content_image/363559.jpg content_image/363563.jpg content_image/363565.jpg
<img src='content_image/363559.jpg'>

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 

<img src='content_image/363563.jpg'>

and assume that J$_{c}$ ( H ) and J$_{c}$ ( B ) are identical at applied fields above H$_{f}$ : 

<img src='content_image/363565.jpg'>

