A SIX-FOLD GENERALIZATION OF IONOSPHERIC RECIPROCITY

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Abstract
In general, reciprocity is not possible in an anisotropic ionosphere, but when certain conditions are satisfied relating to the direction of propagation of the electro-magnetic waves and to the direction of the imposed earth's magnetic field, reciprocity is possible. This is simply expressed in terms of equalities between certain reflection coefficients for two distinct modes of propagation. The mathematical nature of reciprocity is obscured by working in three-dimensional space, so a complete generalization of the whole process is here undertaken, extending the theory to n-dimensional space. First-order differential equations are employed, from which general conditions are deduced that yield reciprocity. What are termed energy and reciprocity invariants are deduced, which in turn yield very simple results in terms of the coefficients of solutions of the propagation equations at all points of the general inhomogeneous stratified medium.

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