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Simulation and Analysis of Magnetic Reconnection in a Laboratory Plasma Astrophysics Experiment

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Simulation and Analysis of Magnetic Reconnection in a Laboratory Plasma Astrophysics Experiment Simulation and Analysis of Magnetic Reconnection in a Laboratory Plasma Astrophysics Experiment by Nicholas Arnold Echlin Murphy A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Astronomy) at the University of Wisconsin – Madison 2009 i Abstract Magnetic reconnection is an inherently multiscale process in which small-scale physics and large-scale dynamics both play important roles. To address the interplay between local and global effects, extended magnetohydrodynamic (MHD) simulations of the Magnetic Recon- nection Experiment (MRX) are presented using the NIMROD code. Both the “pull” and “push” modes of operation are simulated with and without two-fluid effects in the general- ized Ohm’s law. The pull reconnection rate is slowed by the presence of high downstream pressure. Because of the lesser volume available on the inboard side of the current sheet, density is depleted more quickly from the inboard upstream region than the outboard up- stream region during pull reconnection, resulting in a radially inward drift of the current sheet. A buildup of pressure on the inboard side of the current sheet during push recon- nection displaces the X-point towards the outboard side of the current sheet. Two-fluid simulations show good agreement with experimental observations of the quadrupole out- of-plane magnetic field associated with two-fluid reconnection. However, geometric effects are found to be more important in determining the reconnection rate than the inclusion of two-fluid effects. Communication between small and large scales is primarily due to pressure gradients that develop from a pileup of reconnection exhaust which then feed back on the reconnection process. Magnetic reconnection with asymmetry in the outflow direction occurs in many situ- ations in both nature and the laboratory. A control volume analysis is performed for the case of steady antiparallel magnetic reconnection with asymmetric downstream pressure to find approximate relations for conservation of mass, momentum, and energy in the resis- tive magnetohydrodynamic (MHD) framework. These relationships are used to derive the ii outflow velocity from each side. The reconnection rate is not greatly affected except when outflow from both sides of the current sheet is blocked. Instead of bidirectional Alfv´enic jets, reconnection with asymmetric downstream pressure can result in one Alfv´enic jet and one sub-Alfv´enic jet. A similar model is presented for reconnection in cylindrical geometry when the outflow is aligned with the radial direction. The predictions of these models are tested using resistive MHD simulations of driven asymmetric magnetic reconnection. iii To my friends Karin Lathin and Joseph Lindstrom, for everything they have done for others iv Dr. McCoy: “I knew it was wrong. I shouldn’t have done it!” Captain Kirk: “What’s that?” Dr. McCoy: “I should have never reconnected his mouth.” —Star Trek, Episode #56, “Spock’s Brain” “Resistance is futile.” —The Borg, kindly reminding us of the need to in- clude additional terms in our generalized Ohm’s law v Acknowledgements I would first like to thank Carl Sovinec and Ellen Zweibel for the support and assistance they have ceaselessly provided as my advisors. Without their guidance and patience, this thesis would not have been possible. What they have taught me will last throughout my entire career as a scientist. The faculty of the Department of Astronomy must also be acknowledged for giving me the education and training necessary to be a professional astronomer. I would like to thank Linda Sparke for her idea during my first year to consider working with “Ellen’s friends in engineering,” an idea that has turned out to be quite fruitful. Discussions with Alex Lazarian during classes and seminars have improved my understanding of astrophysical magnetic fields and turbulence, and have given me a new appreciation of dust. Much of my knowledge of how to do astrophysical research came from working with Joseph Cassinelli during my first year in Madison. I thank my thesis committee (Joseph Cassinelli, Sebastian Heinz, Carl Sovinec, Rich Townsend, and Ellen Zweibel) for valuable comments on this manuscript. I also acknowledge the help I have received from the plasma physics community in Madison, especially for making an astronomy graduate student feel welcome. In particular, I would like to thank Stewart Prager, Yi-Min Huang, Vladimir Mirnov, Chris Hegna, Fatima Ebrahimi, Adam Bayliss, and Ping Zhu. This simulations performed for this thesis used the NIMROD code, and I must thank all of those who have contributed to its development, in- cluding Carl Sovinec, Dalton Schnack, Dylan Brennan, Scott Kruger, Dan Barnes, Charlson vi Kim, Alan Glasser, and the rest of the NIMROD team. In the greater plasma physics com- munity, I must also thank Paul Cassak, Masaaki Yamada, Hantao Ji, Stefan Gerhardt, Yang Ren, Alexey Kuritsyn, Michiaki Inomoto, Seth Dorfman, Michael Brown, Chris Cothran, Michael Schaffer, Michael Shay, Brian Sullivan, Amitava Bhattacharjee, and Marc Swisdak. My thesis research was supported by the Center for Magnetic Self-Organization in Labo- ratory and Astrophysical Plasmas (CMSO). In addition to financial support, I found the CMSO to be a great community full of wonderful researchers dedicated to building bridges between laboratory and astrophysical plasma physics. This is a largely computational thesis, and hence I must state my appreciation for the system administration skills of Stephan Jansen, who has kept the astronomy depart- ment network running smoothly. The astronomy department staff throughout my tenure as a graduate student have been wonderful, including Steve Anderson, Angela Normington, Lynn Thiele, and John Varda. I also thank Jane Schwantz and Dale Schutte from plasma physics. I must also express appreciation for several faculty from the University of Michigan and elsewhere during my time as an undergraduate, especially John Monnier, Hugh Aller, Joel Bregman, Rachel Somerville, Joel Smoller, and Jack Baldwin. I thank Hugh Aller in particular for his Astronomy 160 class which convinced me to go into astronomy. I must also thank fellow students and post-docs for their contribution to the warm atmosphere of Wisconsin astronomy and physics, including (in the Department of Astron- omy) Kat Barger, Andrey Beresnyak, Tom Bethell, Ella Braden, Blakesley Burkhart, Laura Chomiuk, Steve Crawford, Claudia Cyganowski, Kate Dellenbusch, Katie Devine, John Ev- erett, Andy Fox, Emily Freeland, Sam Friedman, Aaron Geller, Natalie Gosnell, Kelley Hess, Alex Hill, Tabetha Hole, Ryan Keenan, Amanda Kepley, Min-Young Lee, Tommy Nelson, Lou Nigra, Matt Povich, Andrew Schechtman-Rook, Paul Sell, Elizabeth Stanway, vii Aaron Steffen, Jennifer Stone, Laura Trouille, Christer Watson, Kyle Westfall, Isak Wold, Corey Wood, and (in the Departments of Physics and Engineering Physics) Chris Carey, Jim Reynolds, Jacob King, John O’Bryan, Eric Howell, Bonita Burke, Mark Schlutt, Tom Bird, Matt Palotti, Daniel Lecoanet, Tim Tharp, and Hillary Stephens. I must also thank the many friends I have made outside of graduate school for helping to make my Madison experience memorable. From the Emma Goldman (now Audre Lorde) Co-op, I thank Joseph Lindstrom, Max Camp, Lauren Nielsen, Alex Hojem, Jana Grcevich, Summer Wilken, Cedric Lawson, Renee Gasch, Sylvia Jones, Kelly Rentscher, Brian Jordan, Mingwei Huang, Aaron Blecher, Ben Luedcke, Betsy Levine, Anne Seeber, Tom Ebersole, Sara Edquist, Lindsey Saunders, Nick Mader, Ali Muldrow, and many others. From Madison Community Co-op, I thank Stefanie Jones, Kathy Parker, Gabriel Heck, C. J. Carter, Lauren Allen, Rick White, Steve McClure, and Liz Shaffer-Wishner. From the Teaching Assistants’ Association, I thank Claiborne Hill, Samaa Abdurraqib, Aaron Bibb, Rob Henn, Chris Bolander, Mark Supanich, Jay Gates, Stephanie Eastwood, Paul Reckner, Adam Berliner, Jason Murcko, Aaron Bibb, Peter Brinson, Sherry Johnson, Tim Frandy, Julien Colvin (with whom I got my picture taken with George Takei!), and Boian Popunkiov. From the rest of the Madison community, I thank Lori Nitzel, Austin King, Maura McCormick, Kyle Novak, Kerean Grant Povich, Trevor Irwin, Jon Bohman, Sean Hedican, and Christina Vandenhouten. To the members of Alliance for Animals, thank you for hosting numerous vegan dinners, where I always ate more than I should have, but never enough! I would like to thank my family for their support, for putting up with me not calling home often enough, and for being there whenever I needed to visit or talk. Thank you Mom and Dad, Ron, Ellen, and Sue. And finally, I would like to thank my partner throughout most of graduate school, Sonja, for her patience, compassion, and understanding. viii Contents Abstract i 1 Introduction 1 1.1 Introduction.................................... 2 1.2 ModelsofMagneticReconnection . .... 5 1.2.1 TheSweet-ParkerModel . .. .. 7 1.2.2 ThePetschekModel ........................... 13 1.2.3 Enhanced Resistivity from Small-Scale Instabilities .......... 14 1.2.4 TurbulentReconnection . 16 1.2.5 Two-FluidReconnection . 17 1.2.6 AsymmetricReconnection . 21 1.3 The Interplay Between Small and Large Scales During Magnetic Reconnection 23 1.4 IntroductiontoNIMROD . .. .. 24 1.5 OverviewofThesis ................................ 27 References........................................ 28 2 Global Axisymmetric Simulations of Two-Fluid Reconnection in an Ex- perimentally Relevant Geometry 38 ix 2.1 Introduction...................................
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