title: ÐÑÐ¾Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð´Ð»Ð¸Ð½Ð½ÑÐ¹ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐµÑÐºÐ¸ Ð¼Ð¾Ð´ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐ¹ Ð´Ð¶Ð¾Ð·ÐµÑÑÐ¾Ð½Ð¾Ð²ÑÐºÐ¸Ð¹ ÐºÐ¾Ð½ÑÐ°ÐºÑ
title: Ð¼Ð¾Ð½Ð¾Ð³ÑÐ°ÑÐ¸Ñ
titleType: Subtitle
title: Penetration of a Magnetic Field into a Long Periodically Modulated Josephson Contact
Creators: name: ÐÐµÐ»Ð¸ÐºÐ¼Ð°Ð½, ÐÐ°ÑÐº
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2024
Subjects: Ð¡Ð²ÐµÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ¸
ÐÐ°Ð³Ð½Ð¸ÑÐ½Ð¾Ðµ Ð¿Ð¾Ð»Ðµ

description: Ð¤Ð¸Ð·Ð¸ÐºÐ° Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð², Ð¿ÑÐ¾Ð¸ÑÑÐ¾Ð´ÑÑÐ¸Ñ Ð² Ð¾Ð±ÑÑÐ½ÑÑ ÑÐ²ÐµÑÑÐ¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ°Ñ (ÑÑÑÐµÐºÑ ÐÐµÐ¹ÑÐ½ÐµÑÐ°, Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð¸ÑÑÐµÐ¹, Ð¸Ñ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð´ÑÑÐ³ Ñ Ð´ÑÑÐ³Ð¾Ð¼ Ð¸ Ñ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÐ¼ Ð¿Ð¾Ð»ÐµÐ¼), Ð¿Ð¾Ð½ÑÑÐ½Ð°, Ð¸ Ð¸Ñ ÑÐµÐ¾ÑÐ¸Ñ, Ð±Ð°Ð·Ð¸ÑÑÑÑÐ°ÑÑÑ Ð½Ð° ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸ÑÑ ÐÐ¸Ð½Ð·Ð±ÑÑÐ³Ð°-ÐÐ°Ð½Ð´Ð°Ñ, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð° ÐµÑÐµ Ð´Ð¾ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ ÑÐµÐ¾ÑÐ¸Ð¸ ÐÐÐ¨. Ð ÐºÐµÑÐ°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÐÐ¢Ð¡Ð ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ ÑÑÐ¸Ñ ÑÐ²Ð»ÐµÐ½Ð¸Ð¹ ÑÑÐ°Ð»ÐºÐ¸Ð²Ð°ÐµÑÑÑ Ñ ÑÑÑÐ´Ð½Ð¾ÑÑÑÐ¼Ð¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐ²ÑÐ·Ð°Ð½Ñ Ñ ÑÑÐµÐ¸ÑÑÐ¾Ð¹ ÑÑÑÑÐºÑÑÑÐ¾Ð¹ ÑÑÐµÐ´Ñ. Ð¢Ð¾ÐºÐ¾Ð²ÑÐµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¾ÑÐ»Ð¸ÑÐ°ÑÑÑÑ Ð¿Ð¾ ÑÐ²Ð¾ÐµÐ¹ ÑÑÑÑÐºÑÑÑÐµ Ð¾Ñ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ Ð² Ð¾Ð±ÑÑÐ½ÑÑ ÑÐ²ÐµÑÑÐ¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ°Ñ. Ð£ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÐ¸Ð½Ð·Ð±ÑÑÐ³Ð°-ÐÐ°Ð½Ð´Ð°Ñ Ð½ÐµÐ¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ñ Ð² ÑÑÐ¾Ð¹ ÑÐ¸ÑÑÐ°ÑÐ¸Ð¸. Ð Ð½Ð°ÑÑÐ¾ÑÑÐµÐ¹ Ð¼Ð¾Ð½Ð¾Ð³ÑÐ°ÑÐ¸Ð¸ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ ÑÐ°Ðº Ð½Ð°Ð·ÑÐ²Ð°ÐµÐ¼ÑÐ¹ Ð´Ð»Ð¸Ð½Ð½ÑÐ¹ Ð´Ð¶Ð¾Ð·ÐµÑÑÐ¾Ð½Ð¾Ð²ÑÐºÐ¸Ð¹ ÐºÐ¾Ð½ÑÐ°ÐºÑ, Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ñ Ð²ÑÐµ Ð¿ÑÐ¾ÑÐµÑÑÑ, Ð¸Ð¼ÐµÑÑÐ¸Ðµ Ð¼ÐµÑÑÐ¾ Ð² ÑÐ²ÐµÑÑÐ¿ÑÐ¾Ð²Ð¾Ð´ÑÑÐ¸Ñ Ð¾Ð±ÑÐ°Ð·ÑÐ°Ñ: Ð²ÑÑÐ°Ð»ÐºÐ¸Ð²Ð°Ð½Ð¸Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ, Ð²Ð¾Ð·Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ðµ Ð²Ð¸ÑÑÐµÐ¹, Ð¸Ñ Ð¿Ð¸Ð½Ð½Ð¸Ð½Ð³ Ð¸ Ð²ÑÐµ ÑÐ²ÑÐ·Ð°Ð½Ð½ÑÐµ Ñ ÑÑÐ¸Ð¼ ÑÐµÐ½Ð¾Ð¼ÐµÐ½Ñ, Ð² ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸ Ð¿ÑÐ¾Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ðµ Ð² ÐºÐ¾Ð½ÑÐ°ÐºÑ Ð²Ð½ÐµÑÐ½ÐµÐ³Ð¾ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ. ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸ Ð¶Ðµ ÑÑÐ° Ð·Ð°Ð´Ð°ÑÐ° ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾ Ð¿ÑÐ¾ÑÐµ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¸ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð´Ð»Ñ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð³Ð¾ ÑÐ²ÐµÑÑÐ¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐ°. ÐÐ½Ð° Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ ÑÐµÑÐµÐ½Ð° Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾ ÑÐ¾ÑÐ½Ð¾, ÑÑÐ¾ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ð¿ÑÐ¾ÑÐ»ÐµÐ´Ð¸ÑÑ Ð¿ÑÐ¾Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² ÑÐ°ÐºÐ¾Ð¹ ÐºÐ¾Ð½ÑÐ°ÐºÑ, ÑÐ°ÑÑÑÐ¸ÑÐ°ÑÑ Ð²ÑÑ ÐºÑÐ¸Ð²ÑÑ Ð½Ð°Ð¼Ð°Ð³Ð½Ð¸ÑÐ¸Ð²Ð°Ð½Ð¸Ñ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÑ Ð²Ð¸ÑÑÐµÐ²Ð¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½ ÑÐ°ÐºÐ¶Ðµ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð²Ð¸ÑÑÐµÐ¹ Ð¿ÑÐ¸ Ð¿ÑÐ¾ÑÐµÐºÐ°Ð½Ð¸Ð¸ Ð¿Ð¾ Ð¾Ð±ÑÐ°Ð·ÑÑ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÐºÐ°, ÑÑÐ¾ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð¾ ÑÐ°ÑÑÑÐ¸ÑÐ°ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¾ÐºÐ° Ð² ÑÐ°Ð·Ð½ÑÑ ÑÐ»ÑÑÐ°ÑÑ.
description: The physics of the processes occurring in conventional superconductors (the Meissner effect, the formation of vortices, their interaction with each other and with the magnetic field) is understandable, and their theory, based on the Ginsburg-Landau equations, was built even before the creation of the BCS theory. In ceramic HTSCs, the theoretical description of these phenomena faces difficulties related to the cellular structure of the medium. The current states differ in their structure from those existing in conventional superconductors. The Ginsburg-Landau equations are not applicable in
this situation. This monograph examines the so-called long Josephson contact, in which all the processes taking place in superconducting samples are possible: the expulsion of a magnetic field, the appearance of vortices, their pinning and all related phenomena, in particular the penetration of an external magnetic field into contact. Mathematically, this problem is much simpler than a similar problem for a three-dimensional superconductor. It can be solved accurately enough, which makes it possible to trace the penetration of a magnetic field into such a contact, calculate the entire magnetization curve and investigate the dynamics of the vortex distribution. An analysis of the behavior of vortices when the transport current flows through the sample was also carried out, which made it possible to calculate the values of the critical current in different cases.