Generation of harmonic Langmuir mode by beam-plasma instability

Abstract

In this article, numerical solutions of the generalized weak turbulence equation [P. H. Yoon, Phys. Plasmas 7, 4858 (2000)] are carried out. In the generalized weak turbulence theory, the generation of the 2ωpe-harmonic Langmuir mode is treated as a fundamental process in turbulent beam-plasma interaction process, in addition to, and concomitant to, the well-known nonlinear processes such as Langmuir and ion-sound mode coupling and wave-particle interactions. The present numerical analysis shows that the harmonic mode, which is a solution to a nonlinear dispersion equation, hence a “nonlinear” eigenmode, grows primarily due to an induced emission process, which is a “linear” wave-particle interaction process. The harmonic Langmuir mode generation has been observed since the late 1960s in laboratory experiments, simulations, and in space. However, adequate and quantitative theoretical explanation has not been forthcoming. The present work represents a step toward an understanding of such a phenomenon.

Excitation of waves at 2 <i>ω<sub>p,e</sub></i> and back propagating waves at <i>ω<sub>p,e</sub></i>: a parametric study

“…We can consider the point I L / n e k T e = 1 as a characteristic endpoint of the weak turbulence. Our simulations show qualitatively similar results to those of Ziebell et al (2001) and Gaelzer et al (2002) who studied a weak beam-plasma instability solving numerically the equations of (generalized) weak plasma turbulence kinetic theory. Further comparisons of Vlasov simulations and the work of Ziebell et al (2001) and Gaelzer et al (2002) requires the use of comparable plasma parameters and is out of the scope of this paper.…”

“…The third component present in our model is an electron beam with variable initial parameters. We compare the results of our numerical experiments for 2 ω p,e waves with the theoretical predictions of Yoon's theory (Yoon, 2000;Ziebell et al, 2001;Gaelzer et al, 2002). In addition, we briefly discuss the growth rate of −ω p,e waves.…”

“…(3) has been derived as an approximate solution of the non-linear eigenmode analysis retaining the nonlinear wave coupling term which arises from the presence of a broad spectrum of incoherent Langmuir waves (Gaelzer et al, 2002;Yoon, 2000). The numerical simulations carried out in this paper show that the main parameter that governs the plasma properties is the time averaged energy I L…”

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

“…10 appeared in the year 2002, with the discussion of the time evolution of beam-plasma instability, taking into account fundamental and harmonics L waves and S waves, and by incorporating quasilinear effect of induced emission and the nonlinear effects of three-wave decay and scattering. 41 Reference 41 did not take into account spontaneous effects, included in the general formalism after Ref. 11, but only collective nonlinear effects.…”

Formation of quasi-power law weak Langmuir turbulence spectrum by harmonic generation

“…Recently, however, a theory of harmonic generation in turbulent plasmas was developed by the author and his colleagues (Yoon, 2000;Gaelzer et al, 2002Gaelzer et al, , 2003Yoon et al, 2003;Umeda et al, 2003), in which these modes are considered as eigenmodes of nonlinear plasma system. This approach was prompted by recent simulations (Schriver et al, 2000;Kasaba et al, 2001) which show that harmonic modes persist even in late nonlinear phase when the coherent phase space structure is no longer apparent, and when the plasma has entered a stage which can be genuinely characterized by random-phases.…”