Magnetic and temperature dependencies of magnetization harmonics of a thin superconducting disk in the model of critical state with critical current density, inversely proportional to field stength squared

Background. Research of the magnetic properties of critical state of the hard superconductors of the II type, in particular high-temperature superconductors (HTSC) is important because of their practical application in electro- and radio measuring equipment. For this purpose it is necessary to know a response of various structures and HTSC geometrical forms to ac and dc magnetic fields. The purpose of this work is mathematical modeling of magnetization harmonics of a hard superconductor of the II type in the form of a thin disk in apprroximation of field shielding in the sample center within the model of critical state with dependence of critical density of current on intensity of the magnetic field of $J_c \sim \gamma / H^2$ type. The specified dependence was used to describe the critical state of superconductors at the large density of Abrikosov vortex and to describe the magnetic properties of ceramic HTSC. Materials and methods. The initial curve and branches of the hysteresis loop of magnetization of critical state of a thin superconducting disk were calculated analytically. Calculations of the magnetic field and temperature dependencies of the first and the highest harmonics of magnetization were carried out numerically in MathCad system. Results. The authors calculated the hysteresis curves of magnetization and a number of dependencies of the real and imaginary parts of the first and the highest harmonics of magnetization from sizes taking into account intensity of ac and dc magnetic field, and temperature. It is discovered that the dependencies of amplitudes of harmonics of magnetization are influenced strongly by the amplitude of the ac magnetic field, qualitatively changing the specified dependencies of the dc field for small and large amplitudes of the ac field. The results of this work are compared to the experimental data obtained for polycrystalline high-temperature superconductors from another work. Conclusions. The received curves of the first and third harmonics of magnetization qualitatively coincide with experimental data of the work by one of the authors of the present work, in which the author researched the response signal harmonics proportional to harmonics of magnetization of polycrystalline disks in weak magnetic fields and estimated a $\gamma$ model parameters.