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General approximate formula relating Dante flux to “true” hohlraum flux

General approximate formula relating Dante flux to “true” hohlraum flux. Per Lindl 2004, where F = ratio of recirculating flux to spot flux , f (f’) = fraction of total wall area (of area seen by Dante) illuminated by beams.

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General approximate formula relating Dante flux to “true” hohlraum flux

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  1. General approximate formula relating Dante flux to “true” hohlraum flux Per Lindl 2004, where F = ratio of recirculating flux to spot flux , f (f’) = fraction of total wall area (of area seen by Dante) illuminated by beams Dante higher (lower) if f’> (<) f, corresponding to low (high) angle view thru NEL halfraum LEH Hence: If Dante sampling perfect (f’ = f) and/or in limit F >> 1 (large albedo, small LEH): Dante slightly overestimates (“LEH correction”) If Dante sees only unilluminated wall (f’ = 0): Dante underestimates (“albedo correction”)

  2. Dante for LLNL NEL halfraums should give higher T than true Tr because f’/f > 1 at 22° view angle f’/f for 2-9 ns LLNL halfraums f’/f ≈ 0 for LANL halfraums For AH/AW = 0.1 As time progresses, F increases and TDante will approach Tr as expected Limit of albedo corrected (f’=0) Corresponding view angle (LLNL halfraums) 30° 21.6° 0° > 30° Ratio of spot fraction viewed vs true spot fraction

  3. x% change in fraction of spot seen by Dante in NEL halfraums translates into ≈ (x/5)% change in Dante Tr where f’ = fraction of wall area seen by Dante that is illuminated by beams where f = fraction of total wall area illuminated by beams Substituting for IW: Hence change in Dante flux DIDante for spot fraction change Df’ given by: Example for Tr = 1.8 heV, t = 0.5 ns: For NEL scale 1 halfraum with 75% LEH, f = .03, f’ ≈ 0.15, hence: Hence, if Df’/f’ = 0.1: Potential for inaccuracy greatest for lower albedos (F small) and f’ > f Setting Df’ = f’:

  4. Summary • For sparsely illuminated hohlraums (f small), Dante view of unilluminated wall (f’ = 0) is preferable (i.e. uncertainty Df’ = 0) • e.g. LANL NEL halfraums had f’ = 0 • Partial view of isolated spot leads to TDante > Tr (LLNL halfraums) • For densely illuminated hohlraums (e.g. with 40 Omega or 192 NIF beams), f is large and f’/f will be clustered around 1 (better sampling), mitigating Dante error • Equations approximate as assumes IW uniform (no wall gradients) • In reality, wall area nearest LEH will be cooler, so effective f larger, effective f’/f smaller, and TDante/Tr will be closer to 1 per Slide 2

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