Magnetospheric MHD Oscillations
A Linear Theory

A groundbreaking new theory of the magnetosphere

The magnetosphere is the region around Earth in which our planet?s magnetic field exerts its influence to trap charged particles. Waves in this magnetosphere, known as magnetohydrodynamic (MHD) oscillations, are caused by interactions between these charged particles, Solar wind pulses, and the magnetic field. The predictable interval between these oscillations enables them to serve as tools for understanding the magnetospheric plasma which comprises the field.

Magnetospheric MHD Oscillations offers a comprehensive overview of the theory underlying these waves and their periodicity. Emphasizing the spatial structure of the oscillations, it advances a theory of MHD oscillation that promises to have significant ramifications in astronomy and beyond.

Magnetospheric MHD Oscillations readers will also find:

• Theorizing of direct relevance to current satellite missions, such as THEMIS and the Van Allen Probe
• In-depth discussion of topics including Alfven resonance, waveguides in plasma filaments, and many more
• Detailed appendices including key calculations and statistical parameters

Magnetospheric MDH Oscillations is ideal for plasma physicists, theoretical physicists, applied mathematicians, and advanced graduate students in these and related subfields.

List of Figures xi

List of Tables xxv

Author Biography xxvii

Preface xxix

Acknowledgements xxxi

Acronyms xxxiii

Symbols xxxv

Introduction xxxix

1 Hydromagnetic Oscillations in Homogeneous Plasma 1

2 MHD Oscillations in 1D-Inhomogeneous Model Magnetosphere 10

2.1 A Qualitative Picture of MHD Wave Propagation in a 1D-Inhomogeneous Plasma 12

2.2 Model of a Smooth Transition Layer and Basic Equations for MHD Oscillations 15

2.3 FMS Wave Reflected from the Transition Layer in a Cold Plasma. Alfvén Resonance 16

2.4 Alfvén Resonance Excited by a Wave Impulse 20

2.5 Energy Balance in the Problem of an Incident FMS Wave Reflected from the Transition Layer Containing an Alfvén Resonance Point 25

2.6 FMS Wave Reflected from the Transition Layer in a ‘warm’ Plasma. Alfvén and Magnetosonic Resonances 30

2.7 Alfvén Resonance in Non-ideal Plasma. Kinetic Alfvén Waves 37

2.8 FMS Waveguide 43

2.9 Waveguide for Quasilongitudinal Alfvén Waves 47

2.10 Waveguides for Kinetic Alfvén Waves in a ‘cold’ Plasma. Waveguide Mode Attenuation 49

2.11 Waveguide for Kinetic Alfvén and FMS Waves in a ‘warm’ Plasma. Waveguide Mode Resonance 51

2.12 Waveguides in Plasma Filaments 54

2.13 FMS Wave Passing Through a Tangential Discontinuity 62

2.14 Unstable MHD Shear Flows in the Presence/Absence of Boundary Walls 70

2.15 Geotail Instability Due to Shear Flow at the Magnetopause 83

2.16 Kelvin–Helmholtz Instability in the Geotail Low-Latitude Boundary Layer 98

2.17 Cherenkov Radiation of the Fast Magnetoacoustic Waves 111

2.18 MHD Oscillation Field Penetrating from the Magnetosphere to Ground 115

3 MHD Oscillations in 2D-Inhomogeneous Models 133

3.1 Resonance Between FMS and Kinetic Alfvén Waves in a Dipole-Like Magnetosphere 137

3.2 Alfvén Resonance in a Dipole-Like Magnetosphere 146

3.3 Resonant Alfvén Waves Excited in a Dipole-Like Magnetosphere by Broadband Sources 158

3.4 Magnetosonic Resonance in a Dipole-Like Magnetosphere 164

3.5 FMS Oscillations in a Dipole-Like Magnetosphere 178

3.6 FMS Resonators in Earth’s Magnetosphere 185

3.7 Monochromatic Transverse-Small-Scale Alfvén Waves with m ≫ 1ina Dipole-Like Magnetosphere 200

3.8 Electromagnetic Oscillations Induced at Earth Surface by Magnetospheric Standing High-m Alfvén Waves 226

3.9 Linear Transformation of Standing High-m Alfvén Waves Near the Toroidal Resonance Surface 232

3.10 Magnetospheric Resonator for Standing High-m Alfvén Waves 238

3.11 High-m Alfvén Waves Generated in the Magnetosphere by Stochastic Sources 241

3.12 Broadband Standing High-m Alfvén Waves Generated by Correlated Sources 251

3.13 Model Equation to Determine the Transverse Structure of Standing Alfvén Waves in the Magnetosphere 260

3.14 Spatial Structure of Alfvén Oscillations Excited in the Magnetosphere by Localised Monochromatic Source 275

3.15 High-m Alfvén Oscillations Generated in the Magnetosphere by Localised Pulse Sources 282

3.16 Ballooning Instability of Alfvén and SMS Oscillations on Field Lines Crossing the Current Sheet 298

3.17 Coupled Alfvén and SMS Oscillation Modes in the Geotail 315

4 MHD Oscillations in 3D-Inhomogeneous Models of the Magnetosphere 329

4.1 MHD Oscillation Properties in Non-homogeneous Models of the Magnetosphere of Different Dimension 329

4.2 Coordinate System 330

4.3 Basic Equations 331

4.4 Qualitative Investigation of the Equation for Characteristics 334

4.5 Wave Singularity in the 3D-Inhomogeneous Magnetosphere 337

5 Conclusion 341

Appendixes 349

References 372

Index 401

Anatoly Leonovich, PhD, was a Researcher at the Insitute of Solar-Terrestrial Physics, Russian Academy of Science, Irkutsk, Russia. He researched and published widely on the theory of magnetospheric magnetohydrodynamic oscillations.

Vitalii Mazur, PhD, was a renowned theoretical physicist at the Irkutsk Institute of Solar-Terrestrial Physics and held, at the same time, a professorship at the Irkutsk State University, Russia. His research was focused on the theory of magnetohydrodynamic oscillations of the Earth's magnetosphere. He supervised numerous students, among them the coauthors of this book Anatoly Leonovich and Dmitri Klimushkin.

Dmitri Klimushkin, PhD, is a Researcher at the Institute of Solar-Terrestrial Physics, Russian Academy of Science, Irkutsk, Russia. His research focuses on the wave-particle interactions in the magnetosphere.