When a short electron beam propagates in an underdense plasma(plasma density n0 < beam density nb) with adownward density transition, it is known that some background plasmaelectrons are trapped and accelerated by the plasma wakefield. The beamquality of the trapped plasma electrons is severely affected by thewakefield that is generated by the driving electron beam, so dynamicsand instabilities of the driver beam are very important. In this paper,we present some simulation results on the self-trapping and driver beamdynamics
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