On the Magnetic Energy of Supraconductors

Abstract

A long stretched supraconductive body (wire), placed longitudinally in a homogeneous magnetic field of slowly increasing strength H0 loses its supraconductivity when the field strength reaches a certain critical value Ho = Hc. Measurements by de Haas and Voogd [1] disclosed that the case is different when the direction of the wire is transverse: then the transition takes place at a value of the applied field H0 lower than Hc. By H0 is meant the field as it would be if the supraconductor were absent. When it is present, the strength H is in general different from H0 and varies from point to point, because the field cannot penetrate into the supraconductive material, so that the lines of induction are crowded at its surface. These conditions caused Von Laue [2] to enunciate the following hypothesis: A supraconductive body begins its transition into the normal state when the strongest part of the magnetic field H at its surface reaches the critical value H = Hc. Subsequent measurements by de Haas and co-workers on circular and elliptic cylinders [3] and on spheres4 confirmed Von Laue's rule, so that it must be regarded as firmly established experimentally. Recently it has gained added theoretical importance, having been made by Landau [5] the starting point of interesting considerations on the structure of supraconductors during the process of transition. The theoretical reasons for the dependence of the critical field Hc on the temperature were cleared up in a significant paper by Gorter and Casimir [6], in which these authors also attempted a theoretical derivation of Von Laue's rule. However, this part of their work is, in our opinion, unconvincing and open to certain objections. In view of the great importance of the subject it seemed desirable to study it more closely in order to remove all doubts which may arise. The purpose of the present paper is to supply this want and to modify the derivation of Von Laue's rule in such a way as to meet the objections.

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