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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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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 two laser beamlets with certain frequency difference $deltaomega_0$ for parametric instabilities is presented. It suggests that the two beamlets will be decoupled when $deltaomega_0$ is larger than certain thresholds, which are derived for stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), and two plasmon decay (TPD), respectively. In this case, the parametric instabilities for the two beamlets develop independently and can be controlled at a low level provided the laser intensity for individual beamlet is low enough. Secondly, numerical simulations of parametric instabilities with two or more beamlets ($Nsim20$) have been carried out and the above theory model is validated. Simulations confirm that the development of parametric instabilities with multiple beamlets can be controlled at a low level, provided the threshold conditions for $deltaomega_0$ is satisfied, even though the total laser intensity is as high as $sim10^{15}$W/cm$^2$. With such a laser beam structure of multiple frequency components ($Ngtrsim20$) and total bandwidth of a few percentages ($gtrsim4%$), the parametric instabilities can be well-controlled.
New class instabilities is identified in Hall plasmas in configurations with open magnetic field lines. It is shown that sheath resistivity results in a robust instability driven by the equilibrium electric field. It is conjectured that these instabilities play a crucial role in anomalous transport in Hall plasmas devices.
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 laser-driven plasma dynamics. Emphasis is placed on studying the different modes in the laser-plasma system and identifying the absolute and convective nature of the unstable modes in a parameter map spanned by the normalized laser vector potential and the plasma density. Implications for the ultraintense laser-plasma experiments are pointed out.
Counterstreaming plasma structures are widely present in laboratory experiments and astrophysical systems, and they are investigated either to prevent unstable modes arising in beam-plasma experiments or to prove the existence of large scale magnetic fields in astrophysical objects. Filamentation instability arises in a counterstreaming plasma and is responsible for the magnetization of the plasma. Filamentationally unstable mode is described by assuming that each of the counterstreaming plasmas has an isotropic Lorentzian (kappa) distribution. In this case, the filamentation instability growth rate can reach a maximum value markedly larger than that for a a plasma with a Maxwellian distribution function. This behaviour is opposite to what was observed for the Weibel instability growth rate in a bi-kappa plasma, which is always smaller than that obtained for a bi-Maxwellian plasma. The approach is further generalized for a counterstreaming plasma with a bi-kappa temperature anisotropy. In this case, the filamentation instability growth rate is enhanced by the Weibel effect when the plasma is hotter in the streaming direction, and the growth rate becomes even larger. These effects improve significantly the efficiency of the magnetic field generation, and provide further support for the potential role of the Weibel-type instabilities in the fast magnetization scenarios.
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.
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