Accurate Symbolic Solution of Ginzburg-Landau Equations in the Circular Cell Approximation by Variational Method: Magnetization of Ideal Type II Superconductor ()
ABSTRACT
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.
Share and Cite:
Chevtchenko, O. (2017) Accurate Symbolic Solution of Ginzburg-Landau Equations in the Circular Cell Approximation by Variational Method: Magnetization of Ideal Type II Superconductor.
Journal of Modern Physics,
8, 982-1011. doi:
10.4236/jmp.2017.86062.
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