Critical field enhancement due to field penetration in fine-filament superconductors

In samples in which at least one dimension, say 2R, is comparable to a penetration depth, lambda(sub L), the flux-exclusion volume at fields below H(sub c1) is less than the true sample volume. This volume erosion has two important consequences: (1) it causes the Meissner susceptibility to be less than the standard value -- for example, for a field-parallel plate, by a factor 1-(1/x)tanh(x), where x = R/lambda(sub L); (2) it reduces the flux-exclusion energy density (based on the initial sample volume) by the square of that factor. In the latter case it calls for an enhanced applied field strength to terminate the Meissner state -- that enhancement factor being accordingly 1/the square root of 1-(1/x)tanh(x). Both of these effects become more and more pronounced as T approaches (Tc), since the field penetration depth increases with temperature according to 1/the square root of 1-t(sup 4), where t (identical to) T/(Tc). The susceptibility-depletion and field-enhancement effects have been studied on a series of very fine filament composites (with NbTi filament diameters ranging from 0.5 to 11.6 microns), prepared from 23,000-filament NbTi/CuMn strands from which (to avoid unwanted proximity effect coupling) the Cu was removed by etching and replaced by epoxy. For example, at 4.2 K in the finest-filament material, susceptibility was found to be 1/15 of the Meissner value, and the sample exhibited a lower critical applied field of 607 gauss.