Calculation of hysteresis losses in hard superconductors carrying ac: isolated conductors and edges of thin sheets

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Abstract
Two methods of calculating hysteresis losses in hard superconductors are described. The London model is assumed in which the critical current density is taken independent of magnetic field. Losses in isolated wires of different cross section are considered but it is found that losses for solid wires vary by at most a factor of 3 for different shaped wires of the same current-carrying capacity. The loss at saturation current is usually 04-06 Ic2μ0/π. Losses at the edges of thin sheets are also calculated and a fourth-power dependence on current (for low current) is found. Three systems are examined: a slit parallel to the current in a wide sheet (Lc similar, equals μ0j2g2π3 F4/24), one pair of the edges of two wide strips set back-to-back and carrying antiparallel currents (Lc similar, equals μ0πj2s2 F4/6) and a long thin wall parallel to the current flow on a wide sheet (Lc similar, equals μ0π3j2a2 F4/3). Lc is the loss per cycle per unit length, F is the current peak as a fraction of saturation current, g the width of the slit, s the spacing of strips, a the height of the asperity and j the critical current density per unit width. All in MKS units.

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