In-plane fluxon in layered superconductors with arbitrary number of layers

I derive an approximate analytic solution for the in-plane vortex (fluxon) in layered superconductors and stacked Josephson junctions (SJJ's) with arbitrary number of layers. The validity of the solution is verified by numerical simulation. It is shown that in SJJ's with large number of thin layers, phase/current and magnetic field of the fluxon are decoupled from each other. The variation of phase/current is confined within the Josephson penetration depth, $\lambda_J$, along the layers, while magnetic field decays at the effective London penetration depth, $\lambda_c \gg \lambda_J$. For comparison with real high-$T_c$ superconducting samples, large scale numerical simulations with up to 600 SJJ's and with in-plane length up to 4000 $\lambda_J$%, are presented. It is shown, that the most striking feature of the fluxon is a Josephson core, manifesting itself as a sharp peak in magnetic induction at the fluxon center.Comment: 4 pages, 4 figures. Was presented in part at the First Euroconference on Vortex Matter in Superconductors (Crete, September 1999