title: ÐÑÐ¾Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾ÑÐ¾ÐºÐ° Ð² Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ²ÑÐ·Ð½ÑÐµ ÑÐ²ÐµÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Penetration of magnetic flux into non-simply connected superconductors
Creators: name: ÐÐµÑÑÐµÐ½ÐµÐ², ÐÐ³Ð¾Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: ÑÐ²ÐµÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ¸ I Ð¸ II ÑÐ¾Ð´Ð°
ÑÐ²ÐµÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾ÑÑÑ
ÑÐ²ÐµÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´ÑÑÐµÐµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ðµ
ÑÐ¼ÐµÑÐ°Ð½Ð½Ð¾Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ðµ
Ð½Ð°Ð¼Ð°Ð³Ð½Ð¸ÑÐµÐ½Ð½Ð¾ÑÑÑ
Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÐµ Ð¿Ð¾Ð»Ñ
ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐ°
ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ¾Ðº
ÑÑÑÐµÐºÑÐ¾Ð¼ ÐÐµÐ¹ÑÑÐ½ÐµÑÐ°
Ð½Ð¸Ð·ÐºÐ¾ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐ½ÑÐµ ÑÐ²ÐµÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ¸
type-I and II superconductor
superconductivity
superconducting state
mixed state
magnetization
magnetic fields
critical temperature
critical current
Meissner effect
Low-Temperature Superconductivity

description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº ÑÐ²ÐµÑÑÐ¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ¾Ð² I Ð¸ II ÑÐ¾Ð´Ð°, Ð² Ð²Ð¸Ð´Ðµ ÑÐ¿Ð»Ð¾ÑÐ½ÑÑ Ð´Ð¸ÑÐºÐ¾Ð² Ð¸ Ð´Ð¸ÑÐºÐ¾Ð² Ñ Ð¾ÑÐ²ÐµÑÑÑÐ¸ÐµÐ¼. Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ðµ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÑ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐµÐ¹ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° M Ð¾Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð¸ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°. ÐÐ·Ð¼ÐµÑÐµÐ½Ð¸Ñ Ð±ÑÐ»Ð¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð²Ð¸Ð±ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¼Ð°Ð³Ð½Ð¸ÑÐ¾Ð¼ÐµÑÑÐ°. ÐÐ· Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐµÐ¹ Ð(Ð¢) Ð±ÑÐ»Ð° Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð° ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐ° Ð¸Ð½Ð´Ð¸Ñ 3.3Ð Ð¸ Ð½Ð¸Ð¾Ð±Ð¸Ñ 9Ð. ÐÐ° Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑÑ Ð(Ð) Ð´Ð»Ñ In Ð´Ð¸ÑÐºÐ° Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÑÑÑ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¿ÑÐ¾Ð¼ÐµÐ¶ÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¸ Ð½ÐµÐ¾Ð±ÑÑÐ½Ð°Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑ Ð(Ð) Ð¿ÑÐ¸ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸Ð¸ Ð¿Ð¾Ð»Ñ Ð² Ð²Ð¸Ð´Ðµ Ð¿Ð¾Ð»ÑÐºÑÑÐ³Ð°. ÐÐ±Ð»Ð¸Ð·Ð¸ Hc Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÑÑÑâÑÑÑÐµÐºÑ Ð¿ÐµÑÐµÐ¾ÑÐ»Ð°Ð¶Ð´ÐµÐ½Ð¸Ñâ Ð¸ Ð¾ÑÑÑÑÑÑÐ²Ð¸Ðµ Ð·Ð°ÑÐ²Ð°ÑÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° Ð¿ÑÐ¸ H=0. ÐÐ»Ñ In Ð´Ð¸ÑÐºÐ° Ñ Ð¾ÑÐ²ÐµÑÑÑÐ¸ÐµÐ¼ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð(Ð) Ð¾ÑÐµÐ½Ñ Ð±Ð»Ð¸Ð·ÐºÐ¸ Ðº ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ°Ð¼ Ð´Ð»Ñ ÑÐ¿Ð»Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð´Ð¸ÑÐºÐ°, Ð½Ð¾ ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ðµ Ð¾ÑÐ»Ð¸ÑÐ¸Ðµ ÑÐ¾ÑÑÐ¾Ð¸Ñ Ð² Ð±Ð¾Ð»ÑÑÐ¾Ð¼ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¸ Ð·Ð°ÑÐ²Ð°ÑÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð¿ÑÐ¸ Ð=0. ÐÐ»Ñ ÑÐ²ÐµÑÑÐ¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ° II ÑÐ¾Ð´Ð° Ð½Ð¸Ð¾Ð±Ð¸Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ M(H) Ð´Ð»Ñ ÑÐ¿Ð»Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð´Ð¸ÑÐºÐ° Ð¸ Ð´Ð¸ÑÐºÐ° Ñ Ð¾ÑÐ²ÐµÑÑÑÐ¸ÐµÐ¼ Ð¾ÑÐµÐ½Ñ Ð±Ð»Ð¸Ð·ÐºÐ¸. ÐÐ° Ð½Ð¸Ñ Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÑÑÑ Ð±Ð¾Ð»ÑÑÐ°Ñ Ð½ÐµÐ¾Ð±ÑÐ°ÑÐ¸Ð¼Ð¾ÑÑÑ Ð¸ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ðµ ÑÐºÐ°ÑÐºÐ¾Ð² Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾ÑÐ¾ÐºÐ° Ð¿ÑÐ¸ Ð¿Ð¾Ð½Ð¸Ð¶ÐµÐ½Ð¸Ð¸ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ. Ð¢Ð°ÐºÐ¾Ðµ ÑÐ¾Ð²Ð¿Ð°Ð´ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐºÐ°Ð·ÑÐ²Ð°ÑÑ Ð½Ð° ÑÐ¾, ÑÑÐ¾ Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ð¹ Ð²ÐºÐ»Ð°Ð´ Ð² Ð½Ð°Ð¼Ð°Ð³Ð½Ð¸ÑÐµÐ½Ð½Ð¾ÑÑÑ Ð²Ð½Ð¾ÑÑÑ ÑÐºÑÐ°Ð½Ð¸ÑÑÑÑÐ¸Ðµ ÑÐ¾ÐºÐ¸, ÑÐµÐºÑÑÐ¸Ðµ Ð¿Ð¾ Ð¿ÐµÑÐ¸ÑÐµÑÐ¸Ð¸ Ð¾Ð±ÑÐ°Ð·ÑÐ°, ÑÑÐ¾ ÑÐ¾Ð³Ð»Ð°ÑÑÐµÑÑÑ Ñ Ð¼Ð¾Ð´ÐµÐ»ÑÑ ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ. ÐÐ»Ð¸Ð·ÐºÐ¸Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ Ð¿Ð¾Ð»ÐµÐ¹ ÑÐºÐ°ÑÐºÐ¾Ð² Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾ÑÐ¾ÐºÐ° ÑÐºÐ°Ð·ÑÐ²Ð°ÐµÑ Ð½Ð° ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ðµ ÑÐºÐ°ÑÐºÐ¾Ð² Ð¿Ð¾ÑÐ¾ÐºÐ° Ñ Ð²Ð½ÐµÑÐ½ÐµÐ³Ð¾ ÐºÑÐ°Ñ Ð¾Ð±ÑÐ°Ð·ÑÐ°.
ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð¿ÑÐ¸ Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ»Ð¾Ð¶Ð½ÑÑ ÑÐ²ÐµÑÑÐ¿ÑÐ¾Ð²Ð¾Ð´ÑÑÐ¸Ñ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ ÑÐ¸ÑÑÐµÐ¼.
description: The work is devoted to the study of the magnetic characteristics of type I and type II superconductors, in the form of solid disks and disks with a hole.The purpose of the work is to obtain experimental dependences of the magnetic moment M on temperature and magnetic field and conduct a comparative analysis.The measurements were taken using a sensitive vibratory magnetometer. The critical temperature of indium is 3.3k and niobium's 9k and it was determined from the M(T) dependences. A linear dependence inthe intermediate state region and an unusual M(H) dependence with a decreasing field in the form of a semicircle are observed in the M(H) dependences for the In disk. Near Hc, there is a âsupercooling effectâ and the absence of a captured moment at H=0. For an In disk with a hole, the dependences M(H) are very close to the results for a solid disk, but the significant difference is in the large value of the captured field at H=0.For a type II niobium superconductor, the dependences M(H) for a solid disk and a disk with a hole are very close. They show great irreversibility and the development of magnetic flux jumps with decreasing temperature. Such a coincidence of the results indicates that the main contribution to the magnetization is made by the screening currents flowing around the periphery of the sample, which is consistent with the critical state model. Close values of the fields of magnetic flux jumps indicate the development of flux jumps from the outer edge of the sample.
The results can be used in the design of complex superconducting magnetic systems.