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Ultrasound Velocity Measurement in a Liquid Metal Electrode
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Electron magnetohydrodynamics: dynamics and turbulence.

Maxim Lyutikov1

  • 1Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, Indiana 47907-2036, USA and The Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street Toronto, Ontario, Canada M5S 3H8.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
PubMed
Summary

Electron magnetohydrodynamics (EMHD) turbulence differs significantly from MHD. Whistler mode interactions in EMHD exhibit unique properties, leading to distinct turbulent cascades and spectra, unlike Alfvén turbulence.

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Area of Science:

  • Plasma Physics
  • Fluid Dynamics
  • Astrophysical Plasmas

Background:

  • Electron magnetohydrodynamics (EMHD) describes plasma dynamics where electron inertia is negligible.
  • Whistler modes are fundamental wave phenomena in magnetized plasmas.
  • Understanding turbulent cascades is crucial for astrophysical and laboratory plasmas.

Purpose of the Study:

  • Investigate the dynamics and turbulent interactions of whistler modes in EMHD.
  • Determine the validity of energy and relaxation principles in EMHD.
  • Characterize the nonlinear interactions and cascade properties of whistler turbulence.

Main Methods:

  • Analysis of nonlinear solutions and wave interactions.
  • Derivation of the Hamiltonian formulation of EMHD.
  • Numerical solution of the kinetic equation.
  • Analytical estimation of magnetic fluctuation spectra.

Main Results:

  • No energy principle exists in EMHD; stationary configurations are neutrally stable.
  • Harmonic whistlers are exact nonlinear solutions; interactions depend on wave vector and frequency.
  • Three-wave decay is possible, coupling modes with different wave numbers and angles.
  • EMHD turbulence cascades over a broad range of angles, potentially forming anisotropic structures.
  • Predicted magnetic fluctuation spectrum for quasi-isotropic cascade is proportional to k(-2).

Conclusions:

  • EMHD turbulence exhibits distinct properties compared to MHD, precluding direct transfer of Alfvén turbulence characteristics.
  • The relaxation principle remains valid, guiding evolution towards Taylor-Beltrami states.
  • Whistler mode interactions are complex, leading to unique cascade dynamics and spectral properties.