Onset of Vortices in Thin Superconducting Strips and Wires
  Spontaneous nucleation and the consequent penetration of vortices into thin superconducting films and wires, subjected to a magnetic field, can be considered as a nonlinear stage of primary instability of the current-carrying superconducting state. The development of the instability leads to the formation of a chain of vortices in strips and helicoidal vortex lines in wires. The boundary of instability was obtained analytically. The nonlinear stage was investigated by simulations of the time-dependent generalized Ginzburg-Landau equation. 
I. Aranson, M. Gitterman and B. Ya. Shapiro, (Dept. of Physics and   Jack and Pearl Resnick Inst. of Advanced Technology, Ba...