We have studied the variety of the plasma discharge process of neutral gases by an electron beam injected parallel to the external magnetic field[1]. Then various unstable waves are generated by the interaction between the beam and the dischage plasma. On the condition of higher gas pressure and lower magnetic field, low frequency unstable waves excited strongly. The anomalous diffusion due to these waves duffuse the generated plasma perpendicular to the magnetic field[2]. We attempt the theoretical and numerical analysis of low frequency unstable waves in the presence of the applied high frequency (HF) field. The frequencies of the HF field are taken on the neiborhood of the frequencies of Bernstein mode or Trivelpiece-Gould mode as the normal modes in a plasma. These analyses are performed by taking the boundary condition perpendicular to the magnetic field as the cylindrical electron beam and plasma column, i.e., the nonlocal theory. The ponderomotive forces due to the pump the HF field and fields of both lower and higher sideband waves are taken in nonlinear termes. The numerical results show the suppression of unstable ion cyclotron harmonic waves or unstable lower hybrid waves. Therefore, low frequency unstable waves are suppressed by the ponderomotive forces of pump HF fields, and almost low frequnecy unstable waves generated in the discharge plasma by an electron beam can be numerically suppressed by the applied HF fields. These results are partially compared with the experimental results, and the experimental verification will also be performed from now.

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