SIMULATION OF A MAGNETRON USING DISCRETE MODULATED CURRENT SOURCES by Sulmer A. Fernández Gutierrez A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering Boise State University May 2014 © 2014 Sulmer A. Fernández Gutierrez ALL RIGHTS RESERVED BOISE STATE UNIVERSITY GRADUATE COLLEGE DEFENSE COMMITTEE AND FINAL READING APPROVALS of the dissertation submitted by Sulmer A. Fernández Gutierrez Dissertation Title: Simulation of a Magnetron Using Discrete Modulated Current Sources Date of Final Oral Examination: 12 March 2014 The following individuals read and discussed the dissertation submitted by student Sulmer A. Fernández Gutierrez, and they evaluated her presentation and response to questions during the final oral examination. They found that the student passed the final oral examination. Jim Browning, Ph.D. Chair, Supervisory Committee Kris Campbell, Ph.D. Member, Supervisory Committee Wan Kuang, Ph.D. Member, Supervisory Committee Mark Gilmore, Ph.D. External Examiner The final reading approval of the dissertation was granted by Jim Browning, Ph.D., Chair of the Supervisory Committee. The dissertation was approved for the Graduate College by John R. Pelton, Ph.D., Dean of the Graduate College. DEDICATION I dedicate this dissertation to my parents, Sulmer and Juan, for their unconditional love, endless support, and encouragement throughout my studies and life. They taught me that even the largest task can be accomplished if it is done one step at a time. I also dedicate this dissertation to my little sister, Cindy, for her love and friendship during my studies and throughout the years. iv ACKNOWLEDGEMENTS I would like to thank Dr. Jim Browning for serving as my major professor and guide through my Ph.D. program. It was a pleasure to be his first Ph.D. student; I truly appreciate all the time and advice he gave me throughout my time at Boise State University. The enthusiasm he has for his research was motivational and encouraging for me, even during tough times in the Ph.D. pursuit. Thanks for all the valuable insights and support, which were a major contribution to complete this dissertation. I would also like to thank Dr. Kris Campbell, Dr. Wan Kuang, and Dr. Mark Gilmore for being willing to serve as members of my committee. I would also like to acknowledge all the faculty and staff that I worked with at Boise State University, took classes from, and met throughout my graduate studies. They were wonderful people and a real pleasure to know. I also acknowledge the funding sources that made my Ph.D. work possible. The first year this research was funded by the Air Force Office of Scientific Research (ASFOR) under Contract No. FA9550-09-C-0141. The remaining time to completion was funded by the Electrical and Computer Engineering (ECE) Department at Boise State University. I would like to thank Dr. Jack Watrous for his help, expertise, advice, and useful discussions about magnetrons. I would also like to acknowledge Tech-X Corporation, especially Dr. David Smithe, Dr. Ming-Chieh Lin, and Dr. Peter Stoltz for their support and advice and for setting up the original magnetron model in VORPAL; their help was v instrumental in this dissertation. Dr. David Smithe, thank you for the professional advice, time you took speaking with me, and overall friendliness. Thank you to my MVEDs research group: Peter, Marcus, and Tyler, you were always open for discussion, helping me find errors, and checking my work. I appreciate your assistance and friendship. Although, we worked in different projects, we were always able to collaborate with each other. Finally, I would like to thank my family and friends (too many to list here but you know who you are!) for providing support and friendship that I needed during my studies, and also during my study breaks. For anyone else, whom I forgot to mention here, many thanks. vi ABSTRACT Magnetrons are microwave oscillators and are extensively used for commercial and military applications requiring power levels from the kilowatt to the megawatt range. It has been proposed that the use of gated field emitters with a faceted cathode in place of the conventional thermionic cathode could be used to control the current injection in a magnetron, both temporally and spatially. In this research, this concept is studied using the 2-D particle trajectory simulation Lorentz2E and the 3-D particle-in-cell (PIC) code VORPAL. The magnetron studied is a ten cavity, rising sun magnetron, which can be modeled easily using a 2-D simulation. The 2-D particle trajectory code is used to model the electron injection from gated field emitters in a slit type structure, which is used to protect the gated field emitters. VORPAL is used to study the magnetron performance for a cylindrical, a five-sided, and a ten-sided cathode. Finally, VORPAL is used to simulate a modulated, addressable, ten-sided cathode. The aspects of magnetron performance for which improvements are desired include mode control, efficiency, start oscillation time, and phase control. The simulation results show that the modulated, addressable cathode reduces startup time from 100 ns to 35 ns, increases the power density, controls the RF phase, and allows active phase control during oscillation. vii TABLE OF CONTENTS DEDICATION .................................................................................................................... iv ACKNOWLEDGEMENTS .................................................................................................. v ABSTRACT ....................................................................................................................... vii LIST OF TABLES .............................................................................................................. xi LIST OF FIGURES ............................................................................................................ xii CHAPTER ONE: INTRODUCTION ................................................................................... 1 1.1 Overview and Introduction ............................................................................ 1 1.2 Motivation and Contributions ........................................................................ 5 1.3 Dissertation Organization .............................................................................. 6 CHAPTER TWO: BACKGROUND..................................................................................... 8 2.1 Magnetron Operating Characteristics ............................................................. 8 2.2 Cylindrical Magnetron ................................................................................. 12 2.3 Magnetron Resonant Circuit and Modes of Operation .................................. 14 2.4 The Hartree and Hull Cutoff Condition ........................................................ 17 2.5 The Diocotron Instability ............................................................................. 19 2.6 Stability and Mode Separation ..................................................................... 22 CHAPTER THREE: LORENTZ2E SIMULATION ........................................................... 30 3.1 Overview ..................................................................................................... 30 3.2 Software ...................................................................................................... 30 viii 3.3 Simulation Setup and Procedures ................................................................. 31 3.4 Electron Trajectory Analysis ....................................................................... 34 3.5 Sensitivity Simulations ................................................................................ 35 CHAPTER FOUR: LORENTZ2E SIMULATION RESULTS ............................................ 37 4.1 Overview ..................................................................................................... 37 4.2 Energy Distribution Analysis ....................................................................... 37 4.3 Electron Velocity ......................................................................................... 39 4.4 Sensitivity Simulations ................................................................................ 41 4.5 Summary of Results .................................................................................... 54 CHAPTER FIVE: VORPAL SIMULATION SETUP ......................................................... 56 5.1 Overview ..................................................................................................... 56 5.2 Software ...................................................................................................... 56 5.3 Finite Difference Time Domain (FDTD) Technique .................................... 57 5.4 Numerical Stability ...................................................................................... 60 5.5 Boundary Conditions ................................................................................... 61 5.6 Dey-Mittra Cut Cell Algorithm .................................................................... 62 5.7 Integration of the Equations of Motion ........................................................ 64 5.8 Modeling of a 2-D Ten Cavity Rising Sun Magnetron ................................. 64 5.9 Simulation Setup and Procedures ................................................................. 67 5.10 Rising Sun Magnetron Model with