Stimulated Raman scattering in the relativistic regime in near-critical plasmas

Interaction of a high-intensity short laser pulse with near-critical plasmas allows us to achieve extremely high coupling efficiency and transfer laser energy to energetic ions. One-dimensional particle-in-cell simulations are considered to detail the processes involved in the energy transfer. A confrontation of the numerical results with the theory highlights a key role played by the process of stimulated Raman scattering in the relativistic regime. The interaction of a 1 ps laser pulse ($I\sim 6\times {10}^{18}\mathrm{W}{\text{cm}}^{-2}$ with an undercritical ($0.5n_c$) homogeneous plasma leads to a very high plasma absorption reaching 68% of the laser pulse energy. This permits a homogeneous electron heating all along the plasma and an efficient ion acceleration at the plasma edges and in cavities.

Figure 1

Laser pulse interaction with a homogeneous plasma slab and Poynting fluxes measured at the left and right boundaries of the simulation box. (a) and (d) give the amplitudes of forward $E_{+}$ and backward $E_{-}$ propagating waves, respectively, as a function of the longitudinal position $x$ and time $t$. The vertical dashed lines delimit the plasma density $n_p$ where $n_p<0.1n_c$. (b) and (c display the instantaneous (solid line) and cumulated (dashed red line) Poynting fluxes through the right (b) and left (c) boundaries of the simulation box.

Figure 2

Time-frequency analysis of the electromagnetic field leaving out (a) the left boundary and (b) the right boundary of the simulation box. Both panels are normalized to the same scale.

Figure 3

Time-frequency analysis of the (a) forward-propagating $E_{+}$, (b) backward-propagating $E_{-}$, and (c) electrostatic $E_x$ fields at the distance of $3{\lambda }_0$ from the left plasma edge ($x=353{\lambda }_0$). All three panels are normalized using the same scale.

Figure 4

Time evolution of the spatial spectra of the (a) forward-propagating $E_{+}$, (b) backward-propagating $E_{-}$, and (c) electrostatic $E_x$ fields in the plasma, in the interval (350–375) ${\lambda }_0$. All three panels are normalized using the same scale. The blue crosses in (a) and (b) give the theoretical values of the wave number $k_0$ and $|k_s|$ in the plasma of the laser wave (${\omega }_0$) and the scattered wave (${\omega }_s=0.53{\omega }_0$), respectively.

Figure 5

Comparison of the (a) electrostatic wave number $k_p$ and (b) frequency $\mathrm{Re}{\omega }_p$ as a function of the growth rate $\mathrm{\Gamma }=\mathrm{Im}{\omega }_p$ from the solution of Eq. (6) (blue dots) and as a function of FFT amplitude from simulation analysis (solid red curve) in the plasma range $x=(350–375){\lambda }_0$ and at $t\approx 414T_0$.

Figure 6

(a) Electron energy density as a function of space and time and (b) cumulated electron (red) and ion (blue) energy as a function of time. The vertical dashed lines delimit the plasma density $n_p$ where $n_p<0.1n_c$. The solid green line [corresponding to the (2)-(3) boundary line in Fig. 1] shows the arrival of the high-amplitude laser pulse. The dashed blue line [corresponding to the (0)-(1) boundary line in Fig. 1] shows the triggering of the backscattered electromagnetic waves by the plasma.

Figure 7

(a) Longitudinal electron phase space, (b) electrostatic field $E_x$, and forward-propagating field $E_{+}$ at the plasma front ($350–385{\lambda }_0$) at $t\approx 414T_0$.

Figure 8

(a) Electron and (b) ion distribution functions computed at $t\approx 700T_0$ and $t\approx 1528T_0$, respectively.

Figure 9

Ion energy density as a function of space and time. The vertical dashed lines delimit the plasma density $n_p$ where $n_p<0.1n_c$. The solid green line [corresponding to the (2)-(3) boundary line in Fig. 1] shows the arrival of the high-amplitude laser pulse. The dashed blue line [corresponding to the (0)-(1) boundary line in Fig. 1] shows the triggering of the backscattered electromagnetic waves by the plasma.

Figure 10

Interaction energy balance as a function of the laser pulse intensity: $A, R$, and $T$ are respectively the plasma kinetic energy, the reflected and transmitted laser energy at the end of the simulation ($t_s\approx 1528T_0$). These quantities are normalised to the total laser pulse energy. The plasma density is $0.5n_c$ and the length is $150{\lambda }_0$.