Superconducting Sphere Research Articles

Superconductivity applied to gravimetry

A gravimeter has been developed which uses the levitation of a superconducting sphere by the field of persistent current magnets. Instabilities in the field have been reduced to the point where environmental noise on local gravity is greater than the instrument noise. In present results the persistent currents are decaying at a rate of 2 parts in 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> /yr. Concurrent measurements of magnetic field and gravimeter signal allows for correction of this drift. The device is being applied to geophysical problems through measurements of: secular variations in local gravity, tides of the solid earth, effects of oceans and atmosphere on local gravity, and normal modes of the earth.

The Modelling of Oceans by Spherical Caps

Summary We have solved a variety of axisymetric induction problems by a functional analytic method due to Hutson, Kendall and Malin which extends to high frequency the radius of convergence of Price'sfirst method. In the present paper the choice of acceleration parameter and the rate of convergence are discussed in greater detail. The problems treated have involved a cap of a sphere of variable electrical surface conductivity to model a shelving ocean, with a superconducting sphere below to model the conducting Earth. Electric currents are induced in both by an external magnetic field, uniform in space, and varying sinusoidally in time. This problem has previously been extensively studied but the following new points have emerged from our computations: 1. When a superconducting sphere is placed beneath an otherwise isolated spherical cap the distribution of electric current over the cap is modified as though the conductivity of the cap had been reduced. A physical explanation is suggested for this effect. 2. Let the line across which a reversal of the vertical component of induced magnetic field occurs be l. Suppose that the ocean bed begins to shelve upwards to its margin along a line. Then the position of l, even at moderate (4h) frequencies, may be only very loosely related to the position of. In general, the position of l will vary with time, and will also depend upon a number of other parameters. An alternative solution in one case is presented by using Legendre series. The results for series of various lengths are compared with the functional analytic solution, thus enabling an estimate to be made of the number of terms which must be included to give any required accuracy. This comparison shows that a large number of terms must often be taken, and it follows that the Legendre polynomial method must be used with caution for induction problems even for moderately high frequency.

Proximity effect in superconductors: Calculation of the transition temperature

The problem of the calculation of the transition temperature in the proximity effect is considered. From the variational principle of Silvert and Cooper we derive a simpler variational principle which is useful in obtaining a rapid numerical estimate of the transition temperature as well as the qualitative features of the solution. Approximate and exact solutions for the transition temperature and the order parameter are obtained in the clean limit, the geometry investigated being that of a superconducting sphere embedded in an infinite normal matrix. The results for the transition temperature do not display the unphysical behavior found in previous work in the clean limit and suggest that there is a critical radius for the sphere below which the sample is normal at all temperatures. The results for the order parameter show that the nonanalytic behavior discovered by Silvert and Cooper is a relatively small effect in the case investigated.

Effects of the particle number nonconservation on the one-nucleon transfer reactions in spherical superconductor nuclei

The spectroscopic factors of one-nucleon transfer reactions for nuclei, usually treated with the superconductivity techniques, are calculated in a simple model conserving the particle number operator. States of even nuclei are approximated by superpositions of components of zero- and two-quasi-particle excitations, corresponding to the correct number of particles. Analogously states of odd nuclei are taken to be components of one-quasi-particle states with a fixed number of particles. Numerical values are obtained for stripping and pick-up reactions on even and odd tin isotopes. They are compared with the results of the corresponding quasi-particle theory and with the experimental data.

Conservation of the Number of Particles in the Tamm-Dancoff Approximation for Spherical Superconductor Nuclei

A modified Tamm-Dancoff approximation for spherical superconductor nuclei is formulated. The approximation consists in diagonalizing the nuclear Hamiltonian in the space spanned by the components of zero-and two-quasiparticle excitations corresponding to a fixed particle number ("projected states"). Thus, spurious states arising from the Bogoliubov-Valatin canonical transformation, which are present in the usual Tamm-Dancoff approximation, are completely eliminated. Matrix elements between "projected states" are evaluated by the Bayman projection method of the generating functions. The model is applied to the calculation of the low-lying excited states of the tin isotope with $A=116$, and the results are compared with the corresponding ones obtained in the Tamm-Dancoff approximation. Our conclusion is that the effect of the particle-number nonconservation is important mainly for the energies of the highest levels. This becomes particularly clear for the $J=0$ case.

A Superconducting Gravimeter

A gravimeter is constructed which uses the near perfect stability of superconducting persistent currents to make it a device with exceptional stability. A superconducting sphere is levitated in the magnetic field generated by two superconducting coils. Changes in gravitational or inertial forces in the vertical direction are measured as changes in the vertical position of the sphere or as changes in a feedback force, independent of the primary supporting force, which holds the sphere in a fixed position. In its present state of development the instrument produces data which, when compared to calculated earth tides, set an upper limit on the drift rate of ±6 parts in 109 of g/day. Several possible sources of drift are discussed.

The superconducting gravimeter

The superconducting gravimeter is a spring type gravimeter in which the mechanical spring is replaced by a magnetic levitation of a superconducting sphere in the field of superconducting, persistent current coils. The object is to utilize the perfect stability of supercurrents to create a perfectly stable spring. The magnetic levitation is designed to provide independent adjustment of the total levitating force and the force gradient so that it can support the full weight of the sphere and still yield a large displacement for a small change in gravity. The gravimeters provide unequaled long term stability so that instrumental noise can be either below geophysical and cultural noise or indistinguishable from it over periods ranging from years to minutes. This article reviews the construction and operating characteristics of the instruments, and the range of research problems to which it has been and can be applied. Support for operation of the instruments in the United States has been limited so that operation of multiple instruments for periods much longer than a year has not been possible. However, some of the most appropriate applications of the instrument will require records of several years from arrays of instruments. Commercial versions of the instruments have now been purchased in sufficient numbers elsewhere in the world so that a world-wide array has been organized to maintain instruments and share data over a period of six years.

Field line trajectories in a Skornyakov trap

Skornyakov has proposed a magnetic trap in which a spiral conductor connects diametrally opposite points on the inside surface of a superconducting sphere. He has argued that such a system will have nested toroidal magnetic surfaces and that these surfaces will have favourable stability properties both in terms of ‘average minimum B’ and of ‘shear’. Further he has maintained that the field distribution in such a trap can be closely reproduced by substituting an outer return spiral for the superconducting sphere and traps of this technically simpler type have been constructed. In this note we discuss the results of numerical calculations of the trajectories of magnetic field lines in such a two-spiral trap. We find that there are always some field lines originating near the centre of the system which leave it after one or two transits across the machine. Other lines are contained but trace out surfaces which are not topologically toroidal. Thus traps of the two-spiral type will not contain plasma effectively.

Magnetic energy and electron inertia in a superconducting sphere

The hypothesis that the magnetic energy of a current circuit is the kinetic energy of the effective conduction electrons, developed in a previous Monograph,1 is applied to the case of a conducting sphere without resistivity in a uniform magnetic field. A surface current is induced which prevents the growth of a magnetic field within the sphere, and expressions are found for the number and velocity of effective conduction electrons which carry the current. It is found that these electrons are in stable radial equilibrium, moving in circular orbits under the action of magnetic forces.The well-known Meissner effect in pure superconductors is shown to be an expected rather than an unexpected phenomenon, since its absence would require, under certain conditions, a supercurrent lacking equilibrium.The theory is shown to lead, by means of a simple assumption, to the basic equations of the London theory of superconductivity, but with a different interpretation of the velocity parameter. Finally, the inertial supercurrent and magnetic field which should be produced by the steady rotation of a superconducting sphere, as deduced by the new theory, are shown to be exactly the same as those forecast by the London theory.

Permanent Magnetic Moments of a Superconducting Sphere

The magnetic flux retained by a polycrystalline sphere of pure tin has been studied by two experimental methods. It is shown that the amount of flux retained by the superconducting sphere exhibits a reproducible dependence on the temperature at which the transition is allowed to occur. The specimen shows a 99.9% Meissner effect for transitions well below the critical temperature, but near to ${T}_{c}$ the percent of residual flux increases several hundred-fold. The residual flux is constant as long as the temperature of the specimen is constant, but the flux is not necessarily conserved when the temperature is perturbed.

Adiabatic Magnetization of a Superconducting Sphere

Measurements are reported of the temperature changes accompanying suppression of the superconductivity of a lead sphere by adiabatic magnetization. Observations were made in the temperature range 2.1\ifmmode^\circ\else\textdegree\fi{}K to 4.3\ifmmode^\circ\else\textdegree\fi{}K for magnetizations into the complete range of the intermediate state. The magnetic fields were applied as step functions of time, and allowance was made for the resulting eddy-current heating. After magnetization, practically complete temperature equilibrium was established in the order of 15 seconds. Temperature changes observed on magnetization were in quantitative agreement with values predicted from calorimetric data and demonstrate a linear relationship between the applied magnetic field and the fraction of normal metal produced in the intermediate state.

Magnetic Moments and Eddy Current Damping in Spherical Superconductors

Magnetic Moments and Eddy Current Damping in Spherical Superconductors

Superconductors in Alternating Magnetic Fields

A method of studying magnetic properties in alternating fields and its application to the intermediate state of a superconducting sphere are described. It is shown that the behaviour of the sphere in alternating fields of frequencies between 10 and 100 is different from that in very slowly varying fields, the difference becoming less for lower frequencies and for smaller radius. When the specimen is in the intermediate state, energy losses are produced in it by the alternating field, showing that the induced currents are out of phase with the alternating field. The induced currents do not, however, flow in the same way as in a homogeneous isotropic conductor, and this is probably on account of an anisotropic structure of the specimen when in the intermediate state. This structure depends strongly on the amplitude of the alternating field in such a way that the effective average conductivity is increased with decreasing amplitude, and this amplitude effect depends on the size of the specimen. Evidence is given for a time lag in the magnetocaloric effect, and this time lag decreases with decrease of the size of the specimen, being of order sec. for a sphere of about 1 cm. diameter.In conclusion I wish to thank Prof. Lord Rutherford and Dr Cockcroft for their interest in this work; Dr Peierls for suggesting the experiment and for much valuable advice and assistance; Mr Shire for advice on some technical points; and various members of the staff of the Royal Society Mond Laboratory for help in the measurements.

On the gradual penetration of a magnetic field into a superconductive tin sphere

5 1. Introdzlction. In the experiments of W. J. d e H a a s and 0. A. G u i n a u 1) 8) on the penetration of a magnetic field into a superconducting sphere there were two points that needed further investigation. a) When in a constant magnetic field a superconducting sphere was heated, so as to pass to the non-superconductive state, it was observed that, especially in the beginning of the transition region, a considerable time was required, before the final state of the induction at the temperature in question .was reached. Now the question presented itself whether the phenomenon was due only to the fact, that temperature equilibrium set in very slowly, or whether it was a property of the intermediate state of the superconducting body, which seemed more probable, the effect having also been observed by other investigators 8). In this case it should also be observed at constant temperature, when the external field was increased. b) As is well known from the measurements of d e H a a s and G u i n a u a), the induction of the sphere in the intermediate state can be represented by the formula B = 3H,, 2H,, which has been discussed by L o n d o n 4) and P e i e r 1 s 6), and one should expect the induction in the sphere to be homogeneous from the beginning of the penetration at II, = 213 Hk. In a longitudinal canal, however, the fieldstrength remained zero, after the field at the equator had reached the value Hk and had begun to penetrate into the sphere. In experiments of d e H a a s and Mrs. C a s i m i r-J o n k e r 6) on a transverse tin-cylinder the same phenomenon had been observed. So it seemed necessary to investigate whether this was due to the shape of the hole (a long