Theory of the Fireball

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w Q P/Po 1 0.1 0.01 T 4,000 6,000 8,000 4,000 6,000 8,000 I.z',OOO 4,000 6,000 8, ooo 12,000 -1 Table V. Absorption Coefficients in Visible (cm ) 7 . 8-7 4 .2-7 4 1.05-7 4.3-5 ~ . 6 - ~ 13 7.5-5 3 .6'4 6.7-4 12-4 5 .3-4 6 1.2-2 1.5-2 O K 2 1.7-8 0.8 3.3-8 4 o.90-8 -6 1.0-5 ~ 6 ' ~ 5 .7-6 1o.T6 4 . 8-6 2 . 8'5 1.25-~ ~ 6 ' ~ 0. 48'3 1 . 30-~ 0. 7S3 2-5/8 52& ~ 6 6 11-3 ~ 0. 68"2 35 -7 4 . 8'5 6 .4-4 0.85'~ 16'~ 2. 8-6 4.7-5 0 .68-3 3 -l/8 8900 -6 3 1-2 4x00'~ 26 -5 46 -4 1. 42-2 goo-8 25-6 -, 34-5 0.91'~ \
of about 200 from 4000 to 600o0, about 10 from 6000 to &looo except for the lowest density, and 10 to 50 from 8000 to 12,000°. In most cases, the dependence on wave length is slight until the rapid increase of absorption in the ultraviolet which sets in at about 2.5 ev for kOOOO, 3 ev at 6000 and 8000°, and not at aU at 12,000'. Tne especially strong 0 increase for 4000 is due to the Schumam-Runge bands, which are not very sensitive to temperature*" see Sec. 4c) .' 2 In Sec. 5d we shall need the mean free path in @/cm , suitably averaged over the "transparent" region. From Table V it appears that a reasonable estimate of this region is from hv = 1/2 to 2-3/4 ev. We have averaged p/p as calculated from Table V, with the weighting factor 3 -u k X booo ue Y u= hv (4.9) which does not vary much (from 0.84 to 1.33) between 1-1/8 and 2-5/8 ev. The result is given . i n Table VI. *After completion of this paper, I received new absorption coefficients by F . R . Gilmore , cf ref 23. Aside from including the absorption by NO2 ( see Sec. ha), Gilmore includes the free-f ree absorption in the field of neutrals, ba ed on ref . 18, and also new data on f nmbers for the important bands.2f; The most important change is a reduction in the f nmber of the IT2 first positive system from 0.02 to 0.0028, which w ill substantially reduce the absorption in the visible . Unfortunately, this will further raise the theoretical radiating temperature ( Sec . 5d) , which ,is already higher than observed. 'Some recent Avco-Everett experiments may indicate that the free-free electron transitions in the field of the I? atom qe enhanced in the visible as compared to the infrared. This may compensate to some extent for the reduction of the N2 first positive bands (see footnote above) 39
Page 1 and 2: , - Ip.L ,. : CIC-14 REPORT COLLECT
Page 3: LA-3064 UC-34, PHYSICS TID-4500 (30
Page 6 and 7: i.e., the part which has not yet be
Page 9: 1. INTRODUCTION 2. PHASES IN DETELO
Page 12 and 13: 6 radiation .(Stage A of Sec. 2) is
Page 14 and 15: frequency, the opacity, which is su
Page 16 and 17: elations as (3.2) between shock rad
Page 18 and 19: in this case there is no Stage D 11
Page 20 and 21: highest possible density of about l
Page 22 and 23: \ and the average of y' is taken ov
Page 24 and 25: The radius R is given R3 = I"- P P
Page 26 and 27: T-R -10 (3.16) 8 The numerical calc
Page 28 and 29: Since the interesting values of R a
Page 30 and 31: Most of the radiation comes from a
Page 32 and 33: higher frequency (above, and Sec. L
Page 34 and 35: 4. ABSORPTION coEFF1c1ms a. Infrare
Page 36 and 37: (3.21), it is small compared to the
Page 38 and 39: hv (ev) P/Po = 1 ff N2 0- Table N.
Page 42 and 43: Table VI. Average Mean Free Paths (
Page 44 and 45: The fraction of the Planck spectm b
Page 46 and 47: The W beyond 3.5 ev will be strongl
Page 48 and 49: The equation of continuity is aH aJ
Page 50 and 51: U" J, A Ho - H(T1) To determine u w
Page 52 and 53: temperature is aromd Tb, and in whi
Page 54 and 55: internal energy in that sFhere; in
Page 56 and 57: y integrating (5.8); it depends on
Page 58 and 59: a log I1 - y' - 1 a log p at - y' a
Page 60 and 61: 2 vitn A = 0.1G q/cm and n = 6.3. T
Page 62 and 63: or a radiating temperature of 10,80
Page 64 and 65: assuming the strong shock relation
Page 66 and 67: pressure is larger than pa, (5.50)
Page 68 and 69: inconsistency in our apyroximations
Page 70 and 71: G. We& Cool-ing Wave In Stage C I1
Page 72 and 73: 6. EFFECT OF THREE DDENSIOUS a. Ini
Page 74 and 75: 6. Sinrinkage of Isotnemal Sphere W
Page 76 and 77: Pa f(x) = - P and obtain the simple
Page 78 and 79: From y = 1.18, y=l-A Y= -1 2.2 - 0*
Page 80 and 81: where Re is the outer edge of the l
Page 82 and 83: esult of the three-dimensional cons
Page 84 and 85: 4 dF: = - 4KaT at where a is the St
Page 86 and 87: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 . REF

Theory of the Fireball

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