- Open Access
Self-generation of phase coherence in parallel Alfvén turbulence
Earth, Planets and Space volume 57, pagese9–e12(2005)
Nonlinear evolution of Alfvén turbulence is discussed within the framework of the derivative nonlinear Schroedinger equation (DNLS), a subset of the hall-MHD equation set, which includes quasi-parallel propagating right- and left-hand polarized Alfvén wave modes. By numerically time integrating the equation with periodic boundary conditions, we discuss relationship between generation of wave phase coherence and self-organization of the system due to birth of Alfvén solitons.
Carreras, B. A., V. E. Lynch, and G. M. Zaslavsky, Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model, Phys. Plasmas, 8(12), 5096–5103, 2001.
del-Castillo-Negrete, D., B. A. Carreras, and V. E. Lynch, Fractional diffusion in plasma turbulence, Phys. Plasmas, 11(8), 3854–3864, 2004.
Champeaux, S. et al., Remarks on the parallel propagating of small-amplitude dispersive Alfvén waves, Nonl. Proc. in Geophys., 6, 169–178, 1999.
Chen, X. J. and W. K. Lam, Inverse scattaring transform for the derivative nonlinear Schrodinger equations with nonvanishing boundary conditions, Phys. Rev. E, 69, art. no. 066604, 2004.
Ghosh, S. and K. Papadopoulos, The onset of Alfvénic turbulence, Phys. Fluids., 30(5), 1371–1387, 1987.
Hada, T., Nonlinear evolution of Alfvén waves in space plasmas, in Nonlinear Processes in Physics, edited by A. S. Fokas, D. J. Kaup, A. C. Newell, and V. E. Zhakarov, pp. 169–174, Springer-Verlag, 1992.
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.
Kaup, D. J. and A. C. Newell, An exact solution for a derivative nonlinear Schrodinger equation, J. Math. Phys, 19, 798–801, 1978.
Kawata, T. and H. Inoue, Exact solution of the derivative nonlinear Schrödinger equation under the nonvanishing conditions. J. Phys. Soc. Japan, 44, 1968–1976, 1978.
Kawata, T., J. -I. Sakai, and N. Kobayashi, Inverse method for the mixed nonlinear Schrodinger equation and soliton solutions. J. Phys. Soc. Japan, 48, 1371–1379, 1980.
Koga, D. and T. Hada, Phase coherence of foreshock MHD waves: wavelet analysis, Space. Sci. Rev, 107, 495–498, 2003.
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.
Medvedev, M. D., P. H. Diamond, V. I. Shevchenko, and V. L. Galinsky, Dissipative dynamics of collisionless nonlinear Alfvén wave trains, Phys. Rev. Lett., 78(26), 4934–4937, 1997.
Metzler, R. and T. F. Nonnenmacher, Fractional diffusion, waiting-time distributions, and Cattaneo-type equations, Phys. Rev. E, 57(6), 6409–6414, 1998.
Mio, K., T. Ogino, K. Minami, and S. Takeda, Modified nonlinear Schroedinger equation for Alfvén waves propagating along the magnetic field in cold plasmas. J. Phys. Soc. Japan, 41, 265–271, 1976.
Mjølhus, E., Application off the reductive perturbation method to long hy-dromagnetic waves parallel to the magnetic field in a cold plasma, Report no. 48, Department of applied mathematics, Univ. Bergen, Norway, 1974.
Mjølhus, E., On the modulational instability of hydromagnetic waves parallel to the magnetic field, J. Plasma. Phys., 16, 321–334, 1976.
Mjølhus, E. and T. Hada, Soliton theory of quasi-parallel Alfvén waves, in Nonlinear Waves and Chaos in Space Plasmas, edited by T. Hada and H. Matsumoto, pp. 121–169, Terrapub, Tokyo, 1997.
Mjølhus, E. and J. Wyller, Nonlinear Alfvén waves in a finite beta plasma, J. Plasma Phys., 40, 299–318, 1988.
Rogister, A., Parallel propagation of nonlinear low-frequency waves in high-β plasma, Phys. Fluids, 14, 2733–2739, 1971.
Sakai, J. -I. and B. Sonnerup, Modulational instability of finite amplitude dispersive Alfvén waves, J. Geophys. Res, 88, 9069–9078, 1983.
Spangler, S. R., The evolution of nonlinear Alfvén waves subject to growth and damping, Phys. Fluids, 29(8), 2535–2547, 1986.
Spangler, S. R., Kinetic effects on Alfvén-wave nonlinearity, 2. The modified nonlinear-wave equation, Phys. Fluids, B2(2), 407–418, 1990.
Spangler, S. R. and J. P. Sheerin, Properties of Alfvén solitons in a finite-beta plasma, J. Plasma Phys., 27, 193–198, 1982.
Zimbardo, G., A. Greco, and P. Veltri, Superballistic transport in tearing driven magnetic turbulence, Phys. Plasmas, 7(4), 1071–1074, 2000.
About this article
Cite this article
Nariyuki, Y., Hada, T. Self-generation of phase coherence in parallel Alfvén turbulence. Earth Planet Sp 57, e9–e12 (2005). https://doi.org/10.1186/BF03352580
- Alfvén waves
- complex system