Numerical solutions to the initial value problem have been obtained for the guided (toroidal) and isotropic (poloidal) electric fields of hydromagnetic waves for the asymmetric case. The cylindrical model of the inner magnetosphere has been used in which the field lines are arcs of circles and the surface of the earth is planar. The cases considered have the initial disturbance completely restricted to either the guided or isotropic field components to emphasize the effect of coupling. The development of the system has been calculated for asymmetric modes of order m = 1 to 10, corresponding to from one to ten full waves in longitude and the lowest order (n =1) field-line mode, corresponding to a half-wave along a field line. The initial isotropic (east-west) electric-field component is in an eigenstate of the symmetric or uncoupled poloidal mode. In this case, when the coupling is reduced to zero, the isotropic electric field simply oscillates harmonically. The initial guided (north-south) electric-field component is defined to increase radially and towards higher latitudes. As a check on the numerical solutions, the total energy of the system is continually calculated and compared with the initial energy. Although no damping is included in the problem, the poloidal-mode energy decays with time, as has been shown theoretically. The toroidal mode reaches maximum amplitude in regions of relatively narrow latitudinal extent. The large spatial variation of the magnetic field in these resonance regions must be associated with large field aligned currents. (Author).

Here is a fascinating text that integrates topics pertaining to all scales of the MHD-waves, emphasizing the linkages between the ULF-waves below the ionosphere on the ground and magnetospheric MHD-waves. It will be most helpful to graduate and post-graduate students, familiar with advanced calculus, who study the science of MHD-waves in the magnetosphere and ionosphere. The book deals with Ultra-Low-Frequency (ULF)-electromagnetic waves observed on the Earth and in Space.

A disturbance in the exosphere generates waves in three partially separable modes. These modes are described by considering the vorticity about a line of force, the two-dimensional divergence of velocity in the plane perpendicular to the line of force, and the component of velocity along the line of force. The propagation of vorticity is one-dimensional and there is no geometrical attenuation; energy is lost only through the finite conductivity of the medium. The propagation of the longitudinal velocity component is almost one-dimensional but is heavily damped at high frequencies. In a gravitational field, the medium is no longer uniform and at low frequencies the modes are coupled in a complicated way. For parallel magnetic and gravitational fields, the vorticity mode is still separable and gravity leads to anisotropic dispersion in the other modes.-p.i.

A disturbance in the exosphere generates waves in three partially separable modes. These modes are described by considering the vorticity about a line of force, the two-dimensional divergence of velocity in the plane perpendicular to the line of force, and the component of velocity along the line of force. The propagation of vorticity is one-dimensional and there is no geometrical attenuation; energy is lost only through the finite conductivity of the medium. The propagation of the longitudinal velocity component is almost one-dimensional but is heavily damped at high frequencies. In a gravitational field, the medium is no longer uniform and at low frequencies the modes are coupled in a complicated way. For parallel magnetic and gravitational fields, the vorticity mode is still separable and gravity leads to anisotropic dispersion in the other modes.