Nonlinear mechanism for the generation of electromagnetic fields in a magnetized plasma by the beatings of waves
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INEAR PHENOMENA
Nonlinear Mechanism for the Generation of Electromagnetic Fields in a Magnetized Plasma by the Beatings of Waves G. D. Aburjania, G. Z. Machabeli, and O. A. Kharshiladze Vekua Institute of Applied Mathematics, Tbilisi State University, Tbilisi, 380043 Georgia Received July 27, 2005; in final form, November 7, 2005
Abstract—The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process. PACS numbers: 52.35.–g, 52.35.Hr, 52.35.Mw DOI: 10.1134/S1063780X06070063
1. INTRODUCTION The formation of a “plasmon condensate” in a weakly turbulent plasma is a well-known paradoxical phenomenon [1] in which the main nonlinear process— the decay of a Langmuir wave l into a Langmuir wave l ' and an ion acoustic wave s (l l ' + s) [2]—gives rise to a wave energy flux toward the long-wavelength region, where there is no efficient mechanism for wave absorption. As the energy is pumped into Langmuir turbulence, it is stored in the long-wavelength region. Vedenov and Rudakov [3] showed that, because of the development of modulational instability, a uniformly distributed plasmon background can break into plasmon bunches. Zakharov [4] studied the modulational instability in its nonlinear stage, which is characterized by Langmuir wave collapse. The collapse leads the formation of cavities—regions with depressed ion density and elevated field (i.e., with elevated plasmon density). Galeev et al. [5] supposed that the modulational instability can eliminate the problem of plasmon condensate because of the reduction in the spatial scales of the waves. In [6–8], a theory of Langmuir turbulence was developed that takes into account the wave energy flux to smaller scales due to Langmuir wave collapse and the subsequent onset of a linear mechanism for plasmon absorption. All the papers cited above were aimed at studying turbulence in an unmagnetized plasma. In this case, the weak turbulence parameter W/nT should satisfy the 2 2 2 2 condition W/nT ω Be /ω pe (provided that ω Be /ω pe 2
2
k 0 λ D ), where W = ε0E2/2 is the wave energy density, E is the electric field amplitude, ε0 is the dielectric constant, ωBe = eB0/m is the electron gyrofrequency, ωpe =
[e2n/(ε0m)]1/2 is the electron Langmuir frequency, n is the electron density, m is the mass of an electron, T is the electron temperature, k0 is the characteristic wavenumber in the turbulence spectrum, and λD = [ε0T/(e2n)]1/2 is the electron Debye radius. This condition, however, substantially limits the applicability of the results obtained in solving relevant prob
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