Physics of Magnetic Flux Tubes

Preface Contents 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 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 Problems Appendix 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-Burgers 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 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 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 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 References 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 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 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 - Burgers' 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 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 References 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 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 Combinations 13.3 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 Plage 15.5.3 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 Alfven 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 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 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 Instabilities 22.4.3 Z-pinches 22.5 Tadpoles 22.6 Problems References 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 References Index

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