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DOCTORAL THESIS June 2010 David Belohrad

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DOCTORAL THESIS June 2010 David Belohrad Czech Technical University in Prague Faculty of Electrical Engineering Department of Measurement DOCTORAL THESIS CERN-THESIS-2010-131 05/10/2010 June 2010 David Bˇelohrad Czech Technical University in Prague Faculty of Electrical Engineering Department of Measurement Fast Beam Intensity Measurements for the LHC Doctoral Thesis David Bˇelohrad Geneva, April 2010 Ph.D. Programme: Electrical Engineering and Information Technology Branch of study: Measurement and Instrumentation Supervisor: doc. Ing. Petr Kaˇspar,CSc. DEDICATION Writing this thesis was a long term competition with myself. Competition full of slow and painful learning, searching for correct answers, and frustration in times when the inspiration betrayed me. The winners are however those who sustain. I want to dedicate this thesis to my wife, Barbora, without whom this thesis might not have been written, and to whom I am greatly indebted. You have been with me all the distressful way through, seamlessly taking care of our family affairs, and providing me with all those essential little things which allowed me to finish the task. Thank you for your love, support, and source of encouragement and inspiration that you have always given me. Thank you as well for your insistence, which boosted me in the rainy days. I want to dedicate this thesis to my son Erik as well. Thank you for your patience. I promise to spend more time with you. I love you both 1 ACKNOWLEDGEMENT I want to sincerely thank to my supervisor, Assoc. Prof. Petr Kaˇspar, for his supreme guidance during my research and study. He was always accessible and willing to help me in research and in technical matters related to the university. I want to sincerely thank to following people as well: To Ulrich Raich, Rhodri Jones, Lars Søby and Patrick Odier for their excellent • advices and fruitful discussions, and for providing great working environment To Serge Mathot for his comments in the matters of brazing and material science • To Wilhelmus Vollenberg for provided information about various coatings types and • theirs usage To Bernard Henrist for his comments on baking technology used at CERN • To Bernard Jeanneret for his comments on vacuum chamber calculus and for his • patience with me and to all my colleagues at work, who create a great working team with whom is • pleasure to work 3 CONTENTS 1 List of Symbols 7 2 List of Abbreviations 11 3 Introduction 15 4 Current state of the problem 17 4.1 Beam theory as seen by an electronics engineer . 18 4.1.1 Beam Current . 18 4.1.2 Wall Image Current . 23 4.1.3 Particle beams and noise sources . 27 4.2 Non-intercepting beam intensity measurements . 30 4.2.1 Wall current monitors . 30 4.2.2 DC current transformers . 32 4.2.3 The fast beam current transformers . 33 4.3 Fast beam intensity measurements at CERN . 48 4.3.1 Types of the beams produced at CERN . 49 4.3.2 LINAC and LEIR FBCTs . 50 4.3.3 FBCTs in the transfer lines and circular accelerators . 52 4.4 The LHC intensity measurement . 56 4.4.1 Functional specification of the intensity measurement using FBCTs 57 4.4.2 The LHC injection scenarios . 60 5 Detailed objectives for this work 63 6 Analysis of the requirements for the intensity measurement 65 6.1 Determination of the required dynamic ranges . 65 6.1.1 Input signal definition . 65 6.1.2 Dynamic range of the beam signal . 67 6.2 Determination of the transformer bandwidth . 68 6.2.1 The LHC pilot bunch . 69 6.2.2 Injection of multiple batches into the LHC . 74 6.2.3 The high frequency cut-off estimation . 84 7 The FBCTs 91 7.1 Mechanical design of the FBCT . 91 7.1.1 Supporting elements . 93 7.1.2 Magnetic Circuit of the Measurement device . 95 7.2 The vacuum chamber fabrication technological processes . 98 7.2.1 The vacuum chamber . 98 7.2.2 Titanium coating . 100 8 Analysis and implementation of the electronic chain 105 8.1 Acquisition system . 107 8.2 RF signal distribution . 108 8.2.1 Principle of operation . 108 5 CONTENTS 8.2.2 Filtering . 111 8.2.3 Hardware implementation . 113 8.2.4 Electrical properties . 114 8.3 Machine protection system - beam circulating flag detector . 117 8.3.1 Hardware implementation . 117 8.3.2 Algorithm of detection . 118 8.3.3 Physical realisation . 119 8.4 The calibration . 119 8.4.1 Calibration turn . 119 8.4.2 Pulse Current Generator . 121 8.4.3 Implementation of the Calibrator . 131 8.4.4 Measured results . 132 9 Achieved results 135 10 Conclusions and outcomes from the dissertation thesis 141 10.1 My contribution to the work . 146 10.2 Theses for future work . 147 11 PhD student publications 149 11.1 Publications related to the dissertation . 149 11.2 Other publications . 149 12 References 151 13 Appendices 157 13.1 Background information . 157 13.1.1 Particle accelerators . 157 13.2 Simplified mechanical acceptance calculation for the BCTRs . 163 13.3 Photographs . 167 6 1 LIST OF SYMBOLS Laplace Operator L 1 − Inverse Laplace Operator L φ Unity vector of angular component in cylindrical coordinate system ρ Unity vector of radial component in cylindrical coordinate system dB A vector element of magnetic induction T er Unity vector in the radial direction of the cylindrical coordinate system − e Unity vector in Cartesian coordinates: x; y; z h i 2 j Vector of current density Am− 1 v Vector of velocity ms− z Unity vector of z component in cyl. and Cartesian coordinate systems − Φ Unity vector in angular direction of the cylindrical coordinate system − Fs Vector of Lorentz force N B Vector of magnetic flux density T 1 E Vector of electric field V m− F1; F2 Vectors of force N F Force N ~ The reduced Planck's constant eV s α Generalised angle rad β Relativistic factor v=c βx;y Optical beta-function m δ Dirac pulse δ Momentum offset at the injection p − Time constant s Transverse emittance at specific energy mrad 1 0 Permittivity of vacuum F m− n Normalised transversal emittance mrad γ Relativistic factor −1 λN Number of charges per unit length m− 1 µ Absolute permeability Hm− 1 µ0 Permeability of vacuum Hm− µ Relative permeability r − ν Time constant of a first order low-pass filter s 1 ! Angular frequency rads− 1 !0 Angular revolution frequency rads− 1 !s Synchrotron oscillation angular frequency rads− φ(t) Gaussian distribution function σ Longitudinal RMS beam size m σx Standard deviation of x σx;y Transversal RMS beam size m τ Displacement operator in a convolution process 7 List of Symbols τ Time constant of RC circuit s τ(t) Beam lifetime s τs Current amplitude of Synchrotron oscillation A θ Angular deflection rad θ(t) Rounding function ζ Elevation rad a Vacuum chamber radius or general distance m 1 a; b Constants related to bunch width s− a; b Toroid core outer and inner diameter m 1 c Speed of light ms− c Calibration constant k − dl A length element m e Elementary charge C e(k) Measurement relative error in bunch slot k % ec;0 Relative error for the first bunch injected into the LHC % ep;0 Relative error for the LHC pilot bunch % x¯ Mean value of x f0 Revolution frequency Hz fc Low frequency cut-off of a filter or toroid transformer Hz ft Cut-off frequency of a filter Hz g(s) Laplace image of first order low-pass filter. g1(t); g2(t) Partial solution of the convolution integral calculating response of the mea- surement device to the excitation by a beam. h Capacitive pickup electrode length or toroid core width m h(s) Laplace image of a second order filter transfer function H(t) A second order filter transfer function ib(t) Instantaneous beam current A ig(t) Instantaneous bunch current A io(t) Instantaneous beam current including synchrotron oscillation effects A is(t) Instantaneous beam current orbiting on a circular trajectory A imb(t) Instantaneous beam current of multi-bunch beam A j Imaginary number k Harmonic number or bunch slot number − kβ Beta-beating factor −1 kb Boltzmann constant JK− k Parasitic dispersion factor D − l Length m m Bunch number − m Mass kg me Electron mass kg mp Relativistic mass of the proton eV n Period number − 8 n1; n2 Collimator aperture sizes m p Momentum Ns q Charge C qn Generalised charge C qeb Charge present at capacitive pickup plates C r Distance or radius m s Laplace operator sd Total mechanical displacement m sf Surface enclosed by the shape of the ideal bunch C sCO Closed orbit beam excursion m sp;0 Surface enclosed by the shape of the pilot bunch C t Time s u Generic type B uncertainty uA Type A uncertainty uB Type B uncertainty uC Combined type A and B uncertainty 1 v Velocity ms− ∆f Bandwidth Hz 2 Γ Calculated calibration constant bins− Nabla, mathematical operator r Φ Magnitude of magnetic flux W b Φ(!) Fourier transform of Gaussian distribution function ΦT Magnitude of magnetic flux generated in a toroid W b Θ Calculated calibration offset − A Amplifier gain − A Measured binary value corresponding to a calibration current bins Al Magnetic material specific constant, Inductance per square root H A Relative charge m − B Magnetic induction T C Capacitance F Dparasitic Parasitic dispersion of the beam m E Energy eV 1 E Magnitude of electric field V m− E(k) Absolute error of the measurement in bunch slot k − E0 Particle rest energy eV Ei Injection efficiency % Ep Beam energy eV 1 Ex X component of vector of electric field V m− 1 Ey Y component of vector of electric field V m− 1 Ez Z component of vector of electric field V m− E Absolute error for the first bunch injected into the LHC c;0 − 9 List of Symbols Ee(t) Absolute error caused by transient response of the transformer after the injection − Ekin Kinetic energy of particle eV E Absolute error for the LHC pilot bunch p;0 − E Absolute error for
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