 0.1  1  10  0.1  1  3 J sf  (10 10 Am -2 ) d  ( m) x 2 B$_{1}$ = 1 T J$_{1}$ = 10$^{9}$Am$^{-2}$,  = 0.5 J$_{1}$ = 10$^{8}$Am$^{-2}$,  = 1.0 FIG. 2. Comparison of the simulated J$_{sf}$ ( d ) depression (points) to the solution of Eqn. 4 (broken lines) assuming a power-law J$_{c}$ ( B ). After fitting γ ≈ 1 . 2 the solution of the implicit equation is in excellent agreement with the numerical computation. (The α = 0 . 5 data is shifted up by a factor of 2 for clarity.) Combining both equations and inserting the definition of B$_{f}$ results in the implicit equation 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 J$_{c}$ ( H = 0) = J$_{c}$ ( B = B$_{f}$ ) (3) J$_{sf}$ = J$_{c}$ ( B = µ$_{0}$γJ$_{sf}$d/π ) , γ ≈ 1 . 2 . (4) J$_{c}$ ( B ) = J$_{1}$ ( B B$_{1}$ ) − α , (5) 4