MHD theory of field line resonance in the magnetosphere

Abstract

The linearized ideal MHD equations are cast into a set of global differential equations from which the field line resonance equations of the shear Alfven waves and slow magnetosonic waves are naturally obtained for finite pressure plasmas in general magnetic field geometries with flux surfaces. The coupling between the shear Alfven waves and the magnetosonic waves is through the geodesic magnetic field curvature. For axisymmetric magnetospheric equilibria, there is no coupling between the shear Alfven waves and slow magnetosonic waves because the geodesic magnetic field curvature vanishes. The asymptotic singular solutions of the MHD equations near the field line resonant surface are derived. Numerical solutions of the field line resonance equations are performed for the dipole magnetic field, and it is found that the shear Alfven wave field line resonant frequency is proportional to L{sup {minus}4}{rho}{sup {minus}1/2}. The slow magnetosonic wave resonant frequency is much smaller than the Shear Alfven wave resonant frequency and is roughly proportional to P/{rho}L{sup 2}, where L is the equatorial L-shell distance, P is the plasma pressure, and {rho} is the plasma mass density. The results help to understand the continuous spectra observed by AMPTE/CCE.