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VLF and ULF Waves Associated with Magnetospheric Substorms

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VLF and ULF Waves Associated with Magnetospheric Substorms VLF and ULF Waves Associated with Magnetospheric Substorms Andrew B. Collier PhD Thesis Department of Space and Plasma Physics School of Electrical Engineering Royal Institute of Technology Stockholm, Sweden May 2006 Andrew B. Collier VLF and ULF Waves Associated with Magnetospheric Substorms PhD Thesis. Department of Space and Plasma Physics, School of Electrical Engineering, Royal Institute of Technology, Stockholm, Sweden. May 2006. Abstract A magnetospheric substorm is manifested in a variety of phenomena observed both in space and on the ground. Two electromagnetic signatures are the Substorm Chorus Event (SCE) and Pi2 pulsations. The SCE is a Very Low Frequency (VLF) radio phenomenon observed on the ground after the onset of the substorm expansion phase. It consists of a band of VLF chorus with rising upper and lower cutoff frequencies. These emissions are thought to result from Doppler-shifted cyclotron resonance between whistler mode waves and energetic electrons which drift into an observer’s field of view from an injection site around midnight. The ascending frequency of the emission envelope has been attributed to the combined effects of energy dispersion due to gradient and curvature drifts and the modification of the resonance conditions resulting from the radial component of the E B drift. Two numerical models have been developed which × simulate the production of a SCE. One accounts for both radial and azimuthal electron drifts but treats the wave-particle interaction in an approximate fashion, while the other retains only the azimuthal drift but rigorously calculates both the electron anisotropy and the wave growth rate. Results from the latter model indicate that the injected electron population should have an enhanced high-energy tail in order to produce a realistic SCE. Pi2 are damped Ultra Low Frequency (ULF) pulsations with periods between 40 and 150 s. The impulsive metamorphosis of the nightside inner magnetosphere during the onset of the substorm expansion phase is accompanied by a broad spectrum of magnetohydrodynamic (MHD) waves. Over a limited range of local times around midnight these waves excite field line resonances (FLRs) on field lines connected with the auroral zone. Compressional waves propagate into the inner magnetosphere, where they generate cavity mode resonances. The uniform frequency of Pi2 pulsations at middle and low latitudes is a consequence of these cavity modes. A number of Pi2 events were identified at times when the Cluster constellation was located in the nightside inner magnetosphere. Electric and magnetic field data from Cluster were used to establish the existence of both cavity and field line resonances during these events. The associated Poynting flux indicated negligible radial or field-aligned energy flow but an appreciable azimuthal flux directed away from midnight. i ii Acknowledgements I am indebted to a few people who have make this work both possible and pleasurable: my su- pervisor, Professor Arthur R. W. Hughes, for stimulation, guidance, friendship and for sending me to some awesome places; my co-supervisor, Professor Lars G. Blomberg, for his enthusi- astic patronage, helpful advice and being an impeccable host; the various purveyors of data for their indispensable raw produce and generous practical support; Dr P. R. Sutcliffe for his constructive criticism and suggestions for further reading; Professor A. D. M. Walker for a number of highly enlightening discussions; the folk down the corridor, Drs Erhard Mravlag and Judy Stephenson, who have always been good company; Ann Nolte, who cheerfully and efficiently organised flights, hotels, purchase requisitions, and so many other perplexing things; Struan Cockcroft for being great company and an outstanding cocoa mentor; Charles Forman, who must be credited with finally propelling me into the twenty-first century; Tommy Eriks- son, who directed me out of some tight corners and dead ends; the staff of the mechanical and electronic workshop for their support and assistance; my parents for their perennial en- couragement, patience and faith in me; Storm and Emma for their tolerance, stimulation and being the best damn caching partners; and, finally, my running mates: the miles we put in together have kept me sane. A few of you may not have the patience or inclination to read all of this, so here is something for you: 1 9 6 4 8 5 3 2 2 7 5 1 5 9 3 2 5 2 8 5 8 2 4 8 1 5 6 iii iv Contents 1 Introduction 1 1.1 VLFPhenomena .................................. 1 1.2 ULFPhenomena .................................. 1 1.3 Outline........................................ 3 2 The Magnetosphere 4 2.1 Structure ...................................... 4 2.2 MagnetosphericSubstorms . .... 5 2.2.1 ParticleInjections. .. 7 2.2.2 MagneticVariations . .. .. .. 10 3 VLF Waves 14 3.1 TheWhistlerMode................................. 14 3.2 Whistlers ...................................... 16 3.3 Doppler-Shifted Cyclotron Resonance . ........ 16 3.4 Chorus........................................ 18 3.5 SubstormChorusEvents . .. 20 4 ULF Waves 21 4.1 Magnetohydrodynamics . .. 21 4.1.1 MagnetosonicWaves ............................ 24 4.1.2 ShearAlfv´enWaves. 25 4.1.3 PoyntingFlux................................ 25 4.2 ULFPulsations ................................... 26 4.2.1 Classification ................................ 26 4.2.2 MHD Waves in a Box Magnetosphere . 27 4.2.3 MHDWavesinDipoleCoordinates . 27 4.2.4 FieldLineResonance. .. .. .. 30 4.2.5 CavityResonance.............................. 37 4.2.6 EffectsoftheIonosphere . 44 4.3 Pi2Pulsations................................... 49 4.3.1 Observations ................................ 49 4.3.2 Theories................................... 51 5 Instrumentation 53 5.1 Cluster........................................ 53 5.1.1 FGM..................................... 55 5.1.2 EFW..................................... 55 5.2 Polar......................................... 57 5.3 TerrestrialMagnetometers . ..... 57 v 6 Summary 59 6.1 Paper1 ....................................... 59 6.2 Paper2 ....................................... 62 6.3 Paper3 ....................................... 64 6.4 Paper4 ....................................... 66 6.5 Conclusion...................................... 75 A Coordinate Systems 80 A.1 Geophysical Coordinate Systems . ...... 80 A.2 DipoleCoordinates ............................... .. 80 A.3 Mean Field-Aligned Coordinates . ...... 82 B Spectral Techniques 83 B.1 TheFourierTransform .. .. .. .. 83 B.2 TheDiscreteFourierTransform . ..... 85 B.3 Filtering....................................... 87 B.4 ComplexDemodulation. .. 87 C Polarisation Parameters 92 Bibliography 96 vi List of Symbols f frequency ω angular frequency γ growth rate k wave normal vector θ wave normal angle m azimuthal wave number n refractive index R reflection coefficient Π Poynting vector Ω cyclotron frequency ωp plasma frequency Λ normalised frequency W kinetic energy α pitch angle L McIlwain’s parameter λ magnetic latitude r geocentric distance RE mean radius of the Earth (6371km) ν, φ, µ dipole coordinates ρ mass density N number density p pressure v velocity ξ displacement σ conductivity Σ conductance B static magnetic flux density b perturbation magnetic flux density E electric field strength j current density vii viii List of Figures 1.1 SCEsrecordedatSANAE–IV. .. 2 1.2 Pi2 observations in day and night hemispheres. ......... 3 2.1 Theterrestrialmagnetosphere.. ....... 5 2.2 Locations of ACE and WIND with corresponding IMF Bz data. ........ 6 2.3 PolarUVIdata.................................... 8 2.4 SOPA geosynchronous electron flux data. ....... 9 2.5 Model explaining geosynchronous flux dropouts. .......... 10 2.6 Schematic of SCW with associated magnetic perturbations............ 11 2.7 Substorm magnetic bays at selected observatories. ............ 12 2.8 AU and AL indices from the IMAGE magnetometer network. ........ 13 3.1 Whistler ray direction as a function of wave normal angle. ........... 15 3.2 Whistler mode coupling between the atmosphere and the ionosphere. 16 3.3 Spectrogramsofwhistlers. ..... 17 3.4 Spectrogramsofchorus. ... 19 4.1 Coupling between torsional and compressional modes. ............ 29 4.2 Phase relationships for a fundamental toroidal standingwave. ......... 32 4.3 Phase relationships for a second harmonic toroidal standing wave. 33 4.4 Particle density, Alfv´en speed, turning point and FLR frequencies versus L... 35 4.5 Magnetic and electric field perturbations in a fundamental cavity mode. 38 4.6 Field line configuration in a fundamental cavity mode. ........... 39 4.7 Phase relationships for a fundamental radially transverse standing wave. 40 4.8 Phase relationships for a second harmonic radially transverse standing wave. 41 4.9 Dependence of the turning point location on azimuthal wavenumber. 42 4.10 Boundaries of the cavities formed within the magnetosphere. .......... 44 4.11 Polarisation of obliquely incident shear Alfv´en and fast mode waves. 45 4.12 Ionospheric components of a shear Alfv´en wave. ........... 47 5.1 LocationofClusteratperigee.. ...... 54 5.2 Removal of background magnetic field variation. .......... 56 5.3 Stations in the IMAGE magnetometer network. ....... 58 6.1 Simulated evolution of a drifting electron population. .............. 60 6.2 Comparison of simulated SCEs with different injection regions.......... 62 6.3 Lower frequency cutoff caused by upper cutoff in Wk............... 63 6.4 Annualised lightning flash rate density over southern Africa. .......... 65 6.5
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