Theory of the Fireball

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in this case there is no Stage D 11.. At higher elevation, there usually is. The fireball will then remain hot, at about 6000~ or a somewhat lower temperature due to adiabatic expansion in Stage D I1 . The only process which can now lead to further cooling is the rise of the fireball, which leads to further adiabatic expansion and, more important, to turbulent mixing at the surface with the ambient air (Stage E) . The time required for this is typically 10 seconds or more, being determined by buoyancy At very high altitude, the shock wave never plays an important part, but radiation transport continues until the temperature gets too low for effective emission. In other words, Stage A continues to the end.' Of course, a shock does form, but it is, so to speak, an afterthought, and it plays little part in the distribution of energy, At medium altitude, let us say, 10 to 30 kilometers, the stages are much the same as at sea level but the shock wave becomes transparent earlier, i.e., at a higher temperature, because the density is later; this means that the minimum emission comes earlier. Stage C proceeds similarly to sea level, but at the second maximum of radiation the pressure is still much above ambient, therefore Stage C I1 involves a greater radial expansion of the isothermal sphere than at sea level which proceeds simultaneously with the inward motion of the cooling wave. Moreover, there is much adia- 16
We believe that the theory developed in this paper will be useful jn studying the dependence of phenomena on altitude (ambient pressure), but we have not yet exploited it for this purpose. a., Role of NO2 3. RADIATION FRaM BEHDTD THE SHOCK (Stage C I) The diatomic species in equilibrium air, both neutrals and ions, show very little absorption in the visible at temperatures Up to about 16 Iioooo~. This is shown clearly in the tables by Meyerott et We define "the visible" for the purposes of this paper, arbitrarily and incorrectly, as the frequency range hv = 1/2 to 2-3/4 ev i = 4050 to 22,300 an' Then, even at a density as high as lopo (p, = density of air at HIT 3 = 1.29 x w/cm ), the mean free path is never less than 100 meters at k0OO0, 1000 meters at 3000°, and still longer at luwer temperature. Tnese values refer to hv = 2-5/8 ev; for lawer frequencies, the mean free path is even longer. In -the sea-level shock wave from a megaton explosion, the temper- atwe range. from 3000 to 4000' occupies a distance of about 10 meters ( see Sec. 3b). Thus this region is definitely transparent, even at the
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 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 40 and 41: w Q P/Po 1 0.1 0.01 T 4,000 6,000 8
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
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Theory of the Fireball

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