Macroscopic equations for the description of the quasi-static magnetic behaviour of a type II superconductor of arbitrary shape

Labusch, R.; Doyle, T. B.

doi:10.1016/s0921-4534(97)01617-1

Cited by 39 publications

(31 citation statements)

References 6 publications

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“…Next we consider the full, irreversible magnetization curves M (H a ) of pin-free strips and cylinders with cross section 2a × 2b. Appropriate continuum equations and algorithms (which apply also to pinning) have been proposed recently by Labusch and Doyle [19] and by the author [20], based on the Maxwell equations and on constitutive laws which describe flux flow and pinning [or thermal depinning expressed, e.g., by an electric field E(J, B)] and the reversible magnetization in absence of pinning, M (H a ; 0). Here I shall use the method [20] and the model M (H a ; 0), Eq.…”

Section: (Hmentioning

confidence: 99%

“…While method [19] considers a magnetic charge density on the specimen surface which causes an effective field H i (r) inside the superconductor, our method [20] couples the arbitrarily shaped superconductor to the external field B(r, t) via surface screening currents: In a first step the vector potential A(r, t) is calculated for given current density J; then this relation (a matrix) is inverted to obtain J for given A and given H a ; next the induction law is used to obtain the electric field [in our symmetric geometry one has E(J, B) = −∂A/∂t ], and finally the constitutive law E = E(J, B) is used to eliminate A and E and obtain one single integral equation for J(r, t) as a function of H a (t), without having to compute B(r, t) outside the specimen. This method in general is fast and elegant; but so far the algorithm is restricted to moderate aspect ratios, 0.03 ≤ b/a ≤ 30, and to a number of grid points not exceeding 1000 (on a Personal Computer).…”

Section: (Hmentioning

confidence: 99%

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Irreversible magnetization of pin-free type-II superconductors

1999

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The magnetization curve of a type II superconductor in general is hysteretic even when the vortices exhibit no volume or surface pinning. This geometric irreversibility, caused by an edge barrier for flux penetration, is absent only when the superconductor has precisely ellipsoidal shape or is a wedge with a sharp edge where the flux lines can penetrate. A quantitative theory of this irreversibility is presented for pin-free disks and strips with constant thickness. The resulting magnetization loops are compared with the reversible magnetization curves of ideal ellipsoids.PACS numbers: 74.60. Ec, 74.60.Ge, 74.55.+h The magnetic moment of most superconductors is well known to be irreversible. After Abrikosov's [1] prediction of quantized flux lines it became clear [2] that the magnetic hysteresis is caused by pinning of these vortex lines at inhomogeneities in the material. Flux-line pinning and the related critical state [3] were subsequently confirmed quantitatively in numerous papers [4]. However, similar hysteresis effects were also observed [5] in type I superconductors, which do not contain flux lines but normal conducting domains, and in type II superconductors with negligible pinning. In these two cases the magnetic irreversibility is caused by a geometric (specimen-shape dependent) barrier which delays the penetration of magnetic flux but not its exit. In this respect the geometric barrier behaves similar to the Bean-Livingston barrier [6,7] for vortices penetrating a parallel surface.The geometric irreversibility is most pronounced for thin films of constant thickness in a perpendicular field. It is absent only when the superconductor is of exactly ellipsoidal shape or is tapered like a wedge with a sharp edge where flux penetration is facilitated. In ellipsoids the inward directed driving force exerted on the vortex ends by the surface screening currents is exactly compensated by the vortex line tension [8], and thus the magnetization is reversible. In specimens with constant thickness (i.e. rectangular cross-section) this line tension opposes the penetration of flux lines at the four corner lines, thus causing an edge barrier; but as soon as two penetrating vortex segments join at the equator they contract and are driven to the specimen center by the surface currents, see Fig. 1 below. As opposed to this, when the specimen profile is tapered and has a sharp edge, the driving force even in very weak applied field exceeds the restoring force of the line tension such that there is no edge barrier. The resulting absence of hysteresis in wedge-shaped samples was nicely shown by Morozov et al. [9].An elegant analytical theory of the field and current profiles in thin superconductor strips with an edge barrier has been presented by Zeldov et al. [10], see also the extensions [11]. With increasing applied field H a , the magnetic flux does not penetrate until an entry field H en is reached; at H a = H en the flux immediately jumps to the center, from where it gradually fills the entire strip or disk. This ...

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Section: (Hmentioning

confidence: 99%

Section: (Hmentioning

confidence: 99%

Irreversible magnetization of pin-free type-II superconductors

1999

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“…The formulae (7,16,17) are derived essentially from first principles, with no assumptions but the geometry and finite H c1 . They should be used to interpret experiments on superconductors with no or very weak vortex pinning.…”

Section: Pin-free Superconductorsmentioning

confidence: 99%

Superconductors in realistic geometries: geometric edge barrier versus pinning

Brandt

2000

Physica C: Superconductivity

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“…(15). This results in an effective driving current density J H = \7 x H, where H = H(B) = 8(FIV)18B is the "reversible field" obtained from the free energy density F IV of the ideal FLL [38]. The detail that in general B differs from J.loH, only is important at low inductions B < Bel and in the so-called transverse geometry (Sec.…”

Section: T)mentioning

confidence: 99%

“…The detail that in general B differs from J.loH, only is important at low inductions B < Bel and in the so-called transverse geometry (Sec. 6.2, 6.3), where it may lead to a "geometric barrier" which delays the penetration of the first magnetic flux [38,39,40] even in the absence of bulk or surface pinning.…”

Section: T)mentioning

confidence: 99%

Pinning of Vortices and Linear and Nonlinear Ac Susceptibilities in High-T c Superconductors

Brandt¹

2001

High-Tc Superconductors and Related Materials

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Macroscopic equations for the description of the quasi-static magnetic behaviour of a type II superconductor of arbitrary shape

Cited by 39 publications

References 6 publications

Irreversible magnetization of pin-free type-II superconductors

Irreversible magnetization of pin-free type-II superconductors

Superconductors in realistic geometries: geometric edge barrier versus pinning

Pinning of Vortices and Linear and Nonlinear Ac Susceptibilities in High-T c Superconductors

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