Volume 39, Issue 6, 01 May 1968
Index of content:
- SPECIAL SECTION ON APPLIED SUPERCONDUCTIVITY
- PHYSICS REVIEWS
39(1968); http://dx.doi.org/10.1063/1.1656596View Description Hide Description
Although superconductive tunneling has proved to be a very useful tool for investigating the phenomenon of superconductivity, it also has many potential device applications worth further development. Examples of such devices based on the tunneling of normal electrons might include an rf oscillator and amplifier, a low‐temperature thermometer, and a generator and detector of microwave phonons. Examples of devices based on the tunneling of paired electrons, that is, the dc and acJosephson effects, might include a magnetometer, computer elements, a generator and detector of microwave radiation, and a voltage standard. It is the purpose of this paper to briefly review normal electron tunneling as well as the dc and acJosephson effects, how these different tunneling phenomena manifest themselves, and how these manifestations can be used for these several device applications.
39(1968); http://dx.doi.org/10.1063/1.1656597View Description Hide Description
A general physical picture of superconductor weak‐link junctions is outlined with emphasis on phenomena relevant to device applications. The total junction current contains a dissipative quasiparticle component nearly analogous to the current in a normal‐state junction plus an electron‐pair component responsible for superconducting effects such as the Josephson effects.Stochastic relaxation processes such as have been commonly associated with vortex motion and flux flow sometimes perturb the pair current and must also be taken into account.
39(1968); http://dx.doi.org/10.1063/1.1656598View Description Hide Description
Experiments on very thin films and systems composed of small particles have shown transition temperatures significantly higher than the bulk T c . Of the numerous ideas advanced to explain the high T c 's in these films, one of the most exciting is the suggestion of Cohen and Douglass that superconductive pairing can occur across dielectric barriers, and thereby lead to high T c 's. Recent results on the T c of thin superconductors in contact with dielectric barriers, evaporated on cryogenic substrates, are presented. Some representative T c 's obtained in these experiments are Al∼5.7°K, Zn∼1.9°K, Sn∼6°K, In∼4.5°K, and Pb∼7.1°K. In the case of Al, Sn, and Zn these T c 's are much higher than the values found by Buckel and Hilsch for films deposited on quartz at liquid‐helium temperatures. Explanations other than the dielectric barrier idea, such as ``amorphorus structure'' and the suggestion of Ginzburg that surface interactions may modify T c , are also discussed. In the course of these experiments to investigate high T c 's in films it was found that very thin continuous films (∼20 Å or less) could be prepared at cryogenictemperatures. An investigation of superconductivity in these ultrathin films showed that T c was much lower than the T c of the thicker films. This occurred in all the metals measured, which included Pb, Al, Sn, and Bi. An explanation of these results in terms of the destruction of long‐range order in two‐dimensional systems due to fluctuations in the Ginzburg‐Landau order parameter will be discussed. By using this idea and numerical values from the data, estimates can be made of the possibility of obtaining very high T c 's in films approaching a few atomic layers.
39(1968); http://dx.doi.org/10.1063/1.1656599View Description Hide Description
Electrical resistance observed1 in superconductors in the mixed state is interpreted as a measure of the motion of Abrikosov vortices in a direction transverse to the imposed net current. Additional evidence of flow of vortices has been provided by dc transformer action2,3 and by heat transport4 in the direction of vortex flow. The connection between the resistive voltage drop and the flow of vortices is understood5 in terms of the superconducting order parameter, which is a complex number varying in space and time. A vortex, which is formed at one edge of the sample, moves across it, and is destroyed at the other edge, has a ``zipper'' effect on the phase of the order parameter. On one side of the path of the vortex, the phase is raised by π (for a single quantum vortex); on the other side it is lowered by the same amount. This process makes no net change in the physical state of the sample; yet it requires a pulse of voltage difference between the ends of the sample, because the time derivative of phase of the order parameter is proportional6 to electrostatic potential (more generally, to the chemical potential for electrons). A state of steady flow of vortices thus involves a steady difference of potential between the ends of the sample. A voltmeter registers this difference. There is no net induced emf to be registered. The dissipation associated with the electrical resistance of a sample in which there is vortex flow occurs in the form of Joule heating produced by normal (i.e., nonsuper) currents.7 Most of this dissipation is in the cores of the vortices, where the material is at least approximately normal and where the electric field is strongest. The electric field in a moving core is partly induced magnetically but is mostly the gradient of electrostatic potential which is associated with the rapid changes of order parameter on opposite sides of the core. A moving vortex not only produces heat but also carries heat along with it, transversely to the electric current and to the magnetic field. A plausible model for the mechanism of this heat transport is based on the available excited states of the superconducting system of electrons as described by BCS. Each available level has a thermal probability of being occupied. The spectrum of levels available varies from place to place in the material according to the local value of the energy gap, which practically vanishes in the core of each vortex, but is significantly large between cores. A particular excitation can migrate only in regions where the energy gap is less than the excitation energy. Each low‐energy excitation is therefore trapped, rattling about within a definite core. When a core moves, the trapped excitations are carried along. When a vortex is eventually destroyed at the edge of the sample, its trapped excitations are stranded at the last position of the core. As the gap there goes up, so does the energy of each excitation. The excitation probability which corresponded to thermal equilibrium at the orignal energy is excessive at higher energies. Until the energy becomes so great that the excitation is no longer trapped, the excitation probability can readjust only by a net probability of conversion of energy from the electronic excitation into lattice heat. Similarly, when a vortex is formed, its core absorbs heat from the lattice. The net result is transportation of heat from the location of formation to the location of destruction. The detailed mechanisms by which forces are applied to vortices remain obscure. But by thermodynamic arguments8 we find a force in the direction of j×B due to net electrical current and a thermal force in the direction of − ▿T. In a superconductor in which the pinning of vortices is slight, we should be able (at least as laboratory curiosities) to use vortex flow as the basis of an electrically driven low‐temperature refrigerator and of a thermally driven source of electrical energy.
39(1968); http://dx.doi.org/10.1063/1.1656600View Description Hide Description
A review is given of the theoretical and experimental situation concerning the problem of superconductivity in the presence of pair‐breaking perturbations. The problem was first considered by Abrikosov and Gorkov, who advanced a theory which explained the results of the experiments by Matthias and co‐workers on the lowering of T c of superconductors containing small concentrations of magnetic impurities. The theory predicted further that the presence of magnetic scattering centers severely distorts the excitation spectrum of a superconductor and that for sufficiently large spin concentrations the energy gap disappears from the spectrum, even at T=0°K. It has since been found that the AGtheory can be extended to treat other pair‐breaking situations which lead to second‐order superconducting‐normal phase transitions. Examples of these are the vortex state, the surface sheath state, the proximity effect, small superconductors in large magnetic fields, superconductivity in the presence of high currents, and superconductivity in the presence of strong Pauli paramagnetism. In the dirty limit (where the mean free path is much smaller than the zero‐temperature coherence length) the different pair‐breaking regimes are equivalent in that their behavior is specified by a unified single parameter theory. In transforming from one pair‐breaking regime to another, one needs only to change the pair‐breaking parameter. Experimental results from the different depairing regimes are presented and compared with the predictions of the unified theory.
39(1968); http://dx.doi.org/10.1063/1.1656601View Description Hide Description
Superconductors with the highest known transitiontemperatures to date occur in β-tungsten phases which are rich in Nb3Al. It has been found possible to raise the temperature of Nb3Al (T c =18.5°K) to above 20°K by replacing some of the Al with Ge.1 The low values found for the electronic-heat-capacity co-efficient, and the almost temperature-independentmagnetic susceptibility contrast with the corresponding properties of other high-temperature β-tungsten structures such as V3Si. Thus, the location of the Fermi level at a narrow maximum of the density of states in energy which has been used as a model to explain the high specific heat and temperature-dependentsusceptibility of V3Si and the other high-temperature β-tungsten structures2 does not apply to Nb3 (Al, Ge). No distinctive properties of the normal state have as yet been measured. The variation of the transitiontemperature with valence electron count works well on a coarse-grained scale for β-tungsten structures but does not account in detail for the observed transitiontemperature as a function of nominal composition. The effect of stoichiometry, order, strain, and the presence of phases other than β tungsten all play some role in determining the observed transitiontemperature.
39(1968); http://dx.doi.org/10.1063/1.1656602View Description Hide Description
Superconducting magnets have established themselves as useful tools in solid‐state physics, magneto‐optical experiments, NMR,MHD, plasma, and other areas of physics. In high‐energy physics only the bubble‐chamber physicist has shown ample interest in using superconducting magnets. Reasons why there is a reluctance against large superconducting magnets in combination with high‐energy physics experiments and accelerators are discussed. However, in various areas of high‐energy physics superconducting magnets may be utilized, such as accelerator, beam‐transport, and experimental magnets. This paper summarizes physical properties of superconducting systems for experimental and beam transportmagnets in quantitative form. Charging time, field uniformity, resolution, acceptance, solid angle, improvement in optical measurements accuracy, and first‐ and second‐order optics for superconducting magnets, with and without ferromagnetic return paths, will be compared to room and cryogenicmagnets. Summary of experiences with superconducting magnets (energies > 106 J) will be given, as well as irradiation properties of superconducting type II materials and systems. Expected irradiation doses in accelerators and their effect on superconducting systems will be discussed. Lifetime expectancy, economy of operation, and effect of power failures are treated. A short section is devoted to possible design of superconducting magnets with and without ferromagnetic return paths.
- MAGNET MATERIALS
39(1968); http://dx.doi.org/10.1063/1.1656603View Description Hide Description
The superconducting magnetization behavior and transition temperatures of single crystals of Nb were investigated prior to and after a series of fast neutron irradiations (E>1 MeV) in the Oak Ridge Research Reactor at a temperature of 40°C.1 In addition to increases in the upper critical fieldH c2 and small changes in the transition temperature after irradiation, it has been found that defects have been created with the ability to pin magnetic flux as evidenced by an increase in the nonequilibrium behavior of the magnetization.
A greater degree of flux pinning in single‐crystal Nb can be attained by fast‐neutron irradiation than has heretofore been reported for pinning introduced by mechanical deformation, and for fast‐neutron doses of approximately 2×1019 neutrons/cm2 the magnetization approaches that of a completely irreversible type II superconductor. The initial magnetization cycle and subsequent hysteresis loop for an irradiated sample are shown in Fig. 1 as well as the magnetization cycle prior to irradiation. Successive reductions in cross‐sectional area of the highly irradiated sample and subsequent magnetization measurements reveal only a small size dependence of the hysteresis, indicating that rather steep flux gradients can be established even at applied fields close to the upper critical field. From size‐dependent studies of the remanent moment it is concluded that a flux gradient has been established in a macroscopic surface sheath approximately 0.1 mm thick with the corresponding shielding current density calculated to be approximately 2×105 A/cm2.
39(1968); http://dx.doi.org/10.1063/1.1656604View Description Hide Description
A promising new development in practical high‐field superconductors is the technique developed by Tachikawa of the Institute of Metals, Tokyo, Japan, for fabrication of V3Ga in flexible wire or strip form. This can also be made as a composite with copper. The short‐sample characteristic obtained is approximately that of present day commercially manufactured Nb3Sn at magnetic fields of up to 150 kG and is much higher beyond this field. The U.S.S.R. and Japan are manufacturing three element systems of NbZrTi which are comparable in properties with currently available NbTi in the U.S.A., but such systems do not, as yet, appear to offer any significant advantages over NbTi. At present magnets are being fabricated from NbTi, Nb3Sn, or both, usually as composite conductors in intimate contact with copper and frequently with the addition of reinforcing where the operating stress levels are high enough to merit this. The properties of these basic superconductors are well known. NbZr is now obsolescent and current practice favors the use of the cheaper, lighter, and more ductile NbTi. Several recent and highly successful large coils have been fabricated from standard superconductors but improvements in the manufacture of composites of copperclad NbTi with one or more superconducting strands and almost any desired current carrying capacity or size render such stranded conductors obsolescent. Experience with cables and composites has shown that metallurgical‐type diffusion bonds between the superconductors and co‐extruded copper give best performance and are mandatory when superconductors of large cross section are used. Mechanical‐type bonds are being used with success in composities containing small‐cross‐section superconductors. When the highest current density is desired the diffusion‐type bond permits the use of much less copper in the cross section of the composite for the same performance. The techniques of adding additional copper and reinforcement are also being applied to the 1.25 cm wide Nb3Sn ribbons now available so Nb3Sn conductors of almost any strength and current carrying capacity can also be fabricated. In this case, soldering techniques are used to add the additional copper. The most advanced heavy‐section composite conductor yet supplied and tested for large low‐field magnets is the copper‐clad NbTi strip of width 2 in. and thickness 0.1 in. produced for the Argonne National Laboratory 4.8 m i.d. hydrogen bubble‐chamber magnet. This contains six NbTi strips and has been operated in a 60 cm i.d. test coil to 4600 A, while developing maximum fields of 30 kG parallel to the longer dimension of the strip cross section and 19 kG perpendicular to this direction. More advanced large conductors are in production. The most advanced NbTi composite conductors for use in high current density smaller coils of up to 60 cm i.d. at central fields of about 60 kG are of the type being produced for the outer sections of the 88 kG, 50 cm i.d. coils being constructed for the NASA Lewis Research Center by the Avco‐Everett Research Laboratory. The conductors can be wound into stable magnets if suitably cooled. They contain a considerably lower ratio of copper to superconductor than earlier conductors of this type. The increased stability is attained by limiting the temperature rise in the superconductor when sudden movements of flux occur. This is accomplished by using a larger number of superconducting strands for a given total cross section of superconductor so as to maximize the surface‐to‐volume ratio for the superconductor and hence obtain the best possible cooling. Extra superconductor is also being incorporated in the conductors where necessary as a simple and cheap means of providing extra reinforcing in highly stressed conductors. Proposals have been made for hollow copper‐clad conductors in which high‐pressure helium in the dense fluid phase can be circulated so that high heat‐transfer rates can be obtained. Tests on samples of this type of conductor have been made at the Stanford Linear Accelerator Center, and it is hoped that this will allow high current densities to be obtained in larger coils without the necessity for a liquid‐helium tank encasing the complete coil. Present Nb3Sn composite conductors are both more rugged than formerly, more stable in operation, and have a higher current‐carrying capacity. The most advanced conductor of this type has recently been developed by General Electric to meet the Avco‐Everett Research Laboratory requirement for the inner sections of the previously mentioned 50 cm. i.d. 88 kG magnet. The 1.25 cm wide conductor contains outer layers of 0.075 mm thick stainless steel for reinforcing and the superconductor is sandwiched between two layers of 0.05 mm thick copper to provide the electrical protection. The conductor is rated at 300 A for 100 kG and recent tests with 18 cm i.d. counterwound pancakes of this material in Argonne National Laboratory show it to be stable in operation with a smooth reversible transition into the resistive region. Our experiments in Argonne with larger‐size pancaketype coils also show that higher operational stability in 1.25 cm wide copper‐coated Nb3Sn strips can be obtained if a number of narrower parallel superconducting strips are used instead of one superconducting strip occupying the whole width of the superconductor. It is still true at the moment that NbTi composite conductors provide the cheapest means of providing fields of from 60 to 80 kG in medium‐size coils of the order of 20 cm i.d. or larger and that Nb3Sn composite conductors are necessary for the higher fields. The techniques for using Nb3Sn strips in pancake‐type windings to provide the highest fields and highest current densities in coils greater than 5 to 10 cm i.d. are still in their infancy and require considerable development. Although no significant new practical conductors have appeared recently, a great deal has to be done before the potential performance of present materials, as measured by the attainable current densities and maximum attainable magnetic fields reached in short samples, can be realized in practical magnets.
39(1968); http://dx.doi.org/10.1063/1.1656605View Description Hide Description
Composite strip conductors for the two largest superconducting magnets yet to be built are described. The conductors consist of six bands of Nb‐48% Ti alloy buried in 2‐in.‐wide strips of copper. The conductors for the two magnets have, respectively, critical current capacities of 3000 and 5880 A. In addition, the quality of the bond between copper and superconductor is excellent, and the copper conductivity is high. Data are presented for these and other characteristics of the strip as manufactured. The strip conductors are anisotropic in their critical‐current behavior with respect to field orientation. The importance of this fact in designing magnets economically is pointed out. Performance results are given for a 24‐in. i.d. test coil containing a ton of strip. Many strip configurations are possible and can be easily produced Costs of strip of this type will be competitive with present materials.
39(1968); http://dx.doi.org/10.1063/1.1656606View Description Hide Description
Specimens of Ti‐20% V alloy were heat treated to a β‐solid‐solution condition and then aged for several fixed times and temperatures below the β transus. X‐ray and electron diffraction were used to determine the composition and distribution of the metallurgical phases produced by the agingtreatments. These data were correlated with measurements of the superconducting transition temperature and critical current density. In order for these materials to carry resonable supercurrent densities at 4.2°K, it is necessary that the matrix be rich enough in V for the transition temperature to be greater than 4.2°K and that there be present an array of flux‐pinning sites. It was found that aging temperatures of 400°, 500°, or 600°C were required to insure the first condition. The flux pinners produced were ω particles in the case of the 400°C treatment and α precipitates in the case of the 500° and 600°C treatments. In many specimens, the superconducting‐to‐normal transition at a given value of applied field was spread out over a wide range of transport current rather than being abrupt as is usually the case.
39(1968); http://dx.doi.org/10.1063/1.1656607View Description Hide Description
The electromagnetic performance of high‐field type‐II superconductors is significantly affected by structural factors such as crystal size, crystal orientation, or crystal strain. Because the vapor‐deposition process for depositing single‐phase, polycrystalline,stoichiometricNb3Sn on a heated moving substrate permits control of these structural parameters, this technique is used for the deposition of continuously monitored layers of Nb3Sn on long lengths of ribbon substrate. The thickness of teh Nb3Sn layer is controlled and can be readily varied to meet specific magnet requirements. For small‐bore, high‐field, layer‐wound magnets, a family of commerical 0.090‐in.‐wide ribbons has been developed. For larger‐bore magnets, in which ``pancake''‐type construction is desirable, a commercial line of ½‐in.‐wide ribbons is currently being offered. Custom‐size ribbons have been made as narrow as 0.025 in. and niobium stannide has been deposited on wires as thin as 0.005 in. in diameter. This paper describes these different ribbons and discusses their electromagnetic performance. Normalized curves have been developed for calculation of short‐sample critical currents as a function of volume of niobium stannide. For instance. from 20 to 95 kG, normalized critical currentI n (i.e., the ratio of critical current at any desired field to the critical current at 100 kG) can be expressed as follows:.From 95 to 140 kG, the following approximate expression can be used:,where I c is the critical current at the desired magnetic field,I 100 kG is the critical current at 100 kG, and H is the magnetic field in kG. The current density of the Nb3Sn layer in the various types of vapor‐deposited ribbon remains essentially constant. When a constant current density at 100 kG is used for the various Nb3Sn layer thicknesses, the Nb3Sn thickness and the ribbon width can be incorporated into the expression for critical current from 20 kG to 95 kG as follows:.From 95 kG to 140 kG, the following expression applies:,where W is the ribbon width in inches and t is the Nb3Sn layer thickness in inches. These data are discussed in detail. The critical currents obtained in actual magnets are often lower than the short‐sample performance. In many magnet applications, it is economically desirable to obtain the highest possible current density. To achieve these goals, it may be necessary to compromise the amount of normalized metal parallel to the superconductor. Specific examples of optimization of magnetcurrent density as a function of silver plating and cooper cladding of the superconductor ribbon are described.
39(1968); http://dx.doi.org/10.1063/1.1656608View Description Hide Description
A new theory of the stable transition of a superconductor between normal and superconducting states is reviewed and data supporting this theory are presented. Data on copper‐clad Nb‐40% Ti are presented, and the slope for the variation of the critical current with wire diameter is found to be 1.5 for wire diameters between 0.005 and 0.05 cm. For copper‐clad samples of this material, voltage‐current data agree remarkably well with the new theory of stabilization. The importance of the superconducting transitional region is emphasized.
39(1968); http://dx.doi.org/10.1063/1.1656609View Description Hide Description
Composite conductors of copper and titanium‐niobium, either cable or solid, have been fabricated with low‐weight‐percentage Nb alloys in the range 22–28 at.% niobium. The fabrication of such alloys and conductors involves heat treatment in the temperature range 300°–500°C. It has been found that omega‐phase precipitation occurs in all samples. Details as to the size and distribution of omega precipitates will be given as well as the correlation between omega precipitation and critical current densities in the superconductor.
Mechanical and Electrical Properties of Diffusion‐Processed Nb3Sn‐Copper‐Stainless Steel Composite Conductors39(1968); http://dx.doi.org/10.1063/1.1656610View Description Hide Description
Diffusion‐processed Nb3Sn has high current density at high magnetic fields. When combined with copper or copper and stainless steel in the form of a flat laminated tapelike conductor, it also has flexibility, low normal‐state resistance, and the ability to withstand high tensile stress. This paper considers various laminated conductors that have been constructed, with emphasis on mechanical as well as electrical performance characteristics. Design methods and subsequent test evaluation for performance characteristics are discussed.
39(1968); http://dx.doi.org/10.1063/1.1656611View Description Hide Description
In many instances it appears that the limiting performance of a superconductive device is determined by low‐field instabilities rather than by the high‐field current density. If the device is made of flat‐strip superconductors, a further complication may arise from the fact that in the low‐field regions the magnetic field usually is oriented at some nonzero angle to the surface of the strip. To see how these conditions affect the performance of plasma‐plated superconductors, we have measured critical currents in flat strips of Nb 3Sn in transverse applied field, varying the angle θ between the surface of the strip and the magnetic field. When transport current is applied first and the field increased until the specimen undergoes a normal transition, the relationship Hc (IT ) = H 0(IT )+H 1(IT ) cos2θ is roughly obeyed, where IT is the transport current and H 0 and H 1 are found to be of comparable magnitude. When the magnetic field is applied first and the transport current increased to its critical value, virtually no angular dependence is observed. We tentatively explain this result by describing the plasma‐plated material as a matrix of miniature hollow cylinders aligned with the magnetic field. Because of the anisotropy of the plating process the effective wall thickness of the ``cylinders'' varies with the specimen orientation. When the field is applied first, the transport current can find paths around these ``cylinders'' which will not result in locally exceeding the critical current density of the material until nearly all the specimen is critical. However, when the transport current is applied first, the additional shielding currents induced by the magnetic field are forced to travel in paths which are already carrying transport current, and locally the critical current density may be exceeded, precipitating a normal transition before the entire specimen is critical. Further tests are being carried out to determine the effect of heat treatment and strip dimensions on this angular dependence of the critical current. These results should discriminate between our proposed explanation and the possibility that the effect is simply a demagnetization phenomenon.
39(1968); http://dx.doi.org/10.1063/1.1656612View Description Hide Description
Since the discovery of technologically interesting high‐field superconductors in 1961 more than 50 experimental and theoretical publications have appeared which are concerned with the relevant ac loss mechanisms. These papers are reviewed, and certain of the experimental findings are unified in the light of the present day understanding. In many cases seemingly disconnected and even apparently contradictory results are brought into consonance. In this review, theories and models as well as experiments are discussed, and brief mention is made of actual and proposed ac applications. For frequencies with which we are mainly concerned (<104 sec−1) and for fields less than Hc and H c1, respectively, for type I and type II superconductors, ideal homogeneous materials are loss free. Likewise, in dc background fields up to H c3, losses remain negligible if the amplitude of the ac field stays below a value determined by intrinsic critical surface current densities. For larger amplitudes cyclical flux movement takes place inside the superconductor (in the intermediate or mixed state for type I or II, respectively) and flux‐flow and eddy‐current losses appear. In real nonideal superconductors much larger losses appear. These larger losses arise from flux pinning, which also accounts for the large dc transport currents which inhomogeneous materials can support in the mixed state. Although flux‐pinning theories are mostly semiempirical and are incompletely developed they nevertheless provide a good understanding of many loss phenomena. Elastic properties of the fluxoid structure can also lead to resonant losses, as has been predicted and subsequently observed. In addition to direct measurement of losses, experimental work has also been concerned with related factors such as critical currents and fields. Various methods to measure power losses have been employed; in order of popularity they are: (1) Helium boil‐off, (2) Phase shift between current and voltage, (3) Magnetization measurements (hysteresis of B‐H curves), (4) Calorimetry, (5) Q of L‐C circuits, (6) Q of cavities, and (7) Mechanical force or torque measurements. With the exception of (6), these methods are suitable for low frequencies and the first four yield most of the quantitative data. The materials most frequently investigated include pure Nb, Nb alloys with Zr or Ti, and pure Pb. One can distinguish different loss regimes depending on the amplitude Ha of the ac fields: (1) Ha <H c1, (2) H c1<Ha <Hp , (3) Hp <Ha <H c2, and (4) H c2<Ha <H c3. Here Hp is the field of complete penetration, i.e., the field above which the total volume of the superconductor sees an ac field. In general, only the first two regions have been studied extensively because the losses become very large for Ha >Hp . Two important generalizations emerge from the present review of existing data: (1) The losses depend on the peak field to which the superconductor is subjected; it does not matter whether these fields are due to an ac current in the superconductor or are externally applied. (2) The loss per cycle is practically independent of frequency for frequencies less than or approximately equal to 104 sec−1. In agreement with these two points are loss measurements carried out by quasistatic cycling of the magnetic field and results which show that losses are independent of the ac waveform. A plot of all loss measurements as loss per cycle per unit surface area vs peak ac field at the surface exhibits a consistent trend all the way from 10−13 to 10−3 J/cm2/cycle. It shows reasonable agreement with theoretical models for H c1<Ha <Hp , where the loss per cycle, in J/cm2, is 4.22×10−9 (Ha −ΔH)3/jc , with the peak field Ha in oersteds and the critical current density jc in A/cm2. In this formula ΔH is a field step at the surface, due to a superconducting surface current density. Like jc , ΔH may be different from specimen to specimen, and is field dependent, having roughly the size of H c1 at H c1 and getting smaller as the field increases. The measured losses in Nb alloys are almost all in this regime; only a few results are available for Ha >H p and then the losses are proportional to the volume. The much smaller losses in the Meissner effect regime (Ha <H c1) depend strongly on the amount of flux frozen into the specimen. A qualitative discussion connects these losses with flux pinning in the surface. Measurements for pure Nb are usually in this region. These results can be applied in more complicated experimental situations. Superimposed dc fields modify the losses by changing jc and ΔH; a varying temperature has a similar influence. In fact the ac critical current is often limited by thermal runaway. The losses for a solenoid have to be computed by considering the local fields.
39(1968); http://dx.doi.org/10.1063/1.1656613View Description Hide Description
Trapped flux has been shown to be responsible for a large part of the residual ac losses in both types I and II superconductors. The authors have made theoretical and experimental investigations of losses in the 40–400 MHz range to establish a more detailed low‐field model. The surface resistance rs , as given by Pippard, is exceedingly small for Sn, Pb, and other pure metals below about 0.95 Tc at these frequencies. As a consequence, trapped‐flux effects provide the dominant losses in rolled‐foil resonant circuits. The theoreticalmodel is simply Ohmic losses in the normal regions of trapped fluxoids bounded by the penetration depth and the surface. This gives an added resistance rh =rh (0)V(t), where the temperature function is V(t) = (1−t 4)−1/2(1−t 2)−1. The magnitude of the loss is predicted to be proportional to the density of fluxoids trapped, which in turn is assumed proportional to the background magnetic field for low fields. The experimental technique consisted of pulse determinations of circuit Q in the superconducting and normal state as a function of temperature and weak background magnetic field on cooling below Tc . The most detailed effort was made on pure tin foil from 60–350 MHz with background H fields up to 6 G. Data on these and on Sn–In, Pb–Sn, Ta, and Nb samples showed the function V(t) gave the best fit. The flux‐trapping loss was linearly proportional to the cooling field. The Pippard surface‐resistance term was separated out along with a very small residual loss, r 0. The latter was independent of field or temperature and could be annealed out. The Pippard term had a frequency dependence between ν4/3 and ν3/2 as expected. These results differed from Haden et al. in that no break in the decay rate was observed in the pure Sn circuits. This could be explained by the absence of an observable fluxoid core transition. The absence of a strong frequency dependence is consistent with Ohmic loss and ruled out a dominant hysteresis behavior. The nature of the flux‐trapping loss is seen to make it the principle dissipating mechanism for most circuit applications since it resists annealing, does not depend upon impurities, and even though greatly reduced by nulling out external fields, may be partially self‐induced due to thermoelectric effects on cooling.
39(1968); http://dx.doi.org/10.1063/1.1656614View Description Hide Description
The magnetization of hard superconducting wires, in the presence of a transverse magnetic field, can be induced to collapse by the application of a small, local field pulse. Under certain conditions the collapse may propagate along the wire in steps, leaving behind a spatially periodic variation in the remanent magnetization of the wire. The remanent magnetization is associated with discrete vortices of wire. A phenomenological explanation for the formation of the macrovortex structure is proposed. According to this explanation, the energy of magnetization, which is initially stored uniformly over a finite volume, is preferentially dissipated locally during the process of flux jumping, thereby raising the temperature of the region to the critical temperature. Although the formation of the macrovortex structure has thus far been observed only in unclad wire of high pinning strength, it represents a potentially important mechanism for the concentration of energy during a collapse of magnetization.