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Near the resonance (ωo≊ωp) a high-amplitude plasma wave decays into a purely growing electromagnetic perturbation and two Langmuir wave sidebands. The growth rate of the instability γ≃ωpk20v20/ 8k2v2e for a Langmuir pump wave of finite wavenumber k0≳kve/c and the threshold due to the finite extent, x0, of the pump is v20/v2e≳4k2v2e(k2x0+β)/ ω2pβx0; v0 and ve are the oscillatory and thermal velocities of electrons and β is the x component of propagation vector k of the perturbation. This instability may be a possible source of spontaneous generation of random magnetic field in laser-produced plasmas.
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Tripathi et al. (1982) studied this question.
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