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Jun 24, 2017 - DG] 24 Jun 2017. Noname manuscript No. ... details on numerical approaches, see [47] and references therein). On the other hand, an ...
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Three-Dimensional Characterization of Spherical Cryogenic Targets Using Ray Trace Analysis of Multiple Shadowgraph Views
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D. H. Edgell University of Rochester Laboratory for Laser Energetics
17th Target Fabrication Meeting San Diego, CA 1–5 October 2006
Summary
Ray-trace analysis improves ice-layer characterization • Internal reflection of light rays off inner ice surface produce bright rings in backlit shadowgrams that can be measured to ~0.1 nm • Standard method of direct surface reconstruction from bright-ring measurements using linearized formula is limited to low mode numbers • Ray-trace analysis is more accurate and self consistent – reduces standard deviation between calculated and measured bright rings by ~75% – surface reconstructions are well-behaved, using higher-mode numbers
E14938
Collaborators
R. S. Craxton, L. M. Elasky, D. R. Harding, L. S. Iwan, R. L. Keck, L. D. Lund, W. Seka, S. Verbridge, and M. D. Wittman University of Rochester Laboratory for Laser Energetics
Motivation
Ray-trace analysis is more accurate and self-consistent than the standard linearized analysis
• Standard method – linearly relate bright-ring radius to ice-surface radius – linearly fit ice surface to spherical harmonics - limited in accuracy to low-mode numbers - bright rings from different views do not agree at “cross-over” points for nonspherical targets • Ray-trace analysis – ray-tracing self-consistently fits the ice-surface spherical harmonics to the bright rings simultaneously for all views - significantly reduces the standard deviation between measured and predicted bright rings using fitted ice surface
E14939
Diagnostic Setup
Cryogenic target characterization is based on backlit optical shadowgraphy with multiple views
Bright-ring radius measurements are converted to ice-surface radii using a linearized formula derived from spherically symmetric ray-trace modeling. E14942
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Multiple views construct a 3-D representation of the ice surface
The ice surface is directly fit with spherical harmonics to determine the surface-roughness power spectrum
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1S. Pollaine and S. Hatchett, Nucl. Fusion, 44, 117 (2004).
Fitting higher mode numbers leads to unrealistic results
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Poor behavior is due to gaps in data and invalid assumptions of standard method
• False peaks/troughs in 3-D reconstructions occur at gaps in data (particularly the unobservable “polar cap”) – linear Yℓm fit “blows up” trying to best fit the data at gap edges, which always has some scatter • Poor behavior is also due to trying to match ice-surface measurements at “cross-over” points of the views – standard method assumes ice surface is linearly related to bright-ring radius – bright-ring measurements do not necessarily agree at “cross-overs”
E14858
Bright-ring radius cannot be linearly mapped to a single ice-surface radius by a simple formula
• Different views of the same ice surface can have very different bright-ring positions.
E14945
• Ice-surface asymmetries deflect the bright-ring rays from the spherically symmetric predictions.
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• Averaging effect of combining many views is good only for lowest modes (n ≤ 6).
Ray-Trace Analysis
Incorporating the ray-trace model directly into the bright-ring analysis improves the ice-surface fit .FBTVSFE 3BEJVT nN
• Rays are launched backward from measured bright-ring positions – 48 different views – 180 points each
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• Ice-inner-surface spherical harmonics Yℓm’s are nonlinearly fit to produce rays out parallel to rays in – parallel in/out is a good approximation for a quasispherical cryogenic target – maximum peak-to-valley is constrained by observed variance
E14946
Incorporating the ray-trace model directly into the bright-ring analysis improves the ice-surface fit .FBTVSFE 3BEJVT nN
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Incorporating the ray-trace model directly into the bright-ring analysis improves the ice-surface fit .FBTVSFE 3BEJVT nN
DT layers are much more spherical but ray-trace analysis should also improve their characterization
– Standard analysis assumptions more appropriate • In many of the DT targets for OMEGA the bright ring is significantly affected by roughness on the outer surface • Ray-trace analysis should be able to separate outer-surface from innersurface effects on the bright ring – Ice surface rms may be less than reported – Work under progress E15057
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• DT ice layers are much more spherically symmetric than D2 targets (rms
