Geometric averaging factors where is the Legendre mode number and is the ratio of the capsule radius to the source radius, for (a) odd Legendre modes, and (b) even Legendre modes. Branches with are plotted as dashed lines.
Schematic of a spherical capsule in a spherical hohlraum with axisymmetric ring shields occupying and .
Graphical illustration of mode-selective shields as a mask (light blue shaded regions) superimposed on the Legendre modes , , and . The example shown was chosen to have zero content, and clearly nonzero content of and .
Shield solutions with zero content. (a) Shield angular range as a function of , and (b) the corresponding content of the shield solutions in modes 2, 4, and 8.
Mode content of flux to capsule with uniform source emission, as a function of the shield angular range, where all shield solutions have zero content and have been chosen from the positive- portion of Fig. 4(b). The lines represent the view factor numerical results, and the symbols are the analytic results from Eq. (11). The dashed line is the boundary of the shield.
Mode content of flux to capsule with nonuniform source emission (uncorrected ), using the same shield solutions as those plotted in Fig. 5, from the view factor calculation.
Capsule ablation pressure asymmetry modes from 2D LASNEX radiation hydrodynamics simulation, incorporating the shield solutions of Figs. 4 and 5. The applied source asymmetry produces an uncorrected in flux, which corresponds to in ablation pressure asymmetry for this capsule.
Mode content of flux to capsule with uniform source emission, as a function of the total angular range for dual-ring shields, where all shield solutions have and zero , , and content. The placement of the shields with results in zero at the capsule. The solid curve is the numerical view factor result, and the overplotted symbols are the results of Eq. (11).
LASNEX simulations of optimized dual-ring shield geometry. (a) Initial LASNEX setup and (b) resulting capsule ablation pressure modes – as a function of time. The light blue dotted line is the representative radiation temperature near the capsule surface. The uncorrected in ablation pressure has been nearly zeroed during the foot, while the shields are still optically thick.
(a) Geometric averaging factor for modes 14, 28, and 56, illustrating the time-dependent oscillations sampled by the capsule during its implosion. (b) Even Legendre mode content of flux to the capsule for modes 2–100, for the dual-ring configuration of Fig. 9 which was optimized to minimize modes 2–10. The red symbols are the shield transmission modes , the green symbols are the results of a static high resolution view factor calculation , and the blue symbols are flux-weighted view factor results time-integrated over the capsule implosion. Also shown is the approximate NIF capsule requirement as a function of mode number.
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