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Magnetohydrodynamic parametric instabilities of parallel propagating incoherent Alfvén waves


Numerical experiments for parametric instabilities of incoherent Alfvén waves in the context of one dimensional Hall-MHD equation sets are studied. The reason why the decay instability of incoherent waves can be explained in terms of that of the coherent wave is understood through analysis on nonlinearly driven finite amplitude density fluctuations. Numerical results suggest the importance of modulational instabilities of left-hand polarized Alfvén waves.


  • Agim, Y. Z., A. F. Vinas, and M. L. Goldstein, Magnetohydrodynamic and hybrid simulations of broadband fluctuations near interplanetary shocks, J. Geophys. Res., 100(A9), 17081–17106, 1995.

    Article  Google Scholar 

  • Araneda, J. A., Parametric instabilities of parallel propagating Alfvén waves: Kinetic effects in the MHD-model, Phys. Scr., T75, 164–168, 1998.

    Article  Google Scholar 

  • Bruno, R. and V. Carbone, The solar wind turbulece as a turbulence laboratory, Living Rev. Solar Phys., 24, 2005 [Online Article],

  • Bugnon, G., T. Passot, and P. I. Sulem, Landau-fluid simulations of Alfvén wave instabilities in a warm collisionless plasma, Nonl. Proc. Geophys., 11, 609–618, 2004.

    Article  Google Scholar 

  • Chanpeaux, S., D. Laveder, T. Passot, and P. L. Sulem, Remarks on the parallel propagation of small-amplitude dispersive Alfvén waves, Nonl. Proc. Geophys., 6, 169–178, 1999.

    Article  Google Scholar 

  • Del Zanna, L., M. Velli, and P. Londrillo, Parametric decay of circularly polarized Alfvén waves: Multidimensional simulations in periodic and open domains, A & A, 367, 705–718, 2001.

    Article  Google Scholar 

  • Goldstein, M. L., J. P. Eastwood, R. A. Treumann, E. A. Lucek, J. Pickett, and P. Decreau, The near-earth solar wind, Space Sci. Rev., 118, 7–39, 2005.

    Article  Google Scholar 

  • Hada, T., D. Koga, and E. Yamamoto, Phase coherence of MHD waves in the solar wind, Space Sci. Rev., 107(1–2), 463–466, 2003.

    Article  Google Scholar 

  • Hoshino, M. and M. L. Goldstein, Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities, Phys. Fluids B, 1, 1405–1415, 1989.

    Article  Google Scholar 

  • Kuramitsu, Y. and T. Hada, Acceleration of charged particles by large amplitude MHD waves: effect of wave spatial correlation, Geophys. Res. Lett., 27(5), 629–632, 2000.

    Article  Google Scholar 

  • Laveder, D., T. Passot, and P. L. Sulem, Transverse dynamics of dispersive Alfven waves. I. Direct numerical evidence of filamentation, Phys. Plasmas, 9(1), 293–304, 2002.

    Article  Google Scholar 

  • Malara, F. and M. Velli, Parametric instability of a large-amplitude non-monocromatic Alfvén wave, Phys. Plasmas, 3(12), 4427–4433, 1996.

    Article  Google Scholar 

  • Malara, F., L. Primavera, and P. Veltri, Nonlinear evolution of parametric instability of a large-amplitude nonmonocromatic Alfvén wave, Phys. Plasmas, 7(7), 2866–2877, 2000.

    Article  Google Scholar 

  • Nariyuki, Y. and T. Hada, Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfvén waves, Nonl. Proc. Geophys., 13, 425–441, 2006a.

    Article  Google Scholar 

  • Nariyuki, Y. and T. Hada, Kinetically modified parametric instabilities of circularly polarized Alfvén waves: Ion kinetic effects, Phys. Plasmas, 13, 124501, 2006b.

    Article  Google Scholar 

  • Narita, Y., K. H. Glassmeier and R. A. Treumann, Wave-number spectra and intermittency in the terrestrial foreshock region, Phys. Rev. Lett, 97(19), 191101, 2006.

    Article  Google Scholar 

  • Otsuka, F. and T. Hada, Anomalous diffusion of cosmic rays in magnetic field turbulence, Prog. Theor. Phys. Suppl., 162, 204–211, 2006.

    Article  Google Scholar 

  • Shukla, P. K. and Stenflo, L, Filamentation instability of Alfvén waves, Astrophys. Space Sci., 155(1), 145–147, 1989.

    Article  Google Scholar 

  • Suzuki, T. K. and S.-I. Inutsuka, Solar winds driven by nonlinear low frequency Alfvén waves from the photosphere: Parametric study for fast/slow winds and disappearance of solar winds, J. Geophys. Res., 111, A06101, 2006.

    Google Scholar 

  • Terasawa, T., M. Hoshino, J. I. Sakai, and T. Hada, Decay instability of finite-amplitude circulary polarized Alfvén waves: A numerical simulation of stimulated brillouin scattering, J. Geophys. Res., 91, 4171–4187, 1986.

    Article  Google Scholar 

  • Tsiklauri, D., J.-I., Sakai, and S. Saito, Particle-In-Cell of circularly polarized Alfvén phase mixing: A new mechanism for electron acceleration in collisionless plasmas, A & A, 435, 1105–1113, 2005.

    Article  Google Scholar 

  • Tu, C. Y. and E. Marsch, MHD structures, waves and turbulence in the solar-wind-observations and theories, Space Sci. Rev., 73(1–2), 1–210, 1995.

    Article  Google Scholar 

  • Turkmani, R. and U. Torkelsson, Propagation of non-linear circularly polarized Alfvén waves in a homogeneous medium, A & A, 409, 813–820, 2003.

    Article  Google Scholar 

  • Umeki, H. and T. Terasawa, Decay instability of incoherent Alfvén waves in the solar wind, J. Geophys. Res., 97(A3), 3113–3119, 1992.

    Article  Google Scholar 

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Correspondence to Yasuhiro Nariyuki.

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Nariyuki, Y., Hada, T. Magnetohydrodynamic parametric instabilities of parallel propagating incoherent Alfvén waves. Earth Planet Sp 59, e13–e16 (2007).

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Key words

  • Alfvéen waves
  • solar wind