content_image/338284.jpg content_image/338291.jpg content_image/338290.jpg content_image/338292.jpg
Combining both equations 

and inserting the definition of B$_{f}$ results in the implicit equation 

<img src='content_image/338284.jpg'>

<img src='content_image/338291.jpg'>

<img src='content_image/338290.jpg'>

A graphical representation of the derivation is depicted in Fig. 1 and γ is determined by intersecting J$_{sf}$ with J$_{c}$ ( B ). The final result Eqn. 4 allows us to calculate the self-field critical current density as a function of thickness J$_{sf}$ ( d ) for any given J$_{c}$ ( B ). 

We test Eqn. 4 by comparing its solution for a certain J$_{c}$ ( B ) to simulations of J$_{sf}$ ( d ) on a 100 µ m wide film having a thickness between 100 nm and 3 µ m (the typical thickness range in experiments). Inserting, for example, the power-law 

<img src='content_image/338292.jpg'>

