Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for Stimulated Raman Scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with the coherence width $sigma$ of the radiation field, scaling with $1/sigma$ for backscattering (three-wave process), and with $1/sigma^{1/2}$ for direct forward scattering (four-wave process). Our results demonstrate the possibility to control the growth rates of these instabilities by properly using broadband pump radiation fields.
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