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Superconducting Shielding W.O Superconducting shielding W.O. Hamilton To cite this version: W.O. Hamilton. Superconducting shielding. Revue de Physique Appliquée, Société française de physique / EDP, 1970, 5 (1), pp.41-48. 10.1051/rphysap:019700050104100. jpa-00243373 HAL Id: jpa-00243373 https://hal.archives-ouvertes.fr/jpa-00243373 Submitted on 1 Jan 1970 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. REVUE DE PHYSIQUE APPLIQUÉE: TOME 5, FÉVRIER 1970, PAGE 41. SUPERCONDUCTING SHIELDING By W. O. HAMILTON, Stanford University, Department of Physics, Stanford, California (U.S.A.). Abstract. 2014 Superconducting shields offer the possibility of obtaining truly zero magnetic fields due to the phenomenon of flux quantization. They also offer excellent shielding from external time varying fields. Various techniques of superconducting shielding will be surveyed and recent results discussed. 1. Introduction. - Superconductivity has been a field of active research interest since its discovery in 1911. Many of the possible uses of superconducti- vity have been apparent from that time but it has been only recently that science and technology have progressed to the point that it has become absolutely necessary to use superconductors for important and practical measurements which are central to disciplines other than low temperature physics. The various superconducting magnetometers which are now being used in many fields, high field superconducting ma- gnets, superconducting linear accelerators have all opened new research areas and have made the use of low temperature phenomena and techniques even more available. We will discuss the use of super- conducting materials for shielding against electrical and magnetic fields. In many measurements, the use of superconducting shielding provides the only prac- tical solution for shielding large volumes from fluctua- ting fields and it provides the only way to obtain a large region of truly zero magnetic field. II. The Phenomenon of Superconductivity. - Superconductivity is observed in many metals when FIG. 1. they are cooled to the temperature of liquid helium, 4.2 OK. The most striking physical effect seen when current at the surface of the superconductor equals the a material goes into the superconducting state is the critical field the material reverts to the normal state, appearance of zero resistance. Superconducting rings resistance appears and the material behaves like an of tin have been made to carry currents of an amp by ordinary electrical conductor. pulling a permanent magnet out of the ring after it It was thought for many years that the super- has become superconducting. These currents have conducting state could be adequately described by persisted for periods up to a year without any measu- an infinite conductivity. Indeed this is all one need rable decrease. consider for several types of superconducting shielding. This superconducting state can be destroyed by the However a look at Maxwell’s equations is helpful to application of a magnetic field. If the resistance of understand how a superconductor differs from merely a superconductor is measured by a weak current and a perfect conductor. Maxwell’s equation tells us : a magnetic field is applied perpendicular to the super- conducting surface a very sharp transition to a normal state is observed when the field is increased. This and :o field is known as the critical field and it is almost a constant at temperatures well below the superconduc- ting transition temperature. The critical field approa- ches zero as the temperature is raised to approach the which is Ohm’s law. If E is required to be zero superconducting transition temperature. This beha- by Ohm’s law due to 6 being infinite, then Maxwell’s vior is shown in figure 1. equation says that B must be constant in time. Thus The existence of the critical field limits the size of if a changing external magnetic field is incident on a the currents which can be transported by the super- superconductor the superconductor should develop conductor. When the current density is increased screening currents which oppose the change in B. to the point that the magnetic field created by the Since the material has no resistance, the screening Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:019700050104100 42 currents do not die out and the B field in the metal exponentially from the surface of the superconductor, remains constant. The applications ofthis to shielding the magnetic field being pushed out from the interior are obvious and will be discussed in more detail later. of the superconductor by screening currents which In 1933, Meissner examined the magnetic field close flow at the surface. The characteristic length for the when fall between 370 and 500 A in lead. to a superconducting body and found that tin exponential off is becomes superconducting it tends to exclude the The majority of the screening Meissner currents flow magnetic field which was penetrating the metal before in a surface layer of this thickness. The internal the superconducting transition took place. This effect, electric field is zero due to the infinite conductivity. the Meissner effect, cannot be explained simply by For low frequencies then we expect screening currents assuming perfect conductivity. We would expect the to flow in the surface sheath of thickness 500 A. These perfectly conducting material to simply trap whatever currents will exclude the fields from the bulk of the magnetic field happened to penetrate the material material and hence will shield an interior cavity from prior to the superconducting transition. Thus Meiss- these fields. A small interior electric field also arises ner showed that the superconductor also behaves like in this sheath due to the time varying magnetic field the the a perfect diamagnet, tending to exclude all magnetic but it is screened from the bulk of material by fields from its interior. superconducting electrons. Thus we conclude that a Experimentally it was found that a perfect Meissner superconducting shield which is thick compared to effect was extremely difficult to achieve. Most sub- the penetration depth should shield an internal cavity stances tend to exclude some of the applied field when perfectly from slowly time varying fields. they go superconducting, the rest of the field is then The next consideration to ask is just what does These of trapped in the material. regions trapped comprise a slowly varying field. The answer is that magnetic flux are associated with non superconducting the superconducting material begins to look like a inclusions. The perfect conductivity of the material normal metal when the frequencies of the external makes it difficult to eliminate the trapped fields. fields become high enough that the normal skin depth The problem of explaining the apparent diamagne- becomes comparable to the penetration depth. Phy- tism and the perfect conductivity was undertaken by sically this situation arises when one considers what F. and H. London. The results were the famous happens in the superconducting shielding layer. The London equations which do account for the principal time varying currents in this sheath create electric phenomena associated with superconductivity and fields which lag the currents in phase. This in turn which also suggest a very general quantum mechanical causes losses in the superconductor. In the two fluid explanation of superconductivity. Central to this model these electric fields act on the normal electrons interpretation is the concept of a single quantum and create a normal current. At low frequencies mechanical state for the entire macroscopic super- these normal currents are very small. When the nor- conductor. From this idea of a single quantum mal currents become comparable to the superconduc- mechanical state arose F. London’s suggestion that ting screening currents then the material behaves the trapped magnetic flux might be quantized. much like a normal metal. The frequency at which Doll and Nau- In 1961, Deaver and Fairbank and this occurs is approximately 101° Hz in the London which bauer demonstrated that the magnetic flux theory. Thus we expect the superconductor to be could be trapped in a hollow superconducting cylinder an extremely efficient shield of time varying fields up was measured was quantized. The flux quantum to this frequency and from that point on to be no to be : worse than a normal metal. IV. Shielding of D.C. Fields. - The previous discussion has centered on the elimination of time The measurements indicate the validity of the Lon- varying fields. The infinite conductivity of the super- For closed in a don predictions. any path entirely conductor is the only which it has been the magnetic flux linked by the path property superconductor necessary to use to obtain this shielding. We now wish must be an of the flux integer multiple quantum. to examine the Meissner effect to see how it can be The flux then which is observed trapped in the Meissner used to reduce or completely eliminate the effects of effect must be quanta of flux which have experiments the ambient magnetic field on an experiment. become surrounded zero resistance material. We by We discussed earlier the of a d.c. shall see later that this admits the possibility of using penetration magne- tic field into a surface of the the of magnetic flux to completely elimi- layer superconductor. quantization This is about 500 Á thick for lead at 4.2 oK.
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