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On Kinetic Dissipation in Collisionless Turbulent Plasmas ON KINETIC DISSIPATION IN COLLISIONLESS TURBULENT PLASMAS by Tulasi Nandan Parashar A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Spring 2011 c 2011 Tulasi Nandan Parashar All Rights Reserved ON KINETIC DISSIPATION IN COLLISIONLESS TURBULENT PLASMAS by Tulasi Nandan Parashar Approved: George Hadjipanayis, Ph.D. Chair of the Department of Physics & Astronomy Approved: George Watson, Ph.D. Dean of the College of Arts & Sciences Approved: Charles G. Riordan, Ph.D. Vice Provost for Graduate and Professional Education I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Michael A Shay, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: William H Matthaeus, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Dermott Mullan, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Stanley Owocki, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: James MacDonald, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: I. Pablo Huq, Ph.D. Member of dissertation committee ACKNOWLEDGEMENTS I have heard some people say that the acknowledgment section of a document should not be very personal but I believe in the opposite. My journey to this milestone of my life would not have been the same if not for the people around me. I consider myself to be one of the luckiest graduate students because I had the opportunity to work with my advisers Mike Shay and Bill Matthaeus. Whatever I know about plasma physics, turbulence theory, space physics and plasma compu- tation theory, I owe to them. They have an immense role in igniting and shaping my interest in a field that I entered with a completely blank slate. I do not think a simple thank you or a simple statement of acknowledgment could do justice to their role in helping me to grow not just as a student and a potential scientist but also as a person. I hope I make them proud by putting whatever they have taught me to good use throughout my life. I was lucky to get a chance to collaborate with Paul Cassak and Sergio Servidio when they were postdoctoral fellows in our group. I bugged them a lot with millions of simple queries every single day they were here. Kittipat, John, Doug, Minping and Ben Breech were very helpful in countless discussions about basic physics and computations. I wish to especially thank my committee members for their invaluable input to this thesis. I am really indebted to them for pointing out a few aspects in the background material that I had glossed over. Their discussions have helped me make this thesis more streamlined and more relevant. I believe this has really helped in making this thesis a much better document than it originally was. iv For the past few years, Daniel DeMarco very patiently listened to my com- plaints and problems about computers and very patiently and promptly fixed them, every single time, over and over again. I was never able to create a problem big enough that he could not fix quickly. I still remember that the first communication that I received, some time in the first week of February 2005, from UD about my application was from some Maura Perkins. She's been a life saver ever since. Betty Baringer's role in taking the pain out of the financial nuances is one which I think is hard to match by anyone. Debra and Mrs. Long, other than being my "Good Morning Ladies", were of great help with every thing else. Susan, Dennis, Dave Johnson, Tom Reed & Tom Reilly were very helpful whenever I went to them for any kind of help. This 6 year long journey would be almost impossible to finish if it was not for my friends. The list is so long that I would not attempt to include the names in here because this is no Oscar acceptance speech and I'm afraid I might miss one or two names. Friends, you know who you are and you know how much I value your support through the years!!! Thanks :-) Lastly but most importantly I should mention the real force behind my ener- gies: my family. It is with their support, encouragement and love that I have made progress over the last 13 years of my life while living away from them. Trying to thank them would be like trying to describe the sun as a candle. So I'll simply say: Ma, papa, sisters and Tintin: I love you all. v Dedicated to: The four people to whom I owe most of what I am and most of what I know Ma, Papa, Mike & Bill vi The voice on the solar wind breathed to them again. \I hope you are comfortable." It said. ... \And I would like to congratulate you on the accuracy of your deductions." - The Hitchhiker's Guide to the Galaxy. vii TABLE OF CONTENTS LIST OF FIGURES ::::::::::::::::::::::::::::::: xii LIST OF TABLES :::::::::::::::::::::::::::::::: xvii ABSTRACT ::::::::::::::::::::::::::::::::::: xviii Chapter 1 INTRODUCTION :::::::::::::::::::::::::::::: 6 1.1 A brief tour of the heliosphere :::::::::::::::::::::: 6 1.2 Spacecraft Observations ::::::::::::::::::::::::: 12 1.3 Coronal Observations ::::::::::::::::::::::::::: 13 1.3.1 Waves in solar corona ::::::::::::::::::::::: 13 1.3.2 Reconnection ::::::::::::::::::::::::::: 14 1.3.3 Heating :::::::::::::::::::::::::::::: 16 1.4 Solar Wind Observations ::::::::::::::::::::::::: 18 1.4.1 Waves in the solar wind ::::::::::::::::::::: 18 1.4.2 Turbulence :::::::::::::::::::::::::::: 20 1.4.3 Reconnection ::::::::::::::::::::::::::: 22 1.4.4 Heating :::::::::::::::::::::::::::::: 24 1.4.4.1 Protons ::::::::::::::::::::::::: 26 1.4.4.2 Heavy ions ::::::::::::::::::::::: 28 1.5 Heating Mechanisms ::::::::::::::::::::::::::: 28 1.5.1 Wave Mechanisms :::::::::::::::::::::::: 30 1.5.1.1 Cyclotron Resonance :::::::::::::::::: 31 viii 1.5.1.2 Waves in expanding box :::::::::::::::: 33 1.5.1.3 Dissipation or Dispersion? KAWs or Whistlers? ::: 34 1.5.2 Non-wave Mechanisms :::::::::::::::::::::: 38 1.5.2.1 Current sheets & reconnection sites :::::::::: 38 1.5.2.2 Energization by trapping in magnetic islands :::: 40 1.5.2.3 Stochastic heating ::::::::::::::::::: 40 1.6 Summary ::::::::::::::::::::::::::::::::: 41 2 HYBRID CODE ::::::::::::::::::::::::::::::: 44 2.1 Various plasma descriptions ::::::::::::::::::::::: 45 2.1.1 Fluid description ::::::::::::::::::::::::: 45 2.1.2 Fully kinetic description ::::::::::::::::::::: 47 2.1.2.1 Vlasov :::::::::::::::::::::::::: 47 2.1.2.2 Particle In Cell ::::::::::::::::::::: 48 2.1.3 Compromise Models ::::::::::::::::::::::: 49 2.1.3.1 Gyrokinetics :::::::::::::::::::::: 49 2.1.3.2 Hybrid Vlasov ::::::::::::::::::::: 52 2.1.3.3 Hybrid PIC ::::::::::::::::::::::: 52 2.2 Hybrid Code P3D ::::::::::::::::::::::::::::: 53 2.2.1 Electron Physics ::::::::::::::::::::::::: 54 2.2.2 Code details :::::::::::::::::::::::::::: 55 2.2.2.1 Particle Stepping :::::::::::::::::::: 57 2.2.2.2 Particle Moments :::::::::::::::::::: 59 2.2.2.3 Field stepping :::::::::::::::::::::: 60 2.2.3 Analysis :::::::::::::::::::::::::::::: 61 3 PROBLEM SETUP ::::::::::::::::::::::::::::: 65 4 THE ORSZAG TANG VORTEX: TURBULENT DECAY OF ix ENERGY ::::::::::::::::::::::::::::::::::: 68 4.1 Hybrid Simulation Model ::::::::::::::::::::::::: 69 4.2 Results and Discussion :::::::::::::::::::::::::: 72 5 THE ORSZAG-TANG VORTEX: K-! SPECTRA :::::::::: 85 5.1 k − ! spectra of OTV :::::::::::::::::::::::::: 88 5.2 Probability Density Functions (PDFs) ::::::::::::::::: 89 5.3 Conclusions :::::::::::::::::::::::::::::::: 92 6 QUASI STEADY STATE TURBULENCE: TIME INDEPENDENT DRIVING ::::::::::::::::::::::: 94 6.1 Introduction :::::::::::::::::::::::::::::::: 94 6.2 Simulation details ::::::::::::::::::::::::::::: 96 6.3 Results ::::::::::::::::::::::::::::::::::: 97 6.4 Conclusions :::::::::::::::::::::::::::::::: 101 7 QUASI STEADY STATE TURBULENCE: TIME DEPENDENT DRIVING ::::::::::::::::::::::::::::::::::: 105 7.1 Introduction :::::::::::::::::::::::::::::::: 105 7.2 Simulation details ::::::::::::::::::::::::::::: 106 7.3 Results ::::::::::::::::::::::::::::::::::: 108 7.4 Conclusions :::::::::::::::::::::::::::::::: 113 8 CONCLUSIONS AND FUTURE DIRECTIONS :::::::::: 117 Appendix A TWO FLUID DISPERSION RELATION AND WAVES :::::: 122 B HYBRID CODE RUN SEQUENCE ::::::::::::::::::: 125 B.1 Algorithm ::::::::::::::::::::::::::::::::: 125 B.2 Normalization ::::::::::::::::::::::::::::::: 129 C PERMISSION LETTERS ::::::::::::::::::::::::: 133 C.1 Permission Letter from Kazunari Shibata :::::::::::::::: 133 C.2 Permission Letter from Steven Cranmer :::::::::::::::::
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