Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T16:08:13.186Z Has data issue: false hasContentIssue false
  • English
  • Français

Superconducting cylinders

Published online by Cambridge University Press:  24 October 2008

D. Shoenberg
D. Shoenberg
Affiliation:
Trinity College, Exhibition of 1851 Senior Student
Get access Rights & Permissions [Opens in a new window]

Extract

The magnetization curves of short tin, lead and tantalum cylinders were measured by the force method, and it was shown that although for tin there was no appreciable hysteresis in the transverse position, there was a very marked hysteresis in the longitudinal position, of the same form at different temperatures but depending on the sharpness of the cylinder rims. Lead and tantalum showed additional temperature dependent features which could be attributed to impurities.

The hysteresis due to shape in the longitudinal cylinder is analogous to the hysteresis of alloy ellipsoids, in that the magnetization for a given field always lies within a certain boundary curve and varies “classically” within this boundary. This analogy suggests that the mechanism of the shape hysteresis for a pure superconductor may be similar to the sponge mechanism proposed by Mendelssohn for alloys, but it is also possible that the hysteresis is due to the formation of macroscopic superconducting rings. The considerations which fix the boundary curve are probably similar to those in the superconducting ring, and in this connection some new measurements on a lead ring are reported. The paper concludes with a discussion of the time lag between magnetization and field, and it is suggested that this is not a primary phenomenon.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 2 , April 1937 , pp. 260 - 276
Copyright
Copyright © Cambridge Philosophical Society 1937

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

* Shoenberg, , Proc. Roy. Soc. A, 155 (1936), 712.CrossRefGoogle Scholar This contains references to earlier work.

† Peierls, , Proc. Roy. Soc. A, 155 (1936), 613;CrossRefGoogle ScholarLondon, , Physica, 3 (1936), 450.Google Scholar

‡ Rjabinin, and Schubnikow, , Phys. Zeit. d. Sow. Union, 6 (1934), 557;Google ScholarMendelssohn, and Pontius, , Physica, 3 (1936), 327;CrossRefGoogle ScholarNature, 138 (1936), 29.CrossRefGoogle Scholar

* Strictly speaking, what we measure is not exactly the magnetic dipole moment, owing to the contribution to the observed force of higher order moments produced in a non-ellipsoidal specimen. No correction has been made for the influence of these higher order moments, but the correction is probably always small and does not invalidate any of our conclusions.

* Mendelssohn, and Pontius, (Nature, 138 (1936), 29)CrossRefGoogle Scholar have published a B-H curve for a short tin cylinder, and, apart from the time-lag effects, its general form is confirmed by our Fig. 1.

† No great accuracy is claimed either for the temperature or the absolute field values given in this and other diagrams.

* We verified that the magnetization remains zero for several minutes in this region, so the phenomenon has not the character of a time lag between magnetization and field.

† A similar effect has been reported by Mendelssohn and Pontius (loc. cit.).

‡ See Shoenberg (loc. cit.), p. 721, Fig. 3.

* It will be noticed that the maximum of the curve and the form of the hysteresis are not exactly the same as in Fig. 1, although the same specimen was used. Probably these features are very sensitive to the exact position of the specimen in the field, which cannot be exactly reproduced after removing and replacing the specimen.

* See Shoenberg (loc. cit.), footnote p. 720; in the experiment mentioned there we obtained results exactly like those described here for a pure cylinder.

† This was done by filing, and care was taken to avoid filing any regions other than those at the rims, i.e. the end faces were left flat over nearly their whole areas.

* Lead has a large critical field at 4·2° K., and so gives easily measurable forces, while the use of tin involves pumping (introducing difficulties of temperature control), and the critical fields are less than half those of lead. The previous experiments with lead spheres had suggested that the lead was rather pure.

† The absence of a tail for our lead sphere, and the comparatively slight hysteresis found in our lead sphere, may of course be because different samples of the same batch of lead have different degrees of purity, so that the lead sphere was accidently much purer than all the cylinders.

* The word impurity is used in a general sense, i.e. the hysteresis may be caused by the mechanical state of the tantalum rather than chemical impurities (cf. Mendelssohn, and Moore, , Phil. Mag. 21 (1936), 532).CrossRefGoogle Scholar

* It is no doubt because of this method of definition that the maximum value of − 4πσ/H c is about 1 in this case, although it is only 0·88 for the similar tin cylinder. Mendelssohn and Moore (loc. cit.) have shown that the critical fields for reappearance of resistance are much higher, and so the “average” value of critical field may be rather higher than our extrapolated values.

† Proc. Roy. Soc. 152 (1935), 34.Google Scholar

‡ The rounding-off referred to here is that unavoidably produced in the making of the cylinder, and should not be confused with the rounding-off deliberately introduced in the experiments of § 5.

* If a substance has volume susceptibility χ, then the slope k of the magnetization curve of an ellipsoid of demagnetizing coefficient N is given by 1/k = N + 1/χ. For the ascending branch of the curve χ = − ¼π, while for the slope of the descending branch χ = ∞ (see Peierls, loc. cit., p. 624), hence we can obtain − 4πk. The value of N is determined from formulae given in Clerk, Maxwell'sElectricity and Magnetism, 2 (Oxford, 1873), 64–5.Google Scholar

† Probably the ascending and descending branches are not exactly linear, so that the slopes of the assumed straight lines are smaller than the actual slopes of the curve near the axis of abscissae. The experimental accuracy is not sufficient, however, to show this slight curvature of the magnetization curves.

* Phys. Zeit. d. Sow. Union, 10 (1936), 231.Google Scholar The question, however, of how the current in the ring adjusts itself to values on the boundary curve (different from those given by the law of induction) is still an open one; the explanation suggested by the authors is not necessarily the correct one.

† Owing to the thinness of the lead wire (0·35 mm. diameter) from which the ring was made, the ring is thinner in some places than others and the slopes of the various linear portions do not agree well with theory. The discrepancies are however such as can be attributed to lack of uniformity of the ring.

* For a uniform ring the theory requires the return curve to be linear, and the fact that this is not so for the cylinder (see Fig. 3) suggests that the inside surface at which the field is just H c is different for different external fields, or in other words that the distribution of the superconducting regions changes with reduction of field.

* References in § 1.

† Similar effects were found with the lead ring mentioned in § 9.

‡ Less marked time effects were found also at the beginning of the return curve.