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Applied and Computational Math Seminar

Static currents in type-1 superconductors

Manas Rachh (Flatiron Institute)

Location:  Hill 705
Date & time: Wednesday, 31 January 2024 at 11:00AM - 12:00PM

In this talk, we describe the classical magneto-static approach to the theory of type-I superconductors. The magnetic field and the current in type-I superconductors are related by the London equations and tend to decay exponentially inside the superconducting material with support of the fields contained primarily in O(λ_L) neighborhood of the superconductor. We present a Debye source based integral representation for the numerical solution of the London equations, and demonstrate the efficacy of our approach for moderate values of λ_L on complex three dimensional geometries. However, for typical materials λ_L ∼ O(10−7), which makes the PDE and integral equation increasingly difficult to solve in the limit λ_L → 0 due to the presence of two different length scales in the problem. We derive a limiting PDE and a corresponding integral equation, and show that the solutions of this limiting PDE and integral equations are O(λ_L) accurate as compared to the corresponding solutions of the London equations and the Debye source integral equations respectively. We demonstrate the effectiveness of this asymptotic approach both in terms of speed and accuracy through several numerical examples.

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