Parametric pulse amplification by acoustic quasimodes in electron-positron plasma

In a recent paper, M. R. Edwards, N. J. Fisch, and J. M. Mikhailova [Phys. Rev. Lett. 116, 015004 (2016)] reported that in electron-positron plasma stimulated Brillouin scattering is drastically enhanced, while stimulated Raman scattering is completely absent. However, when theory was compared to particle-in-cell (PIC) simulations, a discrepancy by at least a factor four appeared. Authors correctly argued that the disparity might be due to the fluid approximation of the low-frequency mode. They noted that a more precise analytic description of the acoustic resonance requires a kinetic approach, which was beyond the scope of the mentioned paper. Here we deliver the so-far-missing kinetic calculation. It shows quite good agreement with the PIC simulations presented in the above-mentioned paper by Edwards et al. The principal result of enhancement of Brillouin scattering and absence of Raman scattering remains valid. The Brillouin enhancement factors depend on electron temperature and background particle density. These dependencies as well as the transition to the well-known behavior of electron-ion plasma are discussed. It is also shown that pulse amplification in electron-positron plasma crosses over to the strong-coupling regime when the pump amplitude becomes large. Then, the fluid approximation becomes acceptable again.

Figure 1

Numerical (graphical) procedure for solving Eq. (9). Shown are the areas $\text{Re}\left(\mathrm{\Delta }\right)\ge 0$ (yellow) with the borderlines of $\text{Re}\left(\mathrm{\Delta }\right)=0$ on the one hand and the areas $\text{Im}\left(\mathrm{\Delta }\right)\ge 0$ (blue) with the borderlines of $\text{Im}\left(\mathrm{\Delta }\right)=0$ on the other hand, for $S=k{\lambda }_{De}=0.1$ and $\alpha =\beta =1$. The function $\mathrm{\Delta }\left(\zeta \right)$ is defined in (9), and $x=\text{Re}\left(\zeta \right)$, $y=-\text{Im}\left(\zeta \right)$.

Figure 2

Growth rate $\mathrm{\Gamma }$ vs mass ratio $\beta$ obtained by solving different dispersion relations. In dashed red and dashed blue fluid predictions are shown for Raman and Brillouin instability, respectively. The solutions of Eq. (28) with kinetic susceptibilities (29) are depicted by black dots for Raman and the solid black line for Brillouin, respectively. Parameters are $\alpha =1$, $T_e=20$ eV, $n_0={10}^{19}{\mathrm{cm}}^{-3}$, and laser intensity $I={10}^{14}{\mathrm{W}/\mathrm{cm}}^2$.

Figure 3

Growth rate $\mathrm{\Gamma }$ vs mass ratio $\beta$ in kinetic description (28) for different temperatures $T$, namely 20 eV (solid lines), 70 eV (dotted lines), and 120 eV (dashed lines), respectively. The temperature ratio is fixed to $\alpha =1$. Shown are the Brillouin growth rates in black (within the shaded area), as well as the Raman growth rates in red. Other parameters are $n_0={10}^{19}{\mathrm{cm}}^{-3}$ and $I={10}^{14}{\text{W}/\mathrm{cm}}^2$.

Figure 4

Growth rate $\mathrm{\Gamma }$ vs mass ratio $\beta$ in kinetic description (28) for different background densities. Shown is the Brillouin growth rate (black lines) in comparison to the Raman growth rate (red lines). The solid lines are for $n_0={10}^{19}{\mathrm{cm}}^{-3}$ while the dashed lines are for $n_0={10}^{20}{\mathrm{cm}}^{-3}$. Other parameters are $\alpha =1$, $T=20$ eV, and $I={10}^{14}{\mathrm{W}/\mathrm{cm}}^2$.

Figure 5

Growth rate $\mathrm{\Gamma }$ in dependence of pump amplitude $a_0$ for an $e\text{−}p$ plasma ($\beta =1$). The solid line represents the kinetic Brillouin growth rate $\mathrm{\Gamma }$ as obtained from Eq. (28). The dashed line follows from the fluid description with susceptibilities (32). Parameters are $\alpha =1$, $T=20$ eV, and $n_0={10}^{19}{\mathrm{cm}}^{-3}$.