TL;DR: In this paper, the authors considered the effects of lattice rigidity on the summation of pinning forces and showed that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument.
Abstract: This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical...
TL;DR: In this article, the average force of a single-particle pinning can be inferred from a simple summing procedure and has a domelike dependence on magnetic field, which can be used to define the boundaries between the regions of collective and single particle pinning, where the possible break-off of the flux line lattice from the lines of magnetic force is taken into consideration.
Abstract: Large and randomly arranged pinning centers cause a strong deformation of a flux line lattice, so that each pinning center acts on the lattice with a maximum force. The average force for such single-particle pinning can be inferred from a simple summing procedure and has a domelike dependence on magnetic field. Pinning centers of average force, such as clusters of dislocations, strongly deform the flux line lattice only in weak fields and in fields close to the critical field, where there is a peak in the dependence of the critical current on magnetic field. In the range of intermediate fields there is a weak collective pinning. A large concentration of weak centers leads to collective pinning in all fields. In this case, near the critical field a critical current peak should be observed. To explain this peak and to define the boundaries between the regions of collective and single-particle pinning the possible break-off of the flux line lattice from the lines of magnetic force should be taken into consideration, which leads to extra softening of the lattice.
TL;DR: A microstructure is realized which leads to very strong high-temperature flux pinning in YBa and Cu crystals, and causes a considerable enlargement of the irreversibility region in the H-T plane.
Abstract: We report the realization of a microstructure which leads to very strong high-temperature flux pinning in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ crystals. Aligned discontinuous columns of damaged material, about 50 \AA{} in diameter and more than 15 \ensuremath{\mu}m long, are produced by 580-MeV Sn-ion irradiation. The enhancement of flux pinning is largest when the applied magnetic field is aligned with these tracks. At high temperatures and fields the pinning is much greater than that produced by random point defects, and causes a considerable enlargement of the irreversibility region in the H-T plane.
TL;DR: In this paper, it was shown that the peak in Fp scales as [Hc2(T)]2.5 if the temperature is changed; the maximum value of Fp occurred at the same value of reduced field regardless of temperature.
Abstract: For all hard high‐field superconductors examined to date, there is a maximum in the pinning force density Fp as a function of the reduced magnetic field h. Fietz and Webb first demonstrated in dilute Nb alloys that the peak in Fp scales as [Hc2(T)]2.5 if the temperature is changed; the maximum value of Fp occurred at the same value of reduced field regardless of temperature. Recent data on the temperature dependence of pinning in Nb3Sn, Nb–25% Zr and a Nb–Ti alloy, which exhibits the ``peak effect'', are analyzed to show that similar scaling laws are obeyed by these materials. All presently available evidence indicates however that the reduced field hp at which the maximum Fp occurs, as well as the height and shape of this maximum, can be altered by metallurgical treatment. Apparently weak pinning defects, or widely spaced ones, produce a small peak in Fp(h) at high h whereas strong closely spaced pins produce a large peak in Fp(h) at low h without producing much change in Fp(h) at high h. A model which p...
TL;DR: In this article, expressions for flux-pinning in type II superconductors are derived from considerations of the nature of the interaction between individual flux-lines and pinning-centres, and of the geometry of th...
Abstract: Expressions for flux-pinning in type II superconductors are derived from considerations of the nature of the interaction between individual flux-lines and pinning-centres, and of the geometry of th...