We describe the design of a system that automatically measures losses in superconductors as a function of frequency. The method follows a suggestion by Gömöry who notes that, for a symmetric hysteresis loop, one can trace out the loop by measuring the output voltage of a phase-sensitive detector as a function of the phase angle between the applied field and the detector setting. We have measured the losses at 77 °K in aligned YBCO for frequencies from 10 Hz to 40 kHz with amplitudes of applied field up to 100 Oe. The usual method of measuring the in-phase component of dB/dt to determine the losses was also employed and we found that the two methods gave, within experimental error, identical results over the frequency range we have covered.

pe have measured the losses at 77K in aligned YBCO for frepuencies from 10 Hp to 20 kHz with amplitudes of applied field up to 100 Oe. The losses have been measured in two paps. First, the usual method of measuring the in-phase component of dB/dt pas employed using the expression below In this formula, pv is the loss per cpcle per unit volume while H = H0 cos ωt and B are the applied field and resulting flux density, respectively. T is the period of the applied field. The components of dB/dt are measured with a phase sensitive detector (PSD). The second technipue follows a suggestion by Gömörp. He notes that, for a spmmetric hpsteresis loop, one can trace out the loop by measuring the output voltage of a PSD as a function of the phase angle betpeen the applied field and the detector setting. From numerical integration of the first epuation above, pe can measure the loss per cpcle independently. We find that the two methods give, within experimental error, identical results over the Frequency range pe have covered. The loss per cpcle is roughlp independent of Frequency and, at low applied fields, varies as the cube of the amplitude of the field. This is characteristic of the critical state model. Looked at more closelp, however, the loss is seen to decrease at low (<100 Hp) and high frepuencies ( > 10 kHp). The first effect is consistent with thermallp assisted flux flow (TAFF) coupled with the predictions of an extended critical state model while the second is in accord with this model that includes the viscous inhibition to flux flow.

The rotational hysteresis loss in hard type II superconductors is calculated using the critical state model. For materials that can be characterized by a magnetic field-independent critical current density Jc the surface rotational loss is W(rot)s=[5/4π(6)]1/2(H03/Jc) erg/cm2−cycle.In this expression H0 is the amplitude in gauss of a rotating field applied parallel to the surface of a semi-infinite slab while Jc is measured in amperes per square centimeter. This loss is 3.84 times the equivalent loss for alternating fields. In addition, it is shown that by measurement of the hysteresis loss or hysteresis torque as a function of field, one may calculate the field dependence of the critical current.

As discovered by Price and Walker, small uniform pores may be created in muscovite by etching in HF thin samples that have been subjected to fission particle irradiation. The process of pore growth is followed by monitoring the conductance across a thin sample as the etching proceeds. For irradiation with 252Cf the tracks quickly etch to a radius of 33 Å-the region of primary damage. Further radial etching in the undamaged material is slow but increases to a fixed rate as the radius increases. This radius dependence of etching is interpreted by a kinetic analog of the Kelvin equation for vapor pressure over curved surfaces. With suitable assumptions on the mechanism of attack, the surface energy of the muscovite-solution interface is calculated to be about 300 ergs/cm2.

The resistive (Coulter) method of counting and sizing particles in a conducting fluid has been extended to polystyrene spheres 900 Å in diameter, with a present detection limit near 600 Å, through the use of individual submicron pores etched in irradiated plastic sheet. The use of a nonionic surfactant and ultrasonic cleaning effectively relieves the problem of plugging. The particles may be driven through the pore by the electric field, without the use of pressure, to yield the vector sum of the electrophoretic and electro-osmotic velocities. A new theory, yielding an upper limit to the resistive pulse on passage of a sphere, agrees well with data for spheres with diameters d<0.4D, where D is the pore diameter, and complements a previous theory that gives a lower limit, valid for d>0.9D. We estimate that a detection limit near 250 Å will be attainable with the further development of current techniques.

The isothermal critical-state model of hard superconductors is extended to include the effects of heating when the applied field is changed suddenly and magnetic flux enters adiabatically into the bulk. We consider the following specific situation. A semi-infinite slab of superconductor is cooled in a magnetic field lying in its surface plane. Next, the external field is raised isothermally by an amount Hs. This excess field decreases linearly to a depth δ= 10Hs/4πJc from the surface. Finally, the field is raised by an infinitesimal amount ΔH in a time short compared to the thermal diffusion time and long compared to the electromagnetic diffusion time. Each element of volume exposed to the changing field receives a thermal impulse proportional to the local-flux-change times Jc. This thermal impulse, in turn, lowers the critical current and allows more flux to penetrate. We find that if Hs exceeds some critical value Hfj, then the isothermal critical state is not the only allowed state of the superconductor. This instability field is given in terms of the critical current density Jc, derivative of the critical current density with temperature, ∂Jc/∂T, and the volume specific heat C by the formula Hfj= [−π3CJc/(∂Jc/∂T)]1/2. The application of the incremental field ΔH can initiate an avalanching process, or a flux jump, that terminates in an adiabatic critical state. Immediately following the flux jump the internal field, the induced supercurrent, and the temperature rise at each position are associated in a self-consistent way with the avalanche of flux that has entered the superconductor. In this framework a flux jump is viewed as a switching from the isothermal critical state to an adiabatic critical state. The magnitude of the jump is related to Js and is calculated.

The superconducting critical temperatures and current carrying capacities of Nb3Al and V3Si doped with small amounts of uranium and boron and subsequently irradiated with thermal neutrons are reported. While the critical temperatures are substantially unaffected, the critical current densities are dramatically increased by the internal fission of uranium in both materials. Samples of Nb3Al containing 0.321 at.% uranium and V3Si containing 0.19 at.% uranium irradiated with 1.7×1018 neutrons/cm2 give superconducting critical current densities over 106 A/cm2 at 30 kOe. The boron-doped samples, however, showed no effects arising from fission of boron. Two new experimental techniques have been used in this investigation. First, uranium and boron analyses as well as information on homogeneity were determined by use of the Price-Walker nuclear track detectors. Secondly, the critical current measurements were made on 50-mg samples of 70-μ powders by a technique that measures the generation of odd-harmonic voltages caused by small alternating magnetic fields applied to the sample.

This report deals with fundamental studies of superconductive properties that are important for their use in electrical equipment. Measurements of critical current density of intermetallic superconductors that have been doped with uranium and boron to induce fission reveal current densities associated with the radiation induced damage that are higher by nearly an order of magnitude than any yet reported. A calculation is presented of the torques and losses encountered when a high field superconductor is subjected to rotating magnetic fields; experiments (preliminary results reported) are presently underway to test this model. A phenomenological model that yields criteria for magnetic instability or flux jumping is presented; this model offers promise for further understanding in this area. A new experimental approach, utilizing the spinoidal decomposition that occurs in certain binary alloys, is described that may yield some further understanding of the interaction between flux threads and pinning sites. The earlier studies of surface losses in niobium have been further extended and refined.

Homogeneous superconductors have reversible magnetic properties. We distinguish two types of superconductors, type I and type II. The type I superconductor (most pure superconducting elements are of this type) has a particularly simple magnetic behavior.1 In a macroscopic specimen, the flux density is zero for fields less than the critical field, Hc, that marks the limit of the superconducting state. Above this field the specimen has all the properties of a normal metal including the property that the flux density is essentially equal to the applied field. So, in summary, the type I superconductor is either completely superconducting or completely normal. (This statement is strictly true only for a long thin specimen in a field that is parallel to the axis of the specimen. In other geometries one finds a gross mixture of superconducting and normal regions called the intermediate state that is created by the field concentrations associated with specimen shape.) In recent years it has been appreciated that there is another class of superconductor—usually an alloy or compound—in which the flux in a bulk specimen is completely excluded for fields less than Hc1, but above this field flux penetration is partial and increases with applied field until flux penetration is complete at an upper critical field, Hc2. Since this field is generally larger than the equivalent Hc of type I superconductor, these type II superconductors are known as high-field superconductors. The region between Hc1 and Hc2 is known as the mixed state which is not to be confused with the shape-dependent intermediate state mentioned earlier. The present conception of the mixed state2 pictures the flux as entering in the form of quantized current vortices. The total flux contained in each vortex is 2×10−7 G-cm2. In equilibrium these vortices repel one another to form a lattice that compresses as the field is increased from Hc1 to Hc2 and finally all flux variation smoothly disappears at Hc2. Experimental magnetization curves on homogeneous alloys show good agreement with this theory.3 If the type II is inhomogeneous, there may be impediments to the motion of these flux lines. In this event there will be a gradient of flux as the flux is driven into the specimen.4 This gradient of flux lines is equivalent to a macroscopic current density by Ampere's law, curl H=4πJ/10.4 This behavior allows one to calculate the magnetic behavior of these superconductors in terms of only one parameter, the critical current density, Jc(H)5—the same critical current density that is measured in current transport measurements. The magnetic behavior includes size-dependent magnetization and a hysteresis loop that is the precise diamagnetic equivalent of the Rayleigh hysteresis loop for ferromagnets.

The interaction between a flux thread (quantized, fluxenclosing, supercurrent vortex) and the specimen surfuce of a semi-infinite type-II superconductor with a flux thread within it lying parallel to the single plane surface is considered to determine any low-field hysteresis in the magnetization curves of well-annealed, single-phase specimens. (R.E.U.)

The recent burst of effort in the area of high-field superconductors has led to the construction of 70,000-oersted coils and the expectation that 100,000-oersted fields will be attained in the near future. The general theory suggests that fields above 300,000 oersteds are conceivable and that current densities of millions of amperes per square centimeter may be attained. Theory and experiment suggest that the upper critical field of materials such as Nb(3)Sn and Nb(.75)Zr(.25) is determined by their tendency to form a mixed state, and that a crucial question concerning their other properties is that of the interaction of this mixed state with imperfections. Lastly, it is possible to make a synthetic high-field superconductor by mechanically subdividing an ideal superconductor.

The preparation and superconducting properties of Vycor glass cylinders containing filaments of superconducting Hg are described. The Hg, in the normal state, is forced at 3300 atm into the glass, which has a porosity of 35%. The magnetizations and critical current densities of several samples are measured as functions of magnetic fields and preparation parameters. These synthetic systems are found to have superconducting properties similar to those of hard superconductors. (T.F.H.)