Theory and measurements of convective Raman side scatter in inertial confinement fusion experiments

Raman side scatter, whereby scattered light is resonant while propagating perpendicularly to a density gradient in a plasma, was identified experimentally in planar-target experiments at the National Ignition Facility at intensities orders of magnitudes below the threshold for absolute instability. We have derived a new theoretical description of convective Raman side scatter below the absolute threshold, validated by numerical simulations. We show that inertial confinement fusion experiments at full ignition scale, i.e., with mm-scale spot sizes and density scale lengths, are prone to increased coupling losses from Raman side scatter as the instability can extend from the absolute regime near the quarter-critical density to the convective regime at lower electron densities.

Figure 1

(a) Polar view (Lambert azimuthal projection) of the NIF's 96 southern hemisphere beams. (b) Target alignment and geometry; a tilt was used to vary the angle ${\theta }_{\mathrm{out}}$ between the target surface and the FABS diagnostics (located in the quads 36B and 31B).

Figure 2

(a) Expected exit angle for Raman side scatter [Eq. (1)] for two electron temperatures, $T_e=3$ and 5 keV (bracketing the $\sim 4$ keV estimated temperature in the experiments), and FABS measurements at four collection angles ${\theta }_{\mathrm{out}}=[{59}^{\circ },{50}^{\circ },{30}^{\circ },0^{\circ }]$. (b) Laser pulse shape for collection at ${\theta }_{\mathrm{out}}={50}^{\circ }$ (in this case the target was horizontal and the data were collected in FABS 36B). (c) SRS spectrum from the ${50}^{\circ }$ collection angle with all quads turned on, showing the same observed wavelength wether the outer cones ($44.5^{\circ }$ and ${50}^{\circ }$ incidence) or inner cones ($23.5^{\circ }$ and ${30}^{\circ }$) were shot. (d) Same as (c) with selected quads turned off as indicated [the selected quads are highlighted in Fig. 1].

Figure 3

(a) SRS resonance away from the turning point, as given by the Rosenbluth formula when refraction can be neglected (1D problem); the length of the resonance region is approximately $\mathrm{\Delta }l$ along the path of the scattered light. (b) Tangential side-scatter geometry, where the resonance occurs at the turning point; refraction moves the scattered light away from the resonance and leads to a finite convective gain $G$ and resonance region, defined by $\mathrm{\Delta }z$ and $\mathrm{\Delta }x$. (c) Side-scatter gain [numerical solution from Eqs. (6) and (7)] vs. wavelength and laser intensity for $L=800$ $\mu \mathrm{m}$, $T_e=4$ keV and ${\theta }_{0v}={50}^{\circ }$; the region of absolute instability is marked in white, and the orange region corresponds to our experimental observations (with intensities ranging from 2.2 to $1\times {10}^{14}$ W/${\mathrm{cm}}^2$ to account for the $\sim 50\%$ laser absorption at higher densities). (d) Size of the resonance region $\mathrm{\Delta }x$ and $\mathrm{\Delta }z$ [Eqs. (8) and (9)], and size of the NIF beams projected along the $x$ direction (dotted line).