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Electron Density Fluctuations and Fluctuation-Induced Transport in the Reversed-Field Pinch

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Electron Density Fluctuations and Fluctuation-Induced Transport in the Reversed-Field Pinch ELECTRON DENSITY FLUCTUATIONS AND FLUCTUATION-INDUCED TRANSPORT IN THE REVERSED-FIELD PINCH by Nicholas E. Lanier A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) at the University of Wisconsin–Madison 1999 i ELECTRON DENSITY FLUCTUATIONS AND FLUCTUATION- INDUCED TRANSPORT IN THE REVERSED-FIELD PINCH Nicholas E. Lanier Under the supervision of Professor Stewart C. Prager At the University of Wisconsin–Madison An extensive study on the origin of density fluctuations and their role in particle transport has been investigated in the Madison Symmetric Torus reversed-field pinch. The principal physics goals that motivate this work are: investigating the nature of particle transport in a stochastic field, uncovering the relationship between density fluctuations and magnetic field fluctuations arising from tearing and reconnection, identifying the mechanisms by which a single tearing mode in a stochastic medium can affect particle transport. Following are the primary physics results of this work. Measurements of the radial electron flux profiles indicate that confinement in the core is improved during pulsed poloidal current drive experiments. Correlations between density and magnetic fluctuations demonstrate that the origin of the large amplitude density fluctuations can be directly attributed to the core-resonant tearing modes, and that these fluctuations are advective in the plasma edge; however, these fluctuations appear compressional in the core, provided the nonlinear terms are small. Correlations between density and radial velocity fluctuations indicate that although the fluctuations from the core-resonant modes dominate at the edge, their relative phase is such that they do not cause transport there, consistent with the expectation that core modes do not destroy edge magnetic surfaces. This is not the case in the plasma core, where the density and radial velocity fluctuations are in phase, indicating that ii these fluctuations couple to induce transport. Measurements during PPCD discharges show a large reduction in density fluctuations associated with the core-resonant modes. Furthermore, the phase of these fluctuations in the core changes to be π/2 relative to the radial velocity fluctuations, indicating these fluctuations no longer couple to induce transport. iii Acknowledgements Although my defense was only two hours, it represented the culmination of a long and challenging path. In pursuing my degree, there have been many noteworthy individuals that have offered support and direction, and although I have done the work, they have made this possible, and I wish to acknowledge their efforts. Prior to my graduate career, five individuals stand out as being very influential in my progress in physics. Mr. Larry Dean, my high-school physics teacher who started my formal training in physics, Russ Coverdale, the academic advisor at Purdue, who stuck me in the Honors curriculum and forced me to swim. Still as an undergraduate, my first real world work experience was obtained with Dr. John Molitoris, may he always have a place to sit, and Dr. Paul Springer, who showed the faith in my leadership skills by sending me to Russia to run some great physics experiments. Finally I’d like to thank Dr. C. Choi, who introduced me to plasma physics and opened the door to my coming to Wisconsin. iv My years at Wisconsin have been the most enjoyable of my life and the MST group has been a principal reason for that. Faculty such as Sam Hokin, Paul Terry, James Callen, and Chris Hegna (if not he should be) have really worked to expand my plasma physics knowledge. I am especially grateful for the efforts of my advisor Stewart Prager, Cary Forest, and Darren Craig (who will be faculty someday, no doubt about it). MST staff like John Sarff, who introduced me to PPCD, Dan “former vacuum man now diversifying into computer repair” Den Hartog, Genady “come with an envelope leave with a solution” Fiksel have really fostered my experimental talents. Not to be underestimated are the benefits gained from working with David “the Texan” Brower and Yong “lip smackin’ good” Jiang. Finally, I thank Dale, Larry, Paul, Mikey, Kay, John, Don and the rest of the MST support crew for helping to turn my ideas into reality. By far the most outstanding aspect of MST life are the graduate students. In my six years here, students like, James “Jimbo” Chapman, Carl “the only man I’ve seen argue (and win) with Callen” Sovinec, Jay “the Mason” Anderson, Ted “Ironman” Biewer, Brett “the big lovable vacuum Nazi” Chapman, Ching- Shih “LT” Chaing, Alex “BA” Hansen, Derek “the Bavenator” Baver, Paul “Wrong glass sir” Fontana, Cavendish “the Dishman” Mckay, Susanna “nickname pending” Castillo, and of course Neal “it’ll happen someday” Crocker, have made my career here unforgettable. I have no wish to leave such a remarkable set of individuals, but my development as a physicist requires it. Finally I’d like to thank those outside my work life, my parents who not so jokingly quote that I was bred for science, my sister Catherine, my friends, Scott v Kruger, Paul Ohmann, Brian Totten, others that have been supportive of my efforts here. I have been truly blessed. In memory of Katherine Nicole Lanier (December 20, 1996) vi Table of Contents Abstract . i Acknowledgements . iii Table of Contents . vi List of Tables . xii List of Figures . xiii 1 Introduction 1 1.1 The Reversed Field Pinch . 3 1.2 Magnetic Island Formation and Stochasticity . 6 1.3 Stochastic Transport . 8 1.4 Fluctuation-Induced Radial Particle Flux . 10 1.5 Controlling Fluctuations. 11 1.6 Overview of Thesis. 13 References. 15 vii 2 The Far-Infrared Laser System 17 2.1 Plasma Interferometry Theory . 17 2.2 The Far-Infrared Laser Interferometer . 20 2.2.1 Diagnostic Overview . 20 2.2.2 The CO2 Pumping Laser . 22 2.2.3 The Twin Far-Infrared Laser . 24 2.2.4 Power Distribution . 26 2.2.5 Detection Electronics . 30 2.3 Digital Phase Extraction . 32 2.4 Summary . 37 References. 37 3 Neutral Hydrogen Density In MST 39 3.1 Hydrogen Fueling in MST . 40 3.1.1 The Fueling Cycle . 40 3.1.2 Franck-Condon Neutrals . 42 3.1.3 Neutral Penetration . 42 3.1.4 Measuring Neutral Density . 45 3.2 The Hα Array . 46 3.2.1 Alignment and Calibration . 48 3.3 Hα Emission . 50 viii 3.3.1 Hα Behavior in Standard Discharges . 50 3.3.2 Hα Behavior in PPCD Discharges . 53 3.4 Neutral Particle Density . 55 3.4.1 Neutral Particle Profiles in Standard and PPCD Discharges . 55 3.4.2 Neutral Particle Losses . 59 3.4.3 Neutral Particle Population and CHERS . 59 3.5 Summary . 61 References . 62 4 Impurity Behavior In MST 64 4.1 Introduction . 65 4.2 Atomic Physics . 66 4.2.1 Ionization . 67 4.2.2 Radiative and Dielectronic Recombination . 68 4.2.3 Charge Exchange Recombination. 69 4.3 Charge State Equilibrium (Coronal or LTE) . 71 4.4 Electron Impact Excitation and Line Emission . 72 4.5 The ROSS Filtered Spectrometer . 74 4.5.1 Filter Characteristics . 74 4.5.2 The Soft X-ray Diodes. 76 4.5.3 Diagnostic Geometry and Light Collection. 77 ix 4.5.4 Deciphering Impurity Line Emission . 78 4.5.5 Line Contamination . 79 4.6 Impurity Effects . 80 4.6.1 Impurity Concentration in Standard Discharges . 80 4.6.2 Impurity Concentration in PPCD Discharges . 83 4.6.3 Electron Sourcing From Impurities . 88 4.6.4 Impurity Radiation . 90 4.7 Estimating Impurity Confinement Times . 91 4.8 Summary . 93 References . 94 5 Radial Electron Flux Profile Measurements 96 5.1 Equilibrium Electron Density Behavior . 97 5.1.1 Density Profiles in Standard Discharges . 97 5.1.2 Density Profiles During PPCD . 100 5.2 Radial Particle Flux . 103 5.2.1 Extracting Radial Particle Flux . 103 5.2.2 Radial Particle Flux in Standard and PPCD Discharges . 104 5.2.3 Particle Confinement Times . 106 5.3 Convective Power Loss. 107 5.4 Summary . 108 x References . 109 6 Fluctuations and Fluctuation-Induced Particle Transport 110 6.1 Electron Density Fluctuations . 111 6.1.1 Chord-Integrated Fluctuation Amplitude . 112 6.1.2 Frequency Spectrum . 114 6.1.3 Wave Number Content . ..
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