Fine structures on the zero field steps of long Josephson tunnel junctions are simulated for junctions with the bias current injected into the junction at the edges. These structures are due to the coupling between self-generated plasma oscillations and the traveling fluxon. The plasma oscillations are generated by the interaction of the bias current with the fluxon at the junction edges. On the first zero field step, the voltages of successive fine structures are given by Vn=[h-bar]/2e(2omegap/n), where n is an even integer. Applied Physics Letters is copyrighted by The American Institute of Physics.