3D MODELING, ANALYSIS, AND DESIGN OF A TRAVELING-WAVE TUBE USING A MODIFIED RING-BAR STRUCTURE WITH RECTANGULAR TRANSMISSION LINES GEOMETRY by SADIQ ALI ALHUWAIDI B.S., University of Colorado, Boulder, 2011 M.S., University of Colorado, Colorado Springs, 2014 A dissertation submitted to the Graduate Faculty of the University of Colorado Colorado Springs in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Electrical and Computer Engineering 2017 © 2017 SADIQ ALI ALHUWAIDI ALL RIGHTS RESERVED This dissertation for the Doctor of Philosophy degree by Sadiq Ali Alhuwaidi has been approved for the Department of Electrical and Computer Engineering by Heather Song, Chair T.S. Kalkur Charlie Wang John Lindsey Zbigniew Celinski Date 12/05/2017 ii Alhuwaidi, Sadiq Ali (Ph.D. Engineering - Electrical Engineering) 3D Modeling, Analysis, and Design of a Traveling-Wave Tube Using a Modified Ring- Bar Structure with Rectangular Transmission Lines Geometry Dissertation directed by Associate Professor Heather Song. ABSTRACT A novel slow-wave structure of the traveling-wave tube consisting of rings and rectangular coupled transmission lines is modeled, analyzed, and designed in the frequency range of 1.89-2.72 GHz. The dispersion and interaction impedance characteristics are investigated using High Frequency Structure Simulator, HFSS, and a power run is carried out using Finite-Difference Time-Domain (FDTD) code, VSim. The performance of the design providing a better output power, gain, bandwidth, and efficiency is compared to the conventional and existing designs by implementing cold- and hot-test simulations. In addition, an electron gun and periodic permanent magnet, PPM, is designed using EGUN code and ANSYS Maxwell, respectively. The electron beam has a beam voltage of 262 kV, beam current of 12 A, cathode emission density of 5.968 , and minimum radius of A 2.0 mm. The required gun parameters and magnetic field levels,c including the geometrical quantities, are calculated to produce the appropriate electron flow and achieve adequate beam stability. Iterations and analysis of those quantities are provided to properly understand the procedure of the design. iii DEDICATION This dissertation is dedicated to the memory of my grandmother, Zainab, who always prayed for me, to my beloved parents, Ali and Balkess, without whom none of this work would be possible, to my wife, Maryam, and son, Jafar, for supporting me in all my endeavors, to my sister and brothers for standing by me, and to the memory of my uncle, Naeem. iv ACKNOWLEDGMENTS I owe thanks to many people for helping me prepare this work. Unfortunately, limited space dictates that only a few of them can receive a formal acknowledgment. But this is not taken as a disparagement of those whose contributions remain anonymous. My gratitude is immeasurable. My foremost appreciation goes to my academic advisor Dr. Heather Song for her fundamental role in my doctoral work. I am deeply indebted to her for the non-stop accompaniment of my progress during the research and providing all conditions to keep my work running. I would like to thank Dr. T.S. Kalkur for his excellent guidance throughout my degree, and particularly the courses taken with him. I would like to express my gratitude to Dr. John Lindsey for the substantial influence that his courses have had on my knowledge. In addition, I gratefully acknowledge my Ph.D. committee members, Dr. Charlie Wang and Dr. Zbigniew Celinski, for their time and valuable suggestions of the dissertation. I am grateful to Tech-X Corporation for giving me VSim software to pursue my research towards my doctoral degree. Finally, this work would not be accomplished without my parents, brothers, sister, and wife, who cheered me up, supported me academically and emotionally through the rough road to finish this dissertation, and stood by me. v TABLE OF CONTENTS CHAPTER I. INTRODUCTION........................................................................................................ 1 1.1 Early Milestones of Traveling-Wave Tube........................................................... 1 1.2 Classical Types of Electronics .............................................................................. 4 1.2.1 Solid State Devices ........................................................................................ 4 1.2.2 Vacuum Devices ............................................................................................ 5 1.3 Domain of Vacuum Tubes .................................................................................. 10 1.4 Literature Work ................................................................................................... 11 1.5 Novelty of Proposed Work ................................................................................. 14 1.6 Overview of Dissertation .................................................................................... 16 II. BACKGROUND AND THEORY ........................................................................... 17 2.1 Basic Operation of Traveling-Wave Tube .......................................................... 17 2.2 Electron Dynamics .............................................................................................. 23 2.2.1 Electric Field ................................................................................................ 23 2.2.2 Magnetic Field ............................................................................................. 29 2.3 Source of Electrons ............................................................................................. 30 2.3.1 Cathode ........................................................................................................ 31 2.3.2 Thermionic Emission ................................................................................... 32 2.3.3 Schottky Effect............................................................................................. 39 2.3.4 Space Charge Limitation.............................................................................. 42 2.3.5 Life Expectancy ........................................................................................... 45 2.4 Electron Gun and Focusing Structure ................................................................. 46 vi 2.4.1 Electron Guns............................................................................................... 47 2.4.2 Focusing Structure ....................................................................................... 60 2.4.2.1 Uniform-Field Focusing........................................................................ 61 2.4.2.2 Periodic Permanent Magnet (PPM) Focusing....................................... 70 2.5 Traveling Wave Interaction ................................................................................ 79 2.5.1 Electronic, Circuit, and Determinantal Equations ....................................... 79 2.5.1.1 Electronic Equation ............................................................................... 80 2.5.1.2 Circuit Equation .................................................................................... 82 2.5.1.3 Determinantal Equation ........................................................................ 85 2.5.2 Synchronous Condition ................................................................................ 86 2.5.3 Nonsynchronous Condition ......................................................................... 90 2.6 TWT Slow-Wave Circuits .................................................................................. 91 2.6.1 Wave Velocities ........................................................................................... 92 2.6.2 Dispersion .................................................................................................... 94 2.6.2.1 Coaxial Transmission Line ................................................................... 94 2.6.2.2 Rectangular Waveguide ........................................................................ 96 2.6.3 Bandwidth .................................................................................................. 102 2.6.4 Power ......................................................................................................... 109 2.6.4.1 Backward Wave Oscillations and Suppression to Peak Power .......... 109 2.6.4.2 Typical Support Techniques to Average Power ................................. 113 2.6.5 Attenuators and Severs .............................................................................. 118 2.6.6 Ring-Bar and Ring-Loop TWT .................................................................. 120 2.7 Collector ............................................................................................................ 123 vii 2.8 Transmission Line Fundamentals ..................................................................... 128 III. ELECTRON GUN AND FOCUSING STRUCTURE DESIGNS ........................ 133 3.1 Overview ........................................................................................................... 133 3.2 Design Specifications........................................................................................ 135 3.2.1 First Electron Gun Design ......................................................................... 135 3.2.2 Electron Gun Design of the Proposed Novel Slow-Wave Structure ......... 135 3.3 Calculations......................................................................................................