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Energy transfer in Hall-MHD turbulence: cascades, backscatter, and dynamo action

Published online by Cambridge University Press:  01 June 2007

PABLO D. MININNI ,
ALEXANDROS ALEXAKIS  and
ANNICK POUQUET
PABLO D. MININNI
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA (mininni@ucar.edu, alexakis@ucar.edu, pouquet@ucar.edu)
ALEXANDROS ALEXAKIS
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA (mininni@ucar.edu, alexakis@ucar.edu, pouquet@ucar.edu)
ANNICK POUQUET
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA (mininni@ucar.edu, alexakis@ucar.edu, pouquet@ucar.edu)
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Abstract

Scale interactions in Hall magnetohydrodynamics (MHDs) are studied using both the mean field theory derivation of transport coefficients, and direct numerical simulations in three space dimensions. In the magnetically dominated regime, the eddy resistivity is found to be negative definite, leading to large-scale instabilities. A direct cascade of the total energy is observed, although as the amplitude of the Hall effect is increased, backscatter of magnetic energy to large scales is found, a feature not present in MHD flows. The coupling between the magnetic and velocity fields is different than in the MHD case, and backscatter of energy from small-scale magnetic fields to large-scale flows is also observed. For the magnetic helicity, a strong quenching of its transfer is found. We also discuss non-helical magnetically forced Hall-MHD simulations where growth of a large-scale magnetic field is observed.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 3 , June 2007 , pp. 377 - 401
Copyright
Copyright © Cambridge University Press 2006

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References

Alexakis, A., Mininni, P. D. and Pouquet, A. 2005a Phys. Rev. Lett. 95, 264503.CrossRefGoogle Scholar
Alexakis, A., Mininni, P. D. and Pouquet, A. 2005b Phys. Rev. E 72, 046301.Google Scholar
Archontis, V., Dorch, S. B. F. and Nordlund, A. 2003 Astron. Astrophys. 410, 759.CrossRefGoogle Scholar
Balbus, S. A. and Terquem, C. 2001 Astrophys. J. 552, 235.CrossRefGoogle Scholar
Bhattacharjee, A., Ma, Z. W. and Wang, X. 1999 J. Geophys. Res. 104, 14543.CrossRefGoogle Scholar
Birn, J., Drake, J. F., Shay, M. A., Rogers, B. N., Denton, R. E., Hesse, M., Kuznetsova, M., Ma, Z. W., Bhattacharjee, A., Otto, A. and Pritchett, P. L. 2001 J. Geophys. Res. 106, 3715.CrossRefGoogle Scholar
Blackman, E. G. and Field, G. B. 1999 Astrophys. J. 521, 597.CrossRefGoogle Scholar
Blackman, E. G. and Field, G. B. 2002 Phys. Rev. Lett. 89, 265007.CrossRefGoogle Scholar
Brandenburg, A. 2001 Astrophys. J. 550, 824.CrossRefGoogle Scholar
Brandenburg, A. and Subramanian, K. 2005 Phys. Rep. 417, 1.CrossRefGoogle Scholar
Chen, Q., Chen, S. and Eyink, G. L. 2003a Phys. Fluids 15, 361.CrossRefGoogle Scholar
Chen, Q., Chen, S., Eyink, G. L. and Holm, D. D. 2003b Phys. Rev. Lett. 90, 214503.CrossRefGoogle Scholar
Debliquy, O., Verma, M. K. and Carati, D. 2005 Phys. Plasmas 12, 042309.CrossRefGoogle Scholar
Ding, W. X., Brower, D. L., Craig, D., Deng, B. H., Fiksel, G., Mirnov, V., Prager, S. C., Sarff, J. S. and Svidzinski, V. 2004 Phys. Rev. Lett. 93, 045002.CrossRefGoogle Scholar
Domaradzki, J. A. and Rogallo, R. S. 1990 Phys. Fluids 2, 413.CrossRefGoogle Scholar
Galanti, B., Kleeorin, N. and Rogachevskii, I. 1995 Phys. Plasmas 2, 4161.CrossRefGoogle Scholar
Ghosh, S., Siregar, E., Roberts, D. A. and Goldstein, M. L. 1996 J. Geophys. Res. 101, 2493.CrossRefGoogle Scholar
Gruzinov, A. V. and Diamond, P. H. 1995 Phys. Plasmas 2, 1941.CrossRefGoogle Scholar
Helmis, G. 1968 Mon. sber. Deutsch. Akad. Wiss. Berlin 10, 280.Google Scholar
Iroshnikov, P. S. 1963 Sov. Astron. 7, 566.Google Scholar
Ji, H. 1999 Phys. Rev. Lett. 83, 3198.CrossRefGoogle Scholar
Kraichnan, R. H. 1965 Phys. Fluids 8, 1385.CrossRefGoogle Scholar
Krause, F. and Raedler, K.-H. 1980 Mean-field Magnetohydrodynamics and Dynamo Theory. New York: Pergamon.Google Scholar
Lanotte, A., Noullez, A., Vergassola, M. and Wirth, A. 1999 Geophys. Astrophys. Fluid Dyn. 91, 131.CrossRefGoogle Scholar
Laveder, D., Passot, T. and Sulem, P. L. 2002a Phys. Plasmas 9, 293.CrossRefGoogle Scholar
Laveder, D., Passot, T. and Sulem, P. L. 2002b Phys. Plasmas 9, 305.CrossRefGoogle Scholar
Lesieur, M. 1997 Turbulence in Fluids. Dordrecht: Kluwer Academic.CrossRefGoogle Scholar
Mahajan, S. M., Mininni, P. D. and Gómez, D. O. 2005a Astrophys. J. 619, 1014.CrossRefGoogle Scholar
Mahajan, S. M., Shatasvili, N. L., Mikeladze, S. V. and Sigua, K. I. 2005b Astrophys. J. 634, 419.CrossRefGoogle Scholar
Mahajan, S. M. and Yoshida, Z. 1998 Phys. Rev. Lett. 81, 4863.CrossRefGoogle Scholar
Meneguzzi, M., Frisch, U. and Pouquet, A. 1981 Phys. Rev. Lett. 47, 1060.CrossRefGoogle Scholar
Mininni, P. D., Alexakis, A. and Pouquet, A. 2005a Phys. Rev. E 72, 046302.Google Scholar
Mininni, P. D., Gómez, D. O. and Mahajan, S. M. 2002 Astrophys. J. 567, L81.CrossRefGoogle Scholar
Mininni, P. D., Gómez, D. O. and Mahajan, S. M. 2003a Astrophys. J. 587, 472.CrossRefGoogle Scholar
Mininni, P. D., Gómez, D. O. and Mahajan, S. M. 2003b Astrophys. J. 584, 1120.CrossRefGoogle Scholar
Mininni, P. D., Gómez, D. O. and Mahajan, S. M. 2005b Astrophys. J. 619, 1019.CrossRefGoogle Scholar
Mirnov, V. V., Hegna, C. C. and Prager, S. C. 2003 Plasma Phys. Rep. 29, 566.CrossRefGoogle Scholar
Morales, L., Dasso, S. and Gómez, D. 2005 J. Geophys. Res. 110, A04204.CrossRefGoogle Scholar
Numata, R., Yoshida, Z. and Hayashi, T. 2004 Comp. Phys. Comm. 164, 291.CrossRefGoogle Scholar
Ohkitani, K. and Kida, S. 1992 Phys. Fluids A 4, 794.CrossRefGoogle Scholar
Ohsaki, S. 2005 Phys. Plasmas 12, 032306.CrossRefGoogle Scholar
Pouquet, A., Frisch, U. and Léorat, J. 1976 J. Fluid Mech. 77, 321.CrossRefGoogle Scholar
Rezeau, L. and Belmont, G. 2001 Space Sci. Rev. 95, 427.CrossRefGoogle Scholar
Rheinhardt, M. and Geppert, U. 2002 Phys. Rev. Lett. 88, 101103.CrossRefGoogle Scholar
Sano, T. and Stone, J. M. 2002 Astrophys. J. 570, 314.CrossRefGoogle Scholar
Seehafer, N. 1996 Phys. Rev. E 53, 1283.Google Scholar
Shay, M. A., Drake, J. F., Rogers, B. N. and Denton, R. E. 2001 J. Geophys. Res. 106, 3759.CrossRefGoogle Scholar
Smith, D., Ghosh, S., Dmitruk, P. and Matthaeus, W. H. 2004 J. Geophys. Res. 31, L02805.Google Scholar
Steenbeck, M., Krause, F. and Rädler, K.-H. 1966 Z. Naturforsch. 21a, 369.CrossRefGoogle Scholar
Turner, L. 1986 IEEE Trans. Plasma Sci. 14, 849.CrossRefGoogle Scholar
Verma, M. 2004 Phys. Rep. 401, 229.CrossRefGoogle Scholar
Waleffe, F. 1991 Phys. Fluids A 4, 350.CrossRefGoogle Scholar
Wang, X., Bhattacharjee, A. and Ma, Z. W. 2001 Phys. Rev. Lett. 87, 265003.CrossRefGoogle Scholar
Yeung, P. K., Brasseur, J. and Wang, Q. 1995 J. Fluid Mech. 283, 43.CrossRefGoogle Scholar
Zeldovich, Y. B., Ruzmaikin, A. A. and Sokoloff, D. D. 1983 Magnetic Fields in Astrophysics. New York: Gordon and Breach.Google Scholar
Zhou, Y. 1993 Phys. Fluids A 5, 2511.CrossRefGoogle Scholar