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 0.4-0.6 I c z p~/ n. Losses at theedges 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 (L e-poj2g2r3F4/24), one pair of the edges of two wide strips set back-to-back and carrying antiparallel currents (Le 2 ponj2s2F4/6) and a long thin wall parallel to the current flow on a wide sheet (L c~p~. r r 3 j 2 a 2 F ' i / 3). Le 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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Pickup coils are widely used for measurements of magnetic susceptibility and hysteretic losses in magnetic and superconducting materials. A general formulation for the calibration of such pickup coils with different geometries is presented. Although the procedure described here is general and can be applied to any coil and sample, special emphasis has been placed on the calibration of saddlelike coils usually used to measure ac losses of long superconductors under ac fields perpendicular to their long dimension. Numerical simulations and experimental measurements have been carried out in order to determine the geometrical limitations of the pickup coil/sample configurations. This is especially important when simple coils of small dimensions and number of turns are used and/or samples of high demagnetization factor are measured. Superconductors of different geometry, in particular, wires and tapes under parallel and perpendicular fields, have been analyzed.

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