Cylindrical Hall – MHD Waves: A Nonlinear Solution

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.