Abstract
Magnetic fields of laboratory, planetary, stellar, and galactic plasmas commonly exhibit significant order on large temporal or spatial scales compared to the otherwise random motions within the hosting system. Such ordered fields can be measured in the case of planets, stars, and galaxies, or inferred indirectly by the action of their dynamical influence, such as jets. Whether large scale fields are amplified in situ or a remnant from previous stages of an object’s history is often debated for objects without a definitive magnetic activity cycle. Magnetic helicity, a measure of twist and linkage of magnetic field lines, is a unifying tool for understanding large scale field evolution for both mechanisms of origin. Its importance stems from its two basic properties: (1) magnetic helicity is typically better conserved than magnetic energy; and (2) the magnetic energy associated with a fixed amount of magnetic helicity is minimized when the system relaxes this helical structure to the largest scale available. Here I discuss how magnetic helicity has come to help us understand the saturation of and sustenance of large scale dynamos, the need for either local or global helicity fluxes to avoid dynamo quenching, and the associated observational consequences. I also discuss how magnetic helicity acts as a hindrance to turbulent diffusion of large scale fields, and thus a helper for fossil remnant large scale field origin models in some contexts. I briefly discuss the connection between large scale fields and accretion disk theory as well. The goal here is to provide a conceptual primer to help the reader efficiently penetrate the literature.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
K. Asada, M. Inoue, M. Nakamura, S. Kameno, H. Nagai, Astrophys. J. 682, 798 (2008)
S.A. Balbus, Annu. Rev. Astron. Astrophys. 41, 555 (2003)
S.A. Balbus, J.F. Hawley, Astrophys. J. 376, 214 (1991)
S.A. Balbus, J.F. Hawley, Rev. Mod. Phys. 70, 1 (1998)
R. Beck, Space Sci. Rev. 166, 215 (2012)
P.M. Bellan, Spheromaks (Imperial College Press, London, 2000)
M.A. Berger, G.B. Field, J. Fluid Mech. 147, 133 (1984)
P. Bhat, K. Subramanian, Mon. Not. R. Astron. Soc. 429, 2469 (2013)
P. Bhat, E.G. Blackman, K. Subramanian, Mon. Not. R. Astron. Soc. 438, 2954 (2014)
A. Bhattacharjee, E. Hameiri, Phys. Rev. Lett. 57, 206 (1986)
E.G. Blackman, Recent developments in magnetic dynamo theory, in Lecture Notes in Physics, vol. 614, 2003, p. 432
E.G. Blackman, Plasma Phys. Control. Fusion 46, 423 (2004)
E.G. Blackman, G.B. Field, Astrophys. J. Lett. 534, 984 (2000a)
E.G. Blackman, G.B. Field, Mon. Not. R. Astron. Soc. 318, 724 (2000b)
E.G. Blackman, G.B. Field, Phys. Rev. Lett. 89, 265007 (2002)
E.G. Blackman, G.B. Field, Phys. Plasmas 11, 3264 (2004)
E.G. Blackman, A. Brandenburg, Astrophys. J. 579, 359 (2002)
E.G. Blackman, A. Brandenburg, Astrophys. J. Lett. 584, L99 (2003)
E.G. Blackman, A. Hubbard, Mon. Not. R. Astron. Soc. (2014, drafted for submission)
E.G. Blackman, M.E. Pessah, Astrophys. J. 704, L113 (2009)
E.G. Blackman, K. Subramanian, Mon. Not. R. Astron. Soc. 429, 1398, BS13 (2013)
E.G. Blackman, A. Frank, C. Welch, Astrophys. J. 546, 288 (2001)
R.D. Blandford, D.G. Payne, Mon. Not. R. Astron. Soc. 199, 883 (1982)
J. Braithwaite, H.C. Spruit, Nature 431, 819 (2004)
A. Brandenburg, in Theory of Black Hole Accretion Disks, ed. by M.A. Abramowicz, G. Bjornsson, J.E. Pringle (Cambridge University Press, Cambridge, 1998), p. 61
A. Brandenburg, Astrophys. J. 550, 824 (2001)
A. Brandenburg, Astrophys. J. 625, 539 (2005)
A. Brandenburg, Astrophys. J. 697, 1206 (2009)
A. Brandenburg, K.J. Donner, Mon. Not. R. Astron. Soc. 288, L29 (1997)
A. Brandenburg, A. Lazarian, Space Sci. Rev. 178, 163 (2013)
A. Brandenburg, K. Subramanian, Phys. Rep. 417, 1 (2005)
A. Brandenburg, A. Nordlund, R.F. Stein, U. Torkelsson, Astrophys. J. 446, 741 (1995)
A. Brandenburg, D. Sokoloff, K. Subramanian, Space Sci. Rev. 169, 123 (2012)
A. Brandenburg, K. Subramanian, A. Balogh, M.L. Goldstein, Astrophys. J. 734, 9 (2011)
A. Brandenburg, D. Sokoloff, K. Subramanian, Space Sci. Rev. 169, 123 (2012)
V. Bujarrabal, A. Castro-Carrizo, J. Alcolea, C. Sánchez Contreras, Astron Astrophys. 377, 868 (2001)
S. Candelaresi, A. Hubbard, A. Brandenburg, D. Mitra, Phys. Plasmas 18, 012903 (2011)
J. Chae, Y.-J. Moon, Y.-D. Park, Sol. Phys. 223, 39 (2004)
L. Chamandy, K. Subramanian, A. Shukurov, Mon. Not. R. Astron. Soc. 428, 3569 (2013)
P. Charbonneau, SASS 39 (2013)
C.J. Copi, F. Ferrer, T. Vachaspati, A. Achúcarro, Phys. Rev. Lett. 101, 171302 (2008)
A. Díaz-Gil, J. García-Bellido, M. García Pérez, A. González-Arroyo, Phys. Rev. Lett. 100, 241301 (2008)
S.W. Davis, J.M. Stone, M.E. Pessah, Astrophys. J. 713, 52 (2010)
P. Démoulin, M.A. Berger, Sol. Phys. 215, 203 (2003)
F. Del Sordo, G. Guerrero, A. Brandenburg, Mon. Not. R. Astron. Soc. 429, 1686 (2013)
M. Dikpati, P.A. Gilman, Space Sci. Rev. 144, 67 (2009)
F. Ebrahimi, A. Bhattacharjee, Phys. Rev. Lett. 112, 125003 (2014)
G. Field, AIPC 144, 324 (1986)
G.B. Field, E.G. Blackman, Astrophys. J. 572, 685 (2002)
G.B. Field, S.M. Carroll, Phys. Rev. D, Part. Fields 62, 103008 (2000)
G.B. Field, R.D. Rogers, Astrophys. J. 403, 94 (1993)
J.M. Finn, T.M. Antonsen, Comments Plasma Phys. Control. Fusion 9, 111123 (1985)
D.C. Gabuzda, D.M. Christodoulou, I. Contopoulos, D. Kazanas, Int. J. Mod. Phys. Conf. Ser. 355, 012019 (2012)
D.C. Gabuzda, V.M. Vitrishchak, M. Mahmud, S.P. O’Sullivan, Mon. Not. R. Astron. Soc. 384, 1003 (2008)
S.E. Gibson et al., Astrophys. J. 574, 1021 (2002)
G.A. Glatzmaier, Annu. Rev. Earth Planet. Sci. 30, 237 (2002)
O. Gressel, Mon. Not. R. Astron. Soc. 405, 41 (2010)
A.V. Gruzinov, P.H. Diamond, Phys. Plasmas 3, 1853 (1996)
X. Guan, C.F. Gammie, Astrophys. J. 728, 130 (2011)
J. Hao, M. Zhang, Astrophys. J. 733, L27 (2011)
T. Heinemann, J.C. McWilliams, A.A. Schekochihin, Phys. Rev. Lett. 107, 255004 (2011)
A. Hubbard, A. Brandenburg, Geophys. Astrophys. Fluid Dyn. 104, 577 (2010)
A. Hubbard, A. Brandenburg, Astrophys. J. 727, 11 (2011)
H. Ji, S.C. Prager, Magnetohydrodynamics 38, 191 (2002)
T. Kahniashvili, A.G. Tevzadze, A. Brandenburg, A. Neronov, Phys. Rev. D 87, 083007 (2013)
A.P. Kazantsev, J. Exp. Theor. Phys. 26, 1031 (1968)
P.J. Käpylä, M.J. Korpi, A. Brandenburg, Astron. Astrophys. 491, 353 (2008)
P.J. Käpylä, M.J. Korpi, Mon. Not. R. Astron. Soc. 413, 901 (2011)
K. Kemel, A. Brandenburg, H. Ji, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 84, 056407 (2011)
N.I. Kleeorin, A.A. Ruzmaikin, Magnetohydrodynamics 18, 116 (1982)
F. Krause, K.H. Rädler, Mean Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Elmsford, 1980)
A. Konigl, Astrophys. J. 342, 208 (1989)
R.M. Kulsrud, E.G. Zweibel, Rep. Prog. Phys. 71, 046901 (2008)
R.M. Kulsrud, R. Cen, J.P. Ostriker, D. Ryu, Astrophys. J. 480, 481 (1997)
G. Lesur, G.I. Ogilvie, Astron. Astrophys. 488, 451 (2008)
E.-K. Lim, H. Jeong, J. Chae, Y.-J. Moon, Astrophys. J. 656, 1167 (2007)
R.V.E. Lovelace, D.M. Rothstein, G.S. Bisnovatyi-Kogan, Astrophys. J. 701, 885 (2009)
D. Lynden-Bell, Mon. Not. R. Astron. Soc. 369, 1167 (2006)
M. Lyutikov, V.I. Pariev, D.C. Gabuzda, Mon. Not. R. Astron. Soc. 360, 869 (2005)
J. Maron, E.G. Blackman, Astrophys. J. 566, L41 (2002)
S.F. Martin, A.H. McAllister, Geophys. Monogr. 99, 127 (1997)
D. Mitra, A. Brandenburg, Mon. Not. R. Astron. Soc. 420, 2170 (2012)
D. Mitra, S. Candelaresi, P. Chatterjee, R. Tavakol, A. Brandenburg, Astron. Nachr. 331, 130 (2010)
H.K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, 1978)
S. Ortolani, D.D. Schnack, Magnetohydrodynamics of Plasma Relaxation (World Scientific, Singapore, 1993)
K. Park, E.G. Blackman, Mon. Not. R. Astron. Soc. 423, 2120 (2012)
E.N. Parker, Clarendon/Oxford University Press, Oxford/New York, 1979, 858 pp.
R.F. Penna, R. Narayan, A. Sądowski, Mon. Not. R. Astron. Soc. 436, 3741 (2013)
M.E. Pessah, C.-K. Chan, D. Psaltis, Phys. Rev. Lett. 97, 221103 (2006)
A.A. Pevtsov, R.C. Canfield, T. Sakurai, M. Hagino, Astrophys. J. 677, 719 (2008)
A. Pouquet, U. Frisch, J. Leorat, J. Fluid Mech. 77, 321 (1976)
H. Ji, S.C. Prager, J.S. Sarff, Phys. Rev. Lett. 74, 2945 (1995)
R.E. Pudritz, M.J. Hardcastle, D.C. Gabuzda, Space Sci. Rev. 169, 27 (2012)
P.H. Roberts, E.M. King, Rev. Plasma Phys. 76, 096801 (2013)
G. Rüdiger, L.L. Kichatinov, Astron. Astrophys. 269, 581 (1993)
D.M. Rust, Geophys. Monogr. 111, 221 (1999)
D.M. Rust, A. Kumar, Astrophys. J. 464, L199 (1996)
A.A. Ruzmaikin, D.D. Sokolov, A.M. Shukurov (eds.), Magnetic Fields of Galaxies (Kluwer Academic, Dordrecht, 1988)
A. Shukurov, Lect. Notes Phys. 664, 113 (2005)
A. Shukurov, D. Sokoloff, K. Subramanian, A. Brandenburg, Astron. Astrophys. 448, L33 (2006)
A.A. Schekochihin, S.C. Cowley, G.W. Hammett, J.L. Maron, J.C. McWilliams, New J. Phys. 4, 84 (2002)
C.J. Schrijver, C. Zwaan, Solar and Stellar Magnetic Activity (Cambridge University Press, Cambridge, 2000)
P.W. Schuck, Astrophys. J. 632, L53 (2005)
V.B. Semikoz, D.D. Sokoloff, J.W.F. Valle, J. Cosmol. Astropart. Phys. 6, 8 (2012)
J.B. Simon, J.F. Hawley, K. Beckwith, Astrophys. J. 730, 94 (2011)
K.A. Sorathia, C.S. Reynolds, J.M. Stone, K. Beckwith, Astrophys. J. 749, 189 (2012)
S. Sridhar, N.K. Singh, ArXiv e-prints (2013)
H.R. Strauss, Phys. Fluids 28, 2786 (1985)
H.R. Strauss, Phys. Fluids 29, 3008 (1986)
K. Subramanian, Phys. Rev. Lett. 90, 245003 (2003)
K. Subramanian, Astron. Nachr. 331, 110 (2010)
K. Subramanian, A. Brandenburg, Astrophys. J. Lett. 648, L71 (2006)
S. Sur, A. Shukurov, K. Subramanian, Mon. Not. R. Astron. Soc. 377, 874 (2007)
T.K. Suzuki, S.-i. Inutsuka, arXiv:1309.6916 (2013)
J.B. Taylor, Phys. Rev. Lett. 33, 1139 (1974)
J.B. Taylor, Rev. Mod. Phys. 58, 741 (1986)
A.G. Tevzadze, L. Kisslinger, A. Brandenburg, T. Kahniashvili, Astrophys. J. 759, 54 (2012)
S.M. Tobias, F. Cattaneo, N.H. Brummell, Astrophys. J. 685, 596 (2008)
C.L. Van Eck et al., Astrophys. J. 728, 97 (2011)
E.T. Vishniac, Astrophys. J. 696, 1021 (2009)
E.T. Vishniac, A. Brandenburg, Astrophys. J. 475, 263 (1997)
E.T. Vishniac, J. Cho, Astrophys. J. 550, 752 (2001)
E.T. Vishniac, D. Shapovalov, Astrophys. J. 780, 144 (2014)
Y.-M. Wang, N.R. Sheeley Jr., Astrophys. J. 599, 1404 (2003)
L.M. Widrow, D. Ryu, D.R.G. Schleicher, K. Subramanian, C.G. Tsagas, R.A. Treumann, Space Sci. Rev. 166, 37 (2012)
L. Woltjer, Proc. Natl. Acad. Sci. USA 44, 489 (1958a)
L. Woltjer, Proc. Natl. Acad. Sci. USA 44, 833 (1958b)
T.A. Yousef, A. Brandenburg, G. Rüdiger, Astron. Astrophys. 411, 321 (2003)
T.A. Yousef, T. Heinemann, A.A. Schekochihin, N. Kleeorin, I. Rogachevskii, A.B. Iskakov, S.C. Cowley, J.C. McWilliams, Ph R L 100, 184501 (2008)
H. Zhang, S. Yang, Y. Gao, J. Su, D.D. Sokoloff, K. Kuzanyan, Astrophys. J. 719, 1955 (2010)
H. Zhang, D. Moss, N. Kleeorin, K. Kuzanyan, I. Rogachevskii, D. Sokoloff, Y. Gao, H. Xu, Astrophys. J. 751, 47 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this chapter
Cite this chapter
Blackman, E.G. (2016). Magnetic Helicity and Large Scale Magnetic Fields: A Primer. In: Balogh, A., Bykov, A., Eastwood, J., Kaastra, J. (eds) Multi-scale Structure Formation and Dynamics in Cosmic Plasmas. Space Sciences Series of ISSI, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3547-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4939-3547-5_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-3546-8
Online ISBN: 978-1-4939-3547-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)