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Numerical modeling of Hohlraum radiation conditions: Spatial and spectral variations due to sample position, beam pointing, and Hohlraum geometry
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View: Figures


Image of FIG. 1.
FIG. 1.

(Color) Hohlraum images generated with the VISRAD view-factor code, relevant to the experiments discussed in Ref. 4. The top panel shows the OMEGA beam pointing into the Hohlraum cylinder seen side on. Note that the cone 2 beams on each side are pulled back so that the beams from both cones make a single ring on each side of the Hohlraum. The middle panel shows the same target model, but from the position of the DANTE diagnostic. The lower panel shows the DANTE view again, but with the beams hidden, and with the wall temperature at displayed as a color map (the dynamic range in this, and all other, temperature color maps shown in the paper is ). Note the ring of laser hot spots on each side of the Hohlraum. Note also in all of these images how structures in the model seen from the back, or outside, are rendered as transparent mesh to allow for an unobstructed view of the interior of the Hohlraum. This convention will be used throughout the paper. Finally, we point out that the “front,” DANTE-facing, LEH is in the upper right in this, and all similar figures throughout the paper, and the inner and outer edges of the front LEH lip are highlighted in white.

Image of FIG. 2.
FIG. 2.

Schematic of the view-factor calculation for an arbitrary geometry. The flux from any source element onto any other surface element is proportional to the cosine of the angle between the line of centers of the two elements and the surface normal of the source element (because the source element is assumed to be a Lambertian emitter) and also to the cosine of the line of centers and the normal of the surface element (accounting for the projected cross section of the surface element as seen by the source). The line of centers is indicated by the dashed line while the two surface normals are indicated by arrows.

Image of FIG. 3.
FIG. 3.

The top panel shows the assumed x-ray conversion efficiency (dashed line) and calculated albedo (solid line), used as inputs to the view-factor simulations, the results of which are shown in the lower panel. In the lower panel, the filled squares with error bars are the DANTE temperature measurements from Ref. 4 while the open squares are the simulated DANTE temperatures from the view-factor calculations. The circles are the simulated radiation temperatures at the midplane wall of the Hohlraum.

Image of FIG. 4.
FIG. 4.

The simulated DANTE spectrum (solid black) along with the equivalent blackbody spectrum (dashed black) for in the VISRADHohlraum simulation and the simulated spectrum incident on the Hohlraum wall at the midplane (solid gray) along with its equivalent blackbody spectrum (dashed gray) from the same simulation time. Note that the radiation temperatures are for DANTE and for the midplane wall.

Image of FIG. 5.
FIG. 5.

(Color) The DANTE views of the Hohlraum in the two cases with different beam pointings (top two panels). As in the bottom panel of Fig. 1, we show a color map of emission temperature at , and hide the beams for clarity. The color scale spans from . The lower panel shows the trends of DANTE temperature (squares) and midplane temperature (circles) as the beam pointing is changed. The filled symbols represent the simulation time ( and ) and the open symbols represent the simulation time ( and ). The original model, used to reproduce the experiments reported on in Ref. 4 has a mean laser spot position of from the LEH plane. The first variation is shown in the top panel and the second variation is shown in the middle panel. We note that in this last case, the cone 2 beams from either side of the Hohlraum hit the wall almost exactly at the midplane, creating a single, combined ring of hot spots.

Image of FIG. 6.
FIG. 6.

(Color) VISRAD simulations of Hohlraums with fuel capsules. The capsules are centered in the Hohlraums and have a diameter of and an albedo of . The top panel shows the “single ring” pointing (compare to the bottom panel in Fig. 1) while the bottom panel shows the “nominal” pointing (compare to the top panel in Fig. 5) in which two rings are formed by pointing both the cone 2 and cone 3 beams at the LEH center.

Image of FIG. 7.
FIG. 7.

Calculated radiation temperature vs time for the VISRAD simulations shown in Fig. 6. The top panel is for the “single ring” pointing while the bottom panel is for the “nominal” pointing. In each panel, we show the DANTE temperature for the empty (i.e., no capsule) Hohlraum as a solid line and for the Hohlraum containing a capsule as a dashed line. The radiation temperature seen by a wall-mounted sample at the midplane is denoted by a dotted line for the empty Hohlraum and by a dash-dot line for the Hohlraum with a capsule.

Image of FIG. 8.
FIG. 8.

Radiation temperature as a function of sample orientation for a planar sample located at the center of a Hohlraum. The angle plotted along the axis is the angle between the sample normal and the Hohlraum axis, so that 0° is LEH facing, while 90° is wall facing. The filled symbols are the results from , while the open symbols are from . For comparison, the radiation temperatures at these two times for a sample on the wall of the Hohlraum at the midplane (discussed in Sec. II) are 188 and (denoted by Xs); nearly identical to the centrally located, wall-facing (90°) results shown here. Finally, we note that the DANTE temperatures for these two times are 202 and , respectively. In this, and all other figures showing temperature trends in the remainder of the paper, the left-hand axis refers to the values at (solid symbols), while the right-hand axis refers to the values at (open symbols).

Image of FIG. 9.
FIG. 9.

Comparison of the spectrum incident on a sample at the center of a Hohlraum (at ) when it is oriented toward the LEH (dashed line, 0° case in the previous figure) vs the spectrum when the sample is oriented toward the Hohlraum wall (solid line, 90° case in the previous figure). The LEH-facing sample has a modestly harder spectrum, though the radiation temperature onto each is nearly identical ( vs ).

Image of FIG. 10.
FIG. 10.

(Color) The DANTE view at of a halfraum simulation, created by dividing the Hohlraum shown in Fig. 1 in half with a gold disk. Note that from this viewing angle, some of the laser hot spots on the far side of the Hohlraum, caused by beams entering the Hohlraum through the far LEH, are visible [in Fig. 1(c)], which is, of course, not the case with the dividing disk present (as in this figure).

Image of FIG. 11.
FIG. 11.

(Color) Series of halfraum simulations in which the beam pointing was varied. The images show the DANTE view at . The top panel has the beam pointing pulled back from the nominal position, shown in Fig. 10. Recall that “nominal” means that the cone 3 beams cross the halfraum axis at the LEH plane and the cone 2 beams cross the axis outside the LEH. The middle panel has the beam pointing farther into the halfraum than the nominal case, and the bottom panel has the pointing farther than the nominal case.

Image of FIG. 12.
FIG. 12.

The radiation temperature on a sample mounted on the end of a halfraum (circles) and measured by DANTE (squares) for the four different beam pointings shown in Figs. 10 and 11 at two different simulation times: (filled symbols; left-hand axis) and (open symbols; right-hand axis). The mean laser spot position is measured with respect to the LEH plane, so deeper pointings are further right.

Image of FIG. 13.
FIG. 13.

Same as Fig. 12, but with no LEH lip (i.e., 100% LEH).

Image of FIG. 14.
FIG. 14.

Same as Fig. 12, but with the two beam cones making two different rings of hot spots, and using the three-quarter LEH.

Image of FIG. 15.
FIG. 15.

Temperature as a function of halfraum length for four simulations having identical beam pointings with respect to the LEH [nominal beam pointing regardless of halfraum length (top)] and with the beam pointing varying according to halfraum length (bottom). The solid symbols are from a simulation time of (left-hand axis) while the open symbols are from (right-hand axis). The squares are DANTE temperatures and the circles are sample radiation temperatures.

Image of FIG. 16.
FIG. 16.

(Color) Emission temperature color maps, at , of the Hohlraum simulation with the LEH shields (compare to the otherwise identical simulation shown in the top panel of Fig. 5, but without the LEH shields). The top panel shows the usual DANTE view, while the bottom panel shows a view from near the Hohlraum midplane, looking toward one of the LEHs. Note that the shield subtends an angle almost as large as the LEH, as seen from the midplane, and that it is about as hot as the inside of the LEH lip.

Image of FIG. 17.
FIG. 17.

(Color) Two halfraum simulations with a metal foil just outside the LEH. In the simulation shown in the top two panels (DANTE view on the left and view from the sample position on the right), there are no beams onto the foil. The foil simply acts to absorb and reemit radiation that exits through the LEH. In the bottom two panels, there are ten beams onto the foil, which significantly increase the radiation flux inside the halfraum. The snapshots in the right-hand column show emission temperatures at .

Image of FIG. 18.
FIG. 18.

Comparison of spectra incident on the center of the sample in our standard halfraum at , with the standard beam pointing. The dotted line represents the simulation with no foil, the dashed line (nearly coincident with the dotted line) represents the simulation with a foil outside the LEH, and the solid line is from the simulation with the foil heated by ten beams.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Numerical modeling of Hohlraum radiation conditions: Spatial and spectral variations due to sample position, beam pointing, and Hohlraum geometry