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The effect on parametric instability growth of pump wave incoherence is treated by deriving a set of equations governing the space-time evolution of the ensemble-average coupled-mode amplitudes and intensities. Particular attention is paid to establishing the regions of validity of the statistical description. Thresholds, growth rates, and amplification rates are given for both spatially and temporally incoherent pump waves. Both absolutely and convectively unstable modes are considered. The statistical results are verified where appropriate by numerical integration of the coupled-mode equations with different models of pump incoherence.
Electronic parametric instabilities of an ultrarelativistic circularly polarized laser pulse propagating in underdense plasmas are studied by numerically solving the dispersion relation which includes the effect of the radiation reaction force in las
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 d
The development of parametric instabilities in a large scale inhomogeneous plasma with an incident laser beam composed of multiple-frequency components is studied theoretically and numerically. Firstly, theoretical analyses of the coupling between tw
We report the efficient generation of high-gain parametric down-conversion, including pump depletion, with pump powers as low as 100 $mu$W (energies $0.1$~$mu$J/pulse) and conversion efficiencies up to 33%. In our simple configuration, the pump beam
The statistics of edge-localised plasma instabilities (ELMs) in toroidal magnetically confined fusion plasmas are considered. From first principles, standard experimentally motivated assumptions are shown to determine a specific probability distribut