The Kelvin - Helmholtz Instability on the Kronian Magnetopause
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The Kelvin - Helmholtz Instability On The Kronian Magnetopause Thesis submitted for the degree of Doctor of Philosophy at Imperial College London ~2014~ Jack Cutler Space and Atmospheric Physics research group, Department of Physics, Imperial College London Supervisors: Dr Elizabeth Lucek Prof. Michele Dougherty Abstract It is widely accepted that magnetic reconnection is the most efficient means of transporting solar wind plasma across the terrestrial magnetopause. However, at Saturn’s magnetopause, conditions for reconnection are consideraBly different to those at the Earth, and reconnection seems to play a much less important role in energy transport across the magnetopause at Saturn than at the Earth. Therefore, other transport mechanisms, such as diffusion and ‘viscous’ mechanisms Become relatively more important. The Kelvin-Helmholtz (K-H) instaBility is a prime candidate for such an alternative mechanism, as first suggested By Dungey (1955). The K-H instaBility has Been the suBject of numerous studies at the Earth, But its operation and impact at Saturn is much less well understood. This thesis Builds on work undertaken by previous authors to identify K-H waves on the Kronian magnetopause. These waves were found to exist on the dusk flank magnetopause, which has previously Been thought to Be staBle to the instaBility due to a reduced flow shear Between magnetospheric and magnetosheath plasma compared to the dawn flank. This asymmetry is due to the sense of magnetospheric (sub)corotation with the planet. The frequency with which the magnetopause is seen to Become K-H unstaBle as a function of local time is then investigated, and surprisingly, the dusk flank is found to Be as unstaBle as the dawn flank. It is proposed that this is due to the nature of the magnetic field structure in the outer magnetosphere adjacent to the magnetopause. Viscous interaction causes the magnetic field in the outer magnetosphere to have a larger component parallel to the magnetopause in the equatorial plane on the dawn flank, compared to the dusk flank. This in turn raises the threshold for Boundary instaBility on the dawn flank magnetopause. The final part of the thesis investigates the non-linear behaviour of the instability far along the flanks- more specifically concerning the rolling up of waves into vortices and the plasma mixing that results. 2 Declarations ‘The copyright of this thesis rests with the author and is made available under a Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work’ I also declare that this work is my own and that all else has been appropriately referenced. If any of the authors listed in the bibliography feel that their work has been misinterpreted, then I encourage you to contact me to discuss this. Acknowledgements I would like to thank my supervisors Michele and ElizaBeth for all the guidance and support they have provided me throughout the duration of this PhD, it has been ever so much appreciated. I would also like to thank all the members of the Space and Atmospheric Physics group here at Imperial for all the useful discussions and input I have had from them. Additionally, I would like to say a warm thank you to the members of the Cassini Magnetometer team, who made me feel welcome and at home at all of the conferences I attended with them, in particular Adam Masters, who was always ready to give useful feedBack on any of the presentations I made. I would also like to thank all those I shared an office with, who had to put up with the occasional airing of gym towels over the radiator and my smelly-microwaved food I sometimes ate! I would also like to thank my family, Nicole, and all my friends outside of SPAT who have supported me every inch of way throughout the PhD, and even Before as my time as an undergraduate. 3 Chapter 1: Introduction …..………………….10 1.1 Defining a plasma …..……………….…10 1.2 Single-particle motion …..………………….12 1.2.1 Gyromotion along field lines …..………………….12 1.2.2 Particle drifts …..………………….13 1.2.3 Particle Bounce motion …..………………….15 1.3 Magnetohydrodynamics …..………………….17 1.3.1 Ideal magnetohydrodynamics …..………………….19 1.3.2 Applications of the MHD equations …..………………….22 1.4 Magnetic reconnection …..………………….23 1.5 The solar wind …..………………….25 1.6 Planetary magnetospheres: an introduction …..………………….29 1.6.1 Magnetised planets: a comparison …..………………….30 1.6.2 The ‘open’ and ‘closed’ magnetosphere …..………………….32 1.6.3 The low-latitude boundary layer …..………………….35 1.6.4 The bow shock …..………………….37 1.6.5 The ring current …..………………….38 1.6.6 The magnetotail …..………………….39 1.6.7 The magnetopause …..………………….40 1.6.7.1 Introduction …..………………….40 1.6.7.2 Large scale motion …..………………….40 1.7 The Kronian magnetosphere …..………………….43 1.8 Summary …..………………….56 Chapter 2: Instrumentation …..………………….57 2.1 Dual Technique magnetometer (MAG) …..………………….58 2.1.1 Fluxgate magnetometer …..………………….60 2.1.2 Vector/ scalar helium magnetometer …..………………….63 2.1.3 Magnetometer caliBration …..………………….64 2.2 Cassini plasma spectrometer …..………………….66 2.2.1 Electron spectrometer …..………………….68 2.2.2 Ion mass spectrometer …..………………….70 4 2.3 Coordinate systems …..………………….71 2.4 Michigan solar wind propagation model …..………………….72 Chapter 3: The Kelvin-Helmholtz instability For magnetised plasma ……73 3.1 The magnetopause: wave activity and momentum transfer …………………..74 3.1.1 Solar wind pressure pulses at the Earth …..………………74 3.1.2 SuBcorotating magnetospheric Bulge at Saturn’s magnetopause …78 3.1.3 Reconnection at the magnetopause: Earth and Saturn compared..80 3.1.4 K-H instaBility …..………………….82 3.2 The Kelvin Helmholtz instaBility: Theory …..………………….83 3.2.1 Effect of compressiBility on the instaBility …..………………….85 3.2.2 Effect of finite shear layer on the instaBility …..………………….92 3.3 The K-H instaBilities at planetary magnetopauses …..………………….97 3.3.1 K-H at the Earth …..………………….98 3.3.1.1 In-situ observations …..………………….99 3.3.1.2 Simulations …..………………….102 3.3.2 The K-H instaBility at Saturn …..………………….104 3.3.2.1 The K-H instaBility at Saturn: Simulation results …...105 3.3.3.2 The K-H instaBility at Saturn: direct observations ….114 3.3.4 K-H vortex identification methods …..………………….120 3.4 The K-H instaBility at the magnetopause: Summary and open questions …122 3.5 This thesis: objective and relevance …..………………….122 Chapter 4: Dusk Flank magnetopause surFace waves...…………………124 4.1 Introduction …..…………………124 4.2 OBservations …..…………………127 4.3 Boundary normal analysis …..…………………132 4.4 Discussion of results ..……………………140 4.5 Conclusions ..……………………143 Chapter 5: Kelvin-Helmholtz instability assessment ..…………………145 5.1 Introduction ..……………………145 5.2 Data processing ..……………………147 5 5.3 Methodology ..……………………148 5.4 Presentation of results ..……………………151 5.5 Interpretation of results ..……………………154 5.6 Summary ..……………………158 Chapter 6: K-H Vortices on Saturn’s magnetopause..……………………160 6.1 Introduction ..……………………160 6.2 OBjectives ..……………………166 6.3 Method ..……………………168 6.4 Results ..……………………170 6.5 Discussion ..……………………173 6.6 Summary ..……………………176 Chapter 7: Conclusions ..……………………178 7.1 Summary ..……………………178 7.2 Open questions ..……………………179 7.3 Future work ..……………………180 Appendices A.1 A partial derivation of equation 3.1 ..……………………182 A.2 Minimum variance analysis ..……………………183 Bibliography ..……………………187 6 List oF tables and Figures Figure 1.1: Ion Gyromotion ..……………………14 Figure 1.2: Ion Drifts ..……………………15 Figure 1.3: Radiation Belts ..……………………16 Figure 1.4: Sweet-Parker reconnection ..……………………25 TaBle 1.1: Typical solar wind properties ..……………………26 Figure 1.5: Parker spiral ..……………………28 Figure 1.6: Magnetospheric structure ..……………………30 TaBle 1.2: Planetary magnetic dipoles compared ..……………………31 Figure 1.7: Chapman-Ferraro closed magnetosphere ..……………………32 Figure 1.8: Dungey’s open magnetosphere ..……………………34 Figure 1.9: Electron and ion Boundary layers ..……………………36 Figure 1.10: The Vasyliunas cycle ..……………………43 Figure 1.11: Early spacecraft trajectories at Saturn ..……………………44 Figure 1.12: Plasma regions of Saturn’s magnetosphere ..……………………46 Figure 1.13: Magnetodisc current sheet ..……………………50 Figure 1.14: Magnetospheric plasma flow model ..……………………52 Figure 1.15: Magnetopause models at Saturn ..……………………55 Figure 2.1: Cassini spacecraft schematic ..……………………58 Figure 2.2: Cassini MAG FGM ..……………………60 Figure 2.3: FGM input/ output signal ..……………………62 Figure 2.4: Cassini plasma spectrometer schematic ..……………………67 Figure 3.0: Kelvin-Helmholtz in clouds ..……………………73 Figure 3.1.1: Solar wind pressure pulses ..……………………76 TaBle 3.1: Solar wind properties ..……………………77 Figure 3.1.2: Magnetospheric Bulge ..……………………79 Figure 3.2.1: K-H instaBility: common examples ..……………………83 Figure 3.2.2: PossiBle unstaBle magnetic field configurations ..……………………87 Figure 3.2.3: CompressiBility on staBility ..……………………90 Figure 3.2.4: Growth rate vs. wavenumber: perp. case ..……………………94 Figure 3.2.5: Growth rate vs. wavenumber: para. case ..……………………95 Figure 3.2.6: Magnetic shear on staBility ..……………………96 7 Figure 3.3.1: Voyager 1 magnetic field data ..…………………100 Figure 3.3.2: Boundary layer perturbation ..…………………102 Figure 3.3.3: W+ ion flow velocities ..…………………104 Figure 3.3.4: K-H simulations: Saturn ..…………………106