Solution of Thin Film Magnetization Problems in Type-II Superconductivity

Prigozhin, Leonid

doi:10.1006/jcph.1998.5978

Cited by 64 publications

(86 citation statements)

References 31 publications

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“…It should be emphasized that the above formula for the dependence of j c on ϕ−ψ and Eqs. (3,5,6) hold only if flux cutting does not occur in the superconductor when the critical state is established in it. Flux cutting will only happen if | cot(ϕ − ψ)|, calculated from Eq.…”

Section: Splitting the 3d Problemmentioning

confidence: 99%

Critical state in thin anisotropic superconductors of arbitrary shape

Mikitik¹,

Brandt²

2000

Phys. Rev. B

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A thin flat superconductor of arbitrary shape and with arbitrary in-plane and out-of-plane anisotropy of flux-line pinning is considered, in an external magnetic field normal to its plane. It is shown that the general three-dimensional critical state problem for this superconductor reduces to the two-dimensional problem of an infinitely thin sample of the same shape but with a modified induction dependence of the critical sheet current. The methods of solving the latter problem are well-known. This finding thus enables one to study the critical states in realistic samples of high-Tc superconductors with various types of anisotropic flux-line pinning. As examples, we investigate the critical states of long strips and rectangular platelets of high-Tc superconductors with pinning either by the ab planes or by extended defects aligned with the c axis.

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Section: Splitting the 3d Problemmentioning

confidence: 99%

Critical state in thin anisotropic superconductors of arbitrary shape

Mikitik¹,

Brandt²

2000

Phys. Rev. B

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“…Recently, Prigozhin in [14] reformulated the problem to a variational inequality and established the existence of a unique weak solution to the variational inequality if the space dimension is equal to two. Some numerical issues are discussed in [2] (also see a more recent paper [15]). Surprisingly, we show that the weak solution defined in [14] can be obtained as the limit of the solution to the system (1.1) as p -> +oo.…”

Section: Hf+vxmentioning

confidence: 99%

On a 𝑝-Laplacian type of evolution system and applications to the Bean model in the type-II superconductivity theory

Yin¹

2001

Quart. Appl. Math.

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Abstract.In this paper we study the Cauchy problem for a p-Laplacian type of evolution system H( + V x [|V x H|P~2V x H] = F. This system governs the evolution of a magnetic field H, where the displacement currently is neglected and the electrical resistivity is assumed to be some power of the current density. The existence, uniqueness, and regularity of solutions to the system are established.Furthermore, it is shown that the limit solution as the power p -> oo solves the problem of Bean's model in the type-II superconductivity theory. The result provides us information about how the superconductor material under the external force becomes the normal conductor and vice versa. It also provides an effective method for finding numerical solutions to Bean's model.

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“…The static Bean model for thin films of any shape is computed by Prigozhin using a variational method. 13 …”

Section: Introductionmentioning

confidence: 99%

Thin superconductors and SQUIDs in perpendicular magnetic field

Brandt

2005

Phys. Rev. B

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It is shown how the static and dynamic electromagnetic properties can be calculated for thin flat superconducting films of any shape and size, also multiply connected as used for SQUIDs, and for any value of the effective magnetic London penetration depth Λ. As examples, the distributions of sheet current and magnetic field are obtained for rectangular and circular films without and with slits and holes, in response to an applied perpendicular magnetic field and to magnetic vortices moving in the film. The self energy and interaction of vortices with each other and with an applied magnetic field and/or transport current are given. Due to the long ranging magnetic stray field, these energies depend on the size and shape of the film and on the vortex position even in large films, in contrast to the situation in large bulk superconductors. The focussing of magnetic flux into the central hole of square films without and with a radial slit is compared.

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Solution of Thin Film Magnetization Problems in Type-II Superconductivity

Abstract: A variational formulation and an efficient numerical method are derived for thin film critical-state problems. We use this method to solve problems for various film shapes with either the Bean or Kim current-voltage relation characterizing the superconducting material.

Cited by 64 publications

References 31 publications

Critical state in thin anisotropic superconductors of arbitrary shape

Critical state in thin anisotropic superconductors of arbitrary shape

On a 𝑝-Laplacian type of evolution system and applications to the Bean model in the type-II superconductivity theory

Thin superconductors and SQUIDs in perpendicular magnetic field

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