UCLA Electronic Theses and Dissertations
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UCLA UCLA Electronic Theses and Dissertations Title Photons with a Twist: Coherent Optical Vortices From Relativistic Electron Beams Permalink https://escholarship.org/uc/item/943048wn Author Knyazik, Andrey Publication Date 2013 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California University of California Los Angeles Photons with a Twist: Coherent Optical Vortices From Relativistic Electron Beams A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Andrey Knyazik 2013 c Copyright by Andrey Knyazik 2013 Abstract of the Dissertation Photons with a Twist: Coherent Optical Vortices From Relativistic Electron Beams by Andrey Knyazik Doctor of Philosophy in Physics University of California, Los Angeles, 2013 Professor James B. Rosenzweig, Chair The purpose of this dissertation is to examine a proof of principle experiment and its background that generates and amplifies coherent light that carries orbital angular momentum (OAM) in a single pass via free-electron laser (FEL) at the fundamental operating frequency using the HGHMG (High Gain High Mode Gen- eration) scheme. The background to this experiment was done uniting two rapidly expanding and distinct fields of study: (a) high-order OAM light modes, which interact in new ways with matter, and (b) FELs, in which a relativistic electron beam emits coherent, ultra bright, frequency-tunable light via Bremsstrahlung radiation. Due to the medium less nature of FELs, the OAM light generated via FEL interaction enables new frontiers of exploration at Angstrom wavelengths and femtosecond time scales. This dissertation will be divided into two parts: theory and background necessary to perform a proof of principle experiment de- scribed in Chapters 1 through 3; and physical description of insertion devices and experiment setup, execution and data analysis described in Chapters 4 and 5. ii The dissertation of Andrey Knyazik is approved. Peter M. Felker Pietro Musumeci James B. Rosenzweig, Committee Chair University of California, Los Angeles 2013 iii To my family and friends . who have been there with me throughout my journey and challenged me throughout my life iv Table of Contents 1 Introduction :::::::::::::::::::::::::::::::: 1 1.1 Dissertation Outline.........................6 1.2 Before FELs: Relevant Electromagnetism and Accelerator Physics7 1.2.1 Most Relevant basic Electricity and Magnetism......7 1.2.2 Accelerator Physics Formalism................ 11 1.2.3 Dipoles............................. 13 1.2.4 Chicanes............................ 14 1.2.5 Quadrupoles.......................... 16 1.2.6 Envelope equation and FODO lattice............ 17 1.2.7 Constant Focusing Channel................. 21 1.3 Principles of FEL Operation:..................... 23 1.4 Introduction to higher order light modes, and OAM light..... 30 1.5 Conclusions.............................. 35 2 Dielectric Waveguide Expansion, 3-D Gain Length, and Helical Undulator Focusing ::::::::::::::::::::::::::::: 39 2.1 Dielectric Eigenmode Expansion of High-Gain 3D FEL Equations Quick Overview and Summary.................... 39 2.2 Gain length fitting formula for free-electron lasers......... 42 2.3 Helical Undulator Focusing and Beam Transport.......... 48 2.4 Conclusions.............................. 51 v 3 Charged Particle Radiation and Harmonic Interaction in a He- lical Undulator :::::::::::::::::::::::::::::::: 53 3.1 Charged Particle Radiation..................... 53 3.1.1 Undulator Radiation..................... 56 3.2 Transition Radiation......................... 58 3.2.1 Coherent bunch TR...................... 60 3.3 Harmonic Interaction in a Helical Undulator............ 68 3.4 Conclusions.............................. 74 4 Helical Pre-Buncher Design, Simulation, and Calibration; and Simulation of FEL OAM Experiment at NLCTA ::::::::::: 75 4.1 Helical Pre-Buncher Design..................... 77 4.1.1 Period Doubling........................ 81 4.1.2 Detailed CAD Files...................... 84 4.1.3 Pre-Buncher Simulation Results............... 86 4.2 Undulator Measurement and Tuning................ 88 4.2.1 Hall Probe Results...................... 88 4.2.2 Pulse Wire Method...................... 96 4.3 Simulation results of Pre-Buncher interaction............ 103 4.4 Proposed Phase Diagnostic Methods................ 111 4.4.1 Shack-Hartmann Wavefront Sensor............. 112 4.4.2 Interferometer......................... 113 4.4.3 Triangular Aperture..................... 114 4.5 Conclusions.............................. 117 vi 5 OAM FEL Experiment at the NLCTA Laboratory ::::::: 118 5.1 Introduction............................. 118 5.2 Experimental Design......................... 119 5.3 NLCTA Laboratory Background and parameters.......... 119 5.4 Experimental Results......................... 122 5.4.1 Phase Retrieval Algorithm.................. 126 5.4.2 Effect of Slit on observed intensity profile.......... 131 5.5 Conclusion.............................. 133 5.5.1 Motivation for possible future experiments......... 133 References ::::::::::::::::::::::::::::::::::: 136 vii List of Figures 1.1 Standard Gaussian Distribution...................3 1.2 Dipole Schematic............................ 14 1.3 Chicane Schematic........................... 15 1.4 Trace space ellipse and Twiss parameter definitions......... 20 1.5 Three feeding scenarios of FEL interaction.............. 28 1.6 The pondermotive bucket illustration of FEL interaction in a low gain regime............................... 29 1.7 Laguerre Gaussian mode propagation cartoon, intensity, and phase plots of p=0, l varies......................... 36 1.8 Amplitude of different Laguerre Gaussian modes where p and l vary between 0 and 3......................... 37 3.1 Resonance Undulator Condition.................... 57 4.1 Helical Undulator Diagram...................... 77 4.2 Radia simulation of magnetic field on axis and electron trajectory through the 8 period right-handed helical undulator........ 78 4.3 Radia simulation of electrons traveling on axis through the right- handed 8 period helical pre-buncher................. 79 4.4 Magnet dimensions........................... 81 4.5 Kurchatov Undulator Schematic................... 82 4.6 Radia drawing of magnets in the helical undulator......... 83 4.7 Helical Pre-Buncher Solidworks Drawing............... 86 viii 4.8 Helical Pre-Buncher Schematic.................... 87 4.9 Radia simulation of magnetic field on axis and electron trajectory through the undulator........................ 89 4.10 Radia simulation of electrons traveling on axis through the right- handed helical pre-buncher...................... 90 4.11 Hall probe measurement setup at SLAC.............. 93 4.12 Hall probe measurement summary at SLAC............ 94 4.13 Radia simulation compared with Hall probe measurements.... 95 4.14 Radia simulation compared with Hall probe measurements of K in the wrong orientation scenario.................... 96 4.15 Picture of the pulse wire setup.................... 99 4.16 Pulsed Wire First Integral Vertical Component.......... 100 4.17 Pulsed Wire First Integral Horizontal Component......... 101 4.18 Pulsed Wire Second Integral Vertical Component......... 101 4.19 Pulsed Wire Second Integral Horizontal Component........ 102 4.20 Energy spread as a function of phase................ 106 4.21 Far field undulator radiation after 1.5 m of planar radiator.... 108 4.22 Fundamental bunching factor and OAM undulator power gener- ates as a function of planar radiator length............. 109 4.23 LG mode expected bunching with wrong magnet orientation... 110 4.24 LG mode expected bunching..................... 110 4.25 Shack-Hartmann Setup........................ 112 4.26 Interferometer setup......................... 113 ix 4.27 Idealized fundamental and OAM mode interferometer signal.... 115 4.28 Interference pattern due to a triangular aperture of a fundamental and an OAM mode........................... 116 5.1 Experimental Setup Cartoon..................... 120 5.2 OAM Signal Diagnostic Setup Cartoon................ 124 5.3 Near and Far Field Intensities, and phases calculated using the phase retrieval algorithm....................... 128 5.4 E-field profile calculated at radiator exit and decomposed into LG- modes.................................. 130 5.5 E-field diffraction pattern of OAM mode due to a vertical 200 µm wide slit................................ 132 x List of Tables 2.1 Scaled FEL parameters........................ 44 4.1 NLCTA Original Experiment Undulator Parameters........ 79 4.2 NLCTA Updated Experiment Undulator Parameters....... 84 4.3 Pulse Wire Parameters........................ 98 4.4 Scaled FEL parameters........................ 107 5.1 Relevant Electron Beam, Laser and Undulator Parameters.... 122 xi Acknowledgments It would not be possible for me to complete this work without a plethora of help from multiple individuals I would like to acknowledge. First and foremost I want to thank my advisor Professor James Rosenzweig for generation of multitude of outstanding ideas, and positive attitude. Without his charisma, insight, passion that he instills in all of his graduate students, diplomacy, patience, and ability to guide you in the right direction when youre lost, this work would not have been possible. Without his set-up of the PBPL structure I wouldnt have had the useful interaction with everyone else mentioned here, and none of this would be possible. Second I would