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Description
Nonlinear inverse bremsstrahlung absorption (NLIBA) of intense electromagnetic waves in homogeneous plasmas may have significant impact on many physical phenomena through modifications of the electron distribution function (EDF). These modifications depend on the relevant parameter $ \alpha=\frac{v_0^2}{v_t^2\ } $, where $v_0 $ is the quiver velocity and $v_t $ is the electron thermal velocity. We address in this work the effects of the NLIBA on electron plasma waves (EPW).
The dispersion relation of the EPW is derived from the perturbed Vlasov-Poisson equations and we obtain for the real part, $\omega^2=\omega_p^2+\mathrm{\Gamma}k^2v_t^2 $ and for the imaginary part, the damping rate, $\gamma=\frac{\pi}{2\sqrt{2}}\frac{\omega^3}{\omega_p^2}\frac{\omega_p^2}{k^2v_t^2}\frac{d\hat{F}}{dx}\left(x=\frac{\omega}{\sqrt{2}k v_t}\right) $ where the different parameters have their usual meaning, $\hat{F}\left(\vec{v},\alpha\right)$ is the normalized reduced anisotropic EDF and $\mathrm{\Gamma}\left(\alpha\right)=12\sqrt{2}\displaystyle\int_{0}^{\infty}{x^2\hat{F}\left(x\right)}\mathrm{d}x $ is the polytropic index. For $\alpha \ll 1$, the plasma is Maxwellian and we recover the classical results of Bohm and Gross, and Landau, i. e., $\mathrm{\Gamma}_{Max}=3 $ and $ \frac{\gamma_{Max}}{\omega}=-\sqrt{\frac{\pi}{8}}\frac{\omega_p^3}{k^3v_t^3}\ \exp\left(-\frac{\omega^2}{2k^2v_t^2}\right)$. Solving numerically the Fokker-Planck equation for homogeneous plasmas in presence of strong laser field we calculated the EDF $ \hat{F}\left(\vec{v},\alpha\right)$ which presents strong temperature anisotropy induced by NLIBA. As a consequence, we found strong modification in the dispersion relation of the EPW. For $\alpha=1$ and $\alpha=2$ the polytropic index is $1.6$ and $2.6$ times greater than in the case of a Maxwellian plasma. The anisotropy effects affect also the damping of the EPW. The results for the damping rate are depicted in figure 1 where we give the damping rate normalized to the frequency of the EPW $\omega$ as a function of the dimensionless parameter $kv_t/\omega$. The dotted line corresponds to $\alpha\ll 1$ (Maxwellian plasma), the solid line corresponds to $\alpha=1$ and the dashed line corresponds to $\alpha=2$. We can note the modification of the damping rate. In particular, within the frequency range where these waves are weakly damped, i.e., $\frac{\omega}{\sqrt{2}kv_t}\gg 1$, we found that the damping is significantly greater for large $\alpha$. In particular for $ \frac{kv_t}{\omega}=0.15$ one obtains $\frac{\gamma}{\omega}=1.46\times {10}^{-5}$ instead of $\frac{\gamma\left(\alpha\ll 1\right)}{\omega}=4.6\times {10}^{-8}$ for Maxwellian plasmas. These changes in dispersion and damping of EPW, especially if $\alpha \sim 1$, should amend the thresholds and the growth rates of parametric instabilities involving the EPW in the coupling modes.
This work has been carried out within the framework of the PRFU 2023-2026 (Projet de Recherche et de Formation Universitaire) and under grant agreement No B00L02UN160420230002.
