We report a generation of energetic protons by the interaction of a high-energy electron driving beam with an underdense plasma slab. After an interaction period of approximately 4000 fs, a proton beam with maximum energy greater than 250 MeV can be achieved by applying a driving beam with energy 1.0 GeV to a 200 $mathrm {mu }$m plasma slab. Our two-dimensional particle-in-cell simulations also show that the proton acceleration process can be divided into two stages. In the first stage, a strong positive longitudinal electric field appears near the rear boundary of the plasma slab after the driving beam has passed through it. This acceleration process is similar to the target normal sheath acceleration scheme by the interaction between intense pulsed laser with overdense plasma targets. In the second stage, the accelerated protons experience a long-range acceleration process with a two-stream instability between the high-energy driving beam and the proton beam. Further analyses show that this accelerated proton beam is equipped with the property of good collimation and high energy. This scheme presents a new way for proton or ion acceleration on some special occasions.
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