Evidence from whistlers shows that the outer ionosphere contains columns or ducts of enhanced ionization. The theory of propagation in these ducts shows an upper cutoff frequency at one-half the gyrofrequency. The average propagation velocity for whistlers trapped in the ducts can be approximated by assuming that the energy follows along the ionization maximum with wave normals aligned with the magnetic field.
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R. L. Smith (1961) studied this question.
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