Effect of Laser-Plasma Interactions on Inertial Confinement Fusion ...

Effect of Laser-Plasma Interactions on Inertial Confinement Fusion Hohlraum Dynamics D. J. Strozzi, D. S. Bailey, P. Michel, L. Divol, S. M. Sepke, G. D. Kerbel, C. A. Thomas, J. E. Ralph, J. D. Moody, M. B. Schneider

arXiv:1607.06523v1 [physics.plasm-ph] 21 Jul 2016

Lawrence Livermore National Laboratory, Livermore, CA 94551 (Dated: July 25, 2016) The effects of laser-plasma interactions (LPI) on the dynamics of inertial confinement fusion hohlraums is investigated via a new approach that self-consistently couples reduced LPI models into radiation-hydrodynamics numerical codes. The interplay between hydrodynamics and LPI specifically stimulated Raman scattering (SRS) and crossed-beam energy transfer (CBET) – mostly occurs via momentum and energy deposition into Langmuir and ion acoustic waves. This spatially redistributes energy coupling to the target, which affects the background plasma conditions and thus modifies the laser propagation. This model shows a reduction of CBET, and significant laser energy depletion by Langmuir waves, which reduce the discrepancy between modeling and data from hohlraum experiments on wall x-ray emission and capsule implosion shape.

Indirect-drive inertial confinement fusion has been actively pursued for several decades. It entails compressing thermonuclear fuel (namely deuterium and tritium) to 1000× solid density, with x-rays produced by heating a high-Z (e.g. gold) cylindrical “hohlraum” with highpower lasers. Ignition experiments have been conducted at the National Ignition Facility (NIF) from 2009 to the present [1]. Targets with laser pulses longer than ∼10 ns have used high density hohlraum gas fills ρ > ∼ 0.9 mg/cm3 , typically helium, to tamp expansion of the highZ wall. Laser-plasma interactions (LPI) are a key aspect of these experiments, and are sketched in Fig. 1. Substantial crossed-beam energy transfer (CBET) from the outer cones of laser beams, with angles θ to the hohlraum axis of θ = 44.5◦ and 50◦ , to the inner cones (θ = 23.5◦ and 30◦ ), is needed to control implosion symmetry in these experiments [2]. CBET is a version of stimulated Brillouin scatter (SBS) where the beating of two light waves drives an ion acoustic wave (IAW) which transfers energy to the light wave with lower frequency in the plasma frame [3]. Shots with high fill density also have high backward stimulated Raman scatter (SRS) from the inner beams, or the decay of a laser into a scattered light wave and Langmuir wave (LW). This is detrimental since the scattered light energy does not produce x-rays, and the LW decays to superthermal electrons which can preheat the DT fuel and reduce compression. The LWs do not remove energy from the target, but spatially redistribute its deposition. This alters symmetry of the x-ray drive and resulting implosion. LPI processes have temporal growth rates (1-10 ps) and spatial gain lengths (∼ speckle length in phase-platesmoothed beams, ∼ 160 µm on NIF) much smaller than hydrodynamic scales. Full LPI modeling therefore requires much more detailed and computationally expensive tools than radiation-hydrodynamics codes, such as paraxial-propagation [4] or particle-in-cell codes [5]. Including LPI effects in rad-hydro codes is therefore challenging: coupling a paraxial-propagation and rad-hydro

FIG. 1. Schematic of hohlraum LPI. Arrows indicate direction of wave propagation, and color darkness indicates intensity. Outer beams transfer power to inner beams where they overlap in the LEH. SRS light from inner beams grows continuously along path, with little IB absorption. Langmuir waves are driven by beating of inner-beam laser and SRS light.

model has been done, but is usually impractical on current computers [6]. CBET calculations either postprocess plasma conditions from a hydro simulation with no CBET [2, 7], or are directly implemented “inline” in hydro simulations that describe lasers with ray-tracing [8, 9] or paraxial complex geometric optics [10]. SRS is usually treated by removing the escaping light from the incident laser, though recent work has included SRSproduced superthermal electrons in direct-drive hydrodynamic modeling [11]. In this Letter, we use new, reduced LPI models inline in a rad-hydro code to study the interplay of LPI processes (CBET and backscatter) and hydrodynamics. We find significant impacts on plasma dynamics and hohlraum irradiation symmetry. Namely, LPI-driven plasma waves modify plasma conditions and alter CBET in high-fill-density NIF experiments, where CBET can roughly double the inner-beam power, and inner-beam SRS can exceed half of the incident power. Unlike prior work, CBET and SRS are modeled together and through-

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FIG. 2. Left: measured 30◦ cone SRS spectrum from full aperture backscatter station (FABS) for NIF shot N121130, with cone incident (white) and escaping SRS (red) powers. Right: SRS intensity gain exponent spectrum from Lasnex simulation with inline SRS model (magenta: wavelength of maximum gain).

comparable to other parts of a rad-hydro simulation. We specify the incident laser powers and escaping SRS powers and wavelengths, which are measured on each of the two inner cones and shown for θ = 30◦ in Fig. 2. This shows the measured wavelength of peak SRS is close to the wavelength of peak SRS gain exponent calculated from the simulated plasma conditions. The SRS model is not predictive, but evaluates the development of light and Langmuir waves consistent with given escaping SRS data, and the resulting spatially-varying energy deposition. The 192 NIF beams are grouped into 48 “quads” of four beams with polarization smoothing, i.e. two beams linearly polarized orthogonally to the other two. We treat a quad as one laser, which is unpolarized for the CBET model but linearly polarized for SRS. The inline model for one laser (subscript X = 0) propagating to +z is 23 X gCi gR I0 IR − I0 Ii , ωR ωi i=1 gR −∂z IR = −κR IR + I0 IR , ω0 ωL gR I0 IR , pL = ω0 ωR ωAi pAi = gCi I0 Ii . ω0 ωi

∂z I0 = −κ0 I0 −

out the target volume, with no assumption about where they occur. We show that LW heating reduces CBET to the inner beams, so that CBET and SRS must be considered jointly. The SRS light continues to grow from a “seed” point where it becomes convectively unstable as it propagates out of the hohlraum. The LWs are mostly driven just inside the laser entrance hole (LEH), which they heat. Compared to a model where the escaping SRS light is simply removed from the incident inner beams, the inline SRS model increases the electron temperature in the region where inner and outer beams overlap. Since the LWs are driven close to the LEH, they lead to x-ray drive from the poles rather than the equator. Our findings help explain several discrepancies between NIF data and hohlraum modeling, namely predictions that almost all outer-beam power is transferred to inner beams. Static x-ray imaging (SXI) of emission from the wall shows bright spots corresponding to the outer beams, indicating they are not fully depleted [12]. Capsule implosion shape data is close to round or oblate, whereas traditional modeling predicts a strongly prolate shape. The inline CBET and SRS reduced models quantify the processes sketched in Fig. 1. They solve steady-state coupled-mode equations for light-wave intensities Ii along laser ray paths. We treat the plasma waves with kinetic linear-response theory in the strong damping limit (advection of plasma waves neglected). Within linear theory, the strong damping limit is valid for SRS since the LW kL λDe > 0.25 (λDe is electron Debye length) and innerbeam intensities are below 1015 W/cm2 , so that the spatial Landau damping rate exceeds the SRS growth rate. These models are greatly simplified compared to full LPI models, e.g. by neglecting laser speckles and kinetic nonlinearities. This is required for computation cost to be

(1) (2) (3) (4)

κX is the inverse bremsstrahlung (IB) absorption rate of wave X. X = i 6= 0 for one of the 23 other quads incident on the same LEH as quad 0, and X = R for laser 0’s SRS light wave (red in Fig. 1). For the Langmuir wave (X = L, green in Fig. 1), ~kL = ~k0 − ~kR , ωL = ω0 − ωR , and pL is the power deposition density. The IAW for CBET to laser i (X = Ai, purple in Fig. 1) is analogous, with L → Ai and R → i. The CBET coupling coefficient [13] gCi is 2
πre kAi χe (1 + χI ) 1 + cos2 θi Im , (5) 2 2me c k0 ki 1 + χI + χe ! 1 ωAi − ~kAi · ~u √ χj ≡ − 2 2 Z 0 . (6) 2kAi λDj kAi vT j 2

gCi ≡

kX = |~kX |, ckX /ωX = [1 − ne /ncr,X ]1/2 with ncr,X the critical density for light wave X, ~u is the plasma flow velocity, and re ≈ 2.82 fm is the classical electron radius. cos θi = ~k0 ·~ki /k0 ki , and the factor (1+cos2 θi ) applies for two unpolarized lasers. χj is the susceptibility for species P j, χI = j χj for ion species, λDj = (0 Tj /nj Zj2 e2 )1/2 , vT j = (Tj /mj )1/2 , and Z is the plasma dispersion function. gR is obtained from gCi with ~kAi → ~kL , ωAi → ωL , ~ki → ~kR , 1 + χI → 1, and 1 + cos2 θ → 4. Model (1)–(6) has been implemented in the rad-hydro code Lasnex [14], from which we show results. The code describes a laser by rays which propagate instantly (c → ∞) and carry power along a refracted path. We

3 present axisymmetric 2D simulations, with light-wave intensities found on an auxiliary 3D mesh. The standard LLNL “high-flux model” for hohlraum simulations is used [15], which entails the detailed configuration accounting (DCA) non-LTE treatment of atomic and x-ray physics [16], and Spitzer-H¨ arm electron heat conduction with a flux limit of 0.15 the “free-streaming” value ne Te vT e . We simulate NIF shot N121130 to demonstrate the effects of LPI on hohlraum dynamics. This was one of the first shots in the high-adiabat or “high-foot” campaign, which has led to the highest fusion yields to date on NIF [17]. 1.27 MJ of frequency-tripled “3ω” (λ = 351 nm) laser energy (peak power 350 TW) drove a gold hohlraum filled with 1.45 mg/cm3 of He, and a plastic capsule filled with D-He3 gas instead of DT fuel. Cone wavelengths were chosen to give large CBET to the inner (especially θ = 23.5◦ ) cones: λ23 − λ30 = 0.4 ˚ A, λ30 − λouter = 2.43 ˚ A (at 3ω). The x-ray emission from the imploded hot spot was moderately oblate, with the amplitude of the P2 Legendre mode being -12% of the P0 mode (average radius), using the contour at 17% peak brightness (a standard measure of hotspot shape on NIF). The measured bakscatter showed significant inner-cone SRS, little inner-cone SBS, and little outer-cone SRS or SBS. To quantify the effects of the inline SRS model, we compare two Lasnex simulations that both use the inline CBET model [18]. One uses the inline SRS model. In the other, the escaping SRS light is removed from the incident laser, with no LW deposition. This unrealistic “SRS at lens” model obtains from Eqs. (1)-(6) if gR = δ(~x = ~xlens ) and ωR = ω0 . The second condition means no energy is deposited to the zero-frequency LW, so that the same net laser energy drives both simulations [19]. Figure 3 gives the energetics of the two SRS models. The post-CBET energy on the outers is 60% higher with the inline-SRS than SRS-at-lens model. This is reflected in the synthetic SXI image shown in Fig. 4. This detector images hard (3–5 keV) x-ray emission out of the LEH. The bright (upper, lower) bands represent emission from the (outer, inner) beam spots on the hohlraum wall. The post-LPI energy on the inners (inner transmitted + outer CBET to inner) is (52.9, 71.5)% with the (SRS inline, SRS at lens) models. IB absorption of SRS light is much less than the escaping SRS or LW deposition. The profiles in Fig. 5 illustrate the spatial repartition and deposition of power following the CBET and SRS processes. The left panels show the heating rates from laser IB, LWs, and SRS IB. The LW heating is much stronger than SRS IB, and occurs mostly just inside the LEH. Panel d gives the total heating with the SRS-inline model (sum of left panels), and the SRS-at-lens model (just due to laser IB). The SRS-inline model has more heating in the LEH and outer-beam spots, and less heating in the inner-beam path through the ablator blowoff and wall spots. Panel e shows the SRS power keeps growing until the light exits the hohlraum, i.e. the SRS gain

a) SRS Inline

b) SRS at lens

FIG. 3. Energetics of Lasnex simulations with inline SRS model (top), and SRS removed at lens (bottom). “Outer post CBET:” incident outer-beam energy not transferred to inners. “Inner transmitted”: incident inner energy minus energy to SRS channels. Inner SRS: escaping inner SRS light. SRS IB: SRS light absorbed by IB. Langmuir: energy to LWs. Energies integrated from 10.5 ns (start of SRS) to 14.8 ns (end of laser pulse), and given as percent of incident laser energy during that time (1120 kJ).

FIG. 4. Synthetic static x-ray imager (SXI) output for Lasnex simulations with inline SRS model (left) and SRS at lens model (right). Images are symmetrized in azimuth like the simulations. Reduced CBET to inner beams with the inline SRS model results in brighter outer-beam spots on the gold wall. Detector in NIF lower hemisphere 19◦ to hohlraum axis. X-ray emission integrated over all time and energies 3 to 5 keV. y is roughly parallel to hohlraum axis.

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FIG. 5. Spatial profiles of power densities [W/cm3 ] from Lasnex simulations at 12.6 ns (time of peak escaping SRS). All panels are from SRS-inline model, except top of d) which is from SRS-at-lens model. a) laser IB absorption, b) LW deposition, c) SRS light IB absorption, d) total deposition in SRS-at-lens model (top) and SRS-inline model (bottom). e) SRS light power density. All panels except e) use the same logarithmic color scale. Dashed magenta contours are boundaries of helium fill gas.

rate gR I0 /ω0 dominates the SRS IB rate κR . SRS originates from the “seed” region roughly indicated by red.

FIG. 6. Electron temperature at 12.6 ns from the two Lasnex simulations shown in Fig. 3. r > 0 has SRS removed at lens, r < 0 uses inline SRS model with LW deposition and is significantly hotter around the LEH. Magenta contours are fill gas boundaries as in Fig. 5.

The different heating profiles lead to higher electron temperature in the LEH with the inline-SRS model, as

FIG. 7. P2 Legendre moment of x-ray deposition at ablation front, as fraction of total deposition P0 , for x-ray energies 0.52 keV. P2 < 0 for stronger drive from the equator than the pole. For the inline SRS model, reduced CBET to the inner beams, and depletion by LWs, both reduce the laser intensity at the equator, which makes P2 less negative.

shown in Fig. 6, which results in less CBET to the inners. To see this, recall that in the off-resonant regime vT i  ωAi /kAi appropriate for NIF hohlraums and

5 1/2

one ion species, gCi ∝ (λi − λ0 )Zi ne Ti /(Ti + Zi Te )2 [20]. These results can be compared to measurements of hohlraum electron temperature, which are planned for the near term on NIF. Direct measurement of SRS-driven LWs with Thomson scattering would indicate if they exist near the entrance hole. The net impact of LPI processes on symmetry of the xray drive is shown in Fig. 7. The SRS-inline model (red) gives substantially less equatorial drive than the SRS-atlens model (black). A third simulation (blue) was done to separate the effect of reduced CBET, from LW depletion of the inner beams. This imposed the CBET calculated in the SRS-inline simulation to the incident lasers, and removed the escaping SRS from the incident inners. Comparing the black and blue curves shows the equator drive reduction just due to reduced CBET - the SRS is just removed from the incident laser in these two cases. Similarly, comparing the blue and red curves isolates the reduction due to LW depletion - the same power is transferred to the inners in these two cases. The two effects are roughly comparable. We also see that the LW power is effectively outer-beam power for x-ray symmetry, since they are driven close to the LEH. This is a non-trivial result of the inline SRS model: had the LWs been driven close to the equator wall, they would effectively still be inner-beam power. In conclusion, we have shown the effects of LPI on ignition hohlraum plasma conditions and x-ray drive symmetry. The Langmuir waves driven by inner-beam SRS are produced near the laser entrance hole, where they significantly increase the electron temperature. This reduces CBET to the inner beams. Such interplay of hydrodynamics and LPI requires a self-consistent approach, like the one presented here. The reduced CBET and LW depletion both reduce the inner beam intensity on, and x-ray drive from, the equator wall. Inline modeling of LPI partially resolves the long-standing over-prediction of equator x-ray drive in NIF hohlraums with high gas fill density. Accurate modeling of hohlraum dynamics and SRS requires further examination of electron transport - both heat-carrying and superthermal. The modeling shown here has made two extreme but opposite assumptions: the LW energy is deposited locally, but background thermal conduction is essentially not limited below the Spitzer-Harm value (which can occur due to nonlocal effects, magnetic fields, or the return current instability). Improved electron modeling is the subject of ongoing work. We thank J. A. Harte and G. B. Zimmerman for guidance on Lasnex. This work was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344.

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