Cylindrical Hall - MHD Waves: A Nonlinear Solution

Physics

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Scientific paper

The exact nonlinear cylindrical solution for incompressible Hall - magnetohydrodynamic (HMHD) waves, including dissipation, essentially from electron - neutral collisions, is obtained in a uniformly rotating, weakly ionized plasma such as exists in photospheric flux tubes. The ω - k relation of the waves, called here Hall - MHD waves, demonstrates the dispersive nature of the waves, introduced by the Hall effect, at large axial and radial wavenumbers. The Hall - MHD waves are in general elliptically polarized. The partially ionized plasma supports lower frequency modes, lowered by the factor δ≡ratio of the ion mass density to the neutral particle mass density, as compared to the fully ionized plasma ( δ=1). The relation between the velocity and the magnetic field fluctuations departs significantly from the equipartition found in Alfvén waves. These short-wavelength and arbitrarily large amplitude waves could contribute toward the heating of the solar atmosphere.

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