Accurate Symbolic Solution of Ginzburg-Landau Equations in the Circular Cell Approximation by Variational Method: Magnetization of Ideal Type II Superconductor

• 作者: O. A. Chevtchenko
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: GINZBURG-LANDAU Equations ACCURATE SYMBOLIC Solution CIRCULAR Unit CELL
• 年，卷（期）: xdwlyw_2017,（6）
• 页码范围: 982-1011
• 页数: 30页
• 分类号: O1

摘要

In this paper I access the degree of approximation of known symbolic approach to solving of Ginzburg-Landau (GL) equations using variational method and a concept of vortex lattice with circular unit cells, refine it in a clear and concise way, identify and eliminate the errors. Also, I will improve its accuracy by providing for the first time precise dependencies of the variational parameters;correct and calculate magnetisation, compare it with the one calculated numerically and conclude they agree within 98.5% or better for any value of the GL parameter k and at magnetic field , which is good basis for many engineering applications. As a result, a theoretical tool is developed using known symbolic solutions of GL equations with accuracy surpassing that of any other known symbolic solution and approaching that of numerical one.