Nonlinear transport current flow in superconductors with planar obstacles
Nonlinear transport current flow in superconductors with planar obstacles
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DOI：
10.1103/physrevb.62.4004
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发表时间：
2000-08-01
影响因子：
3.7
通讯作者：
Friesen, M
中科院分区：
文献类型：
--
作者：
Gurevich, A;Friesen, M
我们给出了一种速度图法的详细描述，它使我们能够解析地计算超导体中电场E(R)和输运电流密度J(R)的二维分布，同时考虑了超导体的高度非线性E-J特性。该方法给出了给定边界条件下非线性稳态麦克斯韦方程的唯一解E(R)，指出了临界状态模型的适用范围，指出了临界状态模型的缺陷所在。用速度图法计算J(R)的非线性问题归结为求解电势P_i(E)的线性方程或作为E的函数的电流流函数psi(E)。对于幂规律特性E=E-c(J/J(C))(N)，E(R)和J(R)的计算可以映射到伦敦方程的解上，反屏蔽长度β=(n-1)/2根n在速度图空间(Exey)中。我们给出了求解速度图方程的一般方法，并得到了特定水流的闭合解析解。用该方法计算了具有大角度晶界、微裂纹等宏观平面缺陷的超导体中E(R)和耗散的分布，结果表明，平面障碍物周围的电流图样分裂成J方向不同的磁区，并被电流区隔开。我们计算了电流域壁的结构，其宽度同时取决于电流的几何形状和指数n。这些域壁与Bean模型的电流间断线甚至在极限n-->无穷远的情况下也是不同的。我们得到了无限大超导体中通过长度为2a的平面缺陷的电流的解，结果表明，缺陷引起了强的局域电场增强和E(R)在长度尺度上的长程扰动L(垂直于)类似于a，L(平行)类似于根n远大于垂直于平均电流和平行于平均电流。这种解还显示出平面缺陷附近的大磁通停滞区，临界态极限J(R)的普遍分布，n-->0，以及边缘附近的局部磁通流区。我们对非线性电流的焦耳加热进行了计算，结果表明，平面缺陷会引起显著的超耗散，从而影响超导体的交流损耗和局域热不稳定性。
We present a detailed description of a hodograph method, which enables us to calculate analytically the two-dimensional distributions of the electric field E(r) and transport current density J(r) in superconductors, taking into account their highly nonlinear E-J characteristics. The method gives a unique solution E(r) of nonlinear steady-state Maxwell's equations for given boundary conditions, showing applicability limits of the critical state model and pointing out where it breaks down. The nonlinear problem of calculation of J(r) by the hodograph method reduces to solving a linear equation for the electric potential phi(E), or the current stream function psi(E) as a function of E. For the power-law characteristics E=E-c(J/J(c))(n), calculation of E(r) and J(r) can be mapped onto solutions of the London equation with the inverse screening length beta=(n -1)/2 root n in the hodograph space (ExEy). We give general methods of solving the hodograph equations and obtain closed-form analytical solutions for particular current flows. The method is applied to calculate distributions of E(r) and dissipation in superconductors with macroscopic planar defects, such as high-angle grain boundaries, microcracks, etc. Current patterns around planar obstacles are shown to break up into domains of different orientations of J, separated by current domain walls. We calculate the structure of the current domain walls, whose width depends both on the geometry of current flow and the exponent n. These domain walls differ from the current discontinuity lines of the Bean model even in the limit n-->infinity. We obtained a solution for current flow past a planar defect of length 2a in an infinite superconductor and showed that the defect causes strong local electric-field enhancement and long-range disturbances of E(r) on length scales L(perpendicular to)similar to an much greater than a and L(parallel to)similar to a root n much greater than a perpendicular and parallel to the mean current flow, respectively. This solution also exhibits large stagnation regions of magnetic flux near planar defects, universal distributions of J(r) in the critical state limit, n-->infinity, and local flux flow regions near the edges. We calculate Joule heating for nonlinear current flow and show that planar defects cause significant excess dissipation, which affects ac losses and local thermal instabilities in superconductors.