The minimization of the Ginzburg-Landau (GL) free energy with respect to two independent variables, the vector potential and complex order parameter leads to two independent equations, the GL equations. The equation given by the variation of the vector potential yields an equation similar to the London equation, whereas variation of the order parameter yields anequation describing the spatial dependence of the order parameter, which indicates that the number of superelectrons is not constant but depends on position, which is a feature not included in the London theory. The two GL equations yield two characteristic lengths, the penetration depth of the magnetic field similar in form to the London penetration depth and temperature-dependent GL coherence length, which characterizes the spatial variation of the order parameter.
The heat transfer of superfluid helium (He II) in a rectangular channel has been investigated both experimentally and numerically. The channel end is kept open to a He II bath under an atmospheric pressure condition. A one-dimensional heat transfer model, which can predict the temperature rise at the end of the He II channel and λ-transition heat flux, is proposed in the present study. This model is developed on the basis of heat conduction by taking into account heat transfer not only in the channel but also in the He II bath. The supply of heat to the channel results in a temperature rise at the channel end. Larger temperature rise at the channel end leads to a smaller value of λ-transition heat flux in the channel. In the case of λ-transition heat flux being supplied to the channel, an increase in aspect ratio, which is defined as the ratio of the gap to the length of the channel, results in an increase in the value of temperature rise at the channel end. A satisfactory agreement between the measured data and the results of calculation on the basis of the present model is observed for the range of aspect ratio tested in this study.
The critical current density (Jc) of NbTi/Nb/Cu superconducting sheet is determined by two types of Ti precipitate in NbTi layers. One type is approximately 160nm in thickness and 240nm in length, and is precipitated in the grain boundaries. The other is a few nanometers in thickness and 20 to 30nm in length, and is precipitated in crystal grains. But contribution to the Jc value due to the larger precipitate is relatively small, and consequently the Jc value is as small as one-third of that of commercial NbTi multifilamentary wires. In this study, the sheet was rolled by a reduction of 50% or more after the final aging treatment, and the large precipitates were elongated to a favorable size for pinning sites. Consequently the Jc value in the transverse direction at 5T is remarkably improved to twice that of the conventionally aged specimen. On the other hand, the increased value of the Jc in the longitudinal direction is small in comparison to that in the transverse specimen. This is because there are many deformed sections in the NbTi layers of the longitudinal specimen. The NbTi layers of the transverse specimen have fewer deformed sections than those of the longitudinal specimen. The mechanical elongation of the specimen rolled after aging treatment is decreased to less than 2%, but it is recovered by short heat treatment. The Jc value of the transverse specimen decreases by 5 to 15%, while that of the longitudinal specimen increases by 2 to 12% by applying recovery heat treatment. Since the tensile stress remaining between the Nb layers and Cu layers in the longitudinal direction due to the rolling is relieved by recovery heat treatment, the Jc value of the longitudinal specimen is increased.