Field limit and nano-scale surface topography of superconducting radio-frequency cavity made of extreme type II superconductor

The field limit of superconducting radio-frequency cavity made of type II superconductor with a large Ginzburg-Landau parameter is studied with taking effects of nano-scale surface topography into account. If the surface is ideally flat, the field limit is imposed by the superheating field. On the surface of cavity, however, nano-defects almost continuously distribute and suppress the superheating field everywhere. The field limit is imposed by an effective superheating field given by the product of the superheating field for ideal flat surface and a suppression factor that contains effects of nano-defects. A nano-defect is modeled by a triangular groove with a depth smaller than the penetration depth. An analytical formula for the suppression factor of bulk and multilayer superconductors are derived in the framework of the London theory. As an immediate application, the suppression factor of the dirty Nb processed by the electropolishing is evaluated by using results of surface topographic study. The estimated field limit is consistent with the present record field of nitrogen-doped Nb cavities. Suppression factors of surfaces of other bulk and multilayer superconductors, and those after various surface processing technologies can also be evaluated by using the formula.Comment: 17 pages, 6 figure

Flux trapping in superconducting accelerating cavities during cooling down with a spatial temperature gradient

During the cool-down of a superconducting accelerating cavity, a magnetic flux is trapped as quantized vortices, which yield additional dissipation and contribute to the residual resistance. Recently, cooling down with a large spatial temperature gradient attracts much attention for successful reductions of trapped vortices. The purpose of the present paper is to propose a model to explain the observed efficient flux expulsions and the role of spatial temperature gradient during the cool-down of cavity. In the vicinity of a region with a temperature close to the critical temperature Tc,the critical fields are strongly suppressed and can be smaller than the ambient magnetic field. A region with a lower critical field smaller than the ambient field is in the vortex state. As a material is cooled down, a region with a temperature close Tc associating the vortex state domain sweeps and passes through the material. In this process, vortices contained in the vortex state domain are trapped by pinning centers that randomly distribute in the material. A number of trapped vortices can be naively estimated by using the analogy with the beam-target collision event. Based on this result, the residual resistance is evaluated. We find that a number of trapped vortices and the residual resistance are proportional to the strength of the ambient magnetic field and the inverse of the temperature gradient. The obtained residual resistance agrees well with experimental results. A material property dependence of a number of trapped vortices is also discussed.Comment: 14 pages, 5 figure

Models of the magnetic field enhancement at pits

Models of the magnetic field enhancement at pits are discussed. In order to build a model of pit, parameters that characterize a geometry of edges of pit, such as a curvature radius and a slope angle of edge, should be included, because the magnetic field is enhanced at an edge of a pit. A shape of the bottom of the pit is not important, because the magnetic field attenuates at the bottom. The simplest model of the pit is given by the two-dimensional pit with a triangular section. The well-like pit, which is known to many researchers, is a special case of this model. In this paper, idea and methods to analytically evaluate the magnetic field enhancement factor of such models are mentioned in detail. The well-like pit is considered as an instructive exercise, where the famous results by Shemelin and Padamsee are reproduced analytically. The triangular pit model, which is practically important for studies of the quench of SRF cavity, are discussed in detail. Comparisons between the prediction of the triangular-pit model and the vertical test results are also shown.Comment: 5 pages, 9 figures, the 16th International Conference on RF Superconductivity (SRF 2013), Paris, France, 22-27 September, 201

Superconducting nano-layer coating without insulator

The superconducting nano-layer coating without insulator layer is studied. The magnetic-field distribution and the forces acting on a vortex are derived. Using the derived forces, the vortex-penetration field and the lower critical magnetic field can be discussed. The vortex-penetration field is identical with the multilayer coating, but the lower critical magnetic field is not. Forces acting on a vortex from the boundary of two superconductors play an important role in evaluations of the free energy.Comment: 4 pages, 4 figures, the 27th Linear Accelerator Conference, LINAC14, Geneva, Switzerland, 31 August - 5 September, 201

The Next SRF Technologies

In this talk, I introduce the proposed next superconducting radio-frequency (SRF) technologies that will make it possible to achieve much higher accelerating electric field than the present SRF technologies. Audiences are assumed to be non-experts. We start from a brief review of basics of SRF, history of the high gradient technologies and the layered structure behind it. The multiple benefit of the layered structure is introduced. We then move to the next SRF technologies: superconductor-superconductor (SS) structure and superconductor-insulator-superconductor (SIS) structure. We discuss the SS structure in detail. Experimental results are also introduced and compared with theoretical considerations.Comment: Talk presented at the International Workshop on Future Linear Colliders (LCWS2016), Morioka, Japan, 5-9 December 2016. C16-12-05.

Vortex-penetration field at a groove with a depth smaller than the penetration depth

Analytical formula to evaluate the vortex-penetration field at a groove with a depth smaller than penetration depth is derived, which can be applied to surfaces of cavities or test pieces made from extreme type II superconductors such as nitrogen-doped Nb or alternative materials like Nb3Sn or NbN.Comment: 3 pages, 1 figure, the 27th Linear Accelerator Conference, LINAC14, Geneva, Switzerland, 31 August - 5 September, 201

Multilayer coating for higher accelerating fields in superconducting radio-frequency cavities: a review of theoretical aspects

Theory of the superconductor-insulator-superconductor (S-I-S) multilayer structure in superconducting accelerating cavity application is reviewed. The theoretical field limit, optimum layer thicknesses and material combination, and surface resistance are discussed. Those for the S-S bilayer structure are also reviewed.Comment: 38 pages, 21 figure

Review of the multilayer coating model

The recent theoretical study on the multilayer-coating model published in Applied Physics Letters [1] is reviewed. Magnetic-field attenuation behavior in a multilayer coating model is different from a semi-infinite superconductor and a superconducting thin film. This difference causes that of the vortex-penetration field at which the Bean-Livingston surface barrier disappears. A material with smaller penetration depth, such as a pure Nb, is preferable as the substrate for pushing up the vortex-penetration field of the superconductor layer. The field limit of the whole structure of the multilayer coating model is limited not only by the vortex-penetration field of the superconductor layer, but also by that of the substrate. Appropriate thicknesses of superconductor and insulator layers can be extracted from contour plots of the field limit of the multilayer coating model given in Ref.[1].Comment: 3 pages, 3 figures, the 5th International Particle Accelerator Conference (IPAC14), Dresden, Germany, 15-20 June, 201

Radio-frequency electromagnetic field and vortex penetration in multilayered superconductors

A multilayered structure with a single superconductor layer and a single insulator layer formed on a bulk superconductor is studied. General formulae for the vortex-penetration field of the superconductor layer and the magnetic field on the bulk superconductor, which is shielded by the superconductor and insulator layers, are derived with a rigorous calculation of the magnetic field attenuation in the multilayered structure. The achievable peak surface field depends on the thickness and its material of the superconductor layer, the thickness of the insulator layer and material of the bulk superconductor. The calculation shows a good agreement with an experimental result. A combination of the thicknesses of superconductor and insulator layers to enhance the field limit can be given by the formulae for any given materials.Comment: 4 pages, 4 figures; figure and table are added, discussions extended, references added, to appear in Applied Physics Letter

RF field-attenuation formulae for the multilayer coating model

Formulae that describe the RF electromagnetic field attenuation for the multilayer coating model with a single superconductor layer and a single insulator layer deposited on a bulk superconductor are derived from a rigorous calculation with the Maxwell equations and the London equation.Comment: 3 pages, the 4th International Particle Accelerator Conference (IPAC13), Shanghai, China, 12-17 May, 201