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A Classic Thesis Style Turbulence and Transport Measurements in Alcator C-Mod and Comparisons with Gyrokinetic Simulations by Paul Chappell Ennever B.S. Applied Physics (2009) Columbia University School of Engineering and Applied Science Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2016 © Massachusetts Institute of Technology 2016. All rights reserved. Author................................................................................. Department of Physics February 22nd, 2016 Certifiedby............................................................................. Miklos Porkolab Professor of Physics Thesis Supervisor Acceptedby............................................................................ Nergis Mavalvala Professor of Physics Associate Department Head for Education Turbulence and Transport Measurements in Alcator C-Mod and Comparisons with Gyrokinetic Simulations by Paul Chappell Ennever Submitted to the Department of Physics on February 22nd, 2016, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Turbulence in tokamak plasmas is the primary means by which energy is transported from the core of the plasma to the edge, where it is lost, and is therefore the main limitation of tokamak plasma performance. Dilution of the main-ion species was found to have a stabilizing effect on ion gyroradius scale turbulence in tokamak plasmas. Dilution of deuterium tokamak plasmas is the reduction of the ratio of the deuterium ion density to the electron density, nD=ne, to less than 1.0 through the introduction of low-Z impurity species into the plasma. Controlled dilution experiments were performed on Alcator C-Mod wherein plasmas at a range of electron density and plasma current were seeded with nitrogen while a cryopump held the electron density fixed. The electron density fluctuations due to turbulence were monitored using a phase contrast imaging (PCI) diagnostic, an absolutely calibrated diagnostic that measures the line- integral of the electron density fluctuations along 32 vertical chords. In these experiments the seeding reduced the PCI density fluctuations, and had a stabilizing effect on the ion energy transport. The seeding also reversed the direction of intrinsic rotation in certain cases. Nonlinear simulations using the gyrokinetic turbulence code GYRO were performed using measured kinetic profiles from the dilution experiments both before and after the nitrogen seeding. The GYRO simulations reproduced the observed reduction in the turbulent ion energy transport with the nitrogen seeding. The GYRO simulated turbulent density fluctuations were compared to the PCI measurements using a synthetic diagnostic, and they were found to be consistent. GYRO simulations were also performed varying only the main ion dilution to explore the theoretical effects of the dilution on energy transport. Through this it was found that the dilution reduced the turbulent ion energy transport in a wide variety of cases, but primarily increased the critical gradient at low densities, and primarily reduced the stiffness of the transport at high densities. This dilution effect is related to observations of reductions in energy transport from seeding on other tokamaks, and will likely have an impact on ITER and future fusion reactors. Thesis Supervisor: Miklos Porkolab Professor of Physics 3 ACKNOWLEDGMENTS The work of this thesis could not have been completed alone, and there are many people whose contributions I would like to acknowl- edge. Firstly, I would like to thank my advisor, Professor Miklos Porkolab of MIT, for teaching me so much these past six years, and for supporting me and putting me in touch with others who could help me with things he could not. His help with editing the thesis as well was invaluable in making it a polished document. I would also like to thank the many people from different institutions and fields who helped to make the theoretical and experimental work in this thesis possible. • Doctor Gary Staebler and Doctor Jeff Candy from General Atom- ics, for teaching me the GYRO and TGLF codes, as well as build- ing and maintaining them to be (relatively) simple to use for experimentalists, and answering questions I had about running the codes. • Professor Naoto Tsujii currently at University of Tokyo, for teach- ing me how to operate the PCI system on C-Mod, analyze its data, and writing the tools necessary to run it even after he had gone. • Doctor Eric Edlund from Princeton, for helping me with PCI during the 2014 and 2015 experimental campaigns, including testing and installing the new detector. • Doctor J. Chris Rost of MIT, for maintaining the synthetic PCI diagnostic for GYRO, and for helping me out a lot with writing my first paper. • Doctor Matt Reinke of Oak Ridge, for helping with the impurity analysis, as well as the ion temperature and velocity profile mea- surements, even under difficult experimental circumstances. • All the diagnosticians of the Alcator C-Mod team, in particular Doctor Jerry Hughes for Thomson scattering, Doctor Amanda Hubbard for ECE, Doctor John Rice for HIREX, Doctor Seung Gyou Baek for Reflectometer, Doctor Jim Irby for TCI, and Doc- tor Steve Wolfe for magnetics. • All the members of the core transport group on Alcator C-Mod, in particular Doctor Darin Ernst who helped me understand gyrokinetic theory and helped to maintain the LOKI cluster on which I worked, and Nathan Howard whose work on ETG modes helped me to understand my own results. 5 In addition, I would like to extend a special thanks to my parents, Doctors John and Fanny Ennever, for setting me up for success from the very beginning, and supporting me throughout the many years of schooling that I’ve done. Finally, I would like to thank my fiance, Mei Wei Chen, for her unwavering love, support and patience. I couldn’t have made it this far without her, or her food. 6 CONTENTS 1 introduction 13 1.1 Fusion Energy 13 1.2 Tokamak Energy Transport 14 1.3 Alcator C-Mod 16 1.4 Thesis Outline 18 2 plasma turbulence 23 2.1 Linear Fluid Ion Temperature Gradient Modes 24 2.2 Gyrokinetics 26 2.3 Gyrokinetic Simulation Codes 28 2.4 The Flux-Gradient Relationship 31 2.5 Summary 33 3 phase contrast imaging 39 3.1 The Phase Contrast Imaging Technique 39 3.2 Phase Contrast Imaging on Alcator C-Mod 41 3.3 Absolute Calibration 46 3.4 Synthetic PCI Diagnostic For GYRO 47 3.5 Summary 49 4 ohmic dilution experiments 53 4.1 Motivations For Studying Dilution 53 4.2 Experimental Setup 54 4.3 Experimental Results 58 4.3.1 Effect of Nitrogen Seeding on Energy Transport 59 4.3.2 Effect of Nitrogen Seeding on Density Fluctua- tions 63 4.3.3 Effect of Nitrogen Seeding on Toroidal Rota- tion 67 4.4 Summary and Conclusions 70 5 gyro validation results 77 5.1 Linear GYRO Simulations Of Turbulent Growth Rates 78 5.2 Nonlinear Local GYRO Simulations Of Turbulence 80 5.2.1 Local GYRO Simulations at r/a = 0.8 82 5.2.2 Local GYRO Simulations at r/a = 0.6 84 5.3 TGYRO Profile Modification Using TGLF 88 5.3.1 Simulations With The Nominal Experimental Pro- files 88 5.3.2 Simulations With The TGYRO Flux-Matched Pro- files 89 5.3.3 Simulations With The Average Of TGYRO And Experimental Profiles 90 7 8 contents 5.4 Global Nonlinear GYRO Simulations Of Turbulence 92 5.5 Density Fluctuation Comparisons Between GYRO Sim- ulations And PCI Measurements 95 5.6 Summary And Conclusions 99 6 theoretical study of dilution effect with gyro 105 6.1 Effect Of Dilution On GYRO Linear Growth Rates 105 6.2 Effect of Dilution On GYRO Energy Fluxes 107 6.3 Quanitfying The Effect Of Dilution On GYRO Stiffness And Critical Gradient 112 6.4 Summary and Conclusions 115 7 concusions and future work 119 7.1 Summary of This Thesis Work 119 7.2 Conclusions and Implications 121 7.3 Future Work 122 I Appendix 127 a absolute impurity density measurements 129 a.1 Determination Of Impurity Densities From Zeff And Line Brightnesses 129 a.2 Results Of Impurity Analysis 132 b other factors considered in gyro 135 b.1 Inclusion Of ~E × B~ Shear 135 b.2 Inclusion Of Multiple Impurity Ion Species 136 LISTOFFIGURES Figure 1 Fusion Reaction Rates 14 Figure 2 Tokamak Schematic 15 Figure 3 The LOC And SOC Regimes 16 Figure 4 GYRO 3-D Potential Fluctuations 30 Figure 5 Relationship Between Energy Flux And Tem- perature Gradient 31 Figure 6 GENE Simulations From A JET Discharge Show- ing Stiffness And Critical Gradient 32 Figure 7 PCI Schematic 41 Figure 8 Alcator C-Mod PCI System 42 Figure 9 Alcator C-Mod PCI Beam Path 43 Figure 10 Frequency Response of PCI Detectors 45 Figure 11 Example PCI Calibration Plots 47 Figure 12 Plot Of GYRO Density Fluctuations 48 Figure 13 Plot Of Synthetic PCI Spectra With And With- out ~E × B~ Drifts 49 Figure 14 Magnetic Equilibrium 55 Figure 15 Experimental Traces 56 Figure 16 Experimental Energy Confinement Times 57 Figure 17 Experimental nD=neValues 58 Figure 18 Experimental Energy Confinement Times Ver- sus neq95 60 Figure 19 Gyrobohm Normalized Flux Profiles 61 Figure 20 Example Change in Qi=QGB and a=LTi 61 Figure 21 Changes With Seeding Fluxes And Gradients At r/a = 0.6 62 Figure 22 Changes With Seeding Of Fluxes And Gradi- ents At r/a = 0.8 63 Figure 23 Experimental PCI Spectra 64 Figure 24 Change In High Phase Velocity PCI Feature 64 Figure 25 PCI Reflectometer Time Series Comparison 66 Figure 26 Toroidal Rotation Profiles 68 Figure 27 Toroidal Rotation Versus Effective Collisional- ity 69 Figure 28 Toroidal Rotation Versus nDq95 70 Figure
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