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Density Profiles of Plasmas Confined by the Field of a Levitating, Dipole

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Density Profiles of Plasmas Confined by the Field of a Levitating, Dipole Magnet by Alexander C. Boxer Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2008 c Massachusetts Institute of Technology 2008. All rights reserved. Author.............................................................. Department of Physics September 5, 2008 Certified by. Jay Kesner Senior Research Scientist Thesis Supervisor Certified by. Miklos Porkolab Professor of Physics Thesis Supervisor Accepted by . Thomas Greytak Chairman, Department Committee on Graduate Students 2 Density Profiles of Plasmas Confined by the Field of a Levitating, Dipole Magnet by Alexander C. Boxer Submitted to the Department of Physics on September 5, 2008, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Abstract A 4-channel microwave interferometer (center frequency: 60 GHz) has been con- structed to measure the density profiles of plasmas confined within the Levitated Dipole Experiment (LDX). LDX is the first and only experiment built to study plas- mas confined by the field of a levitating, dipole magnet in a geometry that exploits plasma compressibility to achieve stability. Theoretical predictions|based partly on observations of planetary magnetospheres|suggest that dipole-confined plasmas will be driven by fluctuations into pressure and density profiles that are \stationary" to MHD interchange modes. The stationary pressure profile is characterized by an equal amount of entropy per flux-tube while the stationary density profile is characterized by an equal number of particles per flux-tube. These predictions are of interest to nu- clear fusion research since they imply that the pressure and density profiles of dipole- confined plasmas can be simultaneously peaked and stable. Measurements with the interferometer show that the total density of LDX plasmas is strongly affected by the following parameters: levitated vs. mechanical support of the central dipole coil; input ECRH frequency and power; background pressure of neutral particles; plasma species. The gradients of the density profiles are, however, largely independent of the experimental conditions and approximate the value predicted for the stationary profile. Non-linear analyses suggest that dipole-confined plasmas are maintained in their stationary pressure and density profiles by a process of self-organized convection. We present measurements indicating that this self-organization process is observed in LDX. Thesis Supervisor: Jay Kesner Title: Senior Research Scientist Thesis Supervisor: Miklos Porkolab Title: Professor of Physics 3 4 Acknowledgments This thesis could not have existed without the hard work and vision of the entire LDX team to whom the first thanks is due. To Jay Kesner, for his reassuring and zen-like guidance; to Darren Garnier, who would accept nothing short of excellence from me; to Mike Mauel, for his unwavering enthusiasm: Thank you for allowing me to be a part of the Levitated Dipole Experiment. I would also like to thank our technicians, Rick Lations and Don Strahan, who have always been as quick with a helping hand as with a kind word. And to those LDX'ers who have already moved away|Eugenio Ortiz, Ishtak Karim and Alex Hansen| the welcome you showed me when I arrived has not been forgotten. I would like to thank, especially, my fellow graduate student Jen Ellsworth whose help in many aspects of my research was of great value, but whose friendship I value even more. I was also lucky these last two summers to have worked with two undergraduates, Doug Halket and Tom Sidoti, whose assistance was a great help to me. And thanks is owed as well to LDX's newest graduate student, Ryan Bergmann, for keeping me entertained while I wrote this thesis. More personally, I would like to thank my parents whose love was, for me, both an encouragement and a refuge. And to my sister Abby: how lucky we were to live in the same city and to have had the chance to become this close. What MIT has given me I could happily part with were it not for a few special people whom otherwise I would have not met. Guido Festuccia and Antonello Scardicchio: I think of you both like older brothers. Everything I know about physics I learned from the two of you. But most of all, these years are remarkable to me in that I met the lovely Eva Fast. Living together has been such a wonderful time in my life. Each day a new adventure in our own make-believe world. Each day a new and brighter smile. Be strong, Eva; we'll both muddle-through somehow. 5 6 Contents 1 Introduction 17 2 The Dipole-Confinement Idea 25 2.1 Investigations of the Northern Lights . 25 2.2 The Discovery of the Magnetosphere . 28 2.3 Artificial Radiation Belts: High Altitude Nuclear Detonations . 31 2.4 Insights from Nuclear Fusion Research . 33 2.4.1 The Adiabatic Invariants of Trapped Particles . 33 2.4.2 The Interchange Instability . 39 2.5 The Nature of Dipole Confinement . 45 2.5.1 Collisionless, Single-Particle Approach . 46 2.5.2 Fluid Approach . 51 2.5.3 Consistency at Marginal Stability . 52 2.6 Experimental Investigations . 54 3 LDX: The Levitated Dipole Experiment 59 3.1 Overview . 59 3.2 Theoretical Motivation . 61 3.3 A Path to Fusion Power . 62 3.4 LDX: Major Components . 66 3.4.1 Vacuum Chamber . 66 3.4.2 Floating Coil . 66 3.4.3 Charging Coil . 70 7 3.4.4 Levitation Coil and Laser Positioning System . 70 3.4.5 The Magnetic Field . 71 3.4.6 Microwave Heating . 74 3.5 Diagnostics . 75 3.5.1 Probes . 75 3.5.2 Magnetic Diagnostics . 76 3.5.3 Light Detectors . 77 3.5.4 Vessel Ion Gauge . 77 3.5.5 Microwave Interferometer . 78 3.6 Results from \Supported-Mode" Experiments . 78 4 The LDX Microwave Interferometer 81 4.1 General Remarks . 81 4.2 Design . 82 4.2.1 Overview . 82 4.2.2 Choosing the Frequency . 85 4.2.3 Heterodyning . 87 4.2.4 Power Considerations . 93 4.2.5 Multiple Channels from One Transmitted Beam . 96 4.2.6 Phase Detection in Quadrature . 98 4.3 The Interferometer as Built . 100 4.3.1 Microwave Hardware . 100 4.3.2 IF Hardware . 102 4.4 Measurements and Calibration . 104 4.4.1 Phase-Unfolding . 104 4.4.2 Phase Uncertainty . 106 4.4.3 Calibration . 111 5 From Phase Shifts to Density Profiles 115 5.1 Line-Integrated Densities . 115 5.2 Abel Inversion . 117 8 5.2.1 Statement of the Problem . 117 5.2.2 An Additional Data Point from Probe Measurements . 119 5.2.3 Interpolation and Inversion . 122 5.3 Uncertainties in the Radial Density Profiles . 126 5.3.1 Uncertainties from Abel Inversion . 126 5.3.2 Uncertainties from Refraction . 130 5.4 Uninvertible Density Profiles . 137 6 Density Profiles in LDX 147 6.1 An Observational Atlas . 147 6.2 Line-Integrated Density Trends . 149 6.3 Plasma Current Trends . 155 6.4 Radial Density Profile Trends . 158 6.5 Energy and Particle Balance: First Clues . 168 7 Observations of Plasma Self-Organization 175 7.1 Introduction . 175 7.2 Description of the Phenomenon . 178 7.2.1 Characteristic Features of a Density Transition . 178 7.2.2 The Creation of an Unstable Profile . 182 7.3 Microwave Heating Considerations . 185 7.4 Density Transitions as Plasma Self-Organization . 191 7.4.1 Predictions of Non-Linear MHD Theory . 191 7.4.2 Towards a \Natural" Density Profile . 193 8 Conclusion 199 8.1 Summary . 199 8.2 Future Directions . 201 A Interferometer Hardware 203 B Shot/Time Database 205 9 10 List of Figures 2-1 Kristian Birkeland with his terrella ................... 26 2-2 Comparison of Størmer and Alfv´enorbits . 27 2-3 James Van Allen and Explorer I ..................... 30 2-4 Rayleigh-Taylor instability . 40 2-5 \Good" and \bad" curvature . 41 2-6 Interchange instability . 43 2-7 McIlwain B; L coordinates . 47 3-1 LDX: cutaway photo . 60 3-2 Levitated Dipole Reactor . 65 3-3 LDX: schematic drawing . 67 3-4 F-Coil cross-section . 68 3-5 F-Coil levitating with plasma . 69 3-6 Magnetic Field in LDX . 73 3-7 Location of magnetic diagnostics . 76 4-1 LDX interferometer: illustration . 83 4-2 LDX interferometer: schematic drawing . 90 4-3 Demodulator . 99 4-4 Microwave hardware: internal . 100 4-5 Microwave hardware: external . 101 4-6 IF signal processing box: photo . 102 4-7 IF signal processing box: diagram . 102 4-8 PLL schematic . 103 11 4-9 Raw signal data (shot: 80322020) . 104 4-10 Phase shifts (shot: 80322020) . 105 4-11 Raw signal data (shot: 80516021) . 106 4-12 Phase shifts (shot: 80516021) . 107 4-13 Signal balance (shot: 80322020) . 108 4-14 Signal balance (shot: 80516021) . 109 4-15 Calibration measurements . 113 5-1 Abel inversion geometry . 118 5-2 Chord locations . ..
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