Analytic description of the transport $J_{c}(B)$ dependence of HTS thin films in small magnetic fields

Often, e.g. for deconvolution processes and field distribution calculations, an analytical function for the $J_{c}(B)$ dependence of high-$T_{c}$ thin films is needed. The parameters of these functions should still have a physical meaning regarding the intrinsic and extrinsic sample properties. Starting with the modified Kim model, described by Xu \textit{et al}., we found an excellent function by introducing a sharpness parameter $\beta $. This parameter describes the shape of $J_{c}(B)$ between the low-field plateau (single vortex pinning regime) and the power-law dependence at higher fields. The temperature dependence of all fitting parameters will be discussed. Furthermore, the importance of the field dependence of the $n$ value for distinguishing different pinning regimes will be illustrated.