Conditions of analogy between the propagation of electromagnetic waves and the trajectories of particles of same spin with application to rectifying magnetrons

The object of this article is the study of the biunivocal correspondence established by the Pauli principle between the internal energy of a particle and the frequency of the associated wave in media which are the seat of strong coupling between the particles and when their spins are in a favored direction. In Section I, the determinantal forms of antisymmetrical wave functions are investigated, these being valid both for crystals and for electronic plasmas. It is shown that, starting from this determinant, two complementary series of wave functions can be constructed. Depending on the internal energy, two types of complementary particles are thus obtained: (1) free electrons associated with real waves, and (2) holes associated with evanescent waves. In Section II, a study is made of the mathematical analogy between the Schrödinger equation and the tropospheric propagation equation. It is shown that the potential energy can be assimilated to the refraction modulus and that the group velocity of the propagation around the earth can be assimilated to the group velocity of the complementary particle. By a very simple correspondence, the real modes of propagation predict the formation of holes while the imaginary modes of propagation predict the formation of free electrons. A special study is made of the analogy between the index barriers of the inversion layers and the potential barriers of the barrier layers. This analogy enables the existence to be predicted of purely electronic barrier layers without the need for any material support. In Section III, the rectification and photoconduction properties of these electronic barrier layers in magnetrons and in traveling wave magnetron detectors are considered. Their analogies with and differences from the barrier layers of junctions are examined. Finally, in the conclusion, the advantages and description of radar detection arrangements devised, on these principles, by the Compagnie Générale d- e T.S.F. in Paris, are set out.