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We study long Josephson junctions with the critical current densityalternating along the junction. New equilibrium states, which we call the fieldsynchronized or FS states, are shown to exist if the applied field is fromnarrow intervals centered around equidistant series of resonant fields, $H_m$.The values of $H_m$ are much higher than the flux penetration field, $H_s$. Theflux per period of the alternating critical current density, $\phi_i$, is fixedfor each of the FS states. In the $m$-th FS state the value of $\phi_i$ isequal to an integer amount of flux quanta, $\phi_i =m\phi_0$. Two types ofsingle Josephson vortices carrying fluxes $\phi_0$ or/and $\phi_0/2$ can existin the FS states. Specific stepwise resonances in the current-voltagecharacteristics are caused by periodic motion of these vortices between theedges of the junction.

High-field vortices in Josephson junctions with alternating critical current density