Date of Award


Degree Type


Degree Name

Doctor of Philosophy in Electrical Engineering


Electrical Engineering

First Advisor

Charles Polk


This dissertation is concerned with the analysis of hydromagnetic waves which are generated in various regions of the magnetosphere and propagated to the earth in the extremely low frequency spectrum. Two different aspects of the problem are investigated, namely, propagation through inhomogeneous regions of the ionosphere and propagation and excitation of waves in current carrying regions of the ionosphere and the magnetosphere.

Propagation through inhomogeneous regions is studied by two different methods. With the first met hod, transmission coefficients for hydromagnetic waves are obtained in terms of Airy integral functions by assuming a linearly varying inhomogeneous region. Simplified expressions are obtained by using series and asymptotic approximations. Numerical results are given for typical ionospheric parameters.

The second approach to propagation through inhomogeneous regions employs "Epstein's theory". In this method, the wave equation is transformed into the hypergeometric equation to obtain more tract able solutions for the types of inhomogeneities which are characteristic of the ionosphere. Assuming a hydromagnetic wave incident from above and propagating parallel to the earth's magnetic field, power transmission coefficients are calculated. Complex refractive index profiles are employed in the calculations. These profiles approximate those which are obtained from the dispersion relations for a partially ioni zed plasma and available ionospheric data. The transmission coefficients are calculated for various times of day and show that maximum transmission occurs at about local midnight and minimum transmission at about local noon.

The various mechanisms which may be responsible for the generation and amplification of hydromagnetic waves are examined. The expected characteristics of electromagnetic noise in the earth-ionosphere cavity due to excitation by hydromagnetic waves are compared with experimentally observed data and with characteristics deduced from excitation by worldwide thunderstorm activity.

Propagation of hydromagnetic waves through a current carrying plasma is investigated on the basis of macroscopic equations involving additional terms due to the existence of a constant current density. These equations are derived from the basic plasma equations in which streaming velocities for both electron and ion fluids are allowed. A general dispersion relation for small amplitude waves is, derived from these equations. Approximate solutions of the dispersion relation for certain special cases are obtained.

For transverse propagation (propagation normal to the steady magnetic field), when the currents are also transverse to both, the direction of propagation and the static magnetic field, it is found that amplification takes place. For longitudinal propagation with currents in the transverse plane, the propagation constant remains unaffected. In this case, however, an electric field component along the wave normal is introduced which changes the direction of the ray path. For longitudinal propagation, with currents also along the direction of propagation and the static magnetic field, the propagation constant has a resonance at the ion-cyclotron frequency for both right and left hand polarizations. A nonconvective instability is found to exist in the neighborhood of this frequency for certain values of currents. Numerical results are presented for longitudinal propagation, for data corresponding to the ionospheric and magnetospheric conditions.



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