Areal density non-uniformities seeded by time-dependent drive variations and target imperfections in Inertial Confinement Fusion (ICF) targets can grow in time as the capsule implodes, with growth rates that are amplified by instabilities. Here, we report on the first measurements of the perturbations on the density and areal density profiles induced by the membranes used to hold the capsule within the hohlraum in indirect drive ICF targets. The measurements are based on the reconstruction of the ablator density profiles from 2D radiographs obtained using pinhole imaging coupled to area backlighting, as close as 150 ps to peak compression. Our study shows a clear correlation between the modulations imposed on the areal density and measured neutron yield, and a 3× reduction in the areal density perturbations comparing a high-adiabat vs. low-adiabat pulse shape.
I. INTRODUCTION
In Inertial Confinement Fusion (ICF), implosion, and compression of a deuterium-tritium fuel inner layer and gaseous hot spot are achieved by the rocket effect of ablation of a low Z outer shell, the ablator. At the National Ignition Facility (NIF),1,2 the capsules are held at the center of high-Z hohlraums by thin membranes (tents)3,4 and the implosions are indirectly driven by the x-ray radiation produced by laser beams irradiating the hohlraum inner walls.5
The implosion efficiency depends on keeping the in-flight ablator and fuel as close as possible to spherical at all times while maintaining the required implosion velocity and in-flight aspect ratio. Asymmetries and areal density non-uniformities seeded by time-dependent drive variations and target imperfections grow in time as the capsule implodes, with growth rates that are amplified by instabilities.6 One way to diagnose them is by imaging the self-emission from the implosion core.7 However, this technique, besides only providing information on the shape of the hot emission region at final assembly, presents complications due to competition between emission gradients and reabsorption. Time resolved radiographic imaging,8 being insensitive to this effect, is therefore an important tool for diagnosing the ablator and the shell in ICF implosions.
A recent work has studied the asymmetries imparted by the tents on the shape of the hot spot emission images and of the shell radiographs.9
Here, we report on the first analysis of the perturbations induced by the tents on the in-flight areal density profiles and symmetry. We show that the areal density perturbations increase with the increase in tent thickness and a clear correlation exists between the modulations imposed on the areal density and the measured neutron yield. The paper is organized as follows: the experiments are described in Sec. II. Section III describes how the density profiles are reconstructed from the 2D radiograph. Sections IV and V show the results for low and high adiabat pulse shapes. Section VI discusses the impact on mass remaining and neutron yield. The conclusions are presented in Section VII.
II. EXPERIMENT DESCRIPTION
The measurements reported here are derived from the analysis of 2D x-ray radiographs7,8 produced by a backlighting technique that has been developed to image the imploding ablator in-flight down to a radius of about 150 μm. In a variant of a typical indirect drive5,8,10 experimental setup, 2 quads of the NIF are used to drive an area backlighter foil, located 12 mm from the capsule center, in the equatorial plane. The remaining 184 laser beams illuminate the inside of a gold hohlraum that reemits the laser energy into a blackbody X-ray spectrum. Part of the X-rays are absorbed by the outer layer of the capsule, located at the center of the hohlraum, which is ablated and therefore generates a spherically-symmetric rocket reaction that compresses the capsule. The radiographs of the imploding capsule, viewed along an equatorial (i.e., perpendicular to the hohlraum axis) line of sight, are imaged by an array of pinholes, 20 μm to 25 μm in diameter, and recorded on a gated X-ray detector,11 through a clear, unobstructed, sight provided by two 800 μm × 800 μm diagnostic patches on opposite sides of the hohlraum walls. We record radiographs spaced by 40–50 ps and covering a time interval of about 400–500 ps.
For the experiments of interest here, 35–60 kJ of energy from the 8 NIF backlighter laser beams were focused on a Ge foil, delivering up to 18 TW at an irradiance of 1–3 × 1015 W/cm2, exciting the He-like 2–1 resonance lines at ∼10.2 keV with about 1% efficiency. The targets consist of a 5.75 mm inner-diameter gold hohlraum having lengths ranging from 9.126 mm to 10.130 mm. A plastic shell, ∼2.3 mm diameter (graded Si-doped with a stair-stepped 1%, 2%, 1% graded layered distribution12), with thickness varying from 206.9 μm to 210.7 μm, is placed at the center of the hohlraum and filled with ∼6.7 mg/cm3 of 30/70 mixture of D-3He gas. The hohlraum is driven with either a 21-ns-long, 4-shock Low-Foot pulse,13 or a 15-ns-long, 3-shock High-Foot pulse,14 with energy ranging between 1.31 MJ and 1.36 MJ and power ranging between 337 TW and 367 TW. The capsules are held in place by two thin plastic membranes (tents), with thicknesses between 15 nm and 110 nm.3,15 In one case (shot N130411), a thicker fill tube, acting as a stalk, was used to hold the capsule, instead of the tents.9 The detailed values of the main experimental parameters for each shot are shown in Table I.
Main Laser, capsule and hohlraum parameters, thickness of the membrane supporting the capsule inside the hohlraum, raw, and normalized neutron yield, as discussed in the text, for each shot.
. | Laser . | Capsule . | Hohlraum . | Tent . | Neutron . | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Shot # . | Pulse shape . | Energy . | Peak power . | Abl Thk . | Outer radius . | LEH Diam . | Inner length . | Inner diam . | thickness . | Yield (DD) . | Yielda (DD) . |
. | . | MJ . | TW . | μm . | μm . | mm . | mm . | mm . | nm . | 1011 . | 1011 . |
N130411 | Low-foot | 1.33 | 356 | 211 | 1142 | 3.10 | 9.44 | 5.75 | 0b | 1.57 | 1.57 |
N130630 | Low-foot | 1.36 | 367 | 208 | 1138 | 3.37 | 10.13 | 5.75 | 15 | 2.70 | 3.73 |
N121219 | Low-foot | 1.34 | 345 | 209 | 1130 | 3.10 | 9.13 | 5.75 | 45 | 2.11 | 2.11 |
N121218 | Low-foot | 1.34 | 363 | 209 | 1133 | 3.10 | 9.71 | 5.75 | 48 | 2.27 | 2.27 |
N121210 | Low-foot | 1.33 | 360 | 210 | 1119 | 3.10 | 9.43 | 5.75 | 110 | 1.16 | 1.16 |
N121202 | Low-foot | 1.33 | 365 | 208 | 1111 | 3.10 | 9.43 | 5.75 | 110 | 1.68 | 1.68 |
N130808 | High-foot | 1.33 | 362 | 207 | 1128 | 3.37 | 10.13 | 5.75 | 15 | 1.47 | 3.59 |
N130508 | High-foot | 1.33 | 367 | 207 | 1141 | 3.37 | 10.13 | 5.75 | 45 | 1.52 | 3.71 |
N130303 | High-foot | 1.31 | 337 | 207 | 1107 | 3.10 | 9.43 | 5.75 | 110 | 2.69 | 2.98 |
. | Laser . | Capsule . | Hohlraum . | Tent . | Neutron . | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Shot # . | Pulse shape . | Energy . | Peak power . | Abl Thk . | Outer radius . | LEH Diam . | Inner length . | Inner diam . | thickness . | Yield (DD) . | Yielda (DD) . |
. | . | MJ . | TW . | μm . | μm . | mm . | mm . | mm . | nm . | 1011 . | 1011 . |
N130411 | Low-foot | 1.33 | 356 | 211 | 1142 | 3.10 | 9.44 | 5.75 | 0b | 1.57 | 1.57 |
N130630 | Low-foot | 1.36 | 367 | 208 | 1138 | 3.37 | 10.13 | 5.75 | 15 | 2.70 | 3.73 |
N121219 | Low-foot | 1.34 | 345 | 209 | 1130 | 3.10 | 9.13 | 5.75 | 45 | 2.11 | 2.11 |
N121218 | Low-foot | 1.34 | 363 | 209 | 1133 | 3.10 | 9.71 | 5.75 | 48 | 2.27 | 2.27 |
N121210 | Low-foot | 1.33 | 360 | 210 | 1119 | 3.10 | 9.43 | 5.75 | 110 | 1.16 | 1.16 |
N121202 | Low-foot | 1.33 | 365 | 208 | 1111 | 3.10 | 9.43 | 5.75 | 110 | 1.68 | 1.68 |
N130808 | High-foot | 1.33 | 362 | 207 | 1128 | 3.37 | 10.13 | 5.75 | 15 | 1.47 | 3.59 |
N130508 | High-foot | 1.33 | 367 | 207 | 1141 | 3.37 | 10.13 | 5.75 | 45 | 1.52 | 3.71 |
N130303 | High-foot | 1.31 | 337 | 207 | 1107 | 3.10 | 9.43 | 5.75 | 110 | 2.69 | 2.98 |
Normalized neutron yield to properly compare implosions using hohlraums with different lengths, LEH diameters, and gas fills.
Capsule held in place by oversized fill tube.
III. DENSITY RECONSTRUCTION FROM RADIOGRAPHS AND ANALYSIS METHOD
Prior to the reconstruction of the ablator from the transmission radiographs, these are corrected for backgrounds and backlighter non-uniformities using a recently developed technique that takes advantage of the parallax16 from the different pinholes. This procedure can also be used to increase the signal-to-noise ratio, by combining radiographs from different pinholes.
The ablator density is calculated from the 2D radiographs using both a forward iterative unfolding procedure, the details of which will be discussed in a separate article, and a direct Abel inversion.17 The first approach has the advantage of avoiding data deconvolution to remove spatial blurring due to the pinholes, temporal blurring due to the camera temporal resolution, and the effect of the two-dimensional camera point spread function, as these diagnostic characteristics can be part of the forward unfolding procedure. In the second case, the data have to be deconvolved of any blur prior to undergoing the Abel inversion procedure.12 Both methods allow left-right asymmetry in the reconstructed density profile, in the first case by including the asymmetry in the forward-propagated functions, in the second by using left-right tapered density profiles.17 Once the ablator density ρ(r,θ) is reconstructed, the areal density, defined as , is calculated by numerical integration along the radial coordinate for each angle. The perturbations in areal density are characterized by the fractional amplitude Δ(ρR)/ρR of the ripples in ρR.
This analysis method has been validated against simulations:18 Δ(ρR)/ρR values calculated after the reconstruction of the density from synthetic radiographs of simulated implosions of different capsules match the values from simulations within 3% in Δ(ρR)/ρR under a wide range of tent parameters. The analysis method is illustrated in Fig. 1.
Analysis procedure applied to a simulated in-flight radiograph of a capsule with 50 nm-thick supporting tent and driven by a Low-Foot (LF) pulse. (a) Simulated radiograph. (b) Capsule density, ρ, reconstruction based on unfolding code. (c) The areal density is calculated by numerical integration along the radial coordinate. The fluctuations in areal density are characterized by the fractional amplitude Δ(ρR)/ρR of the perturbations in ρR. On experimental data, the fractional amplitudes are averaged over the 4-locations, one on each quadrant.
Analysis procedure applied to a simulated in-flight radiograph of a capsule with 50 nm-thick supporting tent and driven by a Low-Foot (LF) pulse. (a) Simulated radiograph. (b) Capsule density, ρ, reconstruction based on unfolding code. (c) The areal density is calculated by numerical integration along the radial coordinate. The fluctuations in areal density are characterized by the fractional amplitude Δ(ρR)/ρR of the perturbations in ρR. On experimental data, the fractional amplitudes are averaged over the 4-locations, one on each quadrant.
IV. RESULTS: LOW-FOOT PULSE SHAPE
Figure 2(a) shows the radiograph from shot N121210, at a time corresponding to ∼630 ps prior to bang time. In this particular case, a 110 μm-thick tent was used. Two horizontal and almost parallel features are visible across the radiographs at positions corresponding to about +180 μm and −180 μm on the vertical axis. We proved that the tent induces these features on the radiographs by comparing with a stalk mounted capsule implosion N130411 shown in Figure 2(b) at a similar radius and with similar other shot parameters. In this case, the tent was not used, as the capsule was held at hohlraum center by means of a stalk, and no horizontal features can be seen. As a general comment, the radiographs from shots using a tent show perturbations persisting throughout the implosion. Such perturbations are not visible when no tent was used and are less visible in shots using thinner tents. The implications of tent features on hot spot shape are discussed in Ref. 9.
Comparison of radiographs of imploding capsules supported by tent (a) and by stalk (b). No tent-induced perturbations are seen in the second case.
Comparison of radiographs of imploding capsules supported by tent (a) and by stalk (b). No tent-induced perturbations are seen in the second case.
Figure 3(a) shows the normalized density reconstruction for N121210. The features induced by the 110 nm-thick tent on the radiographs are clearly unfolded in a ring-like pattern that results in the rather sharp 4-fold perturbations in the reconstructed density at ∼45° in each of the four quadrants. These perturbations consist primarily of a deficit in density (“bubble”) with increased density (“spikes”) on either side, characteristic of Rayleigh-Taylor growth. Because the spikes are narrower, they are less visible when seen at the 45° viewing angle. Hence, for the remainder of this paper, we concentrate on quantifying the "bubble" areal density deficit. The areal density ρR is calculated by numerical integration along the radial coordinate for each radiograph. At this point, it is convenient to normalize the areal density to the azimuthal average value. Since the areal density does not depend on the radial coordinate, this allows us to then average the areal density from radiographs at different times and convergence ratios, thereby increasing the signal to noise ratio and emphasizing the areal density asymmetries that are persistent along the ablator trajectory. The result of this procedure is shown in Figure 3(b), for N121210, and shows clear 4-fold perturbations in the ρR profile. Again, the most striking characteristic induced by the tent are the valleys in the ρR profile, i.e., a local mass deficit or bubble. A fractional Δ(ρR)/ρR = 19 ± 2% was measured, for an average center of mass radius of the ablator of 250 μm.
(a) Shell density, ρ, reconstruction from radiograph of imploding capsule supported by 110 nm-thick tent (N121210) (b) Normalized areal density with clear 4-fold perturbations (bubble) seeded by the tent.
(a) Shell density, ρ, reconstruction from radiograph of imploding capsule supported by 110 nm-thick tent (N121210) (b) Normalized areal density with clear 4-fold perturbations (bubble) seeded by the tent.
In Figure 4, we summarize the results obtained by applying this analysis to the experiments listed in Table I. The amplitude of perturbations observed in the frame-averaged ρR profiles increases with the increase in tent thickness and scales as
where d = t/tc, i.e., the tent thickness, t, normalized by a characteristic value tc. The specific values of the parameter tc and the exponent α depend on the implosion parameters, e.g., pulse shape.
The fractional amplitude variation of the areal density versus tent thickness shows increases with increase in tent thickness.
The fractional amplitude variation of the areal density versus tent thickness shows increases with increase in tent thickness.
The meaning of the characteristic thickness tc is clear from the scaling shown in Eq. (1): it represents the thickness at which the fractional amplitude variations in the areal density reach half of their asymptotic value. For t < tc, the growth of the fractional amplitude variations scales nearly linear with the thickness of the tent. In the case of the experiments in Table I, driven by Low-Foot pulse shape and reported in Fig. 4, as solid circles, tc = 30 ± 2 nm, α = 1.3.
V. RESULTS: HIGH-FOOT PULSE SHAPE
Indirect drive implosions on the NIF driven by a high-adiabat, or High-Foot, pulse shape have demonstrated significant alpha-heating.14,19 These pulses are designed to enhance the hydrodynamic stability of the shell by delivering higher initial radiation temperature in the “foot” of the pulse, thereby setting the imploding shell on a higher adiabat, increasing the ablation rate and density scale lengths in the shell.20,21 The instability growth during the shock transit phase is also reduced substantially with the high-foot drive. All of these effects contribute to reduce the hydrodynamic instability growth of the shell perturbations, including those induced by the tent.22
Figure 5(a) shows the simulated transmission radiograph of an implosion using a 50 nm thick tent, and driven by a High-Foot pulse shape. The density reconstruction, following the unfold procedure, is shown in Figure 5(b), emphasizing the reduced growth of the tent-induced perturbations in the High-Foot case when compared to the Low-Foot case of Fig. 1. From the normalized ρR profiles, reported in Figure 5(c), we measure a ∼3× reduction in the Δ(ρR)/ρR when the High-Foot pulse is used.
Analysis procedure applied to a simulated implosion of a capsule with 50 nm-thick supporting tent and driven by a High-Foot (HF) pulse. (a) Simulated radiograph. (b) Capsule density, ρ, reconstruction based on unfolding code. (c) The areal density is calculated by numerical integration along the radial coordinate. The fluctuations in areal density are characterized by the fractional amplitude Δ(ρR)/ρR of the perturbations in ρR. On experimental data, the fractional amplitudes are averaged over the 4-locations, one on each quadrant.
Analysis procedure applied to a simulated implosion of a capsule with 50 nm-thick supporting tent and driven by a High-Foot (HF) pulse. (a) Simulated radiograph. (b) Capsule density, ρ, reconstruction based on unfolding code. (c) The areal density is calculated by numerical integration along the radial coordinate. The fluctuations in areal density are characterized by the fractional amplitude Δ(ρR)/ρR of the perturbations in ρR. On experimental data, the fractional amplitudes are averaged over the 4-locations, one on each quadrant.
Figure 6 shows a comparison of measured radiographs from Low-Foot (left) and High-Foot (right) pulse driven implosions. In this case, the tent thickness was 47 nm and 45 nm, respectively. The tent feature in the radiograph is noticeably reduced in the High-Foot case.
The comparison of radiographs from Low-Foot (a) and High-Foot (b) pulse driven implosions of capsules using 47 nm- and 45 nm-thick tent, respectively.
The comparison of radiographs from Low-Foot (a) and High-Foot (b) pulse driven implosions of capsules using 47 nm- and 45 nm-thick tent, respectively.
For a quantitative comparison, the three implosions listed in Table I and driven by the High-Foot pulse shape have been radiographed and analyzed according to the procedure described earlier. The measured Δ(ρR)/ρR are shown in Figure 4, where the measurements for High-Foot implosions are represented by open circles and are compared to the ones from Low-Foot implosions, represented by solid circles. For the High-Foot pulse, the amplitude of perturbations observed in the frame-averaged ρR profiles also increases with the increase in tent thickness, but at a slower rate, with a reduced scaling exponent α ∼ 1, and an increased characteristic thickness tc = 40 ± 4 nm. We also note that the average reduction in Δ(ρR)/ρR, calculated by the ratio of the two scaling fits, is 3.2, while the ratio of the asymptotic values is 2.9. Both are close to the simulated 3× reduction discussed above.
VI. RESULTS: IMPACT ON MASS AND NEUTRON YIELD
From the density or the areal density reconstruction, one can easily calculate the local loss in unablated mass corresponding to the bubble induced by the tent. The results are summarized in Figure 7, where the fractional mass deficit (%), defined as mass needed to fill the bubble relative to the total unablated mass, is shown vs the tent thickness. The mass deficit rate is represented by the slope of the linear fits to the data and is 5× larger for the Low-Foot pulse shape compared to the High-Foot pulse shape. This represents an additional evidence of the higher hydrodynamic stability of the High-Foot drive.
Fractional mass deficit versus tent thickness. Solid circles = Low-Foot pulse shape; Open circles = High-Foot pulse shape.
Fractional mass deficit versus tent thickness. Solid circles = Low-Foot pulse shape; Open circles = High-Foot pulse shape.
In order to correlate the areal density non-uniformities with capsule performance, Figure 8 reports the measured (DD) neutron yield over expected yield ratio vs the fractional amplitude Δ(ρR)/ρR, for the Low-Foot driven implosions. In this case, the expected yield is calculated from post-shot hohlraum-capsule integrated 2D HYDRA18 simulations that do not account for the tent. The measured over expected yield ratio drops as the ρR perturbations induced by tent increase. The plot shows a reduction in measured-to-simulated yield performance ratio approaching factors up to about 2× when the induced fractional perturbation Δ(ρR)/ρR reaches the 20% value, i.e., for tent thicknesses in the 110 nm range. This is consistent with the areal density asymmetry limiting the compression and eventually breaking up the shell relatively early in its trajectory, thereby significantly reducing the conversion of implosion kinetic energy to hot spot internal energy and limiting the produced neutron yield in the experiments.23 The difference in neutron yield between the two shots with the 110-nm-thick tent case (N121202 and N121210) is attributed to an unexplained ∼2× increase of the m = 2 Fourier mode for the latter shot (m2/m0 = 0.14 vs 0.075) that cannot be accounted for in the 2D HYDRA simulations. In shot N130411, when no tent was present, and a thicker fill tube was used to hold the capsule, the measured DD yield amounts to 20% of the simulated one, indicating that the thicker fill tube had an impact, on the implosion performance, similar to a 110 nm-thick tent.
Measured over expected neutron yield ratio as a function of induced fractional perturbation Δ(ρR)/ρR for Low-Foot implosions.
Measured over expected neutron yield ratio as a function of induced fractional perturbation Δ(ρR)/ρR for Low-Foot implosions.
Further comparison of implosion performance vs fractional perturbation Δ(ρR)/ρR is shown in Figure 9, for all the shots listed in Table I. Here, we have used a normalized neutron yield (Yn*) in order to properly compare implosions using hohlraums with different lengths, LEH diameters, and gas fills. The measured neutron yields have been scaled according to the power balance model (e.g., see Eq. (41) in Ref. 13) to account for hohlraum length and increased losses due to larger LEH. For implosions using the High-Foot pulse shape, which were fielded with ∼1.6× more gas-fill in the hohlraum, we can calculate an additional normalization factor due to the measured 4% lower hohlraum temperature. Given that the implosions velocity scales as v ∼ Φ(4.9/8), being Φ the flux, and Φ ∼ Τρ4, where Τρ is the peak radiation temperature in the hohlraum, and the neutron yield scales as the sixth power of the implosion velocity, Yn ∼ v6,24,25 for the symmetry capsule target platform (or “symcap”)24 used in this paper, we arrive to the neutron yield scaling vs hohlraum temperature: Yn ∼ Τρ14.7. The normalized neutron yields are shown in the last column of Table I. Figure 9 shows linear degradation of the measured yield as the fractional Δ(ρR)/ρR increases above about 5%, with yields reduced as much as 2.3× for the cases when Δ(ρR)/ρR approaches 20% (induced by 110 nm-thick tents). For the High-Foot case (open circles in Fig. 9), we note that the implosions with Δ(ρR)/ρR of < 5% (15 and 45 nm tent) gave about the same yield, consistent with Fig. 8 fit asymptoting for Δ(ρR)/ρR < 10%. The horizontal dashed line in Fig. 9 represents the yield achieved in the shot (N130411) that used the oversized fill tube instead of a tent to hold the capsule, and shows that the stalk had an impact, on the capsule performance, similar to a 18%–19% fractional perturbation Δ(ρR)/ρR.
Normalized (see text) neutron yield vs induced fractional perturbation Δ(ρR)/ρR for Low-Foot pulse shape (solid circles) and High-Foot pulse shape (open circles).
Normalized (see text) neutron yield vs induced fractional perturbation Δ(ρR)/ρR for Low-Foot pulse shape (solid circles) and High-Foot pulse shape (open circles).
VII. CONCLUSIONS
We have reported on the first measurements of the perturbations on the density and areal density profiles and symmetry induced by the membranes used to hold the capsule within the hohlraum in indirect drive ICF targets. The measurements are based on the reconstruction of the ablator density profiles from 2D radiographs obtained using pinhole imaging coupled to area backlighting and as close as 150 ps to peak compression.
The areal density perturbations increase with the increase in tent thickness in both Low- and High-foot cases, but are reduced by a factor of ∼3 when the latter pulse-shape is used. Our study also shows a clear correlation between the modulations imposed on the areal density by the tent and the neutron yield.
ACKNOWLEDGMENTS
This work was performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.