Mathematical modeling of the magnetic properties of axisymmetric hard superconductors of the second kind in the Kim model

Abstract

Authors perform mathematical modeling of magnetic properties, such as current distribution, intrinsic magnetic field and magnetization of a number of axisymmetric superconductors of the second kind, for example, of a sphere with the dependence of the critical current density on the local magnetic field in the Kim model. The simulation is based on equation that is integral with respect to coordinate and differential with respect to time. The equation describes time evolution of the critical current density and is solved numerically for a uniformly varying external magnetic field. The shape of the sample is set using a distorted rectangular irregular mesh with compaction to the edges of the sample. While solving the equation of current motion, the total magnetic field iscalculated at the points of the superconductor to calculate the value of the critical current density. In the article, the obtained solutions are used to visualize the current distribution in the volume of a superconductor and to construct magnetization hysteresis loops. Also, thanks to the calculations of the magnetic field in the center of the sample, the dependencies of the total penetration field for samples with different aspect ratios are obtained.

Simulation of the features of the magnetic properties of axisummetric granules of hard type II superconductors

“…, N z N r . Let us introduce new variables u and v, which were used earlier in [5], different from the variables in [2,3]:…”

“…The solution of equation (3) can be obtained using the Green's function in the cylindrical coordinate system [3,5,9]:…”

“…The numerical calculations performed in this work are based on the works [2,3], in which the magnetic properties of plates, disks, and short cylinders were determined within the Bin and Kim models using the integral equation of the second kind. For ellipsoids of rotation and cylinders, similar calculations are made in works [4,5]. It should be noted that there are other approaches currently used to describe the magnetic properties of finite-size superconductors, based on the stationary [6,7] and non-stationary [8] Ginzburg-Landau N.D. Kuzmichev, A.A. Shushpanov, M.A.…”