F. Irie

Theory of Flux Motion in Non-Ideal Type-II Superconductors

A phenomenological expression of the pinning force density is proposed, and the equation of force balance including this expression is shown to describe well the motion of magnetic fluxoids in non-ideal type-II super-conductors in cooperation with the equation describing the continuity of magnetic flux flow. The parameters related to an individual pinning force and pin distribution are included in the present expression which contains those from the models of Bean-London, Silcox-Rollins and Yasukōchi as its special cases. The calculated magnetizations agree well with observed data by adjusting the parameters. The hysteresis losses in the course of magnetization are calculated and the field dependence of the a.c. losses are explained. The formulas of the a.c. dynamic losses are also shown. The field dependence of the critical current in the resistive state and the relaxation time of flux penetration are calculated and compared with observed data.

Flux-flow type Josephson oscillator for millimeter and submillimeter wave region

An oscillator which utilizes the effect of the vortex motion in long Josephson tunnel junctions, i.e., flux flow, has been presented in millimeter and submillimeter wave region. An electromagnetic wave generated by the oscillator is detected with a small tunnel junction as a detector with a refined coupling configuration. Quantitative evaluation of the detected power showed that the detected power attained the value of 10−6 W in the frequency range between 100 and 400 GHz, which is far superior to previous results. Frequency and magnetic field dependences of the present system were also measured, which showed that the output power was able to be controlled by the dc magnetic field. The present oscillator will be promising as the local oscillator in the integrated Josephson receiver systems.

Flux‐flow‐type Josephson oscillator for millimeter and submillimeter wave region. II. Modeling

A theoretical study is made of a travelling‐wave‐type oscillator, which utilizes a flux flow in a long Josephson junction for use as a local oscillator in the integrated superconducting receiver system. An internal electromagnetic field of the oscillator junction in the flux‐flow state is investigated both numerically and analytically. It is shown that the voltage amplitude of the internal oscillation increases gradually in the direction of the flux flow and reaches a maximum value at the junction end. An equivalent circuit of the oscillator is also obtained, which gives dependences of the emitted radiation on frequency, magnetic field, and load. It is shown that the output power attains the value of the order of 10−6 W in the frequency range between 100 and 500 GHz, and that the output power and the radiation frequency can be controlled by both the bias voltage and the applied magnetic field. These theoretical results explain quantitatively the experimental ones with a Pb‐alloy long junction of length 24 λJ.

Flux-flow-type Josephson oscillator for millimeter and submillimeter wave region. III. Oscillation stability

Numerical as well as experimental studies have been made of the oscillation stability for the travelling‐wave‐type oscillator, which utilizes a vortex motion in a long Josephson junction, i.e., a flux flow. For the Josephson oscillator, a steep current step in a dc I‐V characteristic improves the oscillation stability. Two kinds of effects which degrade the steepness of the current step have been investigated for the long junction of the overlap geometry. One is the self‐field effect which makes the current step inclined, and the other is the resonant motion of the vortices which induces a staircaselike structure on the current step. We have discussed the method for the reduction of these effects and proposed a novel junction geometry without these effects, i.e., an overlap junction with a projection on one junction side. With the new geometry, we have obtained current steps whose slope is about one hundred times steeper than those obtained with the conventional overlap geometry and whose height attains a...

Effect of damping resistance on voltage versus flux relation of a dc SQUID with large inductance and critical current

The effect of a damping resistance on the relation between a voltage V and a magnetic flux Φ of a dc SQUID is studied theoretically for the case with a large SQUID parameter βL=2LI0/Φ0 , where L is a loop inductance, I0 is a critical current, and Φ0 is the flux quantum. An approximate analytical expression for the V‐Φ relation is obtained by replacing the Josephson junctions with ac current generators. It is shown that the V‐Φ relation becomes almost independent of the value of βL in the case of large damping. As a result, the conversion efficiency dV/dΦ is not degraded even for large βL , as is not the case with a conventional SQUID without the damping resistance. This result indicates the possibility to use the SQUID with large βL for the improvement of the coupling between the SQUID and the input coil without the degradation of the conversion efficiency. Effect of the capacitance is also studied. It is shown that the effect of the capacitance becomes remarkable for the case of βc≳0.4 , where βc is the ...

Fluxoid Pinning in Nonideal Type-II Superconductors. I. Force between a Fluxoid and a Lattice Defect

A general expression of the interaction energy between fluxoids and lattice defects is obtained by perturbational calculations of the generalized Ginzburg-Landau equations, which are derived by minimizing the free energy of the mixed state including elastic terms. The present expression is the same as Labuschs obtained only for a special type of lattice defects with a pure shear, but is shown to be applicable to any type of defects. The interaction force between a fluxoid and a lattice defect is derived for some typical types of defects by the use of the present expression of interaction energy, and the results of previous authors are shown to be unsatisfactory, even qualitatively. The present results give the first step for the derivation of a general expression of the so-called “pinning force”, which is the final purpose of this series.

Noise characteristics of a dc SQUID with a resistively shunted inductance

Noise characteristics of a dc SQUID with an inductance shunted by a damping resistance are studied numerically. It is shown that the damping resistance improves considerably the resolution of the SQUID in the case of large β, where β=2LI0/Φ0, I0 is a critical current, L is a loop inductance and Φ0 is the flux quantum. The energy resolutions for β=4 and β=10 are only about 2 and 4 times larger than that for β=1, respectively. Furthermore, the ranges of both the bias current and the external flux, where good resolution is obtained, become very wide compared with the conventional SQUID. Therefore, the SQUID with the damping resistance can be used for large β (or L) without the significant degradation of the resolution, and will much improve the coupling properties between the SQUID and the input circuitry. The numerical simulation results are also compared with analytical ones, and a reasonable agreement is obtained.

On the Resistive State of Current-Carrying Rods of Type 2 Superconductors in Longitudinal Magnetic Fields

The resistive state of the current-carrying type 2 superconducting rod in a longitudinal magnetic field was studied for Pb-T l alloys. The herical structure composed of two kinds of domains was found from the measurement of the potential distribution on the sample surface. The larger domain was confirmed directly to be in a flux flow state and the other domain was estimated to be in a normal state by some theoretical considerations. The direction of the boundary between these domains was dependent only on the direction of magnetic field at the surface.

The effect of demagnetization on the eddy‐current loss in a single‐layered multifilamentary superconducting coil

The demagnetization effect of a single‐layered superconducting coil made of a cylindrical multifilamentary wire on its eddy‐current loss is studied for the case of ac magnetic fields parallel to the coil axis. An expression for an effective demagnetization coefficient of the wire is obtained by taking account of the interaction among turns of the coil. It is shown from this expression that the magnitude of the eddy‐current loss increases remarkably with the distance between neighboring turns of the coil. The experimental loss values of the wires wound into various kinds of coils are within 20% of the theoretical values.

Flux Jumps in Nonideal Type-2 Superconductors. I. Theory of Flux Jumps in Slabs

A theory of flux jumps in a slab of a nonideal type-2 superconductor is developed by the use of a phenomenological theory of flux motion. To include explicitly in the theory the various quantities which are controllable experimentally, the temperature inside the slab is assumed to be approximately uniform. Then a flux jump is characterized by a catastrophically sharp rise of the temperature of the sample. The criteria for the occurrence of flux jumps are derived under such an assumption, together with the relation between the value of external magnetic field, at which a flux jump starts, and the sweeping rate of the external magnetic field. Various behaviors of flux jumps observed experimentally are reasonably explained by the present theory in a quantitative way.