1. oll_DantevsTr-1-05 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 Hence: If Dante sampling perfect (f’ = f) and/or in limit F >> 1 (large albedo, small LEH): Dante slightly overestimates (“LEH correction”) Dante higher (lower) if f’> (<) f, corresponding to low (high) angle view thru NEL halfraum LEH If Dante sees only unilluminated wall (f’ = 0): Dante underestimates (“albedo correction”)

2. oll_DantevsTr-1-05 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 Ratio of spot fraction viewed vs true spot fraction For A H /A W = 0.1 As time progresses, F increases and T Dante will approach T r as expected Limit of albedo corrected (f’=0) 0°21.6° Corresponding view angle (LLNL halfraums) > 30° 30° f’/f ≈ 0 for LANL halfraums

3. oll_DantevsTr-1-05 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 total wall area illuminated by beams where f’ = fraction of wall area seen by Dante that is illuminated by beams Substituting for I W : Hence change in Dante flux  I Dante for spot fraction change  f’ given by: For NEL scale 1 halfraum with 75% LEH, f =.03, f’ ≈ 0.15, hence: Hence, if  f’/f’ = 0.1: Example for T r = 1.8 heV, t = 0.5 ns: Potential for inaccuracy greatest for lower albedos (F small) and f’ > f Setting  f’ = f’:

4. oll_DantevsTr-1-05 4 Summary For sparsely illuminated hohlraums (f small), Dante view of unilluminated wall (f’ = 0) is preferable (i.e. uncertainty  f’ = 0) e.g. LANL NEL halfraums had f’ = 0 Partial view of isolated spot leads to T Dante > T r (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 I W uniform (no wall gradients) In reality, wall area nearest LEH will be cooler, so effective f larger, effective f’/f smaller, and T Dante /T r will be closer to 1 per Slide 2