Multiscale Hall-Magnetohydrodynamic Turbulence in the Solar Wind

The spectra of solar wind magnetic fluctuations exhibit a significant power-law steepening at frequencies f > 1 Hz. The origin of this multiple scaling is investigated through dispersive Hall magnetohydrodynamics. We perform three-dimensional numerical simulations in the framework of a highly turbulent shell model and show that the large-scale magnetic fluctuations are characterized by a k-5/3-type spectrum that steepens at scales smaller than the ion inertial length di, to k-7/3 if the magnetic energy overtakes the kinetic energy, or to k-11/3 in the opposite case. These results are in agreement both with a heuristic description a la Kolmogorov and with the range of power-law indices found in the solar wind.

[1]  William H. Matthaeus,et al.  The equations of reduced magnetohydrodynamics , 1992, Journal of Plasma Physics.

[2]  M. Goldstein,et al.  Properties of the fluctuating magnetic helicity in the inertial and dissipation ranges of solar wind turbulence , 1994 .

[3]  Robert H. Kraichnan,et al.  Inertial‐Range Spectrum of Hydromagnetic Turbulence , 1965 .

[4]  Vincenzo Carbone,et al.  A note on shell models for MHD turbulence , 1998, chao-dyn/9807032.

[5]  Drake,et al.  Two-dimensional electron magnetohydrodynamic turbulence. , 1996, Physical review letters.

[6]  U. Frisch.  Turbulence: The Legacy of A. N. Kolmogorov , 1996 .

[7]  Hui Li,et al.  Solar wind magnetic fluctuation spectra: Dispersion versus damping , 2001 .

[8]  P. Coleman.  Turbulence, viscosity, and dissipation in the solar-wind plasma , 1968 .

[9]  A. Barnes.  Interplanetary Alfvenic fluctuations - A stochastic model , 1981 .

[10]  S. Mahajan,et al.  Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind , 2004 .

[11]  P. D. Mininni,et al.  Direct Simulations of Helical Hall-MHD Turbulence and Dynamo Action , 2004, astro-ph/0410274.

[12]  William H. Matthaeus,et al.  Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind , 1982 .

[13]  Edward J. Smith,et al.  Whistler mode turbulence in the disturbed solar wind , 1982 .

[14]  Annick Pouquet,et al.  Inertial ranges and resistive instabilities in two‐dimensional magnetohydrodynamic turbulence , 1989 .

[15]  V. Carbone,et al.  A shell model for anisotropic magnetohydrodynamic turbulence , 1990 .

[16]  D. A. Roberts,et al.  Simulation of high‐frequency solar wind power spectra using Hall magnetohydrodynamics , 1996 .

[17]  Luca Biferale,et al.  SHELL MODELS OF ENERGY CASCADE IN TURBULENCE , 2003 .

[18]  B. Bavassano,et al.  On the evolution of outward and inward Alfvénic fluctuations in the polar wind , 2000 .

[19]  H. K. Wong,et al.  Observational constraints on the dynamics of the interplanetary magnetic field dissipation range , 1998 .

[20]  W. Matthaeus,et al.  MHD-driven Kinetic Dissipation in the Solar Wind and Corona , 2000 .

[21]  Ashis Bhattacharjee,et al.  Impulsive Magnetic Reconnection in the Earth's Magnetotail and the Solar Corona , 2004 .

[22]  W. Matthaeus,et al.  Magnetohydrodynamic turbulence in the solar wind , 1999 .

[23]  W. Matthaeus,et al.  Parallel and perpendicular cascades in solar wind turbulence , 2005 .

[24]  Spectral energy dynamics in magnetohydrodynamic turbulence. , 2005, Physical review letters.

[25]  W. Matthaeus,et al.  Waves and turbulence in the solar wind , 1992 .

[26]  University of Warwick,et al.  A weak turbulence theory for incompressible magnetohydrodynamics , 2000, Journal of Plasma Physics.

[27]  P. Isenberg,et al.  Generation of the fast solar wind: A review with emphasis on the resonant cyclotron interaction , 2002 .

[28]  P. Frick,et al.  CASCADE AND DYNAMO ACTION IN A SHELL MODEL OF MAGNETOHYDRODYNAMIC TURBULENCE , 1998 .

[29]  W. Matthaeus,et al.  Evidence for the presence of quasi‐two‐dimensional nearly incompressible fluctuations in the solar wind , 1990 .

[30]  S. Cranmer,et al.  Alfvénic Turbulence in the Extended Solar Corona: Kinetic Effects and Proton Heating , 2003, astro-ph/0305134.

[31]  A. Balogh,et al.  Anisotropic turbulent spectra in the terrestrial magnetosheath as seen by the cluster spacecraft. , 2006, Physical review letters.

[32]  L. Davis,et al.  Large-Amplitude Alfvn Waves in the Interplanetary Medium' , 1971 .

[33]  On spectral scaling laws for incompressible anisotropic magnetohydrodynamic turbulence , 2005, physics/0504207.

[34]  Charles W. Smith,et al.  Dissipation of the Perpendicular Turbulent Cascade in the Solar Wind , 2004 .

[35]  Contribution of Cyclotron-resonant Damping to Kinetic Dissipation of Interplanetary Turbulence , 1998, astro-ph/9809017.

[36]  Pierluigi Veltri,et al.  Fully developed anisotropic hydromagnetic turbulence in interplanetary space , 1980 .

[37]  T. Horbury,et al.  Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. , 2005, Physical review letters.

[38]  M. Furukawa,et al.  A Shell Model for the Hall MHD System , 2005 .

[39]  Kathleen E. Hamilton,et al.  Dependence of the Dissipation Range Spectrum of Interplanetary Magnetic Fluctuationson the Rate of Energy Cascade , 2006 .

[40]  S. Galtier.  Wave turbulence in incompressible Hall magnetohydrodynamics , 2006, Journal of Plasma Physics.