Annular long Josephson junctions receive a lot of attention, if fluxon dynamics is to be investigated in a clean continuous system. We examine such contacts theoretically and experimentally taking into account their finite width. The width of the ring is important due to the radially dependent Lorentz contraction of the fluxon at high velocities. For a sufficiently long junction its electrodynamics is described accurately by the one-dimensional perturbed sine-Gordon equation. We found an analytical expression for the effective length L_(eff) of the junction by solving the two-dimensional sine-Gordon equation in polar coordinates using a perturbation approach. The theoretical results are compared with measurements of fluxon steps in linear and annular junctions and good agreement is found.
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