Baseline target for the 2010 ignition campaign. Hohlraum specifications are called out in detail. This is the target Rev5-CH; other targets have different dimensions as specified in Table I. LEH diameter is 57% of the hohlraum diameter, except for the 270 eV Be design for which it is 60%.
Capsule specifics for Rev5CH target. All capsules have the same geometry, with different dimensions and dopant concentrations as specified in Table I.
(i) Laser power to drive the target; (ii) the resulting temperature in the hohlraum (right scale); (iii) ablation pressure in the capsule; (iv) fraction of x-ray energy above 1.8 keV (right scale, × 1000, i.e., peak fraction is 18%). This baseline target uses 1.3 MJ of 0.3 μm light absorbed in the target, at peak power 413 TW. The step in power at 300 ps is the turning on of the outer cone, the pulse for which begins later than the inner cone.
Growth factors for perturbations seeded on the CH surface. (i) Perturbations initially on the outer surface, as they grow to CH/DT interface at peak velocity. (ii) Initially on outer surface, growth to hot-spot boundary at ignition time. (iii) Initially on CH/DT interface, growth to interface at peak velocity. (iv) Initially on CH/DT interface, growth to hot-spot boundary.
Growth factors for perturbations seeded on the DT gas/solid interface. (i) Perturbations as they grow to CH/DT interface at peak velocity. (ii) Growth to hot-spot boundary.
Use of ITF to characterize margin, for the 1.3 MJ-scale Rev5 CH target. The horizontal axis is the margin parameter ignition threshold factor, defined in Eq. (1). Approximately, this is the energy the implosion has, divided by the minimum needed for ignition given the top-level implosion parameters of velocity, adiabat, shape, and mix. Symbols are 200 2D simulations with input parameters distributed according to the expected statistics, except without hot electrons. Curves are mean yield at each ITF, plus or minus the rms deviation around that (curve is smoothed). In 1D with exactly nominal drive, this target has ITF 3.6, and 17.5 MJ yield, as indicated. With the assumed statistics and 3D imperfections, the expected ITF for the best of three shots is 1.46 ± 0.4, while the ITF that is needed for ignition is 1 ± 0.25. The cumulative probability of achieving a given ITF is shown. The probability of ignition at this near-term scale is 0.85, which includes the possibility of physics uncertainties requiring an ITF bigger than unity.
ITF required for ignition when conduction loss from hot-spot is increased. 2D calculations with perturbations in the indicated spherical harmonic mode were run with various amplitudes to find the maximum tolerable ignition-time RMS (dashed curves, showing tolerable RMS around 0.5 at nominal conduction, decreasing as the conduction is increased). The ITF required for ignition increases with conduction multiplier, with all modes requiring the same increased ITF. The right end of all curves corresponds to a 1D calculation, which has I 0 = 5.6 for the design used in this study, and can tolerate conduction multiplier 4.7.
Spot pattern on the hohlraum wall, for the baseline Rev5 pointing. One interesting feature of the pattern is that if the 23.5º beams (the most elliptical spots, near Z=0) are different in brightness than the 30º beams (the less elliptical spots closest to Z=0), then an m=4 azimuthal asymmetry can arise. This feature is intrinsic to the NIF beam geometry.
(Color online) Cone fraction variations that were used to establish the sensitivity of the imploded asymmetry to power ratios in various parts of the pulse. See Fig. 10 for sensitivity to these variations.
(Color online) Sensitivity of imploded hot-spot asymmetry to cone fraction variations during the first three parts of the pulse. For all simulations shown, cone fraction during the fourth pulse was left at nominal. The three groups of points (red squares, blue diamonds, or green circles, respectively) correspond to the three indicated inner cone fractions for the first pulse. Variations within each set show the result of variations in the second and third parts of the pulse, as indicated in Fig. 9. The only case that increases the asymmetry past the allowance is a low cone fraction during the first pulse, with some combinations of second and third pulse variation as well.
Density profile in the ablator for the Rev5 CH target just before peak velocity, when the accelerating implosion is the most unstable. The unstable density profile is a function of the preheat in the ablator and is controlled with the dopant profile. The steepest parts of the density profile in the CH are the boundaries between undoped and doped CH. Density profiles for other targets are very similar, by design.
[From Hammel et al. (Ref. 57)] Mix fraction vs. fuel:ablator density ratio for a variety of target designs. The three square points correspond to one capsule design for three different drive conditions: multiplier 0.83, 0.96, and 1.0 on the peak x-ray flux drive. Decreasing the drive increases the ablator mass remaining and decreases the mix. The two circles are for a design with nominal and “hardened spectrum.” The harder spectrum preheats the ablator reducing its density and increasing the mix growth.
Mix fraction vs. Ge dopant for simulated implosions of the Rev5CH target but with varying Ge fraction. Hydro instabilities were seeded with maximum allowed perturbations on all interfaces, modes 2-1000. Open circles are for the 1.5 MJ scale target and closed points for the 1.3 MJ scale. Vertical error bars show sensitivity to indicated variations in the preheat band of the X-ray drive. Other variations are as indicated. The Ge concentration has been set at the optimum 1.0 at. %. Thicker fuel or ablator increases the clean fraction, but costs implosion velocity.
Increase in adiabat resulting from 300 J of hot electrons at given energy, vs energy. Electrons were deposited in the gas volume above the ablator, with time dependence of SRS from shot N091204 (see Fig. 15).
Sensitivity to time at which hot electrons are created. The relative increase in adiabat for a pulse of hot electrons created at each time is plotted vs. the time of creation. Curves are normalized to the impact at 17 ns, which is when the first shock breaks out of the solid fuel. Two curves are for indicated energy distribution of hot electrons. For reference the laser power and the SRS time dependence from shot N091204 are plotted as well (right hand scale, arbitrary units for SRS). The dot-dash curve labeled Heff is the product of the SRS time dependence and a time-weighting based on the sensitivity curves. The integral of Heff is proportional to the net impact of this time dependence.
Performance of 1.3 MJ CH target vs hot-electrons. Horizontal axis is the energy in hot electrons, over 170 keV, assuming time-dependence as shown in Fig. 15. The baseline of 119 J is indicated, as are the requirement of <180 J, and the nominal PDF describing how many hot electrons are present. Plotted are the median expected yield at given hot electron deposition, and the probability of ignition at given hot electron deposition. The excursion of the PDF at zero represents a 3% probability that the hot electrons are below 7 J, the lowest bin boundary used to plot the PDF.
Hole and tube profile defined as nominal configuration. Note that the vertical scale is expanded relative to horizontal. The glue profile is actually a circular torus. Requirements define the size of the tube, the maximum volume of the hole, any tilt of the hole, and the maximum glue mass.
(Color online) Maximum allowed surface roughness power spectra for trace circumferential lineouts of the indicated surfaces. Surfaces are defined relative to the centroid of the inner surface, so mode 1 is not defined for that surface. The fourth internal surface is so close to the outer surface as not to be visible on this graph.
Maximum allowed power imbalance. Solid curve is power vs time, for time reference. Dashed lines are constraints on power imbalance for individual quads relative to each other (upper curve) and for the cone total power relative to shot-to-shot average on otherwise identical shots (lower curve).
(Color online) Quality of fit to velocity and adiabat for MVSS expansion. Horizontal axis is the value from the set of 1D simulations, and the vertical axis is the MVSS fit from Eqs. (27) and (28). Dots are 10 000 individual simulations, and the line represents a perfect fit. At given value of velocity, the fitted velocity is accurate to 1.7%, and at given adiabat, the fitted adiabat is accurate to 1.3%. This fit is used to consider the impact of changes in statistical ensembles; for baseline statistics, the values from the simulations can be used without using the fit.
(Color online) Statistical distributions for adiabat. (i) (Left-hand scale) Probability distribution function for adiabat as results from variations in Table III, with no hot electrons. This is mostly systematic error; shot-to-shot variability is only 0.03. Note the significant probability of adiabat >1.6, which integrates to 13%. (ii) PDF for adiabat, not including hot electrons, but assuming systematic errors have been reduced by THD experiments, primarily by removing high-adiabat outliers. (iii) Final PDF for adiabat, including hot electrons. (iv) (Right-hand scale) To show replication of systematic errors between subsequent shots, plot shows adiabat on second shot vs adiabat on first shot, for 500 realizations of the statistics behind the systematic errors and shot-to-shot variability.
(Color online) Mix as correlated with implosion velocity, for 1000 realizations of the baseline ensemble. The solid curve is the starting deterministic dependence of mix on velocity, to which random changes are added to represent both systematic errors and shot-to-shot variability.
(Color online) Hot-spot mix as correlated with mix fraction. At mix fraction around 0.4, outlier bubbles begin to penetrate the shell and carry mix into the hot-spot. This is the correlation as implemented in the statistical model, based on analysis of generic surfaces. Shown in red circles are 200 samples of the deterministic fraction—hot-spot mix as a function of mix and velocity. Shown in black +’s are the same 200 samples including statistical variability.
(Color online) Hot-spot mix as correlated with implosion velocity. At given velocity, the mix fraction is determined as illustrated in Fig. 22. Then the hot-spot mix is a baseline velocity-dependent amount for the fill hardware, plus a mix-dependent term, plus random variability. Red circles are the deterministic part given velocity and mix, and black +’s include statistical variability. Both are the same 1000 realizations of the statistics.
Median expected yield (MJ) and probability of ignition vs Hot-spot mix, at nominal implosion velocity, for the 1.3 MJ CH target. Because expected hot-spot mix correlates strongly with velocity, statistics were constrained to nominal velocity in making this plot. The dot-dash curve is the probability distribution function describing the hot-spot mix, for nominal velocity. High probability of ignition requires that experiments and capsule requirements can ensure hot-spot mix to be less than 75 ng, as indicated, although without such experiments there is a probability of the mix being higher than that. These curves represent the average performance over the distribution of the amount of Ge in the hot-spot mix, on average 0.6 at. %. The excursion in the PDF at 200 ng results from a 4% probability that the hot-spot mix at nominal velocity is more than 200 ng.
Probability of ignition of 300 eV 1.3 MJ CH target, and expected mix, vs. implosion velocity. (i) Probability density function for expected velocity according to baseline statistics (arbitrary scale). (ii) Median expected mix fraction at given velocity. Solid is baseline scenario, and dot-dash is alternate scenario with 25% less mix, for (ii)-(iv). (iii) Median expected hot-spot mix at given velocity. (iv) Probability of ignition at given velocity, assuming baseline statistics described in the text. Dot-dash is probability of ignition if mix fraction is reduced by 25%. If higher velocity can be achieved, and the mix is 25% below current baseline expectation, the probability of ignition can be increased considerably.
(Color online) Expected performance of 300 eV 1.3 MJ CH target vs ITF. Expected yield curve is broader than shown in Fig. 6 because this curve includes the uncertainty in ITF required. The width of the curve labeled “Probability of ignition” corresponds to the uncertainty in the ITF that is required. The three probability distributions functions (arbitrary scale) are (i) for the first shot assuming successful completion of the campaign and that all requirements are met; (ii) PDF for achieving the given ITF as the best of three nominally identical shots; and (iii) PDF for iterations of the same shot, for the case where the systematic uncertainties provide a mean ITF of 1.22. The spike in PDF (i) and (ii) at the origin represent the probability of ITF being less than 0.05, which is 3.7% for curve (i), 0.8% for curve (ii), and 10−4 for curve (iii).
Parameters characterizing the designs. For all designs, requirements are set so that the expected mix fraction at nominal velocity is 0.25 + 0.1/–0.05, hot-spot mix mass at nominal velocity is 45-100 ng of CH(0.5%Ge) or Be(1%Cu), and weighted hot-spot deformation is 0.13 ± 0.03. Expected velocity is v0×(1 ± 0.02 systematic, 0.025 shot-to-shot). Expected adiabat is α0 + 0.09 ± 0.05 systematic, 0.03 shot-to-shot. Except for the Be targets, the laser power and energy assume Au hohlraums; a U hohlraum requires 5%–10% less peak power and energy. Where uncertainty is asymmetric, quoted + and − limits are analogous to 1-σ RMS in that they are 15.9% probability intercepts.
Spot sizes for the various designs. These are the radii in the major and minor directions of the 50% intensity contour. Spot sizes are often quoted in the NIC community relative to a “Scale 1” which is listed here as the first row. Scale factors are also listed in each table entry. Note that the LEH diameter is 57% of the hohlraum diameter except for the 270 eV design, for which it is 60%.
The parameters that characterize a 1D implosion, and their assumed variability and uncertainty. Numbers in parentheses are goals, to reduce variability or uncertainty in future campaigns. Systematic uncertainties are accuracy, relative to true 1D optimum, including systematic and surrogacy errors. Note that any systematic error in these quantities relative to the true 3D optimum is included in the uncertainty in mix. Flux multipliers are relative to optimum for shock timing, not true flux. Times and durations are all independently varied, referenced as indicated. The last two parameters in the list are unique to Be, since CH has no contaminants that are significant compared to the assumed oxygen variation. Other places where Be and CH differ are noted.
Low mode sphericity requirements on ablator and ice. For these modes, the power spectrum of ablator thickness modulation is the difference between the tabulated outer power and inner power. The inner surface is the reference that defines the center of the system, so it has no mode 1.
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