Mathematical model of vortex penetration phenomenon

Vortex penetration affects the stability of a superconducting system and limits the possible application of the system. However, the mathematical description to this phenomenon is currently unavailable. Here, I presented a mathematical model in which I considered the effects of bulk pinning and internal field repulsive force on vortex hopping. Thereafter, I proposed a series expansion to the activation energy and derived a general formula to describe the time dependence of the vortex penetration process. With these formulas, I can analyze the experimental data and calculate the activation energy of the vortex penetration phenomenon. The results are accurate for the time dependence of the internal field measurements in a Bi(2)Sr(2)CaCu(2)O(8+x) superconductor. (C) 2011 American Institute of Physics. [doi:10.1063/1.3530579]