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Gyrokinetic Continuum Simulation of Turbulence in Open-Field-Line Plasmas

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Gyrokinetic Continuum Simulation of Turbulence in Open-Field-Line Plasmas Gyrokinetic Continuum Simulation of Turbulence in Open-Field-Line Plasmas Eric Leon Shi A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Astrophysical Sciences Program in Plasma Physics Adviser: Gregory W. Hammett arXiv:1708.07283v1 [physics.plasm-ph] 24 Aug 2017 September 2017 © Copyright by Eric Leon Shi, 2017. All rights reserved. Abstract The properties of the boundary plasma in a tokamak are now recognized to play a key role in determining the achievable fusion power and the lifetimes of plasma-facing com- ponents. Accurate quantitative modeling and improved qualitative understanding of the boundary plasma ultimately require five-dimensional gyrokinetic turbulence simu- lations, which have been successful in predicting turbulence and transport in the core. Gyrokinetic codes for the boundary plasma must be able to handle large-amplitude fluctuations, electromagnetic effects, open and closed magnetic field lines, magnetic X-points, and the dynamics of impurities and neutrals. The additional challenges of boundary-plasma simulation necessitate the development of new gyrokinetic codes or major modifications to existing core gyrokinetic codes. In this thesis, we develop the first gyrokinetic continuum code capable of simu- lating plasma turbulence on open magnetic field lines, which is a key feature of a tokamak scrape-off layer. In contrast to prior attempts at this problem, we use an energy-conserving discontinuous Galerkin discretization in space. To model the in- teraction between the plasma and the wall, we design conducting-sheath boundary conditions that permit local currents into and out of the wall. We start by de- signing spatially one-dimensional kinetic models of parallel SOL dynamics and solve these systems using novel continuum algorithms. By generalizing these algorithms to higher dimensions and adding a model for collisions, we present results from the first gyrokinetic continuum simulations of turbulence on two types of open-field-line systems. The first simulation features uniform and straight field lines, such as found in some linear plasma devices. The second simulation is of a hypothetical model we developed of the NSTX scrape-off layer featuring helical field lines. In the con- text of discontinuous Galerkin methods, we also explore the use of exponentially weighted polynomials for a more efficient velocity-space discretization of the distri- bution function when compared to standard polynomials. We show that standard implementations do not conserve any moments of the distribution function, and we develop a modified algorithm that does. These developments comprise a major step towards a gyrokinetic continuum code for quantitative predictions of turbulence and transport in the boundary plasma of magnetic fusion devices. iii Acknowledgements Many fall in the face of chaos, but not this one... not today. Narrator, Darkest Dungeon After more than six years at Princeton, I am finally ready to move on. Although I am eagerly anticipating what the future holds, I will also miss the tightly structured life that I have become accustomed to over the years. I would not have been able to complete my thesis without the direct support of many people. Of course, I must thank Greg Hammett for being my adviser. Although I did not decide to come to Princeton to work with him (or anyone else) in particular, I realized later on in my graduate career how lucky I was to find an adviser who was an expert in both turbulence and numerical methods, had a code-development project written in a modern programming language, and had the patience to teach a student who knew so little. It is fitting that we both have a tendency to send e-mails well-past midnight. I will be happy if I can one day attain even a small fraction of his level of knowledge, creativity, and intuition. I thank Tim Stoltzfus-Dueck for always making the time to share his incredible knowledge and powerful intuition about plasma physics with me. Tim has been a great mentor and teacher, often meeting with me several times a week, and I owe much of what I learned about SOL physics to him. Tim played an essential role in interpreting the physics of the simulations and suggesting systematic ways to test the code when the results appeared to be incorrect. Tim's commitment to do physics in an objective and transparent way has greatly influenced the way I conduct and present my own work. I hope that Tim will one day use his remarkable aptitude for teaching to train future generations of plasma physicists in edge and SOL physics. I am very grateful to Ammar Hakim for creating the Gkeyll plasma-physics frame- work and for developing some of the additional capabilities required for my thesis. I owe a large part of the timely completion of my thesis (by Princeton standards, at least) to Ammar, who has designed the code with modern and sound software- engineering concepts. I would also like to thank Ammar for teaching me the basics about DG methods and for closely working with me for my second-year project. I thank John Krommes for being an excellent teacher, academic adviser, and even boss. Although he must have been disappointed in how little I learned from his `Irreversible Processes in Plasmas' class when I took it as a second-year student, I hope he recognized that I finally started learning something in the two semesters during which I worked as a grader for his class. As my academic adviser, John always listened intently to whatever dilemmas I brought to him and drew upon his experience to provide profoundly wise advice. I also credit John with instilling a strong belief in adhering to established rules and conventions for technical writing. Unfortunately, I will not return your $31 if you catch five writing mistakes in my thesis. I thank my thesis readers, Stewart Zweben and Matt Kunz, for carefully reading my thesis and providing valuable feedback. Greg Hammett and Tim Stoltzfus-Dueck iv also provided valuable comments for my thesis. I would also like to thank Stewart Zweben (figures 1.2 and 1.3), the IAEA and Thomas Eich (figure 1.4), and Troy Carter and David Schaffner (figures 4.1, 4.2, and 4.14) for permission to use their figures in my thesis to illustrate important results. I thank my other research collaborators for taking the time to learn about my research or code: Qingjiang Pan, Tess Bernard, and Jimmy Juno. I credit Noah Mandell with the formidible task of building the Gkeyll code on various systems. I also thank Dan Ruiz and Jeff Parker for enlisting my help on a side project about DW{ZF interactions. I am very grateful to Curt Hillegas and Matt Kunz for their support for my use of the Perseus cluster at Princeton, which enormously sped up my time to graduate. I also thank Frank Jenko and Jason TenBarge for providing access to additional compu- tational resources. I thank Troy Carter, Amitava Bhattacharjee, Paolo Ricci, Stewart Zweben, Frank Jenko, Bill Tang, Hantao Ji, and Bob Kaita for their encouragement and support. I also acknowledge useful discussions with John Krommes, Troy Carter, Paolo Ricci, Stewart Zweben, Denis St-Onge, Seung-Ho Ku, and Michael Churchill. I thank Dan Ruiz for his consistent friendship over the year and being a great office mate. He probably would have graduated even sooner if he did not have me as an office mate to provide constant distractions. I am in awe of his personal integrity and ability to conjure original research ideas. I am also grateful to the friends I made at Princeton: Mike Hay, Jeff Parker, Seth Davidovits, Lee Ellison, Jake Nichols, Yao Zhou, Kenan Qu, Chang Liu, and Yuan Shi. I thank Beth Leman, Barbara Sarfaty, and Jen Jones for shielding me from the host of complicated administrative details associated with being a graduate student at PPPL. Lastly, I thank my family for their unconditional support. Rita, I would not have been so determined in my goals if I did not have an older sibling to show me what could be achieved. Mom and Dad, thank you for all the sacrifices you have made to help your children pursue their dreams. You have given me so much and have never asked for a single thing in return. This work was funded by the U.S. Department of Energy under Contract No. DE- AC02-09CH11466, through the Max-Planck/Princeton Center for Plasma Physics and the Princeton Plasma Physics Laboratory. Some simulations in Chapters4 and5 were performed on the Perseus cluster at the TIGRESS high-performance computer center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering and the Princeton University Office of Information Technology's Research Computing department. Initial development on the simulations in Chapter4 used the Edison system at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02- 05CH11231. The simulations in Chapters4 and5 also used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. v To my parents. vi Contents Abstract . iii Acknowledgements . iv List of Tables . ix List of Figures . .x 1 Introduction1 1.1 The Boundary Plasma . .1 1.1.1 Basic Features of the SOL . .3 1.1.2 Basic Plasma Physics Experiments . .7 1.2 Boundary-Plasma Modeling . .8 1.2.1 Fluid Modeling . 10 1.2.2 Gyrokinetic Modeling . 11 1.3 Thesis Overview . 17 1.3.1 A Note on Color Maps .
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