Expansion for the superheating field in a semi-infinite film in the weak-$\kappa$ limit

Castillo, Pierre Del

ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 6, pp. 971-993.

Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-$\kappa$ limit. These authors deduced a formal expansion for the superheating field in powers of ${\kappa }^{\frac{1}{2}}$ up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr’s formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers of ${\kappa }^{\frac{1}{2}}$ for the superheating field.

Classification : 34E05, 34E10
Mots clés : superconductivity, Ginzburg-Landau equation, critical field

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