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The long-time evolution of the two-stream instability of a cold ion beampulse propagating though the background plasma is investigated using alarge-scale one-dimensional electrostatic kinetic simulation. The three stagesof the instability are identified and investigated in detail. After the initiallinear growth and saturation by the electron trapping, a portion of theinitially trapped electrons becomes detrapped and moves ahead of the ion beampulse forming a {forerunner} electron beam, which causes a secondary two-streaminstability that preheats the upstream plasma electrons. Consequently, theself-consistent nonlinear-driven turbulent state is set up at the head of theion beam pulse with the saturated plasma wave sustained by the influx of thecold electrons from the upstream of the beam that lasts until the final stagewhen the beam ions become trapped by the plasma wave. The beam ion trappingleads to the nonlinear heating of the beam ions that eventually extinguishesthe instability.

Generation of forerunner electron beam during interaction of ion beam pulse with plasma