FIG. 3. Same as in Fig. 2, but for a generalized Kim-model. Depending on the relative strength of B$_{0}$ to the self-field of the sample, J$_{sf}$ ( d ) is almost constant if B$_{0}$ ≫ B$_{f}$ (squares) or decays rapidly if B$_{0}$ ≪ B$_{f}$ (circles). Equation 4 fully accounts for this behavior.  0.1  1  2  0.1  1  3 J c  (10 10 Am -2 ) d  ( m) J$_{0}$ = 10$^{10}$Am -2 B$_{0}$ = 0.001 B$_{0}$ = 0.01 B$_{0}$ = 0.1 We demonstrated how to calculate J$_{sf}$ ( d ) if a theoretical J$_{c}$ ( B ) is available, but our re- sult is also technologically relevant for investigating the reason of the J$_{sf}$ decrease in coated conductors with thicker superconducting layers. For such an analysis J$_{c}$ ( H ) should be mea- sured on the thinnest sample, where substrate interface effects do not play a role anymore. From this data J$_{c}$ ( B ) is determined down to inductions of about B$_{f}$ of the thinnest film. The remaining uncertainty in J$_{c}$ ( B ) (we suggest to assume a constant J$_{c}$ ( B ) at inductions below B$_{f}$ if no theoretical model is available) will introduce only a minor error in calculating J$_{sf}$ ( d ) for thicker films, provided they carry higher sheet current densities and thus elevate B$_{f}$ above the value of the thinnest film. We wish to emphasize, that the effect of the self-field is not an alternative explanation for a thickness dependent critical current density and will always be present, if the critical current density depends on the magnetic induction. A depression of J$_{sf}$ ( d ) significantly different from that calculated from J$_{c}$ ( B ) is thus indicative of an additional mechanism, such as a change in the material or pinning properties with thickness, determining the performance of the thicker conductor. If, however, the calculated and the measured J$_{sf}$ ( d ) are similar, the self-field controls the thickness dependence. In this case an improvement in 6