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.

Four research areas were investigated: (1). the propagation and coupling of hydromagnetic waves in the magnetosphere. The coupled hydromagnetic equations in the dipole model of the magnetosphere were solved numerically. A reconstruction of the long period waves in an actual geomagnetic storm was demonstrated (2). non-linear wave-particle interactions in the magnetosphere. Anomalous cross-field diffusion of trapped energetic protons may result in proton precipitation in the equatorial region; (3). the filamentation instability of large amplitude hydromagnetic waves in the solar wind plasma. This work is relevant to observations of Alven waves and magnetosonic waves in space plasmas; (4). parametric excitation of whistler waves in the high latitude ionosphere by a high frequency heater transmitting from the ground. It has been shown that whistler waves and Langmuir waves can be excited by ionospheric heaters. The instability which produces these waves offers a potential mechanism to generate large amplitude long period waves in the ionosphere.

This book is a study of plasma waves which are observed in the earth's magnetosphere. The emphasis is on a thorough, but concise, treatment of the necessary theory and the use of this theory to understand the manifold varieties of waves which are observed by ground-based instruments and by satellites. We restrict our treatment to waves with wavelengths short compared with the spatial scales of the background plasma in the mag netosphere. By so doing we exclude large scale magnetohydrodynamic phenomena such as ULF pulsations in the Pc2-5 ranges. The field is an active one and we cannot hope to discuss every wave phenomenon ever observed in the magnetosphere! We try instead to give a good treatment of phenomena which are well understood, and which illustrate as many different parts of the theory as possible. It is thus hoped to put the reader in a position to understand the current literature. The treatment is aimed at a beginning graduate student in the field but it is hoped that it will also be of use as a reference to established workers. A knowledge of electromagnetic theory and some elementary plasma physics is assumed. The mathematical background required in cludes a knowledge of vector calculus, linear algebra, and Fourier trans form theory encountered in standard undergraduate physics curricula. A reasonable acquaintance with the theory of functions of a complex vari able including contour integration and the residue theorem is assumed.

Perturbation electric and magnetic fields carry in excess of 10(exp10) to 10(exp12) W of electrical power between the magnetosphere and high-latitude ionosphere. Most of this power is generated by the solar wind. The ionosphere at large spatial and temporal scales acts as a dissipative slab which can be characterized by its height-integrated Pedersen conductivity sigma p, so that the power flux into the ionosphere due to a quasi-static electric field E is given by sigma (pE2) The energy transferred to the ionosphere by time-varying electromagnetic fields in the form of Alfven waves is more difficult to calculate because density and conductivity gradients can reflect energy. Thus, field resonances and standing wave patterns affect the magnitude and altitude distribution of electrical energy dissipation. We use a numerical model to calculate the frequency-dependent electric field reflection coefficient of the ionosphere and show that the ionosphere does not behave as a simple resistive slab for electric field time scales less than a few seconds. Time variation of spacecraft-measured high-latitude electric and perturbation magnetic fields is difficult to distinguish from spatial structuring that has been Doppler-shifted to a non-zero frequency in the spacecraft frame. However, by calculating the frequency-dependent amplitude and phase relations between fluctuating electric and magnetic fields we are able to show that low frequency fields (

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.

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).