Plasma Waves Generated by Rippled, Magnetically Focused Electron Beams Surrounded by Tenuous Plasmas
The electrostatic instability and the corresponding unstable wave spectrum of a neutralized rippled cylindrical electron beam (finite radius) surrounded by a tenuous plasma (large radius) at rest is investigated. The rippling is due to the imbalance of the centrifugal (defocusing) and Lorentz (focusing) forces acting on the fluid element of beam.
The analysis is carried out for both long and short wavelength surface perturbations. Closed analytical expressions for the growth rates are derived and discussed. It is found that the growth rates are proportional to the relative ripple amplitude and to the effective beam plasma frequency. Because of the "reduction" effect due to the finiteness of the beam radius, the growth rates are larger in the short wavelength limit. The presence of the surrounding plasma is such as to increase the growth rates of the instability.
The generation of unstable surface waves in the presence of a rippled beam-edge (and, correspondingly, a modulated beam particle density) places this process in the class of parametric instabilities.
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