10 9 10 10 10 11 10 -3 10 -2 10 -1 1 J c  (Am -2 ) $_{0}$H,  B  (T) J$_{sf}$ = J$_{c}$ ( H = H$_{f}$ ) J c ( H = H $^{f}$) = J c ( B = B $^{f}$) J$_{c}$ ( H ) J$_{sf}$ J$_{c}$ ( H = 0) J$_{c}$ ( B ) J$_{sf}$ = J$_{c}$ ( B = B$_{f}$ 1.2 $_{0}$J$_{sf}$ d / ) FIG. 1. Approximations made to connect J$_{sf}$ ( d ) and J$_{c}$ ( B ). The simulations of J$_{c}$ ( H ) (solid line) are carried out assuming J$_{c}$ ( B ) ∝ B − 0 . 5 (dotted line) and result in a finite J$_{sf}$ at zero applied field. The simulated J$_{c}$ ( H ) remains approximately at this value up to applied fields of B$_{f}$ , which is found by intersecting J$_{sf}$ (broken line) and J$_{c}$ ( B ), and approaches J$_{c}$ ( B ) above this field. applied fields, on the other hand, the transport current alters the field distribution only marginally and J$_{c}$ ( H ) is identical to J$_{c}$ ( B ). The applied field at which J$_{c}$ ( H ) becomes field dependent and approaches J$_{c}$ ( B ), can be estimated by comparison to the self-field of the film. We use H$_{f}$ = B$_{f}$/µ$_{0}$ = γJ$_{sf}$d/π , which is equivalent to the field scale of thin films $^{8}$, but we replace the constant J$_{c}$ of the Bean model by the average critical current density at zero applied field and include a factor γ , which is approximately 1.2 as determined graphically from Fig. 1 or by least squares fitting (see below). Because the sheet current density J$_{sf}$d controls the self-field of the sample, the thickness dependence J$_{sf}$ ( d ) can be related to J$_{c}$ ( B ) by making the following approximations. We neglect any field dependence of J$_{c}$ ( H ) up to applied fields H = H$_{f}$ , which leads to J$_{c}$ ( H = 0) = J$_{c}$ ( H = H$_{f}$ ) , (1) and assume that J$_{c}$ ( H ) and J$_{c}$ ( B ) are identical at applied fields above H$_{f}$ : J$_{c}$ ( H = H$_{f}$ ) = J$_{c}$ ( B = B$_{f}$ ) . (2) 3