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Astron. Astrophys. 331, 1147-1156 (1998)

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4. Generation of Langmuir waves

Here we consider the full behaviour of collective effects by using a 1-D electrostatic particle code similar to that in the paper by Messerotti and Karlický (1991). The case of an infinite neutral beam will be compared with the pure electron and proton beam cases. The length of the system, which was chosen to be equal to the wavelength of the most unstable wave, was set to 2 [FORMULA]. The proton-electron mass ratio was chosen as 100; the electron and proton beam frequencies are [FORMULA] and [FORMULA]. Cold monoenergetic beams were considered. The time evolution of the electrostatic field energy is shown in Fig. 6. From these results it is evident that Langmuir waves are generated in two steps. Firstly, the neutral beam behaves like a pure electron beam and later on like a proton beam. This means that at the beginning the growth rate of the instability is as high as that for an electron beam. Furthermore, the first saturation level of Langmuir waves is given by electron trapping. On the other hand, the high level of Langmuir waves at the second saturation level is determined by the beam protons. The phase space diagrams (Figs. 7a and 7b) show that firstly electrons are trapped, and after a mixing phase (t= 70-110 T, where T is the plasma period) the proton-beam instability starts and protons are trapped in the intense Langmuir wave. These numerical results fully agree with the theoretical estimates given by formulae for the growth rates, saturation levels and trapping periods, as follows (Mikhailovskii, 1974; Drummond et al., 1970; LeQueau and Roux, 1987):

[EQUATION]

[EQUATION]

where [FORMULA],

[EQUATION]

where [FORMULA] is the growth rate of the two-stream instability, [FORMULA] is the wave energy density at the saturation level, P is the trapping period, [FORMULA] is the mass of beam particles, [FORMULA] is the beam velocity, while k and E are the k-vector and the electric field amplitude of Langmuir waves, respectively.


[FIGURE] Fig. 6. The time evolution of electrostatic field energy in the simulated neutral beam-plasma system.

[FIGURE] Fig. 7a and b. The phase space at times 15.9 T (a), and 159.2 T (b) for the neutral beam-plasma system. The electrons and protons are represented by the smaller and bigger dots respectively.

These considerations are purely intended to indicate some of the complication likely to arise when high densities of coherent plasma waves occur in beam/plasma/gas interaction. We have not considered in any detail how wave scattering may allow stable propagation of beams but we observe that such interaction may determine the ultimate fate of the beam and may be crucial to an understanding of coherent radiation diagnostics such as Type III bursts.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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