Solar magneto-hydrodynamics

I have felt the need for a book on the theory of solar magnetic fields for some time now. Most books about the Sun are written by observers or by theorists from other branches of solar physics, whereas those on magnetohydrodynamics do not deal extensively with solar applications. I had thought of waiting a few decades before attempting to put pen to paper, but one summer Josip Kleczek encouraged an im mediate start 'while your ideas are still fresh'. The book grew out of a postgraduate lecture course at St Andrews, and the resulting period of gestation or 'being with monograph' has lasted several years. The Sun is an amazing object, which has continued to reveal completely unexpected features when observed in greater detail or at new wavelengths. What riches would be in store for us if we could view other stars with as much precision! Stellar physics itself is benefiting greatly from solar discoveries, but, in tum, our understanding of many solar phenomena (such as sunspots, sunspot cycles, the corona and the solar wind) will undoubtedly increase in the future due to their observation under different conditions in other stars. In the 'old days' the solar atmosphere was regarded as a static, plane-parallel structure, heated by the dissipation of sound waves and with its upper layer expanding in a spherically symmetric manner as the solar wind. Outside of sunspots the magnetic field was thOUght to be unimportant with a weak uniform value of a few gauss."

I have felt the need for a book on the theory of solar magnetic fields for some time now. Most books about the Sun are written by observers or by theorists from other branches of solar physics, whereas those on magnetohydrodynamics do not deal extensively with solar applications. I had thought of waiting a few decades before attempting to put pen to paper, but one summer Josip Kleczek encouraged an im mediate start 'while your ideas are still fresh'. The book grew out of a postgraduate lecture course at St Andrews, and the resulting period of gestation or 'being with monograph' has lasted several years. The Sun is an amazing object, which has continued to reveal completely unexpected features when observed in greater detail or at new wavelengths. What riches would be in store for us if we could view other stars with as much precision! Stellar physics itself is benefiting greatly from solar discoveries, but, in tum, our understanding of many solar phenomena (such as sunspots, sunspot cycles, the corona and the solar wind) will undoubtedly increase in the future due to their observation under different conditions in other stars. In the 'old days' the solar atmosphere was regarded as a static, plane-parallel structure, heated by the dissipation of sound waves and with its upper layer expanding in a spherically symmetric manner as the solar wind. Outside of sunspots the magnetic field was thOUght to be unimportant with a weak uniform value of a few gauss.

1. A description of the sun.- 1.1. Brief History.- 1.2. Overall Properties.- 1.2.1. Interior.- 1.2.2. Outer Atmosphere.- 1.3.The Quiet Sun.- 1.3.1. The Interior.- A. The Core.- B. A Model.- C. Convection Zone.- 1.3.2. The Photosphere.- A. Motions.- B. Magnetic Field.- C. A Model.- 1.3.3. The Chromosphere.- 1.3.4. The Corona.- A. At Eclipses.- B. In X-rays.- C. Solar Wind.- 1.4. Transient Features.- 1.4.1. Active Regions.- A. Development.- B. Structure.- C. Loops.- D. Internal Motions.- 1.4.2. Sunspots.- A. Development.- B. Umbra.- C. Penumbra.- D. Motion.- E. Solar Cycle.- 1.4.3. Prominences.- A. Introduction.- B. Properties.- C. Development.- D. Structure.- E. Eruption.- F. Coronal Transients.- 1.4.4. Solar Flares.- A. Basic Description.- B. Ground-Based Observations.- C. Space Observations.- 2. The basic equations of magnetohydrodynamics.- 2.1. Electromagnetic Equations.- 2.1.1. Maxwell's Equations.- 2.1.2. Ohm's Law.- 2.1.3. Generalised Ohm's Law.- 2.1.4. Induction Equation.- 2.1.5. Electrical Conductivity.- 2.2. Plasma Equations.- 2.2.1. Mass Continuity.- 2.2.2. Equation of Motion.- 2.2.3. Perfect Gas Law.- 2.3. Energy Equations.- 2.3.1. Different Forms of Heat Equation.- 2.3.2 Thermal Conduction.- 2.3.3. Radiation.- 2.3.4. Heating.- 2.3.5. Energetics.- 2.4. Summary of Equations.- 2.4.1. Assumptions.- 2.4.2 Reduced Forms of the Equations.- 2.5. Dimensionless Parameters.- 2.6. Consequences of the Induction Equation.- 2.6.1. Diffusive Limit.- 2.6.2. Perfectly Conducting Limit.- 2.7. The Lorentz Force.- 2.8. Some Theorems.- 2.8.1. Cowling's Antidynamo Theorem.- 2.8.2. Taylor-Proudman Theorem.- 2.8.3. Ferraro's Law of Isorotation.- 2.8.4. The Virial Theorem.- 2.9. Summary of Magnetic Flux Tube Behaviour.- 2.9.1. Definitions.- 2.9.2. General Properties.- 2.9.3. Flux Tubes in the Solar Atmosphere.- 2.10. Summary of Current Sheet Behaviour.- 2.10.1. Processes of Formation.- 2.10.2. Properties.- 3. Magnetohydrostatics.- 3.1. Introduction.- 3.2. Plasma Structure in a Prescribed Magnetic Field.- 3.3. The Structure of Magnetic Flux Tubes (Cylindrically Symmetric).- 3.3.1. Purely Axial Field.- 3.3.2. Purely Azimuthal Field.- 3.3.3. Force-Free Fields.- A. Linear Field.- B. Nonlinear Fields.- C. Effect of Twisting a Tube.- D. Effect of Expanding a Tube.- E. A Tube of Non-Uniform Radius.- 3.3.4. Magnetostatic Fields.- 3.4. Current-Free Fields.- 3.5. Force-Free Fields.- 3.5.1. General Theorems.- 3.5.2. Simple Constant-? Solutions.- 3.5.3. General Constant- ? Solutions.- 3.5.4. Non-Constant- ? Solutions.- 3.5.5. Diffusion.- 3.5.6. Coronal Evolution.- 3.6. Magnetohydrostatic Fields.- 4. Waves.- 4.1. Introduction.- 4.1.1. Fundamental Modes.- 4.1.2. Basic Equations.- 4.2. Sound Waves.- 4.3. Magnetic Waves.- 4.3.1. Shear Alfven Waves.- 4.3.2. Compressional Alfven Waves.- 4.4. Internal Gravity Waves.- 4.5. Inertial Waves.- 4.6. Magnetoacoustic Waves.- 4.7. Acoustic-Gravity Waves.- 4.8. Summary of Magnetoacoustic-Gravity Waves.- 4.9. Five-Minute Oscillations.- 4.9.1. Observations.- 4.9.2. Models.- A. Photospheric Ringing.- B. Wave Trapping.- 4.9.3. Wave Generation.- 4.9.4. Strong Magnetic Field Regions.- 4.9.5. The Future.- 4.10. Waves in a Strongly Inhomogeneous Medium.- 4.10.1. Surface Waves on a Magnetic Interface.- 4.10.2. A Twisted Magnetic Flux Tube.- 4.10.3. A Stratified Atmosphere.- 5. Shock waves.- 5.1. Introduction.- 5.1.1. Formation of a Hydrodynamic Shock.- 5.1.2. Effects of a Magnetic Field.- 5.2. Hydrodynamic Shocks.- 5.3. Perpendicular Shocks.- 5.4. Oblique Shocks.- 5.4.1. Jump Relations.- 5.4.2. Slow and Fast Shocks.- 5.4.3. Switch-Off and Switch-On Shocks.- 5.4.4. The Intermediate Wave.- 6. Heating of the upper atmosphere.- 6.1. Introduction.- 6.2. Models for Atmospheric Structure.- 6.2.1. Basic Model.- 6.2.2. Magnetic Field Effects.- 6.2.3. Additional Effects.- 6.3. Acoustic Wave Heating.- 6.3.1. Steepening.- 6.3.2. Propagation and Dissipation.- 6.4. Magnetic Heating.- 6.4.1. Propagation and Dissipation of Magnetic Waves.- 6.4.2. Nonlinear Coupling of Alfven Waves.- 6.4.3. Resonant Absorption of Alfven Waves.- 6.4.4. Magnetic Field Dissipation.- A. Order of Magnitude.- B. Current Sheets.- C. Current Filaments.- 6.5. Coronal Loops.- 6.5.1. Static Energy-Balance Models.- A. Uniform Pressure Loops.- B. Cool Cores.- C. Hydrostatic Equilibrium.- 6.5.2. Flows in Coronal Loops.- 7. Instability.- 7.1. Introduction.- 7.2. Linearised Equations.- 7.3. Normal Mode Method.- 7.3.1. Example: Rayleigh-Taylor Instability.- A. Plasma Supported by a Magnetic Field.- B. Uniform Magnetic Field B0(+) = B0(-).- 7.4. Variational (or Energy) Method.- 7.4.1. Example: Kink Instability.- 7.4.2. Use of the Energy Method.- 7.5. Summary of Instabilities.- 7.5.1. Interchange Instability.- 7.5.2. Rayleigh-Taylor Instability.- 7.5.3. Pinched Discharge.- 7.5.4. Flow Instability.- 7.5.5. Resistive Instability.- 7.5.6. Convective Instability.- 7.5.7. Radiatively-Driven Thermal Instability.- 7.5.8. Other Instabilities.- 8. Sunspots.- 8.1. Magnetoconvection.- 8.1.1. Physical Effects.- 8.1.2. Linear Stability Analysis.- 8.1.3. Magnetic Flux Expulsion and Concentration.- 8.2. Magnetic Buoyancy.- 8.2.1. Qualitative Effect.- 8.2.2. Magnetic Buoyancy Instability.- 8.2.3. The Rise of Flux Tubes in the Sun.- 8.3. Cooling of Sunspots.- 8.4. Equilibrium Structure of Sunspots.- 8.4.1. Magnetohydrostatic Equilibrium.- 8.4.2. Sunspot Stability.- 8.5. The Sunspot Penumbra.- 8.6. Evolution of a Sunspot.- 8.6.1. Formation.- 8.6.2. Decay.- 8.7. Intense Flux Tubes.- 8.7.1. Equilibrium of a Slender Flux Tube.- 8.7.2. Intense Magnetic Field Instability.- 8.7.3. Spicule Generation.- 8.7.4. Tube Waves.- 9. Dynamo theory.- 9.1. Introduction.- 9.2. Cowling's Theorem.- 9.3. Qualitative Dynamo Action.- 9.3.1. Generation of Toroidal and Poloidal Fields.- 9.3.2. Phenomenological Model.- 9.4. Kinematic Dynamos.- 9.4.1. Nearly-Symmetric Dynamo.- 9.4.2. Turbulent Dynamo: Mean-Field Electrodynamics.- 9.4.3. Simple Solution: Dynamo Waves.- 9.4.4. Solar Cycle Models: The ?-? Dynamo.- 9.5. Magnetohydrodynamic Dynamos.- 9.5.1. Modified Kinematic Dynamos.- 9.5.2. Strange Attractors.- 9.5.3. Convective Dynamos.- 9.6. Difficulties with Dynamo Theory.- 10. Solar flares.- 10.1. Magnetic Reconnection.- 10.1.1. Unidirectional Field.- 10.1.2. Diffusion Region.- 10.1.3. The Petschek Mechanism.- 10.1.4. External Region.- 10.2. Simple-Loop Flare.- 10.2.1. Emerging (or Evolving) Flux Model.- 10.2.2. Thermal Nonequilibrium.- 10.2.3. Kink Instability.- 10.2.4. Resistive Kink Instability.- 10.3. Two-Ribbon Flare.- 10.3.1 Existence and Multiplicity of Force-Free Equilibria.- 10.3.2 Eruptive Instability.- 10.3.3 The Main Phase: 'Post'-Flare Loops.- 11. Prominences.- 11.1. Formation.- 11.1.1. Formation in a Loop (Active-Region Prominences).- 11.1.2. Formation in a Coronal Arcade.- 11.1.3. Formation in a Current Sheet.- A. Thermal Nonequilibrium.- B. Line-Tying.- 11.2. Magnetohydrostatics of Support in a Simple Arcade.- 11.2.1. Kippenhahn-Schluter Model.- 11.2.2. Generalised Kippenhahn-Schluter Model.- 11.2.3. The External Field.- 11.2.4. Magnetohydrodynamic Stability.- 11.2.5. Helical Structure.- 11.3. Support in Configurations with Helical Fields.- 11.3.1. Support in a Current Sheet.- 11.3.2. Support in a Horizontal Field.- 11.4. Coronal Transients.- 11.4.1. Twisted Loop Models.- 11.4.2. Untwisted Loop Models.- 11.4.3. Numerical Models.- 11.4.4. Conclusion.- 12. The solar wind.- 12.1. Introduction.- 12.2. Parker's Solution.- 12.3. Models for a Spherical Expansion.- 12.2.1. Energy Equation.- 12.2.2. Two-Fluid Model.- 12.2.3. Magnetic Field.- 12.4. Streamers and Coronal Holes.- 12.4.1. Pneuman-Kopp Model.- A. Basic Model.- B. Angular Momentum Loss.- C. Current Sheet.- 12.4.2. Coronal Hole Models.- 12.5. Extra Effects.- Appendix I. Units.- Appendix II. Useful Values and Expressions.- Appendix III. Notation.- References.