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Physics of Magnetic Flux Tubes (2nd Ed., 2nd ed. 2018) Astrophysics and Space Science Library Series, Vol. 455

Langue : Anglais

Auteur :

Couverture de l’ouvrage Physics of Magnetic Flux Tubes

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.



Chapter 1. The Sun’s Magnetic fields

1.1 The Sun as a Star

1.1.2 Legacy of ancients

1.1.2 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


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


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 Problems

Appendix A. Analogy with Landau Damping

Appendix B. Derivation of Equation for Kink Oscillations from MHD


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


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 Waves

5.8 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


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.


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 Fields

7.1.2 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


Chapter 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


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 condition

9.3 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


Chapter 10. ”Magnetosonic Streaming”

10.1 Secondary Flows - Boundary Layer Effects

10.1.1 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 fragmentation

10.7 Problems


Chapter 11. Moving Magnetic Features (MMFs)

11.1 Types of MMFs and Their General Properties

11.2 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


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


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 Combinations

13.3 Observation of Photospheric Reconnections and Their Impact on Overlying


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


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


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


15.5.1 Mixed Polarity Plage

15.5.2 Unipolar Plage

15.5.3 N-Solitons

15.6 Problems


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


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


Chapter 18. Bow Shocks and Plasma Jetting over Penumbrae

18.1 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


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


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


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 Instabilities

22.4.3 Z-pinches

22.5 Tadpoles

22.6 Problems


Chapter 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 effect

23.1.3 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 Regions

23.9.1 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



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.

Presents vital knowledge for understanding fundamental processes in the solar and stellar atmospheres, as well as in laboratory plasmas and earth's magnetosphere

Covers both theory and observations

Presents theoretical models in analytical and phenomenological forms tailored for practical applications

Provides learning material at the end of the chapters with problems and solutions, and guides researchers how to choose and interpret observational data

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