Physics of Magnetic Flux Tubes

<p>Preface</p> <p>Contents</p> <p>Chapter 1. The Sun’s Magnetic fields</p> <p>1.1 The Sun as a Star</p> 1.1.2 Legacy of ancients<p></p> <p>1.1.2 Hidden interior</p> <p>1.1.3 Magnetic dipole</p> <p>1.2 Magnetic Surface</p> <p>1.2.1 Quiet sun</p> <p>1.2.2 Sunspots and active regions</p> <p>1.2.3 Plages</p> <p>1.2.4 High latitudes and polar regions</p> <p>1.3 Mass Flows</p> <p>1.4 Magnetic Skeleton</p> <p>References</p> <p>Chapter 2. A Quick Look on Small Scale Flux Tubes</p> <p>2.1 Early Years</p> <p>2.1.1 First observational signs of magnetic flux tubes</p> <p>2.1.2 The Sunspot dilemma</p> <p>2.2 Elements of Theory for de facto Flux Tubes</p> <p>2.3 Numerical visualization and Observations</p> <p>2.4 Filamentary Structures in Laboratory and Universe</p> <p>2.5 Problems</p> <p>References</p> <p>Chapter 3. Intrinsic Properties of Flux Tubes - Wave Phenomena</p> <p>3.1 Equations of Motion or How are Tube Waves Excited</p> <p>3.1.1 Equation of Motion for a Single flux tube</p> <p>3.1.2 Macroscopic Motions of an Ensemble of flux tubes</p> <p>3.2 Absorption of Acoustic Waves - Landau Resonance</p> <p>3.3 Effects of Non-collinearity of Flux Tubes</p> <p>3.4 Exact Theory of Linear Oscillations of Magnetic Flux Tube</p> <p>3.5 Radiation of Secondary Waves by Oscillationg Flux Tubes</p> <p>3.6 Scattering of Acoustic Waves and Maximum Energy input</p> <p>3.7 Axisymmetric Oscillations of Flux Tube</p> <p>3.7.1 Types of m = 0 mode</p> <p>3.7.2 Equation of Motion for Sausage Oscillations</p> <p>3.7.3 Dispersion Relation</p> <p>3.7.4 Sausage and and Fast Oscillations in homogeneous flux tube</p> <p>3.7.5 Effects of Radial Inhomogeneities on Sausage oscillations</p> 3.8 Problems<p></p> <p>Appendix A. Analogy with Landau Damping</p> <p>Appendix B. Derivation of Equation for Kink Oscillations from MHD</p> <p>References</p> <p>Chapter 4. Effects of Flux Tube Inhomogeneities and Weak Nonlinearity</p> <p>4.1 Radially Inhomogeneous Flux Tube - Internal Resonances</p> <p>4.1.1 Anomalous resonance in kink oscillations</p> <p>4.1.2 Alfv´en resonance</p> <p>4.2 Boundary Value Problem</p> <p>4.2.1 Phase-mixing in flux tubes</p> <p>4.2.3 Phase-mixed torsional waves</p> <p>4.2.3 Phase-mixed kink oscillations</p> <p>4.3 Longitudinal resonances</p> <p>4.3.1 Loss of radial equilibrium</p> <p>4.3.2 Bullwhip effect</p> <p>4.4 Standing resonances and the temperature jump</p> <p>4.4.1 Growth of the oscillation amplitude - first resonance</p> <p>4.4.2 Spectral density and strong enhancement of the oscillation amplitude</p> <p>4.5 Weakly Nonlinear Waves in Flux Tubes</p> <p>4.5.1 Nonlinear kink oscillations - KdV-B¨urgers equation</p> <p>4.5.2 Possibility of solitary sausage wave</p> <p>4.6 Problems</p> <p>References</p> <p> </p><p>5.1 Kelvin-Helmholtz Instability and Negative Energy Waves</p> <p>5.2 Shear Flow Instabilities in Magnetic Flux Tubes</p> <p>5.2.1 Specifics of Kelvin-Helmholtz instability along flux tubes</p> <p>5.2.2 Flux tubes and Negative Energy Waves (NEWs)</p> <p>5.3 Basic Equations of Flux tube Oscillations with Shear Flows</p> <p>5.4 Dissipative Instabilities of Negative-energy Kink Oscillations</p> <p>5.5 Radiative Instability of Flux Tube Oscillations in Presence of Flows</p> <p>5.5.1 Sausage oscillations</p> <p>5.5.2 Kink oscillations</p> <p>5.6 Parity of Negative and Positive Energy Waves</p> 5.7 Explosive Instability of Negative-energy Waves<p></p> <p>5.8 Sub-critical Mass Flows - Absence of Instabilities</p> <p>5.8.1 Can the Alfv´en waves heat the corona?</p> <p>5.8.2 Effect of mass flows on the efficiency of heating by Alfv´en waves</p> <p>5.9 Phase-Mixed Alfv´en Waves at Sub-alfv´enic Mass Flows</p> <p>5.9.1 Damping rate and height of energy release</p> <p>5.9.2 Observable morphological effects</p> <p>5.10 The Asymptotic Behavior of the Total Energy Flux</p> <p>5.11 The Wave Extinction in the Presence of Downflows</p> <p>5.12 Problems</p> <p>Appendix A. Equation for Alfv´en Waves in the Presence of Parallel Mass Flows</p> <p>References</p> <p>Chapter 6. Collective Phenomena in Rarefied Ensembles of Flux Tubes</p> <p>6.1 Response of Flux Tubes to Propagation of Sound Waves</p> <p>6.1.1 Energy exchange between the waves and ensembles of flux tubes</p> <p>6.1.2 Near-resonance condition</p> <p>6.2 Nonlinear Estimates of the Maximum Energy Input</p> <p>6.3 Axisymmetric Oscilation in Flux Tube Ensembles</p> <p>6.3.1 Equations of motion</p> <p>6.3.2 Dispersion relation - resonance and frequency shift</p> <p>6.4 The Interaction of Unsteady Wave Packets with an Ensemble of Flux Tubes</p> <p>6.5 Spreading of the Energy Absorption Region - ”Clouds of Energy”</p> <p>6.5.1 Large wave packets</p> <p>6.5.2 Short wave packets - energy absorption and release</p> <p>6.6 The Energy Transfer from Unsteady Wave Packets to the Medium</p> <p>6.7 Problems</p> Appendix A.<p></p> <p>References</p> <p>Chapter 7. Effects of Magnetic Flux Tubes in Helioseismology</p> <p>7.1 The Time-distance Tomography</p> 7.1.1 Key Points of Time-distance Analysis with Magnetic Fields<p></p> <p>7.1.2 The Travel Times</p> <p>7.2 The Effects of Horizontal Flows</p> <p>7.3 Effects of Horizontal Magnetic Field</p> <p>7.4 Effects of Background Inhomogeneities</p> <p>7.4.1 Weak Inhomogeneities</p> <p>7.4.2 Variations of Flow Velocities</p> <p>7.5 Practical Use of the Forward-Backward Information</p> <p>7.5.1 Symmetry properties</p> <p>7.5.2 Reconstruction of flow and magnetic fields from observations</p> <p>7.6 Magnetic Corrections in a Vertically Stratified Atmosphere</p> <p>7.7 Estimate of the Energy Flux from Time-distance Analysis</p> <p>7.7.1 Heat and magnetic energy fluxes</p> <p>7.7.2 Contribution of eddy fluxes</p> <p>7.7.3 Reconstruction of energy fluxes from observational data</p> <p>7.8 Raman Spectroscopy of Solar Oscillations</p> <p>7.8.1 Stokes and anti-Stokes satellites</p> <p>7.8.2 Using Raman spectroscopy in observations</p> <p>7.9 Problems</p> References<p></p> <p>Chapter 8. Wave Phenomena in Dense Conglomerate of Flux Tubes</p> <p>8.1 Propagation of MHD Waves in an Ensemble of Closely Packed Flux tubes</p> <p>8.1.1 Basic Equations and Dispersion Relation</p> <p>8.1.2 Spacial Cases</p> <p>8.2 Dissipative processes</p> <p>8.2.1 Weakly Inhomogeneous Medium</p> <p>8.2.2 Medium with Moderate and Strong Inhomogeneities</p> <p>8.2.3 Dissipation by Thermal Conduction</p> <p>8.2.4 Dissipation by Viscosity</p> <p>8.2.5 Total Dissipation Rate</p> <p>8.3 Anomalous Damping at Small Wavevectors</p> <p>8.4 Absorption of p-modes by Sunspots and Active Regions - Observations</p> <p>8.5 The Interpolation Formula and Comparison with Observations</p> <p>8.6 Problems</p> <p>References</p> <p>Chapter 9. NonlinearWave Phenomena in Dense Conglomerate of Flux Tubes</p> <p>9.1 Nonlinear Equations in Strongly Inhomogeneous Medium</p> <p>9.2 Formation of Shocks Across Small Scale Inhomogeneities</p> 9.2.1 Validation of the overturning condition<p></p> <p>9.3 Effect of Inhomogeneities on the Dispersion Properties of the System</p> <p>9.3.1 Basic Equations</p> <p>9.3.2 Dispersion Relation&lt; </p><p>9.3.3 KdV - B¨urgers’ Equation with Strong Inhomogeneities</p> <p>9.4 Numerical Analysis</p> <p>9.4.1 The Model</p> <p>9.4.2 Formation of Shock Waves</p> <p>9.4.3 Energy Dissipation</p> <p>9.5 Problems</p> <p>References</p> <p>Chapter 10. ”Magnetosonic Streaming”</p> 10.1 Secondary Flows - Boundary Layer Effects<p></p> <p>10.1.1 Acoustic Streaming - History and Nature of Faraday’s Effect</p> <p>10.1.2 Secondary Flows In Magnetohydrodynamics</p> <p>10.2 Magnetosonic Streaming due to the Action of Ponderomotive Force</p> <p>10.3 Process of Filamentation and Diffusive Vanishing of Flux Tubes</p> <p>10.3.1 Diffusive broadening of flux tube</p> <p>10.3.2 Quantitative estimates - Lifetimes and spatial scales of flux tubes</p> <p>10.4 Generation of Mass Flows due to the Absorption Mechanisms</p> <p>10.5 Numerical Analysis</p> <p>10.5.1 Basic Equations and Numerical Method</p> <p>10.5.2 Numerical Results</p> 10.6 Intrinsic nature of flux tube fragmentation<p></p> <p>10.7 Problems</p> <p>References</p> <p>Chapter 11. Moving Magnetic Features (MMFs)</p> 11.1 Types of MMFs and Their General Properties<p></p> <p>11.2 Impossibility of the Origin of MMF’s in Conservative Systems</p> <p>11.2.1 The Mechanism</p> <p>11.3 Nonlinear Kink and its Evolution in the Presence of Shear Flows</p> <p>11.4 Soliton and Shocklike Formations along the Flux Tube - Numerical Studies</p> <p>11.5 Observations and Comparison with Theory</p> <p>11.6 Quantitative Analysis</p> <p>11.7 Unification of Known Types of Moving Magnetic Features</p> <p>11.8 Impact of MMFs on the Overlying Atmosphere</p> <p>11.9 Anticorrelation between Population of MMF’s and Coronal Loop Formation</p> <p>11.10 Problems</p> <p>References</p> <p>Chapter 12. Reconnection of Flux Tubes - Specifics of High Plasma ¯</p> <p>12.1 Basics of Magnetic Reconnection</p> <p>12.2 Photospheric Reconnections - No Immediate Gain in Energy&lt; </p><p>12.2.1 Specifics of Photospheric Reconnections</p> <p>12.2.2 Flux Tubes Carrying Different Amount of Magnetic Flux</p> <p>12.2.3 Number of Events - Importance of Noncollinearity of Flux Tubes</p> <p>12.3 Dynamics of the Post-reconnection Products</p> <p>12.3.1 Self-similarity of solution</p> <p>12.3.2 Energy Analysis</p> <p>12.3.3 Transsonic Motion</p> <p>12.4 Dynamics of S-shaped Flux Tubes</p> <p>12.5 Dynamics of-shaped Part of Flux Tube</p> <p>12.6 Problems</p> <p>References</p> <p>Chapter 13. Post-reconnection Processes - Shocks, Jets and Microflares</p> <p>13.1 Key Regularities Observed in the Photosphere/Transition Region</p> <p>13.2 Post-reconnection Shocks and Hydromagnetic Cumulation of Energy</p> <p>13.2.1 Head-on Convergence of Shock-fronts</p> 13.2.2 Energy Distribution between Heat, Jet and Their Combinations<p></p> <p>13.3 Observation of Photospheric Reconnections and Their Impact on Overlying</p> <p>Atmosphere</p> <p>13.3.1 Microflares, jets and their combinations</p> <p>13.3.2 Effects of Converging Supergranular Flows</p> <p>13.4 Key Elements of Energy Production and Observation of Shocks</p> <p>13.5 Explosive Events</p> <p>13.6 Response of the Upper atmosphere to Reconnection of Unipolar Flux Tubes</p> <p>13.7 Problems</p> <p>References</p> <p>Chapter 14. Photospheric Network as Energy Source for Quiet Sun Corona</p> <p>14.1 Post-Reconnection Processes in Arbitrarily Magnetized Environment</p> <p>14.1.1 Magnetic Loop Arcades in The Chromosphere</p> <p>14.1.2 Post-Reconnection Shocks in Chromosphere - Types and Characters</p> <p>14.2 Heights of Shock Formation&lt; </p><p>14.3 Energy Release in the Chromosphere-Transition Region</p> <p>14.3.1 Quantitative Analysis</p> <p>14.3.2 Total Energy Flux In Quiet Sun Atmosphere</p> <p>14.4 Magnetic Energy Avalanche and the Fast Solar Wind</p> <p>14.5 Problems</p> <p>References</p> <p>Chapter 15. Response of the Corona to Magnetic Activity in Underlying</p> <p>Plage Regions</p> <p>15.1 Magnetic Imprint of Plage Regions in the Corona</p> <p>15.2 Coronal Dynamics above Unipolar and Mixed Polarity Plages</p> <p>15.3 Properties of Braidlike Coronal Structures</p> <p>15.4 Comparison of Coronal Emission above Mixed polarity and Unipolar Plages</p> <p>15.5 Energy Extraction Mechanisms from the Ensembles of Photospheric Flux</p> <p>Tubes</p> <p>15.5.1 Mixed Polarity Plage</p> 15.5.2 Unipolar Plage<p></p> <p>15.5.3 N-Solitons</p> <p>15.6 Problems</p> <p>References</p> <p>Chapter 16. Electrodynamic Coupling of Active Region Corona with the Photosphere</p> <p>16.1 The Problem of Multi-face Corona</p> <p>16.2 Emerging Magnetic Flux and Structure Formation in Overlying Atmosphere</p> <p>16.3 Current Drive Mechanisms Associated with the Emerging Magnetic Flux</p> <p>16.3.1 Proper Motion</p> <p>16.3.2 Acoustic Waves</p> <p>16.3.3 Alfv`en Waves</p> <p>16.4 Energy Flow throughout Solar Atmosphere</p> <p>16.4.1 An equivalent circuit - Earlier attempts</p> <p>16.4.2 LRC circuit with mutual inductance (Transition Region)</p> <p>16.5 Energetically Open Circuit</p> <p>16.6 Evolution of Current Systems</p> <p>16.6.1 Linear Regime</p> <p>16.6.2 Nonlinear Regime</p> <p>16.7 Quantitative Analysis</p> <p>16.7.1 Examples</p> <p>16.8 Limiting Currents and Filamentary Structures</p> <p>16.9 Problems</p> <p>Appendix A. Method of slow variables for van der Pol Equation</p> <p>References</p> <p>Chapter 17. Fine Structure of Penumbrae: Formation and Dynamics</p> <p>17.1 Peculiarities of Sunspot Penumbrae - Observations</p> <p>17.2 Dynamics of Penumbral Filaments and On-going Reconnections</p> <p>17.3 Formation of Filamentary Penumbrae</p> <p>17.3.1 Phenomenology of basic mechanism</p> <p>17.3.2 Filamentary structure of sunspot</p> <p>17.3.3 Properties of individual filaments</p> <p>17.4 Screw Pinch Instability and Dark Cores</p> <p>17.4.1 More on substructures of filaments and effects of axial flows</p> <p>17.5 Problems</p> <p>References</p> Chapter 18. Bow Shocks and Plasma Jetting over Penumbrae<p></p> <p>18.1 Response of the Overlying Atmosphere to Penumbral Dynamics</p> <p>18.1.1 Penumbral transients - Double structures and jets</p> <p>18.1.2 Viewing under different angles</p> <p>18.1.3 Brief summary of properties</p> <p>18.2 Phenomenology and Quantitative Analysis</p> <p>18.2.1 Dynamics of S-shaped Filaments</p> <p>18.2.2 Nature of double structures</p> <p>18.3 Bow Shocks</p> <p>18.4 Energy Release and Lifetime of Bright Transients</p> <p>18.5 Problems</p> <p>References</p> <p>Chapter 19. Self-organization in the Corona and Flare Precursors</p> <p>19.1 Well-organized Multi-threaded Coronal Arcades - Slinkies</p> <p>19.2 Essential Difference between ”Regular” and Slinky-Producing Flares</p> <p>19.3 Precursors and Predictability</p> <p>19.4 Exemplary case of X-class Flare and Formation of Slinkies</p> <p>19.5 Phenomenology of Energy Build up and Quantitative Analysis</p> <p>19.6 Recurrent Flares and Echoes</p> <p>19.6.1 Landau damping and Spatio-Temporal Echoes</p> <p>19.6.2 Echo effects in slinkies</p> <p>19.6.3 Spatial and temporal recurrences in flares</p> <p>19.7 Problems</p> <p>References</p> <p>Chapter 20. Quiescent Prominences</p> <p>20.1 Background - Problem of Stability</p> <p>20.2 Large-scale observed regularities</p> <p>20.3 Formation of Prominence Cavity and Helical Structures</p> <p>20.3.1 The case of the 16 August 2007 prominence</p> <p>20.3.2 Phenomenology of cavity formation</p> <p>20.4 Regular Series of Plumes - Multi-mode Regime of Rayleigh-Taylor Instability</p> <p>20.4.1 Practical use</p> <p>20.5 Fast-growing Plumes - Nonlinear Regime</p> <p>20.5.1 Mushroom Formation</p> <p>20.5.2 Two-bubble competition</p> <p>20.6 Greenhouse Effect</p> <p>20.6 Problems</p> <p>References Chapter 21 Mass Flows: From Spicules and Mustaches to Coronal Mass Ejections</p> <p>21.1 Brash-lands of Spicules</p> <p>21.1.1 Appearence and morphology of spicules</p> <p>21.1.2 Physical properties</p> <p>21.1.3 Observations and misconceptions</p> <p>21.1.4 Analytical models</p> <p>21.2 Ellerman Bombs and Severny Moustaches</p> <p>21.2.1 Observations</p> <p>21.2.2 Physical properties and interpretations</p> <p>21.3 Active filaments</p> <p>21.4 Jetting</p> <p>21.4.1 Penumbral jets</p> <p>21.4.2 Transition region and coronal jetting</p> <p>21.4.3 Downflows</p> <p>21.4.4 Polar plumes</p> <p>21.5 Coronal mass ejections</p> <p>21.5.1 Classes</p> <p>21.5.2 Models</p> <p>21.5.3 Controversies</p> <p>21.6 Problems</p> <p>References</p> <p>Chapter 22 The Sun and Laboratory Astrophysics</p> <p>22.1 Magnetic Reconnection Experiments</p> <p>22.1.1 Revealing the fundamental properties of reconnection</p> <p>22.1.2 Verification of the Kruskal-Shafranov stability limit </p><p>22.1.3 Impulsive reconnection</p> <p>22.2 3D-Magnetic reconnection</p> <p>22.2.1 Magnetic Reconnection between Colliding Plasma Plumes</p> <p>22.2.2 Magnetic Reconnection in current carrying flux ropes</p> <p>22.3 Bow shocks and thermal instabilities</p> <p>22.4 Laser experiments on Plasma Instabilities</p> <p>22.4.1 Rayleigh-Taylor Instability</p> 22.4.2 Kelvin-Helmholtz and Explosive Instabilities<p></p> <p>22.4.3 Z-pinches</p> <p>22.5 Tadpoles</p> <p>22.6 Problems</p> References<p></p> <p>Chapter 23. What to Observe</p> <p>23.1 Quiet Sun and Plages</p> <p>23.1.1 Flows along Flux tubes and resulted morphological effect</p> 23.1.2 Bullwhip effect<p></p> <p>23.1.3 Clouds of Energy</p> <p>23.1.4 Formation of Clouds above quiet Sun</p> <p>23.1.5 Space-time cuts revealing the properties of wave packets</p> <p>23.1.6 Chirality of clouds</p> <p>23.1.7 Coronal Holes and comparison with ”out of hole” quite regions</p> <p>23.1.8 Corona above the sequence of alternating unipolar plages. &lt;23.2 Wave Phenomena in and above Sunspots</p> <p>23.2.1 Power spectra of the dominant oscillations in sunspot</p> <p>23.2.2 The f-modes</p> <p>23.2.3 The wave amplitudes in flaring and dormant active regions</p> <p>23.2.4 Shocks at the surface of sunspot</p> <p>23.2.5 Nonlinear waves above active regions</p> <p>23.3 Magnetic Flux Fragmentation</p> <p>23.3.1 Magnetosonic Streaming</p> <p>23.3.2 Lifetime of flux tubes</p> <p>23.4 Moving Magnetic Features</p> <p>23.4.1 Origin, evolution, collapse</p> <p>23.4.2 Effects on Coronal Loop Formation</p> <p>23.5 High-Reconnection and Post-reconnection Processes</p> <p>23.5.1 Dynamics of post-reconnection products</p> <p>23.5.2 Post-reconnection shocks and energy build up throught the atmosphere</p> <p>23.5.3 Triggering jets, microflares and explosive events</p> <p>23.5.4 Magnetic energy avalanche and solar wind</p> <p>23.6 Mystery of Braidlike Structures</p> <p>23.7 Prediction and Expectation of Newly Emerging Sunspots and Pores</p> <p>23.7.1 Observation of emerging fluxes and their coagulation</p> <p>23.7.2 Measuring the mass flows and currents above emerging fluxes</p> <p>23.7.3 Spectroscopic diagnostics of magnetic flux formation</p> <p>23.8 Bow shocks and Precursors of Penumbral Jets</p> 23.9 Flaring, Non-flaring and Slinky Producing Active Regions<p></p> <p>23.9.1 Electric fields and energy fluxes</p> <p>23.9.2 Homologous coronal jets and multiple blobs</p> <p>23.9.3 Echo effects</p> <p>23.10 Prominences</p> <p>23.10.1 Birth and evolution of prominences</p> <p>23.10.2 Onset of various plasma instabilities</p> <p>23.10.3 Exploding prominences</p> <p>23.10.4 Greenhouse-like effects</p> <p>References</p> <p>Index</p>