Physics of Magnetic Flux Ropes

Editors: C. T. Russell, E. R. Priest and L. C. Lee

686pp, American Geophysical Union,Geophysical Monograph No. 58,
Washington DC, 1990



PART 1: Structure, Waves and Instabilities


The equilibrium of magnetic flux ropes, by: E. R. Priest 1
MHD waves on solar magnetic flux tubes, by: J. V. Hollweg 23

Solar flares, by: H. Zirin 33


Ideal instabilities in a magnetic flux tube, by: G. Einaudi 43

Resistive instability, by: K. Schindler and A. Otto 51

Steady magnetic field reconnection, by: B. U. O. Sonnerup, J. Ip and T.D. Phan 63


Magnetic flux tubes: Their origin and appearance, by: V. D. Kuznetsov 77

Magnetic reconnection, coalescence and turbulence in current sheets, by: M. Scholer 85

Wave modes in thick photospheric flux tubes: Classification and diagnostic diagram, by: S. S. Hasan and T. Abdelatif 93

Flux tube waves: A boundary-value problem, by: M. P. Ryutova and I. G. Khijakadze 99

Shock waves in the thin flux tube approximation, by: A. Ferriz Mas 107

PART 2: Photospheric Flux Tubes


Properties and models of photospheric flux tubes, by: B. Roberts 113



The structure of photospheric flux tubes, by: J. H. Thomas 133


On the thin magnetic flux tube approximation, by: A. Ferriz Mas and M. Schussler 141

On the equilibrium of a thin force-free magnetic flux tube in a stratified atmosphere, by: Prasannalakshmi and M. H. Gokhale 149

Diagnosing the fine structure of magnetic fields in the photospheric network on the periphery of active regions, by: V. M. Grigoryev and V. L. Selivanov 153

Dynamical effects and energy transport in intense flux tubes, by: S. S. Hasan 157

Electric currents in unipolar sunspots, by: A. A. Pevtsov and N. L. Peregud 161

Generation of currents in the solar atmosphere by acoustic waves, by: D. D. Ryutov and M. P. Ryutova 167

Magnetic flux tubes and their relation to continuum and photospheric features, by: A. Title, T. Tarbell, K. Topka, D. Cauffinan, C. Balke and G. Sckarmer 171

Waves in solar photospheric flux tubes and their influence on the observable spectrum, by: S. K. Solanki and B. Roberts 181

Quantitative explanation of stokes V asymmetry in solar magnetic flux tubes, by: S. K. Solanki 185

PART 3: Structure and Heating of Coronal Loops


A brief introduction to coronal 'loops', by: R. Rosner 189


Formal mathematical solutions of the force-free equations, spontaneous discontinuities, and dissipation in large-scale magnetic fields, by: E. N. Parker 195

Structure and flows in coronal loops, by: S. K. Antiochos 203


Dynamics of axisymmetric loops, by: R. S. Steinolfson 211

Twisted flux ropes in the solar corona, by: P. K. Browning 219

The observation of possible reconnection events in the boundary changes of solar coronal holes, by: S. W. Kahler and J. D. Moses 229

Quasistatic evolution of a three-dimensional force-free magnetic flux tube or arcade, by: J. J. Aly 235

The quasi-static evolution of magnetic configurations on the sun and solar flares, by: Yu. G. Matyukhin and V. M. Tomozov 241

Quasi-potential-singular-equilibria and evolution of the coronal magnetic field due to photospheric boundary motions, by: T. Amari and J. J. Aly 245

Braided flux ropes and coronal heating, by: M. A. Berger 251

Coronal loop heating by resonant absorption, by: S. Poedts, M. Goossens and W. Kerner 257

Linear evolution of current sheets in sheared force-free magnetic fields with discontinuous connectivity, by: R. Wolfson 263

Dynamics, catastrophe and magnetic energy release of toroidal solar current loops, by: J. Chen 269

An electrodynamical model of solar flares, by: A. I. Podgorny and I. M. Podgorny 279

The flare as a result of cross-interaction of loops, by: A. M. Uralov 285

Effects of plasma mass flow on Alfven wave phase mixing in coronal loops, by: M. Peredo and J. A. Tataronis 289

PART 4: Solar Prominences


Basic properties and models of solar prominences, by: T. G. Forbes 295


Structure and stability of prominences, by: U. Anzer 307

Filament cooling and condensation in a sheared magnetic field, by: G. Van Hoven 315


Fibril structure of solar prominences, by: J. L. Ballester and E. R. Priest 321

Structure of two-dimensional magnetostatic equilibria in the presence of gravity, by: T. Amari and J. J. Aly 327

On driving the eruption of a solar filament, by: V. Gaizauskas 331

Helical flux ropes in solar prominences, by: P. C. H. Martens and A. A. van Ballegooijen 337

PART 5: Coronal Mass Ejections and Magnetic Clouds


Coronal mass ejections and magnetic flux ropes in interplanetary space, by: J. T. Gosling 343


A bubblelike coronal mass ejection flux rope in the solar wind, by: N. U. Crooker, J. T. Gosling, E. J. Smith and C. T. Russell 365

Global configuration of a magnetic cloud, by: L. F. Burlaga, R. P. Lepping and J. A. Jones 373

Effects of the driving mechanisms in MHD simulations of coronal mass ejections, by: J. A. Linker, G. Van Hoven and D. D. Schnack 379

Energetic ion and cosmic ray characteristics of a magnetic cloud, by: T. R. Sanderson, J. Beeck, R. G. Marsden, C. Tranquille, K.P. Wenzel, R. B. McKibben and E. J. Smith 385

Formation of slow shock pairs associated with coronal mass ejections, by: Y. C. Whang 393

PART 6: Flux Ropes in Planetary Ionospheres


The solar wind interaction with unmagnetized planets: A tutorial, by: J. G. Luhmann 401


Magnetic flux ropes in the ionosphere of Venus, by: C. T. Russell 413


'Wave' analysis of Venus ionospheric flux ropes, by: J. G. Luhmann 425

The model of the velocity shear instabilities at Venusian ionopause and the problem of magnetic flux ropes formation, by: E. V. Belova and L. M. Zelenyi 433

PART 7: The Magnetopause


The magnetopause, by: C. T. Russell 439


Observations of flux transfer events: Are FTEs flux ropes, islands, or surface waves? by: R. C. Elphic 455

The theory of FTE: Stochastic percolation model, by: M. M. Kuznetsova and L. M. Zelenyi 473


Imbedded open flux tubes and 'viscous interaction' in the low latitude boundary layer, by: N. U. Crooker 489

Coupling of the tearing mode instability with KH instability at the magnetopause, by: Z. Y. Pu and M. Yei 493

The asymptotic quasistatic state of the vortex induced tearing mode instability at the magnetopause, by: Z. Y. Pu, P. T. Houand and Z. X. Liu 499

A simulation study of particle heat flux and plasma waves associated with magnetic reconnections at the dayside magnetopause, by: D. Q. Ding and L. C. Lee 507

A three-dimensional MHD simulation of the multiple X line reconnection process, by: Z. F. Fu, L. C. Lee and Y. Shi 515

The generation of twisted flux ropes during magnetic reconnection, by: M. A. Berger and A. N. Wright 521

Formation of flux ropes by turbulent reconnection, by: R. L. Lysak and Y. Song 525

The current dynamo effect and its statistical description during 3-D time-dependent reconnection, by: Y. Song and R. L. Lysak 533

PART 8: Magnetospheric Field Aligned Currents and Flux Tubes


Field-aligned currents in the Earth's magnetosphere, by: G. Haerendel 539


Satellite observations of fine-scale structure in auroral field-aligned current system, by: E. M. Dubinin 555


Observations of filamentary field-aligned current coupling between the magnetospheric boundary layer and the ionosphere, by: C. R. Clauer, M. A. McHenry and E. Friis- Christensen 565

Measurement of field-aligned currents by the SABRE coherent scatter radar, by: M. P. Freeman, D. J. Southwood, M. Lester and J. A. Waldock 575

Observations of ionospheric flux ropes above South Pole, by: Z. M. Lin, J. R. Benbrook, E. A. Bering, G. J. Byrne, E. Friis-Christensen, D. Liang, B. Liao and J. Theall 581

DE-2 observations of filamentary currents at ionospheric altitudes, by: M. F. Smith, J. D. Winningham, J. A. Slavin and M. Lockwood 591

A model of FTE footprints in the polar cap, by: F. R. Toffoletto, T. W. Hill and P. H. Reiff 599

Terrestrial ionospheric signatures of field-aligned currents by: E. Friis-Christensen 605

The response of the magnetosphere-ionosphere system to solar wind dynamic pressure variations, by: M. P. Freeman, C. J. Farrugia, S. W. H. Cowley, D. J. Southwood, M. Lockwood and A. Etemadi 611

Magnetopause pressure pulses as a source of localized field-aligned currents in the magnetosphere, by: M. G. Kivelson and D. J. Southwood 619

PART 9: The Magnetotail


Substorms and flux rope structures, by: W. Baumjohann and G. Haerendel 627


Evidence for flux ropes in the Earth's magnetotail, by: D. G. Sibeck 637

Magnetic islands in the near geomagnetic tail and its implications for the mechanism of 1054 UT CDAW 6 substorm, by: N. Lin, R. J. Walker, R. L. McPherron and M. G. Kivelson 647

The magnetic topology of the plasmoid flux rope in a MHD simulation of magnetotail reconnection, by: J. Birn and M. Hesse 655

A 2 1/2-dimensional magnetic field model of plasmoids, by: M. B. Moldwin and W. J. Hughes 663

Magnetic flux ropes in 3-dimensional MHD simulations, by: T. Ogino, R. J. Walker and M. Ashour-Abdalla 669

Parallel electric fields in a simulation of magnetotail reconnection and plasmoid evolution, by: M. Hesse and J. Birn 679


      The American Geophysical Union Chapman Conference on the Physics of Magnetic Flux Ropes was held at the Hamilton Princess Hotel, Hamilton, Bermuda on March 27-31, 1989. Topics discussed ranged from solar flux ropes, such as photospheric flux tubes, coronal loops and prominences, to flux ropes in the solar wind, in planetary ionospheres, at the Earth's magnetopause, in the geomagnetic tail and deep in the Earth's magnetosphere. Papers presented at that conference form the nucleus of this book, but the book is more than just a proceedings of the conference. We have solicited articles from all interested in this topic. Thus, there is some material in the book not discussed at the conference. Even in the case of papers presented at the conference, there is generally a much more detailed and rigorous presentation than was possible in the time allowed by the oral and poster presentations.

      The conference consisted of tutorial presentations, review papers, research reports and discussion. The research reports were presented as either oral or poster presentations. We have attempted to preserve this structure in the book which contains the above three different types of paper, together with many of the questions, answers and comments that took place during the discussion periods following the oral presentations. To capture the discussion, questioners were asked to write out their questions and the presenter was then given the opportunity to prepare a written answer. The book has been divided into parts. In Part 1, we present the papers treating the basic processes occurring in magnetic flux ropes such as the equilibrium of magnetic flux ropes by E. R. Priest, MHD waves on flux ropes by J. V. Hollweg, ideal instabilities by G. Einaudi, resistive instabilities by K. Schindler and A. Otto and reconnection by B. U. O. Sonnerup and colleagues. A paper by H. Zirin on solar flares has been included here because of the basic role flares play in the solar system.

      Part 2 treats the properties and structure of photospheric flux tubes. The thin tube approximation is discussed by B. Roberts as is the fine structure of the photospheric field by J. H. Thomas. Dynamical effects, energy transport, current generation, and waves are all examined.

      Part 3 examines the structure and heating of coronal loops. R. Rosner provides a tutorial overview of coronal loops. E. N. Parker reviews the spontaneous appearance of discontinuities and the resulting dissipation while S. K. Antiochos reviews the structure and flow in the corona. Numerous research reports on the physics of these structures are also reported, including reconnection, quasistatic evolution, and heating.

      Part 4 opens with a tutorial by T. G. Forbes on the properties of solar prominences. This paper is followed by reviews of the structure and stability of prominences by U. Anzer and the cooling and condensation of filaments by G. Van Hoven. Research reports cover fibril structure, equilibria, eruptions and helical flux ropes.

      Part 5 changes scales to examine those larger structures which link the Sun and the Earth's magnetosphere: coronal mass ejections and magnetic clouds. J. T. Gosling presents the energetic particle evidence pertaining to the topological structure of coronal mass ejections while N. U. Crooker and L. F. Burlaga and colleagues discuss magnetic constraints on these structures. also treated in this chapter are MHD simulations of CME's, energetic particles in CME's and slow shocks at CME's.

      Part 6 in contrast, treats the smallest scale flux ropes: those in the Venus ionosphere which are only a few kilometers across. J. G. Luhmann provides an introduction to the solar wind interaction with unmagnetized planets while C. T. Russell reviews the observed properties of ionospheric flux ropes. J. G. Luhmann adds an analysis of the properties of these ropes and E. Belova and L. Zelenyi provide a model for their formation.

      Part 7 takes us to the Earth's magnetopause where reconnection leads to what appears to be rope-like structures. The chapter opens with a brief review of the magnetopause followed by reviews by R. C. Elphic of the phenomenon known as the flux transfer event and of their theory by M. M. Kuznetsova and L. M. Zelenyi. The various reports in this chapter concern the structure of these flux tubes and possible mechanisms for their generation.

      Part 8 moves us into the magnetosphere to examine field-aligned current systems with a tutorial paper by G. Haerendel and a review of satellite observations of the fine-scale structure of auroral field-aligned current systems by E. M. Dubinin. The following reports treat ionospheric observations of possible flux tubes and the response of the magnetosphere- ionosphere system to solar wind dynamic pressure fluctuations which might mimic the expected signature of magnetic flux tubes being dragged through the ionosphere.

      The book closes with a discussion of the magnetotail which itself could be considered to be two giant flux ropes anchored in the earth. W. Baumjohann and G. Haerendel discuss the substorm phenomenon and the formation of flux rope structures. Research reports cover the evidence for flux ropes and the structure of plasmoids which are created during substorms.

      The organizers wish to thank the many people who helped make the conference and this book possible. We are especially appreciative of the referees who spent much time poring over these papers and at times caused the authors to reevaluate their hypotheses. These referees included: T. Amari, R. R. Anderson, S. K. Antiochos, U. Anzer, D. N. Baker, M. A. Berger, J. Birn, J. Brackbill, P. K. Browning, L. F. Burlaga, C. R. Clauer, S. W. H. Cowley, T. E. Cravens, N. U. Crooker, P. Demoulin, D. Q. Ding, J. Drake, T. E. Eastman, P. Edwin, G. Einaudi, R. C. Elphic, D. H. Fairfield, J. A. Fedder, T. G. Forbes, G. E. Francis, V. Gaizauskas, C. K. Goertz, D. J. Gorney, J. T. Gosling, R. A. Greenwald, R. Harrison, J. V. Hollweg, A. Hood, W. J. Hughes, A. J. Hundhausen, S. W. Kahler, J. R. Kan, M. G. Kivelson, L. C. Lee, M. Lockwood, B. C. Low, J. G. Luhmann, R. L. Lysak, U. Matthaeus, M. McHenry, K. L. Miller, E. Neilson, A. Nishida, N. Omidi, E. N. Parker, V. Pizzo, E. R. Priest, P. Pritchett, P. H. Reiff, B. Roberts, R. Rosner, M. P. Ryutova, M. Schussler, Y. Shi, D. G. Sibeck, S. K. Solanki, Y. Song, B. U. . Sonnerup, D. J. Southwood, H. Spence, R. S. Steinolfson, D. W. Swift, M. Temerin, J. H. Thomas, B. T. Tsurutani, A. A. Van Ballegooijen, G. Van Hoven, W. J. Wagner, R. J. Walker, D. F. Webb, Q. C. Wei, D. R. Weimer and R. Wolfson. We would also like to thank the AGU meetings staff, Brenda Weaver and Patrice Dickerson, for their able assistance at the conference, and the AGU publications staff, Patricia Rayner and Lathifah Jocum, for their timely handling of the publication of the book. Finally we are extremely grateful for the assistance of Sarah Suk at UCLA who handled all the correspondence with the attendees at the conference, the UCLA correspondence with AGU and authors, and any necessary retyping of manuscripts. M. Ishiwata is gratefully acknowledged for her redrafting of many figures to improve their readability. All this assistance made our job much easier.

C. T. Russell Institute of Geophysics and Planetary Physics
University of California Los Angeles, CA 90024.

E. R. Priest Applied Mathematics Division University of St.
Andrews North Haugh St. Andrews KY16 9SS Fife, Scotland.

L. C. Lee Geophysical Institute University of Alaska
Fairbanks, AK 99775-0800

March 1990

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