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Large-scale dynamo action driven by forced beating waves in a highly conducting plasma

Part of: 50 years of Mean Field Electrodynamics

Published online by Cambridge University Press:  08 August 2018

Krzysztof A. Mizerski Open the ORCID record for Krzysztof A. Mizerski [Opens in a new window]
Krzysztof A. Mizerski*
Affiliation:
Department of Magnetism, Institute of Geophysics, Polish Academy of Sciences, Ksiecia Janusza 64, 01-452, Warsaw, Poland
*
†Email address for correspondence: kamiz@igf.edu.pl
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Abstract

The aim of this short paper is simply to demonstrate the effect of interactions between distinct waves induced by an oscillatory forcing on generation of the large-scale electromotive force (EMF) in a highly electrically conducting plasma in the dynamical regime, i.e. when the back reaction of the Lorentz force on the flow is included. The mean EMF is induced by waves with distinct but close phase speeds, which are called ‘beating waves’ by analogy with the acoustic effect of ‘beat’, in the presence of a locally uniform seed magnetic field. These waves may have either positive or negative helicity, and it is supposed that waves of a single sign of helicity are preferentially excited by a symmetry-breaking mechanism. The formula for the mean EMF in a highly conducting plasma is derived, conditions relevant to those of the early universe before and during galaxy formation. Within the scope of the weak magnetohydrodynamic turbulence dominated by the linear waves an $\unicode[STIX]{x1D6FC}$-effect, that is generation of the large-scale EMF is studied, which leads to amplification of the seed mean magnetic field. Possible subsequent equilibration due to quenching resulting from the presence of the Lorentz force is briefly discussed.

Keywords

astrophysical plasmasplasma dynamicsplasma instabilities
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 4 , August 2018 , 735840405
Copyright
© Cambridge University Press 2018 

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References

Beck, R., Brandenburg, A., Moss, D., Shukurov, A. & Sokoloff, D. 1996 Galactic magnetism: recent developments and perspectives. Annu. Rev. Astron. Astrophys. 34, 155–206.Google Scholar
Braginskii, S. I. 1964a Self-excitation of a magnetic field during the motion of a highly conducting fluid. Sov. Phys. JETP 20, 726–735.Google Scholar
Braginskii, S. I. 1964b Theory of the hydromagnetic dynamo. Sov. Phys. JETP 20, 1462–1471.Google Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209.Google Scholar
Cattaneo, F. & Hughes, D. W. 2006 Dynamo action in a rotating convective layer. J. Fluid Mech. 553, 401–418.Google Scholar
Davies, C. R. & Hughes, D. W. 2011 The mean electromotive force resulting from magnetic buoyancy instability. Astrophys. J. 727 (112), 12.Google Scholar
Feldman, S. I. & Lin, C. C. 1973 A forcing mechanism for spiral density waves in galaxies. Stud. Appl. Maths 52, 1–20.Google Scholar
Finlay, C. C. 2008 Waves in the presence of magnetic fields, rotation and convection. In Les Houches, Session LXXXVIII, Dynamos (ed. Cardin, Ph. & Cugliandolo, L. F.). Elsevier.Google Scholar
Hughes, D. W. & Cattaneo, F. 2008 The alpha-effect in rotating convection: size matters. J. Fluid Mech. 594, 445–461.Google Scholar
Lehnert, B. 1954 Magnetohydrodynamic waves under the action of the Coriolis force. Astrophys. J. 119, 647–654.Google Scholar
Lesur, G. & Ogilvie, G. I. 2008a Localized magnetorotational instability and its role in the accretion disc dynamo. Mon. Not. R. Astron. Soc. 391, 1437–1450.Google Scholar
Mizerski, K. A. 2018 Large-scale hydro-magnetic dynamo by Lehnert waves in non-resistive plasma. SIAM J. Appl. Maths (SIAP) 78 (3), 1402–1421.Google Scholar
Mizerski, K. A., Bajer, K. & Moffatt, H. K. 2012 The mean electromotive force generated by elliptic instability. J. Fluid Mech. 707, 111–128.Google Scholar
Mizerski, K. A. & Moffatt, H. K. 2018 Dynamo generation of a magnetic field by decaying Lehnert waves in a highly conducting plasma. Geophys. Astrophys. Fluid Dyn. 112 (2), 165–174.Google Scholar
Moffatt, H. K. 1970 Turbulent dynamo action at low magnetic Reynolds number. J. Fluid Mech. 41, 435–452.Google Scholar
Moffatt, H. K. 1972 An approach to a dynamic theory of dynamo action in a rotating conducting fluid. J. Fluid Mech. 53, 385–399.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Moffatt, H. K. & Proctor, M. R. E. 1982 The role of the helicity spectrum function in turbulent dynamo theory. Geophys. Astrophys. Fluid Dyn. 21, 265–283.Google Scholar
Ng, C. S. & Bhattacharjee, A. 1996 Interaction of shear-Alfven wave packets: implication for weak magnetohydrodynamic turbulence in astrophysical plasmas. Astrophys. J. 465, 845–854.Google Scholar
Parker, E. N. 1955 Hydromagnetic dynamo models. Astrophys. J. 122, 293–314.Google Scholar
Rädler, K.-H. 1969 A new turbulent dynamo, I. Monats. Dt. Akad. Wiss. 11, 272–279; (English translation: Roberts and Stix (1971), 301–308).Google Scholar
Rädler, K.-H. 1986 Investigations of spherical mean-field dynamo models. Astron. Nachr. 307, 89–113.Google Scholar
Rädler, K.-H., Kleeorin, N. & Rogachevskii, I. 2003 The mean electromotive force for MHD turbulence: the case of a weak mean magnetic field and slow rotation. Geophys. Astrophys. Fluid Dyn. 97, 249–268.Google Scholar
Roberts, P. H. 1972 Kinematic dynamo models. Phil. Trans. R. Soc. Lond. A 272, 663–698.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2003 Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear. Phys. Rev. E 68, 036301.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2004 Nonlinear theory of a ‘shear-current’ effect and mean field magnetic dynamos. Phys. Rev. E 70, 046310.Google Scholar
Rong, Y., Yi, S.-X., Zhang, S.-N. & Tu, H. 2015 Radial alignment of elliptical galaxies by the tidal force of a cluster of galaxies. Mon. Not. R. Astron. Soc. 451, 2536–2543.Google Scholar
Ruzmaikin, A. A., Shukurov, A. M. & Sokoloff, D. D. 1988 Magnetic Fields of Galaxies. Kluwer Academic Publishers.Google Scholar
Schekochihin, A. A. & Cowley, S. C. 2006 Turbulence, magnetic fields, and plasma physics in clusters of galaxies. Phys. Plasmas 13, 056501.Google Scholar
Spitzer, L. 1962 Physics of Fully Ionized Gases. Wiley.Google Scholar
Steenbeck, M., Kirko, I. M., Gailitis, A., Klawina, A. P., Krause, F., Laumanis, I. J. & Lielausis, O. A. 1967 An experimental verification of the $\unicode[STIX]{x1D6FC}$ -effect. Monats. Dt. Akad. Wiss. 9, 716–719; (English translation: Roberts and Stix (1971), 97–102).Google Scholar
Steenbeck, M. & Krause, F. 1966 The generation of stellar and planetary magnetic fields by turbulent dynamo action. Z. Naturforsch. 21, 1285–1296; (English translation: Roberts and Stix (1971), 49–79).Google Scholar
Steenbeck, M., Krause, F. & Rädler, K.-H. 1966 Berechnung der mittleren Lorentz–Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis–Kräfte beeinflusster Bewegung. Z. Naturforsch. 21, 369–376; (English translation: Roberts and Stix (1971), 29–47).Google Scholar
Tobias, S. M., Cattaneo, F. & Boldyrev, S. 2013 MHD dynamos and turbulence. In Ten Chapters in Turbulence (ed. Davidson, P. A., Kaneda, Y. & Sreenivasan, K. R.), pp. 351–404. Cambridge University Press.Google Scholar
Vainshtein, S. I. & Zel’dovich, Y. B. 1972 Origin of magnetic fields in astrophysics. Sov. Phys. Uspekhi 15, 159–172.Google Scholar
Wesson, P. S. 1982 Galaxies in clusters: alignments, formation from pancakes, and tidal forces. Vistas Astron. 26, 225–241.Google Scholar
Zweibel, E. G. & Heiles, C. 1997 Magnetic fields in galaxies and beyond. Nature 385, 131–136.Google Scholar