Power Dissipation in a Hard Superconducting Tube

Two kinds of dissipation are computed for a macroscopically homogeneous sample subjected to a changing axial magnetic field. Based upon the Anderson-Kim model of critical states, the induction, current density, electric field intensity, and thence the Joulean power density are determined. All are significantly dependent upon radial distance and magnetic history. Reversal of an applied field produces within the sample an interface region in which neighboring fluxoids are in opposite directions. Pairs of opposing fluxoids are presumed to coalesce, giving up their line energles as heat in an annihilation process. By way of illustration, computed values of all these quantities are presented for a typical unannealed ${\mathrm{Nb}}_{0.75}$ ${\mathrm{Zr}}_{0.25}$ sample. If the computed values of dissipation, which are averages in the sense that they are based upon a homogeneous model, are taken to be a measure of the thermal activation of flux motion, then their pattern affords a highly satisfactory explanation of an extensive body of experimental observations.