Physics of Magnetic Flux Tubes

Preface

Contents

Chapter 1. The Sun's Magnetic fields

1.1 The Sun as a Star

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

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-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

5.8 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

About the Author:

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.