Kim model for magnetization of type-II superconductors

Journal Article · Fri Sep 15 00:00:00 EDT 1989 · Journal of Applied Physics; (USA)

DOI:https://doi.org/10.1063/1.344261· OSTI ID:5464844

Chen, D; Goldfarb, R B ^[1]

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1. Electromagnetic Technology Division, National Institute of Standards and Technology, Boulder, Colorado 80303 (US)

We have calculated the initial magnetization curves and complete hysteresis loops for hard type-II superconductors. The critical-current density {ital J}{sub {ital c}} is assumed to be a function of the internal magnetic field {ital H}{sub {ital i}} according to Kim's model, {ital J}{sub {ital c}}({ital H}{sub {ital i}})={ital k}/({ital H}{sub 0}+{vert bar}{ital H}{sub {ital i}}{vert bar}), where {ital k} and {ital H}{sub 0} are constants. As is the case for other critical-state models, additional assumptions are that bulk supercurrent densities are equal to {ital J}{sub {ital c}}, and that the lower critical field is zero. Our analytic solution is for an infinite orthorhombic specimen with finite rectangular cross section, 2{ital a}{times}2{ital b} ({ital a}{le}{ital b}), in which a uniform field {ital H} is applied parallel to the infinite axis. Assuming equal flux penetration from the sides, we reduced the two-dimensional problem to a one-dimensional calculation. The calculated curves are functions of {ital b}/{ital a}, a dimensionless parameter {ital p}=(2{ital ka}){sup 1/2}/{ital H}{sub 0}, and the maximum applied field {ital H}{sub {ital m}}. The field for full penetration is {ital H}{sub {ital p}}={ital H}{sub 0}((1+{ital p}{sup 2}){sup 1/2}{minus}1). A related parameter is {ital H}{sup *}{sub {ital m}}={ital H}{sub 0}((1+2{ital p}{sup 2}){sup 1/2}{minus}1). Hysteresis loops were calculated for the different ranges of {ital H}{sub {ital m}} : {ital H}{sub {ital m}}{lt}{ital H}{sub {ital p}}, {ital H}{sub {ital p}}{lt}{ital H}{sub {ital m}}{lt}{ital H}{sup *}{sub {ital m}}, and {ital H}{sup *}{sub {ital m}}{lt}{ital H}{sub {ital m}}. The equations for an infinite cylindrical specimen of radius {ital a} are the same as those for a specimen with square cross section, {ital a}={ital b}.

• OSTI ID: 5464844
• Journal Information: Journal of Applied Physics; (USA), Journal Name: Journal of Applied Physics; (USA) Vol. 66:6; ISSN 0021-8979; ISSN JAPIA
• Country of Publication: United States
• Language: English

Related Subjects

656100* -- Condensed Matter Physics-- Superconductivity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
CRITICAL CURRENT
CRYSTAL LATTICES
CRYSTAL STRUCTURE
CURRENTS
ELECTRIC CURRENTS
HYSTERESIS
MAGNETIC FIELDS
MAGNETIC PROPERTIES
MAGNETIZATION
MATHEMATICAL MODELS
ONE-DIMENSIONAL CALCULATIONS
ORTHORHOMBIC LATTICES
PHYSICAL PROPERTIES
SUPERCONDUCTORS
TYPE-II SUPERCONDUCTORS