higher and correspondsto the minimum energy for ionization. It depends both on local fields and the energy lost as asingle electron leaves the particulate. From B. Auchmann [62]:Tmin = φ(Q) +W (5.4)where φ(Q) is a coulomb term which depends on the UFO charge and W is the work functionof the dust particulate. The coulomb term describes the additional energy required for anelectron to leave the vicinity of the particulate once it reached the surface. UFOs will only startinteracting with the beam at a distance of about 6σ in the LHC. At that distance, the electricfield from a nominal proton bunch is around 2× 105 V/m. If the UFO is only slightly charged,any electron reaching the surface will be accelerated by the beam and exit the particulate. Whenthe UFO surface field becomes comparable with the electric field from the beam, which happenswhen Q/R2 ∼ 2× 10−5 C/m2, then electrons need to overcome the coulomb attraction fromthe UFO. Hence: φ(Q) = Q · e4piε0R for Q/R2 > 2× 10−5 C/m2φ(Q) = 0 otherwise(5.5)This result is different from what was previously used in the model only by the addition ofthe Q/R2 cutoff value. Note that only the surface field is considered here, which is valid for aconductive UFO or a dielectric UFO if space charge effects are neglected.To estimate the work function W , B. Auchmann [62] considers that the electrons leaving theparticulates are the ones with a practical range (for a given energy) in the material sufficient toreach the surface of the dust particulate. Following the empirical relation described in [64] for0.3 keV to 20 MeV electrons, the practical range L(T ) of electrons in matter is given by:L(T ) = ATρ(1− B1 + CT)(5.6)where A = 5.37× 10−6 kg m−2 eV−1, B = 0.9815, C = 3.123× 10−6 eV−1 and ρ is the densityof the material. From there, the work function of the dust particulate is found by equatingthe practical range at a given energy to the average path length of escaping electrons. Thelatter corresponds to the average distance needed for an electron created anywhere inside adust particulate to reach the surface. To make this calculation, B. Auchmann [62] assumedthat all electrons travel perpendicularly to the proton track, which leads to an average path435.1. UFO Dynamics Simulation Toollength of L(W ) = 0.7358R, such that W = L−1(0.7358R). In order to validate this result andthe main charging mechanism of the model, a beam of high energy protons impinging on a solidsphere of carbon or copper was simulated using FLUKA. The energy and the velocity vector ofthe knock-on electrons leaving the particulate were recorded and used as a benchmark. It wasfound that the average path length given above is not valid for the electron energies consideredhere, and that the correct work function should rather beW = L−1(0.3216R), as explained below.The production angle θz of a δ ray with kinetic energy Te and corresponding momentum peis given by:cos(θz) =(Tepe)(pmaxTmax)(5.7)where pmax is the momentum of an electron with the maximum possible energy transfer [63].Based on the FLUKA simulations performed, one can see from Fig. 5.1 that the electronsreaching the surface of the UFO are distributed between θz = 0 and θz = pi because of multiplecoulomb scattering, making it possible for an electron to be ejected in the opposite directionthan the impinging protons. An important fraction of electrons are leaving at θz = pi/2 andcorrespond to electrons of small energy produced close to the surface, such that their effectivework function is negligible. From the electron energy spectrum obtained with FLUKA, onecan compute the most probable production angle of δ rays based on Eq. (5.7). The result isfound to be smaller than pi/2, as assumed in the previous model, and consistent with the localmaximum of the angular distribution from Fig. 5.1.0.00 0.25 0.50 0.75 1.00z01234Observation densityMaterial : CuR=10 mR=50 mR=100 mFigure 5.1: Angular distribution of electrons as they leave the UFO,where cos(θz) = vz/|v|. The large number of electrons found aroundpi/2 are electrons of small energy close to the surface, while the restof the electrons are subject to numerous random coulomb scatteringbefore leaving the UFO. The most probable production angle computedfrom Eq. (5.7) is shown by the dashed line.445.1. UFO Dynamics Simulation ToolIn fact, the calculation of the average path length done previously overestimates the actualaverage path length of escaping electrons, because electrons of small energy are more probableand can only escape the dust particulate if they are produced close to the surface. To find abetter estimate, the average path length was fitted to match the Qpp calculations from FLUKA(see Fig. 5.2a), which yielded L = 0.3216R. Following these changes to the model, the averagenumber of escaping electrons per passing protons for a neutral UFO agrees well with FLUKAfor different materials, as shown in Fig. 5.2a. The energy spectrum of electrons as they exit thedust particulate also agrees well with FLUKA, as shown in Fig. 5.2b.0 20 40 60 80 100Radius ( m)0.000.010.020.030.040.05Escaping electrons per passing protonCCuFLUKA(a)10 4 10 3 10 2 10 1 100 101 102Energy (MeV)0.0000.0020.0040.0060.0080.0100.0120.014dd(lnE)NeR=10 mR=50 mR=100 m(b)Figure 5.2: Comparison of the current model with FLUKA. (a) Averagenumber of escaping electrons per passing proton for a neutral UFO.The previous model (solid lines) is compared to FLUKA (circles). (b)Energy spectrum of knock-on electrons as they escape the UFO. Theprevious model (dashed lines) is compared to FLUKA (solid lines) forthree UFO radii. The energy cut for electron transport in FLUKA isshown by the black line, at 1 keV. The average path length consideredis L = 0.3216RInelastic Collision RateAs presented in Ch. 3, FLUKA can be used to compute the BLM responses as a function of theloss source location (see Fig. 3.2). Local losses are caused by inelastically scattered protons onthe nuclei of the dust particulate. Assuming that the proton flux density J(x, y) is uniform overthe surface of the UFO, the inelastic collision rate ˙` is:˙` =∫∫J(x, y)Σinel dAds ≈(4R3)Σinel(piR2)J(x, y) (5.8)where Σinel is the macroscopic cross section of the material. Following the new implementation ofthe UFO Dynamics Simulation Tool, the inelastic collision rate can be computed on a bunch-by-455.1. UFO Dynamics Simulation Toolbunch basis. As discussed in Ch. 3, only dBLMS, located at the collimators, have a sufficient timeresolution to observe bunch-by-bunch losses. However, due to multiturn losses, the falling edgeof the measured signal cannot be compared to simulations. In order to do so, elastically scatteredprotons would need to be tracked between the UFO event location and the collimators, which isnot no yet part of the simulation tool. On the other hand, the rising edge of the signal canbe accurately modelled, assuming that the elastic collision rate is proportional to the inelastic one.On 2018-09-30 22:47:52, a UFO event was recorded at 6.5 TeV during a LHC fill in whichtwo bunches had an increased emittance, one horizontally and one vertically. This variationin emittance for two bunches leads to a unique bunch-by-bunch signature of the losses [35],[65], which can be used to validate the simulated inelastic collision rate with two independentmeasurements. The measured losses from local ICBLMs can be directly compared to the totalinelastic collision rate computed from the model, and the rising edge of measured losses atthe collimator dBLMs can be compared to the normalized bunch-by-bunch inelastic collisionrate. Using Monte-Carlo simulations, a UFO candidate for which the inelastic collision ratematches the local ICBLM measurement and the bunch-by-bunch dBLM measurement was found.The algorithm to find this best candidate is discussed in Ch. 6. The parameters of this UFOcandidate are shown in Table 5.1 and the beam parameters used are the ones present in themachine when the event was recorded. Figure 5.3 shows the nuclear collision rate obtained fromthe ICBLM measurements using the FLUKA calibration factor compared to the simulated resultand Fig. 5.4 shows a comparison of the measured bunch-by-bunch losses with the simulatedones for the same event.0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8Time (ms)0.00.51.01.52.02.53.03.54.0Nuclear collision rate (s1 )1e11FLUKA-ICBLMUFO dynamics simulationTable 5.1: Best Candidate ParametersParameterMaterial CuRadius 33 µmInitial Charge −2× 107eInitial x position 1.1 mm off-centerPosition in arc-cell 57.9 mFigure 5.3: Comparison of a simulated UFO candidate with the ICBLMmeasurement for the 2018-09-30 22:47:52 UFO event. The number ofnuclear collision rate for the measurement was computed with FLUKA.The uncertainty is shown by the blue error bars.465.2. Suggested Future Upgrades600 400 200 0 200 400 600 800 1000Time (us)0.00.20.40.60.81.0Normalized losses (a.u.)Normal bunchesH blown upV blown up(a) dBLM measurement600 400 200 0 200 400 600 800 1000Time (us)0.00.20.40.60.81.0Normalized losses (a.u.)Normal bunchesH blown upV blown up(b) SimulationsFigure 5.4: Comparison of the turn-by-turn bunch losses for a simulatedUFO candidate with dBLM measurement with blown-up bunches inthe LHC for the 2018-09-30 22:47:52 UFO event. The first 12 bunchesare shown. Only the relative amplitude of the bunches is relevant here,as the falling edge of the measurements is elongated from multiturnlosses at the collimators.This analysis shows that the model can be used to identify a UFO candidate which reproduceswell the two independent measurements (ICBLM and dBLM) of the same beam-UFO interaction.The result shown in Fig. 5.3 is dependent on the inelastic collision rate and on the energydeposited in ICBLMs. As for the result shown in Fig. 5.4, it is dependent on the elastic collisionrate (detection at the TCP) and is coming from the fine time structure (single bunch interaction)of the UFO event recorded by a dBLM. In both cases, simulations are in very good agreementwith measurements.5.2 Suggested Future UpgradesEven if the current physics of the model was validated using FLUKA, the UFO DynamicsSimulation Tool is not complete. As will be discussed in Ch. 6, the current model fails toexplain some UFO measurements where the signal is positively skewed (i.e.: longer falling edgethan rising edge). Some upgrades which might be able to explain this discrepancy are suggestedbelow.UFO Charging MechanismsAs observed in electron and antiproton storage rings, several charging and discharging mechanismshave to be taken into account for an accurate description of the charge carried by a dustparticulate as a function of time when interacting with a particle beam [15], [66]. Knock-onelectrons, photo electrons and field evaporation lead to an increase of the (positive) charge. Asa counterpart, electron capture and field ionization lead to a decrease of the dust charge. In475.3. Orbiting UFOsthe current model, knock-on electron production is assumed to dominate the charging processand discharging mechanisms are neglected. With the presence of electron clouds all around theLHC, it would be necessary to consider electron capture processes for a positively charged UFO.Considering the high mobility of electrons in comparison with the UFO speed, it is likely thatelectron capture significantly contributes to the time evolution of UFO charges over a few LHCturns.UFO HeatingIt is also known from electron storage rings that beam-dust interaction causes heating of thedust particulate, which either leads to the particulate exploding [67], or melting [16]. However,unlike electron storage rings where the dust is trapped for a long time in the center of the beamafter being ionized, heating effects for UFOs in the LHC are not as critical. This is becauseUFOs get repelled from the beam within few turns, following their ionization. Using roughapproximations, one can verify that heat radiation is only one order of magnitude larger thanthe energy deposition for a dust particulate located 4σ away from the center of the beam [67].For a deeper UFO penetration into the beam, charging and heating processes happen oversimilar time scales, and the heating process would have to be considered. It is possible thatthermal expansion of the dust particulate increases the interaction time with the beam as theUFO is starting to be repelled, leading to a long falling edge of the signal.5.3 Orbiting UFOsBased on experimental observations, the dynamics of UFOs in the LHC has been hypothesizedto follow simple trajectories: falling into the beam due to gravity, getting charged, and repelledby the beam’s electric field. This is inherently different from how dust behaves in electron andantiproton storage rings, where it can be trapped in the beam due to the acquired positive chargeresulting from the beam-dust interaction [14]–[16], [66]. In these accelerators, dust can remain inthe vicinity of the beam for a long period, causing important intensity loss or emittance growth.In the LHC, negatively charged UFOs could lead to a similar phenomenon. The discussionpresented in Ch. 4, shows that this possibility has to be considered. The problem is essentiallythe one of a charged body in orbit in a logarithmic potential, as the beam can be very accuratelymodelled by an infinite charge-carrying wire. This fundamental problem didn’t get a lot ofattention apart from one study regarding the Orbitron from the University of Wisconsin, whereelectrons are injected between two concentric cylinders [68]. Since the dynamics of UFOs in theLHC is not yet completely understood, the possility of having orbiting UFOs has to be studied.In this section, a simple theoretical description of the dynamics of orbiting dust particulatesaround the LHC proton beam is presented. A shape parameter is introduced to study the shapeof the orbits and to derive an analytic expression for the radial oscillation period. The effect ofthe interaction with the beam is also discussed.485.3. Orbiting UFOsFormulation of the ProblemLet’s consider the general problem of a dust particulate of mass m carrying a charge Q, subjectto a central electric potential V (r) and a potential vector ~A. Since gravity has to be taken intoaccount for micrometer-sized dust particulates, the Hamiltonian of the system is:H = 12m∣∣∣~P −Q~A∣∣∣2 +QV (r) +mgy (5.9)where ~P is the momentum and g is the gravitational constant. For small magnetic, HB, andgravitational,Hg, contributions to the Hamiltonian, it is useful to write H = H0 +HB +Hg andtreat them as a perturbation to the basic Hamiltonian H0, which can be written in cylindricalcoordinates (r, φ, z) as:H0 = P2r2m +P 2φ2mr2 +QV (r) (5.10)Using the Lagrangian, one can easily show that Pφ = ∂L∂φ˙ = mr2φ˙ = L is the angular momentumand that Pr = ∂L∂r˙ = mr˙ is the radial momentum. To complete the description of the Hamiltonianof the system, the potential has to be specified. From Eq. (1.10) the potential associated withthe beam’s electric field is:Vbeam(r) = V0[12Ei(− r22σ2)− ln(r/r∞)](5.11)where Ei is the Exponential Integral, Ei(x) = − ∫∞−x e−tt dt and V0 = λ2piε0 with λ being the linearcharge density of the proton beam. When r reaches a few σ, only the logarithmic term remainsin the potential and the beam can be approximated by an infinitely long charge-carrying wire.For the following sections, the potential will be taken as V (r) ≈ −V0 ln(r/r∞) since the dustparticulate will be assumed to remain a few σ away from the beam.Particulate StiffnessThe charge-to-mass ratio Q/m is an important physical quantity, both when studying theformation and the dynamics of dust particulates in EM fields. For this reason, it is interestingto look for a conserved quantity which would be dependent on the charge-to-mass ratio. Theparticulate stiffness is therefore introduced and defined as:S = h2Q/m(5.12)where h is the specific angular momentum h = L/m. S has units of Vm2. With this definition,the basic Hamiltonian in the logarithmic approximation of the beam can be written as:495.3. Orbiting UFOsH0 = P2r2m +Q[ S2r2 − V0 ln(r/r∞)](5.13)= P2r2m +QV˜0(r)where V˜0(r) is the quasi-potential for the basic Hamiltonian. To interpret the physical meaningof S, it is relevant to look at the radial dependency of the electric force in a logarithmic potential.We can write FE = Qλ2piε0r =QV0r = maE , which leads to aE =Q/mr V0. With this, one can rewritethe particulate stiffness by expanding the specific angular momentum as h = L/m = r2φ˙ = vφr,which gives:S = h2Q/m= (vφr)2Q/m= 1aEV0(v2φr)r2 = acaEV0r2 (5.14)where ac is the necessary centripetal acceleration for circular motion at a given radius. Wesee that S describes the balance between the required centripetal force at a given radius andthe electric force at play. Over the course of an orbital period, the different contributions areperfectly compensated so that S remains constant.Case of Charge Carrying Wire Without GravityLet’s look at the basic Hamiltonian for now, neglecting the effect of gravity. With the simple formgiven in Eq. (5.13), the equations of motion can be written down and numerically integrated:r˙ = Prm, φ˙ = Pφmr2P˙r =P 2φmr3−Q ddrV (r) , P˙φ = 0(5.15)In the context of this work, the UFO Dynamics Simulation Tool was used to evaluate theresulting trajectories. The solution to this set of equations is that charged dust will orbit withoscillating radial position. For any logarithmic potential, one can show that the orbits are notnecessarily closed, but are always bounded [69]. For a precise description of the orbits, thequasi-potential from Eq. (5.13), shown in Fig. 5.5, is of particular interest.For a given orbit, the perigee rmin and apogee rmax happen whenever the radial momentumreaches zero. From Eq. (5.13), we therefore see that the turning points for a total energy E anda particulate stiffness S are the roots of:EQ− S2r2 + V0 ln(r/r∞) = 0 (5.16)which leads to rmin =√S/V0W−1(ξ) and rmax =√S/V0W0(ξ) where Wn is nth branch of the Lambert505.3. Orbiting UFOs0.0 0.5 1.0 1.5 2.0 2.5 3.0r (mm)−120−100−80−60−40−200−V˜(r) (V)rcrmaxrmin  S = − 1.0e− 06 Vm2S = − 1.0e− 05 Vm2S = − 1.0e− 04 Vm2Figure 5.5: Quasi potential as a function of r. The minus sign is addedto show the effect on a negative charge. rmin, rmax and rc are shownfor a given pair (E,S).W-Function and ξ = SV0r2∞exp(2EQV0). For a given stiffness, there is a precise energy for whichrmin = rmax = rc, in which case the orbit is circular, with a radius rc. It also corresponds to theextremum of the quasi-potential, found by taking the first derivative:rc =√−S/V0 (5.17)which is real when S and λ are of opposite signs (when the particulate carries a charge oppositeto the one of the beam). For the circular orbit of energy Ec, we see that the angular kineticenergy Kφ,c = Ec +QV0 ln(rc/r∞) = −12QV0 depends only on the charge of the dust particulate.Studying the quasi potential also allows for the definition of the dimensionless shape parameter,κ(E,S):κ = E − Ec2Kφ,c = −EQV0− 12[1 + ln( −SV0r2∞)](5.18)Note that κ is strictly positive, as the circular orbit energy is, by definition, the minimal energyallowed for a given stiffness (recall that the stiffness depends on the angular momentum). For afixed S, κ increases with the difference in energy from the circular orbit and dictates the shapeof the orbit, as can be inferred from [68]. For κ→ 0, the orbit is circular, and for κ→∞, theorbit degenerates into a straight line going through the center of the beam. Fig. 5.6 showsdifferent orbit shapes following κ.515.3. Orbiting UFOs=0.003 =0.143=0.693 =2.443Figure 5.6: Examples of orbits of charged dust particulates aroundthe LHC beam. The shape parameters κ were chosen from [68] forcomparison. The beam screen height is 36.9 mm.Period of Radial OscillationBecause of the cylindrical symmetry, the angular position φ is of little interest for this problem.On the contrary, the radial position is extremely important, especially in the context of theLHC, as beam-dust interaction are highly influenced by the radial position. The period of radialoscillation, T , can be obtained from the Hamiltonian, following:T =√2m∫ rmaxrmindr√E −QV˜0(r)(5.19)Because of the logarithmic potential, this integral cannot be solved analytically and must beevaluated numerically, except for the limit cases of κ→ 0 and κ→∞ [68]. From these limitconditions, it can be inferred that the period T (E,S) follows:T = T0e−E/(QV0)f(κ) for κ > 0 (5.20)where T0 = 2pi√m−2QV0 r∞ and f(κ) is a function of κ only, respecting f(κ → 0) = 1√e andf(κ→∞) = 1√pi. Based on the numerical integration of Eq. (5.19), an approximation of f(κ)525.3. Orbiting UFOsrespecting the boundary conditions is given by:f(κ) ≈( 1√e− 1√pi)eAκ(B−κ) + 1√pi(5.21)where A = 6.1125× 10−2 and B = −19.8135 are dimensionless fitting parameters (like κ). Usingthis approximation, the error is always below 0.014%, over the full domain of κ. The fittingparameters are independent of the parameters of the problem and give the general solution ofEq. (5.19) for a logarithmic potential. The radial period is shown in Fig. 5.7.0 2 4 6 8 1010-310-210-1100101102Radial Period, T (s)S = − 1.0e− 06 Vm2S = − 1.0e− 05 Vm2S = − 1.0e− 04 Vm2Figure 5.7: Radial period as a function of κ for Q/m = −0.01 C/kg.Increasing the absolute value of the charge-to-mass ratio slightly shiftthese curves downward, as a higher angular momentum is required toend up with the same stiffness.Charge-Carrying Wire With GravityBased on observations from the Dynamics Simulation Tool, it seems that the effect of gravity is,to first order, to shift the orbits vertically down. Analytic considerations can be used to supportthis observation. Adding the contribution from gravity, the quasi-potential becomes:V˜g(r, φ) = S(r, φ) 12r2 − V0 ln(r/r∞) +1Q/mgr sin(φ) (5.22)where g is the gravitational constant and S(r, φ) is no longer constant, because of the φdependence of the potential. When gravity is present, there is no inertial reference frame inwhich the angular momentum is perfectly conserved since the angular velocity is higher in thelower half orbit than the upper half. However, there is an inertial reference frame (not centeredwith the orbit) in which the variation of angular momentum is minimized and where S is almostconstant. Let’s imagine a primed coordinate system (r′, φ′) shifted down vertically by a distance535.3. Orbiting UFOsd such that y′ = y + d. We can write:r2 = x2 + y2 = r′2 + d2 − 2y′d = r′2(1 + ′) (5.23)where ′ =(dr′)2 − 2 ( dr′) sin(φ′). The quasi potential in this shifted frame becomes:V˜g(r′, φ′) = Seff(r′, φ′) 12r′2 −V02 ln(r′2(1 + ′)/r∞)+ 1Q/mg(r′ sin(φ′)− d) (5.24)where Seff = S/(1 + ′) is not exactly the particulate stiffness measured in the primed coordinateS ′ = S − (x˙′d)2Q/m[1 + 2(r′2d) (φ˙′x˙′)], but rather the effective one, by identification with the originalpotential. Assuming that d r′, we can use ln(1 + ′) ≈ ′ and write:V˜g(r′, φ′) ≈ V˜0(Seff, r′)− V02 ′ + 1Q/mg(r′ sin(φ′)− d)≈ V˜0(Seff, r′) + V0(dr′)sin(φ′) + 1Q/mg(r′ sin(φ′)− d) (5.25)We see that there is a specific choice of d for which V˜g(r′c, φ′) ≈ V˜0(r′c), showing that the potentialin this shifted frame takes the form of the original potential, without gravity. We get:d = −r′c sin(φ′)V0(Q/m)gr′csin(φ′)− 1 ≈ − gV0(Q/m)r′2c (5.26)where the final result is the averaged value over a full φ′ period. Note that the same resultis obtained if we simply consider that V0(Q/m)gr′c sin(φ′)  1, which is the case, by hypothesis.In this shifted frame, the angular momentum is almost constant for radial positions close tor′c =√−Seff/V0. However, the orbits are not centered around the origin of this frame, asmentioned earlier, but rather around:ycenter = r′c′ − d (5.27)which lies below the beam (ycenter < 0). Lastly, to formally find the condition under which theeffect of gravity can be neglected, one can look at the Taylor expansion of Eq. (5.17) around rc.This leads to:545.3. Orbiting UFOsV˜g(r) ≈ V˜g(rc) +[V˜(1)0 (rc) +1Q/mg sin(φ)](r − rc)+ 12[V˜(2)0 (rc)](r − rc)2 + . . .= V˜g(rc) +1Q/mg sin(φ)(r − rc)− V0r2c(r − rc)2 + . . .= V˜0(rc) +1Q/mgr sin(φ)− V0r2c(r − rc)2 + . . .= V˜0(rc)− V0r2cr2 +[ 1Q/mg sin(φ) + 2V0rc]r − V0 + . . . (5.28)which is identical to the Taylor expansion (to any order) of V˜0(r) around rc, provided that theφ-dependent term in bracket can be neglected. In terms of the parameters of the problem, thismeans that the effect of gravity can be neglected for any φ provided that:1|Q|/mg 2V0rc(5.29)An equivalent requirement is that d 2rc.The LHC caseBased on observations during Run I and Run II operation, no failure cases or unexpectedobservation around LHC operation led to the hypothesis of having orbiting dust particulates,unlike in electron storage rings. However, it is not excluded that some observations could be asymptom of orbiting dust in the LHC. In order to proceed to a quantitative study of orbitingdust in the LHC, more work on the subject would be needed. In the following section, qualitativeconclusions based on tentative simulations are presented to better understand the dynamics oforbiting dust particulates.Tentative SimulationsUsing the UFO Dynamics Simulation Tool, the dynamics of orbiting dust particulates aroundthe LHC was simulated. With or without magnetic field present in the beam pipe, the transversemovement of the dust particulate is very consistent with what was described in the previoussections, which confirms the validity of the approximations used in the mathematical descriptionof the problem. The biggest difference lies in the charging of the dust particulates over time,which causes the shape parameter to change with time. It is useful to describe the motion interms of a succession of instantaneous orbits. When the dust is far away from the beam butnot too close to the beam screen, instantaneous orbit parameters are stationary. However, withevery pass close to the beam, the ionization of the particulate due to secondary electrons causesa very sharp change in the instantaneous orbit parameters, as shown on Fig. 5.8, where thefractional change for Q, S, E and κ is presented.555.3. Orbiting UFOs0 1 2 3 4 5Time (ms)−202468Fractional change (%)Q(t)S(t)E(t)(t)Figure 5.8: Evolution of the instantaneous orbit parameters duringone pass close to the beam. The fractional change is only given as anexample, the precise value is highly influenced by the exact conditionsof the interaction.In general, a dust particulate orbiting around the LHC beam behaves according to one of thefollowing:1. If the interaction is long enough or strong enough because of a very small rmin, theparticulate can become positively charged, at which point it behaves like a UFO and isrepelled from the beam.2. If the interaction is quick enough or weak enough, the charge will remain negative and theshape parameter, κ, will increase over time as shown in Fig. 5.8. This is true because theparticulate charge will only increase (positively) over time, as knock-on electron productionis the predominant charging mechanism for a highly negatively charged dust particulate.a) Since Q only changes during passes close to rmin, the instantaneous orbit will evolvetoward a degenerate orbit with the same rmin. As a result, the minimal distance tothe center of the beam does not decrease over time, but is kept constant.b) Because of the increase in κ, the instantaneous radial period (period of interactionwith the beam) is not constant, but increases over time.c) If the charge increases so much that gravity becomes dominant, the dust is extractedfrom the beam. This will be discussed in more details below.565.3. Orbiting UFOsFigure 5.9: Example trajectory for a negatively charged dust particulateorbiting the LHC beam. With every interaction with the beam, thedust is charged and the instantaneous shape parameter increases. rminis almost constant throughout the event. In the last phase, gravitydominates and prevents the dust from reaching a degenerate orbit,forcing it into the beam screen.Orbits LifetimeThree main mechanisms could lead to a dust particulate leaving the orbit of the beam, namely:the charging of the particulate up to a point where gravity dominates, the particulate hittingthe beam screen, or its thermal breakdown. Using the current UFO model, the lifetime of dustparticulates as a function of their starting position was simulated. If the dust starts outsideof the beam’s vicinity, the orbit can carry on forever, but is difficult to detect as it does notinteract with the beam. If it starts too close to the beam, the ionization is quicker than typicalorbital periods and the dust particulate is sent to the beam screen.4.0 4.5 5.0 5.5 6.0Starting position (beam σ)105106107108Lifetime (LHC turns)1061071081091010Peak Losses (coll./s)LifetimePeak LossesFigure 5.10: Example of the evolution of the lifetime of a large (50 µm)dust particulate orbiting the LHC beam with high Q/m (-1 C/kg). Forsmaller or less charged dust particulates, the lifetime is shorter andthe losses are smaller. 575.3. Orbiting UFOsEffect on the BeamOrbiting dust in the LHC could have three main detrimental effects on the proton beam: beamlosses, E-field kick and emittance growth. Since the dust is generally orbiting a few σ away fromthe center, emittance growth should not be a problem, unlike the case of electron and antiprotonstorage rings. As for beam losses, Fig. 5.10 shows the peak losses expected for the extreme caseof a large dust with a large charge-to-mass ratio. As discussed above, if the interaction with thebeam is strong enough, orbiting dust would leave a similar loss signature than the typical UFOs.Taking the example of Fig. 5.9, it would also be possible to observe several UFO-like spikesover a short time scale, as was already observed in the LHC. An example of the loss signaturefor that case is shown on Fig. 5.11. Finally, because of the high negative charge required for adust particulate to orbit the LHC beam, the beam would be subject to a periodic electric fieldaveraging several kV/m with amplitudes also in the order of kV/m, directed radially toward itscenter. More work on the subject is needed to evaluate the impact of such a field on the beam.0 10 20 30 40 50 60 70Time (ms)0.000.250.500.751.001.251.501.75Beam losses (coll./s)1e10Figure 5.11: Beam losses corresponding to the trajectory shown onFig. 5.9. The dust hits the beam screen after 195 ms.58PART IIUFO Time Profile Analysis59CHAPTER 6Time Profile StudyPrevious work already studied the UFO rate observed along the ring and its correlation withbeam parameters (intensity, energy, bunch spacing, etc.) or exterior factors like electron clouds[12], [23]. The dose deposited by UFOs recorded by the UFO Buster was also extensively studiedin order to assess the risk for magnet quenches and other limitations to LHC operation at higherenergy [11], [13]. However, to better understand UFO dynamics, validate the UFO DynamicsSimulation Tool and understand the origin of UFOs, a thorough investigation of the time profileof UFO losses is necessary, in complement to other UFO dynamics studies [35], [65]. In thecontext of this thesis, UFO time profiles recorded by ICBLMs and dBLMs were analyzed. In thischapter, the UFO Buster time profiles from Run II are analyzed and compared to simulations.A closed expression for UFO losses is proposed and the shape of experimental UFO losses alongstandard arc cell is discussed. Moreover, the time asymmetry observed in the measurement isdiscussed, and an experimental evidence supporting the presence of initially negatively chargedUFOs in the LHC is presented.6.1 Monte-Carlo SimulationsAs mentioned in the previous chapter, UFO dynamics depends on several input parameters. TheUFO properties (mass, material, size), the initial conditions (UFO charge, position, velocity)and the beam properties (energy, intensity, transverse size) all influence the trajectory followedby the dust particulate and the resulting proton losses. For this intricate problem, the effect ofa single parameter cannot be isolated and generalized. As a result, Monte-Carlo simulationsare particularly useful to study UFO dynamics, as they allow for these 9 parameters to varyseparately. The general approach taken in the context of this thesis is to try to understandhow a given range of values for each input parameter (e.g.: limiting the radius to 1-100 µm)influences the distribution of UFO losses obtained when all parameters are allowed to vary.Table 6.1 gives a typical set of input parameters used for UFO Monte-Carlo simulations. Unlessspecified otherwise, the following sections present simulation results in gray, to distinguish themfrom measurements. The charge-to-mass ratios considered are in agreement with the resultsdiscussed in Ch. 4 (see Fig. 4.2) and the beam size is computed from the longitudinal location of606.2. Measurement CollectionTable 6.1: Input parameters for Monte-Carlo simulations.Parameter ValuesUFO Q0/m -10−8 − -100 C/kgUFO Position Top of beam screenUFO Radius 1 µm− 100 µmUFO Material C, Cu, Si, AlBeam Energy 6.5 TeVBeam Intensity 3× 1011 − 3× 1014Longitudinal Position, s 0−106.9 mBeam σx and σy 80 µm− 260 µmthe event, using a normalized emittance of 2.5 µm·rad. Using this approach, it was found thatthe current model can explain most properties of the time profile of UFO losses (event length,amplitude, integrated dose) found in the measurements [70], but that the left-right asymmetryof the time profiles is not yet understood [71]. This is discussed in the following sections.6.2 Measurement CollectionIn total, the UFO Buster was triggered 337,217 times during Run II. The triggering algorithmrequires that two ICBLMs within 40 m of each other pick up a signal which is at least fivetimes greater than the background noise (i.e., > 0.1 Gy/s for signals integrated in 640 µs bins).This condition was defined following UFO studies from Run I [12]. Out of these events, ICBLMtime profiles were only successfully recorded 57,262 times because of priority conflicts withother devices, or because of the dead time of the system.Since other losses can also satisfy the triggering condition from the UFO Buster, not all thetime profiles recorded correspond to UFOs. For this reason, additional filters were applied toeach time profile, ensuring a minimal signal length of 5 data points (5× 80 µs) and a sufficientsignal-to-noise ratio to allow for signal processing down the line. With these filters, the numberof validated UFO time profiles was narrowed down to 3,035. A few additional hundred eventswere then discarded to only keep Gaussian-like profiles. The rejected profiles from this last stepwere individually examined. Requiring a minimal event length certainly introduces a bias in theanalysis, but this condition is necessary to ensure that a meaningful numerical analysis can beperformed, as will be presented in the following sections. The resulting ensemble of validatedevents is only a subset of all UFO events from Run II, some being never detected because oflosses below the detection threshold, others being lost in the recording of the ICBLM file andsome being lost because of a length comparable to the ICBLMs resolution. The assumptionmade in the following sections is that the validated events are representative of most UFOs inthe LHC, which was indirectly validated by comparing with previous analysis of UFO data.616.2. Measurement CollectionThe distribution of measured UFOs along standard arc cells around the LHC is highly influencedby the response of the ICBLMs (see Fig. 3.2), which depends on geometric effects and materialin the neighbouring equipment. In Fig. 6.1 the number of UFOs observed for each ICBLMtype around the LHC is shown. The straight sections are not considered in this analysis. Thehorizontal axis follows each beam in order for the ICBLMs to be grouped by matching betafunctions. Because of the higher sensitivity of ICBLMs located upstream of quadrupole magnets,one expects to detect more UFOs at these BLMs. This is the case, as shown in Fig. 6.1, for bothbeams. Around 30% of arc UFOs are recorded upstream of the quadrupole magnets, originatingfrom somewhere inside the third dipole. Since the role of quadrupoles is inverted between beam1 and beam 2, one can see that for both beams, more UFOs are detected at a common physicallocation (the horizontally defocusing quadrupole for beam 1 at 48 m, and focusing quadrupolefor beam 2 at 100 m). This could be explained by the presence of additional components aroundevery other quadrupole, which would change the response curve of the ICBLMs. This trendshould be further investigated in the future, as it could be linked to the triggering mechanismof UFOs. Another important observation from Fig. 6.1 is the difference in the number of UFOsobserved between both beams at the ICBLM downstream of quadrupole magnets. Based on thelow sensitivity of these ICBLMs, almost no UFOs should be detected at that location, whichis the case for beam 1. For beam 2 however, a significant number of UFOs are detected. It islikely that the difference is coming from accelerator equipment not accounted for in the ICBLMresponse, which needs to be verified.20 40 60 80 100Distance along the beam (m)051015202530UFO Distribution (%) Beam 1Beam 2Figure 6.1: Distribution of arc UFOs along both beams for a regulararc cell during Run II. Only validated events measured during stablebeam are considered. The horizontal axis follows each beam (not theabsolute location in the LHC) from their entrance point in the arc cell,in order for the ICBLMs to be grouped by matching beta functions.626.3. UFO Time Profile: Skewed Gaussian Signal6.3 UFO Time Profile: Skewed Gaussian SignalTo simplify the study of UFO time profiles and compare different UFO events in a systematicway, characteristic values of each time profile were extracted from the measurements using adedicated fit. Data collected during both Run I and Run II showed asymmetric Gaussian losseswith about half the UFO events having a signal with longer rise time (negatively skewed) andhalf having a longer fall time (positively skewed). The rise time, identified in Fig. 6.2, is definedas the time required for the ICBLM signal to rise from 1% to 100 % of its peak value. In thesame way, the fall time is the time required for the signal to drop from 100% to 1% of its peakvalue. Previous work on the subject mentioned the time profile asymmetry of UFO losses [12],[23], but did not explain the origin of this asymmetry. An example for both positively skewedand negatively skewed measurements is also shown in Fig. 6.5.−0.50 0.00 0.50 1.00 1.50 2.00Time (ms)0.000.050.100.150.200.25Signal (Gy/s)Rise Fall ICBLMFW at 1%Binned fitFitFigure 6.2: Typical UFO measurement from ICBLMs (blue). The risetime and fall time of the signal are identified and the fit from Eq.(6.1)is shown (black) and binned (orange).To study this effect in more detail, a skewed normal distribution is proposed to represent UFOlosses. This distribution has a single highest value and a left-right asymmetry following:Φ(t) = Ae−(t−µ)22σ2(1 + erf[α(t− µ)√2σ2])(6.1)where A, σ, µ, α are the amplitude, scale, location and shape parameters, respectively. Theshape parameter is linked to the skewness of the distribution (the third standardized moment),usingγ1 :γ1 =4− pi2(δ√pi/2− δ2)3with δ = α√1 + α2(6.2)As discussed in Ch. 2, the shape of UFO losses is believed to be coming from the convolution636.3. UFO Time Profile: Skewed Gaussian Signalof the UFO trajectory with the beam profile. Due to the interaction with the proton beam,UFOs are ionized, leading to an asymmetry in the incoming and outgoing speed of the dustparticulate with regard to the beam. For simple trajectories, if the entry speed of the UFOin the beam is larger than the exit speed, the losses obtained are positively skewed. On thecontrary, for smaller entry speed than exit speed, the losses are negatively skewed. Eq.(6.2)allows representing both cases, and is found to be in very good agreement with the inelasticcollision rate from the UFO Dynamics Simulation Tool for typical UFO parameters. To fitEq.(6.2) to measurements, the skewed normal distribution is binned in 80 µs bins in the sameway as the ICBLM signal and the best fit is obtained through a standard least square method.In Fig. 6.2, the underlying skewed normal distribution is shown by the black dash curve, and itsbinned version is shown in orange. This skewed Gaussian fit reproduces most measurementsand simulated loss profiles.With this analytic expression, the shape of UFO events is uniquely defined using threeparameters: A, σ and α (µ being a translation parameter), which allows to quantify thevariations between different time profiles. In addition, one can directly find the best matchbetween simulated UFO events and measured UFO events by comparing these 3 parameters. Aleast square method can be used to find the closest match between two time profiles based ontheir fitting parameters. A histogram for each parameter from experimental UFO time profilesis shown in Fig. 6.3 for all arc ICBLMs, separated arc ICBLMs and for all straight sectionICBLMs. The added box plots show the five-number summary (1st, 25th, 50th, 75th, 99thpercentiles from each distribution). Overall, one can see that there is no significant difference inthe time profiles of UFOs observed in the arcs or in the straight sections. When comparingICBLMs along the arc cell, comparison should be made between BLMs of the same family (seeTable 3.1) because of the difference in the response curve of each family, which can introduce abias in the recorded time profiles. One can see that no significant difference is observed betweenindividual BLMs of the same family, despite the fact that the transverse beam shape (circular,horizontal beam, vertical beam) evolves along the arc cell following the beta functions.Based on Monte-Carlo simulations, the event length σ should be strongly influenced by thebeam shape since a vertically larger beam generally leads to longer events. Fig. 6.4 shows thedistribution of σ obtained from Monte-Carlo simulations, assuming uniformly distributed UFOsalong a standard arc cell. Only the events with detectable peak losses (for any ICBLM) areconsidered. Since the bias from varying ICBLM response is not considered in this analysis,Fig. 6.4 gives the underlying distribution of events that could be detected by each BLM, providedthat all events are successfully recorded by the UFO Buster. The effect of the beam shapeon the loss signals is less important than anticipated, mainly because of the wide coverage ofeach ICBLM, which explains the experimental results from Fig. 6.3. For example, the ICBLMlocated downstream of the horizontally focusing quadrupole is expected to detect events up64All Arc BLMs 0 20 40 60 80 100 Straight SectionsDistance along the beam (m)10 410 310 210 1100Amplitude, A (Gy/s)Beam 1Beam 2All Arc BLMs 0 20 40 60 80 100 Straight SectionsDistance along the beam (m)0100200300400500600700Event length,  (s)Beam 1Beam 2All Arc BLMs 0 20 40 60 80 100 Straight SectionsDistance along the beam (m)1.000.750.500.250.000.250.500.751.00SkewnessBeam 1Beam 2All Arc BLMs 0 20 40 60 80 100 Straight SectionsDistance along the beam (m)10 710 610 510 4Integrated dose (Gy)Beam 1Beam 2Figure 6.3: Histogram of the amplitude A, the event length σ, the skewness γ1 and theintegrated dose from the UFO Buster time profiles for both beams. The box plots givethe five-number summary (1st, 25th, 50th, 75th, 99th percentiles) from each distribution.Only validated events measured during stable beam are considered. The histograms areshown for all arc BLMs combined, separated arc cell BLMs and straight section BLMs.Comparison should be made between BLMs of the same family (see Table 3.1) because ofthe difference in the response curve for each family.656.4. Skewness Distributionto 15 m upstream of its location, where the beam shape varies significantly (from horizontallylarger beam, to round beam to vertically larger beam with an almost maximal βy(s)). Forthis reason, the effect of the beam shape on the time profile recorded by different ICBLMsis blurred out or is too small to be detected with the current approach. Extensive FLUKAsimulations combined with the UFO Dynamics Simulation Tool would be needed for a morecomplete understanding of the results shown in Fig. 6.3.All Arc BLMs 0 20 40 60 80 100Distance along the beam (m)0100200300400500600700Event length,  (s)SimulationsFigure 6.4: Distribution of the event length, σ, from Monte-Carlosimulations. The box plots give the five-number summary (1st, 25th,50th, 75th, 99th percentiles) of the distribution.6.4 Skewness DistributionAs shown in Fig. 6.3, the skewness of UFO time profiles collected during Run II is distributedbetween −1 and 1. An example of both positively skewed and negatively skewed measurementsis shown in Fig. 6.5.0.8 0.6 0.4 0.2 0.0 0.2Time (ms)0.000.050.100.150.20Signal (Gy/s)0.4 0.2 0.0 0.2 0.4 0.6Time (ms)0.000.050.100.150.200.250.300.35ICBLMBinned fitFitFigure 6.5: Example of measured UFO events with negative skewness(left) and positive skewness (right). The skewed Gaussian fit is shown,as well as the resulting binned fit. 666.4. Skewness DistributionPrevious UFO studies from Run I reported a similar observation [23], as shown in Fig. 6.6a.The equivalent plot for Run II is presented in Fig. 6.6b. Note that Fig. 6.6a shows an estimateof −γ1 on the vertical axis whereas Fig. 6.6b shows the statistical third standardized moment γ1from the 80 µs binned ICBLM signals. In both cases, there is a slight decrease of the skewnessas a function of the peak loss rate. The distribution observed during Run II is similar to theone observed during Run I.(a)10-3 10-2 10-1 100Peak loss rate [Gy/s]−1.00−0.75−0.50−0.250.000.250.500.751.00Skewness, γ1MeasurementsFit, y= aln(bx)Average (binned)(b)Figure 6.6: Measured skewness and peak loss rate of UFO eventsobserved during (a) Run I, from [23]. (b) Run II. The fit parametersare a = −0.062± 0.007 and b = 56± 11 (Gy/s)−1. Only events withsufficient signal which occurred in stable beam are shown. The orangedots indicate the average skewness and average peak signal of the datawithin the bins defined by the horizontal bars and standard error ofthe mean shown with vertical bars.This is an important observation, as it is inconsistent with the current UFO model, whichcan only account for negatively skewed time profiles. In the model, UFOs generally acquire acharge above +106e following their interaction with the beam. Given the electric field of theLHC beam, this corresponds to an acceleration of 15 km/s2 at the point of closest approach.Comparing this with gravity, and taking into account that UFO signals generally last betweenthree and ten LHC turns, one can calculate that the entry speed of a neutral UFO is around 0.5m/s, while the exit speed is around 5 m/s, leading to a negatively skewed loss signal. If theentry speed of the UFO is larger (because of an initial negative charge, or initial velocity), itpenetrates deeper into the beam, acquires a higher positive charge and is repelled with an evenlarger exit speed. As a result, with the current model, all simulated losses follow a negativelyskewed profile, which is incompatible with measurements. Previous versions of the model alsoonly allowed for negatively skewed profiles [23]. Different hypotheses were tested using the UFODynamics Simulation Tool to identify the source of this discrepancy, most of which led to thevalidation of the model presented in Ch. 5. The main hypotheses to be investigated in the futurein order to explain the positive skewness observed in the measurement are the ones discussed676.5. UFO Chargein section 5.2: considering all charging and discharging mechanisms of the UFO as it interactswith the beam as well as considering the heating of the UFO, which could lead to its thermalexpansion.6.5 UFO ChargeSince the start of UFO studies, it was generally assumed that UFOs are initially neutral(Q0 = 0) and fall into the beam due to gravity. Based on the discussion presented in Ch.4,this assumption appears unlikely due to the presence of multiple charging mechanisms for dustparticulates in the LHC beam pipe. In fact, it was found that the measurements recordedduring Run II have rise times which are too short to be explained by initially neutral UFOs.Fig. 6.7 shows the distribution of rise time from the ICBLMs measurements, compared withsimulation results obtained with initially neutral UFOs (Q0 = 0) and negatively charged UFOs(|Q0/m| > 5× 10−3 C/kg).0.0000.0010.0020.0030.0040.0050.006.Simulations, Q0 =00.0000.0010.0020.0030.0040.0050.006.Simulations, |Q0/m|>  5 · 10−3 C/kg0 100 200 300 400 500 600 700.0.0000.0010.0020.0030.0040.0050.006.ICBLM MeasurementsExclusion region, Q0 =0Rise Time (µs)Observation densityFigure 6.7: Distribution of rise times found in Monte-Carlo simulationsfor initially neutral UFOs (top) and initially negatively chargedUFOs (middle), compared with experimental distribution from ICBLMmeasurements (bottom). Neutral UFOs cannot explain the short risetimes (below 262 µs) observed in measurements.It is found that neutral UFOs only lead to loss profiles with rise times larger than 262 µs. Evenafter excluding ultra-short UFO events in the filtering process of the UFO Buster, more than40% of Run II UFOs are found to have rise times shorter than what can be explained by neutral686.5. UFO ChargeUFOs. However, if an initial charge is added to the UFO, the rise time distribution agrees wellwith the measurements and covers the whole range of values observed experimentally. This resultstrongly suggests that dust particulates interacting with the beam of the LHC must carry aninitial negative charge. This conclusion is consistent with what is expected for a dust-in-plasma,as discussed in Ch.4, and the charge required is in the expected order of magnitude.69ConclusionThe UFO Problem will remain an important concern for LHC operation in the years to come,especially with the High Luminosity upgrade of the LHC, but also for future high intensityand high energy hadron colliders, proton-antiproton colliders and electron storage rings. Thisdissertation addressed important considerations of the current UFO hypothesis and led tosignificant novel contributions about the formation, charging mechanisms and dynamics offalling dust particulates in the LHC.From the theoretical point of view, a new numerical method was developed to accuratelycompute the electric field of the LHC beam in presence of the beam screen. This finding isessential to simulate accurately the dynamics of charged particulates around the beam. Basedon a literature review of cosmic dust and dust-in-plasma observed in laboratory conditions,it was found that the environment of the LHC (due to electron clouds and synchrotronradiation) is conducive to multiple charging mechanisms for dust particulates already presentor being grown in the beam pipe. This case study was discussed for the first time andis a key finding which should be further studied. In addition, it allowed to compute theadhesive forces between UFOs and the conductive beam screen, a critical element in thestudy of plausible UFO release mechanisms. Lastly, the possibility of having negativelycharged dust particulates orbiting the beam of the LHC was suggested for the first time asa plausible alternative to the prevailing hypothesis of dust particulates falling in the protonbeam. The idea was thoroughly discussed and a mathematical description of the orbits was given.Experimentally, the time profile of proton losses from thousands of UFO events were analyzed.Following an intensive validation of the UFO Dynamics Simulation Tool, where numerousupgrades were made and benchmarked against FLUKA, measurements were compared tosimulations. It was found that the very fast rise time of the time profiles of UFO losses measuredduring both Run I and Run II can only be explained by UFOs carrying an initial negativecharge. This result is an important step in understanding UFO dynamics and the triggeringmechanism of UFOs. Moreover, the charge required to explain experimental observations is con-sistent with expectations for dust-in-plasma and the charging mechanisms discussed theoretically.70ConclusionTo further analyze the time profile of UFO losses, a systematic approach was taken, basedon a skewed Gaussian fit which allows describing loss profiles using only three parameters.This simplifies the analysis of time profiles, reduces the amount of data to record and allowsto quantify the match between a UFO candidate and measured proton losses using a leastsquare method. The fitting parameters from thousands of events were analyzed, which showedthat the time asymmetry (positively skewed) of about half the measurements collected duringRun I and Run II cannot be explained with the current UFO model. This critical observationshould be the first focus of future studies as it may lead to an important result about UFOdynamics or UFO release mechanisms, two elements which can significantly influence the timeevolution of proton losses. Bunch-by-bunch losses were also discussed and two novel numericalmethods making use of diamond beam loss monitors were presented. These methods offer apromising way of directly studying UFO dynamics. Efforts should be made toward acquiringlocal bunch-by-bunch loss measurements of sufficient quality before the start of the next LHCrun in 2022. These methods should be further developed and readily applied on measurements,as they could provide the first direct measurement of UFO dynamics to date. This result, inaddition to validating or invalidating the current UFO Hypothesis, would lead to a much betterunderstanding of UFO dynamics.For future work, a large database of simulated trajectories and corresponding losses should becreated to allow for Bayesian inferences about UFOs. Using the fitting parameters presented inthis thesis, the probability that a given UFO event originated from specific UFO candidates couldbe evaluated rigorously. From there, one could infer the distribution of masses, materials, radiiand initial conditions for dust particulates in the LHC, which would be a major advancement inthe understanding of the UFO problem.71Bibliography[1] P. Belanger, “Generalizing the Method of Images for Complex Boundary Conditions :Application on the LHC Beam Screen,” 2019. arXiv: 1905.03405. [Online]. Available:http://cds.cern.ch/record/2677615.[2] A. Ferrari, P. R. Sala, A. 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Available:http://cds.cern.ch/record/2721906.77APPENDIX AAdditional FiguresA.1 Beam Electric Field (sec. 1.4)Figure A.1: Relative error on the potential for a filament placed midwaybetween the boundary and the center (y/R = 0.5)(a) (b)Figure A.2: Comparison of the maximum relative error for the potential everywhereinside the boundary for the case of a cylindrical boundary as a function of the beamlocation. The Matrix method is the one discussed in sec. 1.4). (a) N = 200 (b)N = 50078A.2 UFO Release Mechanism in the LHC (sec. 4.3)(a) Surface separation d = 200 nm (b) Surface separation d = 200 nm(c) Surface separation d = 500 µm (d) Surface separation d = 500 µmFigure A.3: Escape velocity for a charged dust particulate to leavethe beam screen (red) and terminal velocity at 5σ of the beam fordust spontaneously released (blue). (a) and (b) correspond to aninitial surface separation of 200 nm whereas (c) and (d) correspondto an initial surface separation of 500 µm. The charge-to-mass ratioconsidered are the ones allowed from Fig. 4.2.79

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