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The behavior of long annular Josephson junctions with various numbers n of trapped fluxons is studied in the presence of a uniform external magnetic field parallel to the plane of the junction’s tunnel barrier. We report on measurements of the magnetic dependencies of the critical current and current–voltage characteristics with different n. Experimental results are explained by the model assuming that a barrier-parallel magnetic field produces potential wells for fluxons and antifluxons at the opposite locations. We also present numerical simulations using the perturbed sine-Gordon equation with an additional magnetic-field-induced term. Good agreement is found between the measured critical current versus magnetic-field dependencies and the numerical simulations. © 1997 American Institute of Physics.