Cylindrical Hall MHD waves: A nonlinear solution

Abstract

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.