Susceptibility of superconductor disks and rings with and without flux creep
Susceptibility of superconductor disks and rings with and without flux creep
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DOI：
10.1103/physrevb.55.14513
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发表时间：
1997-06-01
影响因子：
3.7
通讯作者：
Brandt, EH
中科院分区：
文献类型：
--
作者：
Brandt, EH
首先，列出了第二类超导体临界电流恒定的Bean假设的一些结果，并导出了窄环的Bean交流磁化率。然后用非线性电流-电压定律E(与J(N)成正比)描述磁通蠕变，由此导出了具有一般孔半径a(1)和一般蠕变指数n的环在恒斜率下的饱和磁矩H-a(T)，然后以运动方程的形式给出了环在垂直外加磁场H-a(T)中的精确表达式，即厚环和薄环中的电流密度或薄环和薄盘中的薄片电流。用这种方法计算了有蠕变和无蠕变的环的一般磁化曲线m(H-a)和交流磁化率chi，也考虑了非常数J(C)(B)。描述了典型的电流和磁场(B)分布。M(H-a)(理想抗磁矩)的初始斜率和完全穿透磁场被表示为内外环半径和a的函数。导出了一个标度律，它表明对于任意的蠕变指数n，复非线性交流极化率chi(H-0，omega)仅取决于交流幅度H-0和交流频率omega/2pi的组合H-0(n-1)/omega。因此，该比例律将欧姆极限(n=1)中的已知依赖项chi=chi(Omega)和Bean极限(n->无穷大)中的chi=chi(H-0)联系在一起。
First some consequences of the Bean assumption of constant critical current Jc in type-II superconductors are listed and the Bean ac susceptibility of narrow rings is derived. Then flux creep is described by a nonlinear current-voltage law E(proportional to)J(n), from which the saturated magnetic moment at constant ramp rate H-a(t) is derived for rings with general hole radius a(1) and general creep exponent n. Next the exact formulation for rings in a perpendicular applied field H-a(t) is presented in the form of an equation of motion for the current density in thick rings and disks or the sheet current in thin rings and disks. This method is used to compute general magnetization curves m(H-a) and ac susceptibilities chi of rings with and without creep, accounting also for nonconstant J(c)(B). Typical current and field (B) profiles are depicted. The initial slope of m(H-a) (the ideal diamagnetic moment) and the field of full penetration are expressed as functions of the inner and outer ring radii al and a. A scaling law is derived which states that for arbitrary creep exponent n the complex nonlinear ac susceptibility chi(H-0,omega) depends only on the combination H-0(n-1)/omega of the ac amplitude H-0 and the ac frequency omega/2 pi. This scaling law thus connects the known dependencies chi = chi(omega) in the ohmic limit(n = 1) and chi = chi(H-0) in the Bean limit (n --> infinity).