Multibeam Stimulated Raman Scattering in Inertial Confinement Fusion Conditions

Stimulated Raman scattering from multiple laser beams arranged in a cone sharing a common daughter wave is investigated for inertial confinement fusion (ICF) conditions in a inhomogeneous plasma. It is found that the shared electron plasma wave (EPW) process, where the lasers collectively drive the same EPW, can lead to an absolute instability when the electron density reaches a matching condition dependent on the cone angle of the laser beams. This mechanism could explain recent experimental observations of hot electrons at early times in ICF experiments, at densities well below quarter critical when two plasmon decay is not expected to occur.

Figure 1

(a) Geometry of collective SRS via a shared EPW: the instability is convective for $n_e<n_{em}({\theta }_v)$ (I), absolute for $n_e=n_{em}({\theta }_v)$ (II), and cannot exist for $n_e>n_{em}({\theta }_v)$ (III). (b) Convective gain vs $n_e$ and ${\theta }_v$, for an overlapped intensity of ${10}^{16}\mathrm{W}/{\mathrm{cm}}^2$ (with polarization smoothing) and $L_n=1\mathrm{mm}$.

Figure 2

(a) Geometry of the dominant SRS side-scatter mode for a single laser beam, azimuthally ($\varphi$) or radially ($\theta$) polarized; $\epsilon$ is the direction of both the laser beam and its scatter light wave’s polarizations. (b) $N_{\mathrm{PS}}$ and $N_{\theta }$ [from Eqs. (6) and (7)] as a function of ${\theta }_v$: the collective shared EPW instability dominates over each individual laser beam’s SRS side-scatter when the number of beams per cone $N$ is larger than $N_{\mathrm{PS}}$ with PS or $N_{\theta }$ with radial polarization. Also shown are the typical number of beams per cone on the NIF, Omega and Laser Megajoule (LMJ, France) facilities.

Figure 3

Experimental signatures of shared EPW SRS vs incident cone angle: (a) scattered light wavelength ${\lambda }_s$; (b) hot electron temperature $T_{\text{hot}}=\frac{1}{2}m({\omega }_{pm}/k_p{)}^2$; (c) scattered light exit angle in vacuum (with respect to $z$, i.e., 180° is pure backscatter).

Figure 4

(a) Overlapped intensities in units of ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ for the four NIF cones of beams, at 23.5°, 30°, 44.5°, and 50° ($\times 10$ for the 23.5° and 30°), and beams overlap geometry (inset). (b)–(d) Simulated $n_e/n_c$ vs $z$ (hohlraum axis) at the LEH for two NIF shots with hohlraum gas fill of $0.6\mathrm{mg}/\mathrm{cc}$ and $0.03\mathrm{mg}/\mathrm{cc}$ (“near-vacuum hohlraum,” NVH) at $t_1=0.2\mathrm{ns}$, $t_2=0.5\mathrm{ns}$, and $t_3=1\mathrm{ns}$. Also shown are the matching densities $n_{em}({\theta }_v)$ [Eq. (1)] for the four cone angles. The 50° cone is 40 times above threshold at $n_{em}(50°)$ between $t_2$ and $t_3$ for the $0.6\mathrm{mg}/\mathrm{cc}$ shot only [after $t_3$, the density bump has both dropped below $n_{em}(50°)$ and moved out of the 50° cone overlap region, shown as a dashed black box between $z=5.5$ and 6.2 mm: multibeam SRS is, thus, expected to stop]. The density in the NVH drops fast enough to stay below $n_{em}$, eliminating the risk of absolute multibeam SRS. This is consistent with the observation of hot electrons on the $0.6\mathrm{mg}/\mathrm{cc}$ shot only, at time $t_2$ for a duration $\le 250\mathrm{ps}$.