Based on a statistic study in a random pin medium, we have proposed a new method to describe current transport properties in high Tc superconductors (HTS). The theoretical results are compared with measured electric field (E) vs. current density (J) curves in a YBCO film with magnetic fields up to 12T. The nonlinear E-J curves can be characterized by a power function [(J-Jcm)/J0]m with three parameters: the minimum value of critical current density (Jc) denoted by Jcm, the variance of the distribution, J0, and exponent, m, which determines the shape of Jc distribution. Magnetic field (B) and temperature (T) dependencies of the E-J curves can be attributed to the thermodynamic properties of Jcm and typical value of Jc, denoted by Jk(≡Jcm+J0) through the corresponding macroscopic pinning force densities JcmB and JkB, respectively, as in the similar form in low Tc superconductors. The present method allows us to estimate the statistic Jc distribution from E-J curves. Moreover, B- and T-dependencies of the E-J curves can be predicted in a (B, T)-plane based on the scaling properties of the pinning force densities. The present method has also been compared with the so called n-value model: E(J)=Ec(J/Jc)n. It has been shown that the value of exponent n and Jc determined by an electric-field criterion, Ec, can be plotted as a function of B and T. Additionally, the relationship between these parameters, n and Jc, and material properties such as pin distribution and its thermodynamic properties can be clarified by this analysis. These results are useful not only to estimate critical current properties in HTS materials but also to design HTS-based devices by taking into account operation conditions such as B, T and power dissipation.
