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Physics of Magnetic Flux Tubes
ISBN-13: 9783319963600 / Angielski / Twarda / 2018 / 747 str.
Physics of Magnetic Flux Tubes
ISBN-13: 9783319963600 / Angielski / Twarda / 2018 / 747 str.
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This book presents the physics of magnetic flux tubes, including their fundamental properties and collective phenomena in an ensemble of flux tubes.
Preface
Contents
Chapter 1. The Sun’s Magnetic fields
1.1 The Sun as a Star
1.1.2 Legacy of ancients1.1.2 Hidden interior
1.1.3 Magnetic dipole
1.2 Magnetic Surface
1.2.1 Quiet sun
1.2.2 Sunspots and active regions
1.2.3 Plages
1.2.4 High latitudes and polar regions
1.3 Mass Flows
1.4 Magnetic Skeleton
References
Chapter 2. A Quick Look on Small Scale Flux Tubes
2.1 Early Years
2.1.1 First observational signs of magnetic flux tubes
2.1.2 The Sunspot dilemma
2.2 Elements of Theory for de facto Flux Tubes
2.3 Numerical visualization and Observations
2.4 Filamentary Structures in Laboratory and Universe
2.5 Problems
References
Chapter 3. Intrinsic Properties of Flux Tubes - Wave Phenomena
3.1 Equations of Motion or How are Tube Waves Excited
3.1.1 Equation of Motion for a Single flux tube
3.1.2 Macroscopic Motions of an Ensemble of flux tubes
3.2 Absorption of Acoustic Waves - Landau Resonance
3.3 Effects of Non-collinearity of Flux Tubes
3.4 Exact Theory of Linear Oscillations of Magnetic Flux Tube
3.5 Radiation of Secondary Waves by Oscillationg Flux Tubes
3.6 Scattering of Acoustic Waves and Maximum Energy input
3.7 Axisymmetric Oscillations of Flux Tube
3.7.1 Types of m = 0 mode
3.7.2 Equation of Motion for Sausage Oscillations
3.7.3 Dispersion Relation
3.7.4 Sausage and and Fast Oscillations in homogeneous flux tube
3.7.5 Effects of Radial Inhomogeneities on Sausage oscillations
3.8 ProblemsAppendix A. Analogy with Landau Damping
Appendix B. Derivation of Equation for Kink Oscillations from MHD
References
Chapter 4. Effects of Flux Tube Inhomogeneities and Weak Nonlinearity
4.1 Radially Inhomogeneous Flux Tube - Internal Resonances
4.1.1 Anomalous resonance in kink oscillations
4.1.2 Alfv´en resonance
4.2 Boundary Value Problem
4.2.1 Phase-mixing in flux tubes
4.2.3 Phase-mixed torsional waves
4.2.3 Phase-mixed kink oscillations
4.3 Longitudinal resonances
4.3.1 Loss of radial equilibrium
4.3.2 Bullwhip effect
4.4 Standing resonances and the temperature jump
4.4.1 Growth of the oscillation amplitude - first resonance
4.4.2 Spectral density and strong enhancement of the oscillation amplitude
4.5 Weakly Nonlinear Waves in Flux Tubes
4.5.1 Nonlinear kink oscillations - KdV-B¨urgers equation
4.5.2 Possibility of solitary sausage wave
4.6 Problems
References
5.1 Kelvin-Helmholtz Instability and Negative Energy Waves
5.2 Shear Flow Instabilities in Magnetic Flux Tubes
5.2.1 Specifics of Kelvin-Helmholtz instability along flux tubes
5.2.2 Flux tubes and Negative Energy Waves (NEWs)
5.3 Basic Equations of Flux tube Oscillations with Shear Flows
5.4 Dissipative Instabilities of Negative-energy Kink Oscillations
5.5 Radiative Instability of Flux Tube Oscillations in Presence of Flows
5.5.1 Sausage oscillations
5.5.2 Kink oscillations
5.6 Parity of Negative and Positive Energy Waves
5.7 Explosive Instability of Negative-energy Waves5.8 Sub-critical Mass Flows - Absence of Instabilities
5.8.1 Can the Alfv´en waves heat the corona?
5.8.2 Effect of mass flows on the efficiency of heating by Alfv´en waves
5.9 Phase-Mixed Alfv´en Waves at Sub-alfv´enic Mass Flows
5.9.1 Damping rate and height of energy release
5.9.2 Observable morphological effects
5.10 The Asymptotic Behavior of the Total Energy Flux
5.11 The Wave Extinction in the Presence of Downflows
5.12 Problems
Appendix A. Equation for Alfv´en Waves in the Presence of Parallel Mass Flows
References
Chapter 6. Collective Phenomena in Rarefied Ensembles of Flux Tubes
6.1 Response of Flux Tubes to Propagation of Sound Waves
6.1.1 Energy exchange between the waves and ensembles of flux tubes
6.1.2 Near-resonance condition
6.2 Nonlinear Estimates of the Maximum Energy Input
6.3 Axisymmetric Oscilation in Flux Tube Ensembles
6.3.1 Equations of motion
6.3.2 Dispersion relation - resonance and frequency shift
6.4 The Interaction of Unsteady Wave Packets with an Ensemble of Flux Tubes
6.5 Spreading of the Energy Absorption Region - ”Clouds of Energy”
6.5.1 Large wave packets
6.5.2 Short wave packets - energy absorption and release
6.6 The Energy Transfer from Unsteady Wave Packets to the Medium
6.7 Problems
Appendix A.References
Chapter 7. Effects of Magnetic Flux Tubes in Helioseismology
7.1 The Time-distance Tomography
7.1.1 Key Points of Time-distance Analysis with Magnetic Fields7.1.2 The Travel Times
7.2 The Effects of Horizontal Flows
7.3 Effects of Horizontal Magnetic Field
7.4 Effects of Background Inhomogeneities
7.4.1 Weak Inhomogeneities
7.4.2 Variations of Flow Velocities
7.5 Practical Use of the Forward-Backward Information
7.5.1 Symmetry properties
7.5.2 Reconstruction of flow and magnetic fields from observations
7.6 Magnetic Corrections in a Vertically Stratified Atmosphere
7.7 Estimate of the Energy Flux from Time-distance Analysis
7.7.1 Heat and magnetic energy fluxes
7.7.2 Contribution of eddy fluxes
7.7.3 Reconstruction of energy fluxes from observational data
7.8 Raman Spectroscopy of Solar Oscillations
7.8.1 Stokes and anti-Stokes satellites
7.8.2 Using Raman spectroscopy in observations
7.9 Problems
ReferencesChapter 8. Wave Phenomena in Dense Conglomerate of Flux Tubes
8.1 Propagation of MHD Waves in an Ensemble of Closely Packed Flux tubes
8.1.1 Basic Equations and Dispersion Relation
8.1.2 Spacial Cases
8.2 Dissipative processes
8.2.1 Weakly Inhomogeneous Medium
8.2.2 Medium with Moderate and Strong Inhomogeneities
8.2.3 Dissipation by Thermal Conduction
8.2.4 Dissipation by Viscosity
8.2.5 Total Dissipation Rate
8.3 Anomalous Damping at Small Wavevectors
8.4 Absorption of p-modes by Sunspots and Active Regions - Observations
8.5 The Interpolation Formula and Comparison with Observations
8.6 Problems
References
Chapter 9. NonlinearWave Phenomena in Dense Conglomerate of Flux Tubes
9.1 Nonlinear Equations in Strongly Inhomogeneous Medium
9.2 Formation of Shocks Across Small Scale Inhomogeneities
9.2.1 Validation of the overturning condition9.3 Effect of Inhomogeneities on the Dispersion Properties of the System
9.3.1 Basic Equations
9.3.2 Dispersion Relation<
9.3.3 KdV - B¨urgers’ Equation with Strong Inhomogeneities
9.4 Numerical Analysis
9.4.1 The Model
9.4.2 Formation of Shock Waves
9.4.3 Energy Dissipation
9.5 Problems
References
Chapter 10. ”Magnetosonic Streaming”
10.1 Secondary Flows - Boundary Layer Effects10.1.1 Acoustic Streaming - History and Nature of Faraday’s Effect
10.1.2 Secondary Flows In Magnetohydrodynamics
10.2 Magnetosonic Streaming due to the Action of Ponderomotive Force
10.3 Process of Filamentation and Diffusive Vanishing of Flux Tubes
10.3.1 Diffusive broadening of flux tube
10.3.2 Quantitative estimates - Lifetimes and spatial scales of flux tubes
10.4 Generation of Mass Flows due to the Absorption Mechanisms
10.5 Numerical Analysis
10.5.1 Basic Equations and Numerical Method
10.5.2 Numerical Results
10.6 Intrinsic nature of flux tube fragmentation10.7 Problems
References
Chapter 11. Moving Magnetic Features (MMFs)
11.1 Types of MMFs and Their General Properties11.2 Impossibility of the Origin of MMF’s in Conservative Systems
11.2.1 The Mechanism
11.3 Nonlinear Kink and its Evolution in the Presence of Shear Flows
11.4 Soliton and Shocklike Formations along the Flux Tube - Numerical Studies
11.5 Observations and Comparison with Theory
11.6 Quantitative Analysis
11.7 Unification of Known Types of Moving Magnetic Features
11.8 Impact of MMFs on the Overlying Atmosphere
11.9 Anticorrelation between Population of MMF’s and Coronal Loop Formation
11.10 Problems
References
Chapter 12. Reconnection of Flux Tubes - Specifics of High Plasma ¯
12.1 Basics of Magnetic Reconnection
12.2 Photospheric Reconnections - No Immediate Gain in Energy<
12.2.1 Specifics of Photospheric Reconnections
12.2.2 Flux Tubes Carrying Different Amount of Magnetic Flux
12.2.3 Number of Events - Importance of Noncollinearity of Flux Tubes
12.3 Dynamics of the Post-reconnection Products
12.3.1 Self-similarity of solution
12.3.2 Energy Analysis
12.3.3 Transsonic Motion
12.4 Dynamics of S-shaped Flux Tubes
12.5 Dynamics of-shaped Part of Flux Tube
12.6 Problems
References
Chapter 13. Post-reconnection Processes - Shocks, Jets and Microflares
13.1 Key Regularities Observed in the Photosphere/Transition Region
13.2 Post-reconnection Shocks and Hydromagnetic Cumulation of Energy
13.2.1 Head-on Convergence of Shock-fronts
13.2.2 Energy Distribution between Heat, Jet and Their Combinations13.3 Observation of Photospheric Reconnections and Their Impact on Overlying
Atmosphere
13.3.1 Microflares, jets and their combinations
13.3.2 Effects of Converging Supergranular Flows
13.4 Key Elements of Energy Production and Observation of Shocks
13.5 Explosive Events
13.6 Response of the Upper atmosphere to Reconnection of Unipolar Flux Tubes
13.7 Problems
References
Chapter 14. Photospheric Network as Energy Source for Quiet Sun Corona
14.1 Post-Reconnection Processes in Arbitrarily Magnetized Environment
14.1.1 Magnetic Loop Arcades in The Chromosphere
14.1.2 Post-Reconnection Shocks in Chromosphere - Types and Characters
14.2 Heights of Shock Formation<
14.3 Energy Release in the Chromosphere-Transition Region
14.3.1 Quantitative Analysis
14.3.2 Total Energy Flux In Quiet Sun Atmosphere
14.4 Magnetic Energy Avalanche and the Fast Solar Wind
14.5 Problems
References
Chapter 15. Response of the Corona to Magnetic Activity in Underlying
Plage Regions
15.1 Magnetic Imprint of Plage Regions in the Corona
15.2 Coronal Dynamics above Unipolar and Mixed Polarity Plages
15.3 Properties of Braidlike Coronal Structures
15.4 Comparison of Coronal Emission above Mixed polarity and Unipolar Plages
15.5 Energy Extraction Mechanisms from the Ensembles of Photospheric Flux
Tubes
15.5.1 Mixed Polarity Plage
15.5.2 Unipolar Plage15.5.3 N-Solitons
15.6 Problems
References
Chapter 16. Electrodynamic Coupling of Active Region Corona with the Photosphere
16.1 The Problem of Multi-face Corona
16.2 Emerging Magnetic Flux and Structure Formation in Overlying Atmosphere
16.3 Current Drive Mechanisms Associated with the Emerging Magnetic Flux
16.3.1 Proper Motion
16.3.2 Acoustic Waves
16.3.3 Alfv`en Waves
16.4 Energy Flow throughout Solar Atmosphere
16.4.1 An equivalent circuit - Earlier attempts
16.4.2 LRC circuit with mutual inductance (Transition Region)
16.5 Energetically Open Circuit
16.6 Evolution of Current Systems
16.6.1 Linear Regime
16.6.2 Nonlinear Regime
16.7 Quantitative Analysis
16.7.1 Examples
16.8 Limiting Currents and Filamentary Structures
16.9 Problems
Appendix A. Method of slow variables for van der Pol Equation
References
Chapter 17. Fine Structure of Penumbrae: Formation and Dynamics
17.1 Peculiarities of Sunspot Penumbrae - Observations
17.2 Dynamics of Penumbral Filaments and On-going Reconnections
17.3 Formation of Filamentary Penumbrae
17.3.1 Phenomenology of basic mechanism
17.3.2 Filamentary structure of sunspot
17.3.3 Properties of individual filaments
17.4 Screw Pinch Instability and Dark Cores
17.4.1 More on substructures of filaments and effects of axial flows
17.5 Problems
References
Chapter 18. Bow Shocks and Plasma Jetting over Penumbrae18.1 Response of the Overlying Atmosphere to Penumbral Dynamics
18.1.1 Penumbral transients - Double structures and jets
18.1.2 Viewing under different angles
18.1.3 Brief summary of properties
18.2 Phenomenology and Quantitative Analysis
18.2.1 Dynamics of S-shaped Filaments
18.2.2 Nature of double structures
18.3 Bow Shocks
18.4 Energy Release and Lifetime of Bright Transients
18.5 Problems
References
Chapter 19. Self-organization in the Corona and Flare Precursors
19.1 Well-organized Multi-threaded Coronal Arcades - Slinkies
19.2 Essential Difference between ”Regular” and Slinky-Producing Flares
19.3 Precursors and Predictability
19.4 Exemplary case of X-class Flare and Formation of Slinkies
19.5 Phenomenology of Energy Build up and Quantitative Analysis
19.6 Recurrent Flares and Echoes
19.6.1 Landau damping and Spatio-Temporal Echoes
19.6.2 Echo effects in slinkies
19.6.3 Spatial and temporal recurrences in flares
19.7 Problems
References
Chapter 20. Quiescent Prominences
20.1 Background - Problem of Stability
20.2 Large-scale observed regularities
20.3 Formation of Prominence Cavity and Helical Structures
20.3.1 The case of the 16 August 2007 prominence
20.3.2 Phenomenology of cavity formation
20.4 Regular Series of Plumes - Multi-mode Regime of Rayleigh-Taylor Instability
20.4.1 Practical use
20.5 Fast-growing Plumes - Nonlinear Regime
20.5.1 Mushroom Formation
20.5.2 Two-bubble competition
20.6 Greenhouse Effect
20.6 Problems
References Chapter 21 Mass Flows: From Spicules and Mustaches to Coronal Mass Ejections
21.1 Brash-lands of Spicules
21.1.1 Appearence and morphology of spicules
21.1.2 Physical properties
21.1.3 Observations and misconceptions
21.1.4 Analytical models
21.2 Ellerman Bombs and Severny Moustaches
21.2.1 Observations
21.2.2 Physical properties and interpretations
21.3 Active filaments
21.4 Jetting
21.4.1 Penumbral jets
21.4.2 Transition region and coronal jetting
21.4.3 Downflows
21.4.4 Polar plumes
21.5 Coronal mass ejections
21.5.1 Classes
21.5.2 Models
21.5.3 Controversies
21.6 Problems
References
Chapter 22 The Sun and Laboratory Astrophysics
22.1 Magnetic Reconnection Experiments
22.1.1 Revealing the fundamental properties of reconnection
22.1.2 Verification of the Kruskal-Shafranov stability limit
22.1.3 Impulsive reconnection
22.2 3D-Magnetic reconnection
22.2.1 Magnetic Reconnection between Colliding Plasma Plumes
22.2.2 Magnetic Reconnection in current carrying flux ropes
22.3 Bow shocks and thermal instabilities
22.4 Laser experiments on Plasma Instabilities
22.4.1 Rayleigh-Taylor Instability
22.4.2 Kelvin-Helmholtz and Explosive Instabilities22.4.3 Z-pinches
22.5 Tadpoles
22.6 Problems
ReferencesChapter 23. What to Observe
23.1 Quiet Sun and Plages
23.1.1 Flows along Flux tubes and resulted morphological effect
23.1.2 Bullwhip effect23.1.3 Clouds of Energy
23.1.4 Formation of Clouds above quiet Sun
23.1.5 Space-time cuts revealing the properties of wave packets
23.1.6 Chirality of clouds
23.1.7 Coronal Holes and comparison with ”out of hole” quite regions
23.1.8 Corona above the sequence of alternating unipolar plages. <23.2 Wave Phenomena in and above Sunspots
23.2.1 Power spectra of the dominant oscillations in sunspot
23.2.2 The f-modes
23.2.3 The wave amplitudes in flaring and dormant active regions
23.2.4 Shocks at the surface of sunspot
23.2.5 Nonlinear waves above active regions
23.3 Magnetic Flux Fragmentation
23.3.1 Magnetosonic Streaming
23.3.2 Lifetime of flux tubes
23.4 Moving Magnetic Features
23.4.1 Origin, evolution, collapse
23.4.2 Effects on Coronal Loop Formation
23.5 High-Reconnection and Post-reconnection Processes
23.5.1 Dynamics of post-reconnection products
23.5.2 Post-reconnection shocks and energy build up throught the atmosphere
23.5.3 Triggering jets, microflares and explosive events
23.5.4 Magnetic energy avalanche and solar wind
23.6 Mystery of Braidlike Structures
23.7 Prediction and Expectation of Newly Emerging Sunspots and Pores
23.7.1 Observation of emerging fluxes and their coagulation
23.7.2 Measuring the mass flows and currents above emerging fluxes
23.7.3 Spectroscopic diagnostics of magnetic flux formation
23.8 Bow shocks and Precursors of Penumbral Jets
23.9 Flaring, Non-flaring and Slinky Producing Active Regions23.9.1 Electric fields and energy fluxes
23.9.2 Homologous coronal jets and multiple blobs
23.9.3 Echo effects
23.10 Prominences
23.10.1 Birth and evolution of prominences
23.10.2 Onset of various plasma instabilities
23.10.3 Exploding prominences
23.10.4 Greenhouse-like effects
References
Index
Margarita Ryutova (Kemoklidze) received her MSc and PhD from the famous Landau Theoretical Department, Kapitsa Institute for Physical Problems, Moscow and worked there until she married and moved to Budker Institute of Nuclear Physics. Since 1994 she lives in the United States where she has been affiliated with Stanford Lockheed Institute for Space Research in Palo Alto and Lawrence Livermore National laboratory.
She has 30 years of experience in teaching undergraduate and graduate courses in Physics and Mathematics. This includes supervising graduate and PhD students. She has published over 100 research papers and reviews in various fields of theoretical and experimental physics such as Statistical Physics, Solar Physics, Laboratory and Plasma Astrophysics, Nonlinear Fluid Dynamics, Solitons, Shocks and Selforganization, Superfluidity and Superconductivity.
Along with research in physics, she works in and has published books and essays on the history of physics and mathematics.
This book presents the physics of magnetic flux tubes, including their fundamental properties and collective phenomena in an ensemble of flux tubes. The physics of magnetic flux tubes is vital for understanding fundamental processes in the solar atmosphere that are shaped and governed by magnetic fields. The concept of magnetic flux tubes is also central to various magnetized media ranging from laboratory plasma and Earth's magnetosphere to planetary, stellar and galactic environments.
The book covers both theory and observations. Theoretical models presented in analytical and phenomenological forms that are tailored to practical applications. These are welded together with empirical data extending from the early pioneering observations to the most recent state-of-the-art data.
This new edition of the book is updated and contains a significant amount of new material throughout as well as four new chapters and 48 problems with solutions. Most problems make use of original papers containing fundamental results. This way, the original paper, often based on complex theory, turns into a convenient tool for practical use and quantitative analysis.
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