The paper presents a study on dynamic stabilization of filamentation instability driven by an electron beam introduced into a plasma. The results presented in the paper demonstrate that the filamentation instability is successfully stabilized by the dynamic stabilization mechanism, in which the electron beam axis oscillates. The dynamic stabilization mechanism for plasma instability was proposed in the paper [Kawata, Phys. Plasmas 19, 024503 (2012)]. In general, instabilities emerge from the perturbations of the physical quantity. Normally the perturbation phase is unknown so that the instability growth rate is discussed. However, if the perturbation phase is known, the instability growth can be controlled by a superimposition of perturbations imposed actively: if the perturbation is introduced by, for example, a driving beam axis oscillation or so, the perturbation phase can be controlled and the instability growth is mitigated by the superimposition of the growing perturbations.

An ultra-intense short-pulsed laser interacting with a uniform underdense plasma with near-critical density is investigated by 2.5-dimensional particle-in-cell simulations. It is found that a collimated proton beam with maximum energy up to the GeV was generated. The corresponding proton acceleration mechanism is analyzed. The laser wakefield acceleration (LWFA) electrons play an important role as a driving beam. Due to the features of LWFA electrons, quasi-monoenergetic distribution and good collimation, the protons can be accelerated for a long distance by the chargeseparated electric field. The proton beam in this regime is also well collimated and the amount can reach several nC. Moreover, it is found that the LWFA electrons can overtake the laser and stand quasi-synchronized in the center of pulse. Therefore the electrons can absorb energy from the laser and transfer it to the protons like in the break-out afterburner (BOA) scheme in laser irradiated on ultra-thin film target.

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