Abstract
Most of the magnetic fields of cosmic objects are generated and maintained by dynamo action of the motions of electrically conducting fluids. A brief survey on observational facts concerning cosmic magnetic fields is given. Some basic principles of magnetofluiddynamics are explained. On this basis essential features of the dynamo theory of cosmic objects are developed, first on the kinematic level and later taking into account the full interaction between magnetic field and motion. Particular attention is paid on mean-field electrodynamics and mean-field magnetofluiddynamics and their application to mean-field dynamo models for objects showing irregular or turbulent motions and magnetic fields. A few explanations are given on dynamos in the Earth and the planets, in the Sun and stellar objects and in galaxies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Krause and K.-H. Rädler: ‘Elektrodynamik der mittleren Felder in turbulenten leitenden Medien und Dynamotheorie’, in Ergebnisse der Plasmaphysik und der Gaselektronik, volume 2, ed. by R. Rompe and M. Steenbeck,( Akademie-Verlag Berlin, 1971) pp. 1–154
F. Krause and K.-H. Rädler: Mean-Field Magnetohydrodynamics and Dynamo Theory, (Akademie-Verlag Berlin and Pergamon Press Oxford, 1980)
H. K. Moffatt: Magnetic Field Generation in Electrically Conducting Fluids. (Cambridge University Press, 1978)
M. R. E. Proctor and A. D. Gilbert: Lectures on Solar and Planetary Dynamos, (Cambridge University Press, 1994)
P. H. Roberts: An Introduction to Magnetohydrodynamics (Longmans, Green and Co. Ltd., 1967)
A. A. Ruzmaikin, A. M. Shukurov, and D. D. Sokolo.: Magnetic Fields of Galaxies, (Astrophysics and Space Science Library Vol. 133. Kluwer Academic Publishers, 1988)
Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokolo.: Magnetic Fields in Astrophysics, (The Fluid Mechanics of Astrophysics and Geophysics Vol.3. Gordon and Breach Science Publishers, 1983)
The Cosmic Dynamo, ed. by F. Krause, K.-H. Rädler, and G. Rüdiger, (Kluwer Academic Publishers Dordrecht Bosten London, 1993)
Stellar Dynamos: Nonlinearity and Chaotic Flows., ed. by M. Nunez and A. FerrizMas, (Astronomical Society of the Pacific, 1999)
Solar and Planetary Dynamos, ed. by M. R. E. Proctor, P. C. Matthews, and A. M. Rucklidge, (Cambridge University Press, 1993)
Stellar and Planetary Magnetism, ed. by A. M. Soward, (Gordon and Breach Science Publishers, 1983)
K.-H. Rädler: Rev. Mod. Astron. 8, 295 (1995)
P. H. Roberts: ‘Dynamo theory’, in Lectures on Applied Mathematics, volume 14, ed. by W. H. Reid, (Amer. Mathematics Soc., Providence, 1971) pp. 129–206
P. H. Roberts: ‘Dynamo theory’, in Astrophysical Fluid Dynamics, ed. by J.-P. Zahn and J. Zinn-Justin, (Elsevier Science Publishers B.V., 1993)
P. H. Roberts: ‘Fundamentals of dynamo theory’, in Lectures on Solar and Planetary Dynamos, ed. by M. R. E. Proctor and A. D. Gilbert, (Cambridge University Press, 1994), pp. 1–58
P. H. Roberts and A. M. Soward: Ann. Rev. Fluid Mech. 24, 459 (1992)
N. O. Weiss: Y. J. Roy. Astron. Soc. 12, 432 (1971)
J. Larmor: How could a rotating body such as the Sun become a magnet?, Rep. Brit. Assoc. Adv. Sc., pp. 159–160 (1919)
H. Bondi and T. Gold: Mon. Not. R. Astron. Soc. 110, 607 (1950)
D. Moss: Mon. Not. R. Astron. Soc. 257, 593 (1992)
K.-H. Rädler: Astron. Nachr. 301, 101 (1980)
K.-H. Rädler: Astron. Nachr. 307, 89 (1986)
K.-H. Rädler:’ On the effect of differential rotation on axisymmetric and non-axisymmetric magnetic fields of cosmical bodies’, in Plasma-Astrophysics (Proceedings of the Joint Varenna-Abastumani International School and Workshop, Sukhumi, ESA SP-251, 1986), pp. 569–574
H.-J. Bräuer and K.-H. Rädler: Astron. Nachr. 308, 27 (1987)
K.-H. Rädler: Astron. Nachr. 295, 73 (1974)
T. G. Cowling: Mon. Not. R. Astron. Soc. 94, 39 (1934)
S. I. Braginskij: Geomagn. Aeron. 4, 732 (1964)
R. Hide and T. N. Palmer: Geophys. Astrophys. Fluid Dyn. 19, 301 (1982)
R. W. James, P. H. Roberts, and D. E. Winch: Geophys. Astrophys. Fluid Dyn. 15, 149 (1980)
D. Lortz: Phys. Fluids 11, 913 (1968)
W. M. Elsasser: Phys.Rev. 69, 106 (1946)
E. C. Bullard and H. Gellman: Phil. Trans. Roy. Soc. A 247, 213 (1954)
F. H. Busse: J. Geophys. Res. 80, 278 (1975)
A. Herzenberg: Phil. Trans. R. Soc. London, Ser. A 250, 543 (1958)
R. D. Gibson: Q. J. Mech. Appl. Math. 21, 243 (1968)
R. D. Gibson: Q. J. Mech. Appl. Math. 21, 257 (1968)
F. J. Lowes and I. Wilkinson: Nature 198, 1158 (1963)
F. J. Lowes and I. Wilkinson: Nature 219, 717 (1968)
Yu. B. Ponomarenko: PMTF 1973(6), 47 (1973) in Russian
G. O. Roberts: Phil. Trans. R. Soc. London, Ser. A 266, 535 (1970)
G. O. Roberts: Phil. Trans. Roy. Soc. London A 271, 411 (1972)
S. Childress and A. D. Gilbert: Stretch, Twist, Fold: The Fast Dynamo, (Lecture Notes in Physics. Springer-Verlag Berlin Heidelberg New York, 1995)
A. Gailitis: Magnetohydrodynamics 6, 14 (1970)
C. L. Pekeris, Y. Accad, and B. Shkoller: Phil. Trans. R. Soc. London, Ser. A 275, 425 (1973)
D. Gubbins: Phil. Trans. R. Soc. London, Ser. A 274, 493 (1973)
S. Kumar and P. H. Roberts: Proc. R. Soc. London, Ser. A 344, 235 (1975)
S. I. Braginskij: Sov. Phys. JETP 20, 726 (1964)
S. I. Braginskij: Sov. Phys. JETP 20, 1462 (1964)
S. I. Braginskij: Phys. Earth Planet. Inter. 11, 191 (1976)
S. I. Braginskij:’ The nonlinear dynamo and model-z’. In Lectures on Solar and Planetary Dynamos, ed. by M. R. E. Proctor and A. D. Gilbert, (Cambridge University Press, 1994) pp. 267–304
M. Steenbeck, F. Krause, and K.-H. Rädler: Z. Naturforsch. 21a, 369 (1966)
E. N. Parker: Astrophys. J. 122, 293 (1955)
O. Lielausis: Astron. Nachr.315, 303 (1994)
A. Gailitis:’ Current status of liquid sodium MHD dynamo experiment in Riga’, in Proceedings of the International Conference ”Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows”(Aussois, France, 1997). pp. 33–38
F. H. Busse: Geophys. J. R. Astron. Soc. 42, 437 (1975)
K.-H. Rädler, E. Apstein, M. Rheinhardt, and M. Schüler: Studia geoph. et geod. 42, 224 (1998)
K.-H. Rädler, E. Apstein, and M. Schüler:’ The alpha-effect in the Karlsruhe dynamo experiment’ in Proceedings of the International Conference ”Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows” Held in Aussois, France, 1997, pp. 9–14
A. Tilgner: Phys. Lett. A 226, 75 (1996)
A. Tilgner: Acta Astron. et Geophys. Univ. Comenianae 19, 51 (1997)
F. Krause and M. Steenbeck: Z. Naturforsch. 22a, 671 (1967)
K.-H. Rädler: Geophys. Astrophys. Fluid Dyn. 20, 191 (1982)
K.-H. Rädler and U. Geppert:’ Turbulent dynamo action in the high-conductivity limit: A hidden dynamo.’, in Stellar Dynamos: Nonlinearity and Chaotic Flows, ed. by M. Nunez and A. Ferriz-Mas, ( ASP Conference Series Vol.178, 1999) pp. 151–163.
K.-H. Rädler:’ Mean-field magnetohydrodynamics as a basis of solar dynamo theory’, in Basic Mechanisms of Solar Activity, ed. by V. Bumba and J. Kleczek, (D. Reidel Publishing Company Dordrecht Holland, 1976) pp. 223–344
T. S. Ivanova and A. A. Ruzmaikin: Sov. Astron. 20, 227 (1976)
K.-H. Rädler: Z. Naturforsch. 23a, 1841 (1968)
K.-H. Rädler: Z. Naturforsch. 23a, 1851 (1968)
Ya. B. Zeldovich: J. Exptl. Theoret. Phys.31, 154 (1956)
E. M. Drobyshevski, E. N. Kolesnikova, and V. S. Yuferev: J. Fluid Mech. 101, 65 (1980)
E. M. Drobyshevski and V. S. Yuferev: J. Fluid Mech. 65, 33 (1974)
M. Steenbeck and F. Krause: Astron. Nachr. 291, 49 (1969)
M. Steenbeck and F. Krause: Astron. Nachr. 291, 271 (1969)
H. K. Moffatt and M. R. E. Proctor: Geophys. Astrophys. Fluid Dyn. 21, 265 (1982)
K.-H. Rädler: Monatsber. Dtsch. Akad. Wiss. Berlin 11, 272 (1969)
K.-H. Rädler: Monatsber. Dtsch. Akad. Wiss. Berlin 12, 468 (1970)
P. H. Roberts: Phil. Trans. R. Soc. London, Ser. A 272, 663 (1972)
A. Brandenburg, I. Tuominen, and K.-H. Rädler: Geophys. Astrophys. Fluid Dyn. 49, 45 (1989)
K.-H. Rädler: Mem. Soc. Roy. Soc. Liege VIII, 109 (1975)
G. Rüdiger: Astron. Nachr. 301, 181 (1980)
G. Rüdiger and D. Elstner: Astron. Astrophys., 1 (1993)
T. T. Ivanova and A. A. Ruzmaikin: Astron. Nachr. 306, 177 (1985)
P. H. Roberts and M. Stix: Astron. Astrophys. 18, 453 (1972)
W. Deinzer and M. Stix: Astron. Astrophys. 12, 111 (1971)
W. Deinzer, H.-U. v. Kusserow, and M. Stix: Astron. Astrophys. 36, 69 (1974)
M. Stix: Astron. Astrophys. 24, 275 (1973)
A. Brandenburg and I. Tuominen:’ The solar dynamo’. In The Sun and Cool Stars: Activity, Magnetism, Dynamos, ed. by I. Tuominen, D. Moss, and G. Rüdiger, (Lecture Notes in Physics, Springer Verlag, 1991)
M. Stix: Geophys. Astrophys. Fluid Dyn. 62, 211 (1991)
M. Stix: Astron. Astrophys. 47, 243 (1975)
M. P. White: Astron. Nachr. 299, 209 (1978)
W. Deinzer, H. Grosser, and D. Schmitt: Astron. Astrophys. 273, 405 (1993)
K.-H. Rädler and E. Wiedemann:’ Mean-field models of galactic dynamos admitting axisymmetric and non-axisymmetric magnetic field structures’ in Galactic and Intergalactic Magnetic Fields (Proceedings of the IAU Symposium No 140, Heidelberg 1990), ed. by R. Beck, P. P. Kronberg, and R. Wielebinski, (Kluwer Academic Publishers, 1990), pp. 107–112
D. Elstner, R. Meinel, and G. Rüdiger: Geophys. Astrophys. Fluid Dyn. 50, 85 (1990)
G. Rüdiger, D. Elstner, and M. Schultz:’ The galactic dynamo: Modes and models’, in The Cosmic Dynamo, ed. by F. Krause, G. Rüdiger, and K.-H. Rädler, (Kluwer Academic Publishers, 1993), pp. 321–331
S. A. Balbus and J. F. Hawley: Rev. Mod. Phys. 70, 1 (1998)
G. Rüdiger and L.L. Kichatinov: Astron. Astrophys. 269, 581 (1993)
G. B. Field, E. G. Blackman, and H. Chou: Astrophys. J. 513, 638 (1999)
G. Rüdiger: Differential Rotation and Stellar Convection, (Akademie Verlag Berlin, 1989)
G. Rüdiger:’ Dynamo theory and the period of the solar cycle’, in Solar Magnetic Fields, ed. by M. Schüssler and W. Schmidt, (Cambridge University Press, 1994), pp. 77–93
A. Brandenburg and I. Tuominen: Geophys. Astrophys. Fluid Dyn. 49, 129 (1989)
R. Hollerbach: Geophys. Astrophys. Fluid Dyn. 60, 245 (1991)
K.-H. Rädler, E. Wiedemann, A. Brandenburg, R. Meinel, and I. Tuominen: Astron. Astrophys. 239, 413 (1990)
D. M. Barker and D. Moss: Astron. Astrophys.283, 1009 (1994)
H. Fuchs, K.-H. Rädler, M. Rheinhardt, and M. Schüler: Chaos, Solitons & Fractals 5, 2013 (1995)
W. V. R. Malkus:’ Energy sources for planetary dynamos’, in Lectures on Solar and Planetary Dynamos, ed by M. R. E. Proctor and A. D. Gilbert, (Cambridge University Press, 1994), pp. 161–179
M. R. E. Proctor:’ Convection and magnetoconvection in a rapidly rotating sphere’, in Lectures on Solar and Planetary Dynamos, ed. by M. R. E. Proctor and A. D. Gilbert, (Cambridge University Press, 1994) pp. 97–115
R. Hollerbach: Phys. Earth Planet. Inter. 98, 163 (1996)
A. M. Soward: Geophys. Astrophys. Fluid Dyn. 62, 191 (1991)
U. Christensen and P. Olson: Geophys. Res. Lett. 25, 1565 (1998)
U. Christensen, P. Olson, and G. A. Glatzmaier: Geophys. J. Int. 138, 393 (1999)
G. A. Glatzmaier and P. H. Roberts: Nature 377, 203 (1995)
G. A. Glatzmaier and P. H. Roberts: Physica D 97, 81 (1996)
G. A. Glatzmaier and P. H. Roberts: Science 274, 1887 (1996)
E. Grote, F. H. Busse, and A. Tilgner: Phys. Earth Planet. Inter. 117, 259 (2000)
W. Kuang and J. Bloxham: Nature 389, 371 (1997)
D. Moss and A. Brandenburg: Geophys. Astrophys. Fluid Dyn. 80, 229 (1995)
F. H. Busse, E. Grote, and A. Tilgner: Studia geoph. et geod. 42, 211 (1998)
D. R. Fearn:’ Nonlinear planetary dynamos’, in Lectures on Solar and Planetary Dynamos, ed. by M. R. E. Proctor and A. D. Gilbert, editors, (Cambridge University Press, 1994), pp. 219–244
E. E. DeLuca and P. A. Gilman: The Solar Dynamo, (The University of Arizona Press Tucson, 1992), pp. 275–303.
P. A. Gilman:’ What can we learn about solar cycle mechanisms from observed velocity fields?’, in The Solar Cycle, ( ASP Conference Series 27, 1992), pp. 241–254
K.-H. Rädler:’ The solar dynamo’, in Inside the Sun, ed. by G. Berthomieu and M. Cribier, (Proceedings of the IAU Colloquium No 121, Kluwer Academic Publishers, 1990), pp. 385–402
R. Rosner and N. O. Weiss:’ The origin of the solar cycle’, in The Solar Cycle, ed. by K. Harvey, (Astronomical Society of the Pacific, 1992), pp. 511–531
M. Stix:’ Dynamo theory and the solar cycle’, in Basic Mechanisms of Solar Activity, ed. by V. Bumba and J. Kleczek, (D. Reidel Publishing Company Dordrecht Holland, 1976), pp. 367–388
N. O. Weiss:’ Solar and stellar dynamos’, in Lectures on Solar and Planetary Dynamos, ed. by M. R. E. Proctor and A. D. Gilbert, (Cambridge University Press, England, 1994), pp. 59–95
K. G. Libbrecht:’ The excitation and damping of solar oscillations’, in Seismology of the Sun and Sun-Like Stars, ed. by E.J. Rolfe, (ESA Publications Division, 1988) pp. 3–10
D. Schmitt:’ The solar dynamo’, in The Cosmic Dynamo, ed. by F Krause, K.-H. Rädler, and G. Rüdiger, (Kluwer Academic Publishers, 1993), pp. 1–12
D. Schmitt, A. Ferriz-Mas, and M. Schüssler:’ An α-effect due to instability of toroidal magnetic flux tubes’, in Solar Magnetic Fields, ed. by M. Schüssler and W. Schmidt, (Cambridge University Press, 1994), pp. 101–103
F. Moreno-Insertis, M. Schüssler, and A. Ferriz-Mas:’ Storage of magnetic flux in the overshoot region’, in The Cosmic Dynamo, ed. by F. Krause, K.-H. Rädler, and G. Rüdiger, (Kluwer Academic Publishers, 1993) pp. 41–44
M. Schüssler:’ Flux tubes and dynamos’, in The Cosmic Dynamo, ed, by F. et Al. Krause, (IAU, 1993) pp. 27–39
A. Brandenburg:’ Simulating the solar dynamo’, In The Cosmic Dynamo, ed. by F. Krause, K.-H. Rädler, and G. Rüdiger, (Kluwer Akademic Publishers, 1993) pp. 111–121
G. Rüdiger and A. Brandenburg: Astron. Astrophys. 296, 557 (1995)
P. Hoyng: Astron. Astrophys. 272, 321 (1993)
P. Hoyng, D. Schmitt, and L. J. W. Teuben: Astron. Astrophys. 289, 265 (1994)
G. Belvedere:’ Solar and stellar cycles’. In Inside the Sun, ed. by M. Cribier and G. Berthomieu, (Kluwer Academic Publishers, 1990) pp. 371–382
E. H. Levy:’ Physical assessment of stellar dynamo theory’, in Cool Stars, Stellar Systems, and the Sun, ed. by M. S. Giampapa and J. A. Bookbinder, (ASP Conference Series 26, 1992) pp. 223–239
N. O. Weiss:’ Dynamo processes in stars’, in Accretion Discs and Magnetic Fields in Astrophysics, ed. by G. Belvedere, (Kluwer Academic Publishers, 1989), pp. 11–29
D. Elstner:’ The galactic dynamo-success and limitations of current models’. in Plasma Turbulence and Energetic Particles in Astrophysics (Proceedings of the International Conference Cracow1999), ed. by M. Ostrowski and R. Schlickeiser, (Colonel, Poland, 1999), pp. 74–83
R. Beck, A. Brandenburg, D. Moss, A. Shukurov, and D. Sokolo.: Ann. Rev. Astron. Astrophys.34, 155 (1996)
R. Wielebinski and F. Krause: The Astron. Astrophys. Rev. 4, 449 (1993)
K. Ferriére: Astron. Astrophys. 310, 438 (1996)
U. Ziegler: Astron. Astrophys. 313, 448 (1996)
D. Schultz, M. Elstner and G. Rüdiger: Astron. Astrophys. (1993)
A. M. Soward: Astron. Nachr. 299, 25 (1978)
D. Moss: Mon. Not. R. Astron. Soc. 297, 860 (1998)
R. Rhode, R. Beck, and D. Elstner: Astron. Astrophys. 350, 423 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rädler, KH. (2000). The Generation of Cosmic Magnetic Fields. In: Page, D., Hirsch, J.G. (eds) From the Sun to the Great Attractor. Lecture Notes in Physics, vol 556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45371-7_3
Download citation
DOI: https://doi.org/10.1007/3-540-45371-7_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41064-5
Online ISBN: 978-3-540-45371-0
eBook Packages: Springer Book Archive