Theory of the Fireball

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higher frequency (above, and Sec. LC). The fraction of the black body spectrum which can be emitted is given, in sufficient approximation, by where 0 *. U, hV 0 o w lJ =- In (3.34) we have neglected the fact that the infrared, below about 1 (3.35) (3.34) ' 1/2 ev, also cannot be emitted (Sec. 4a), and nave approximated ( eU - 1) in tjne Planck spectrum by e-U; both corrections are small. To = 8OWo has been chosen as a reasonable average temperature ( see Sec. 5). Near -1.5 this temperature, varies about as T , so that tne actual radiation to large distances is about Solving (3.32) for p, with po = 1-29 x (normal air density) gives 1
t For p1 = po, T = 0.8, this is 14 bars. At higher temperature (T' > 1) , the ultraviolet can be transported as easily as the visible although it will not escape to large distances (Sec. kc). Then it (,),, is reasonable to use the full black body radiation (3.33) for the emission. Inserting this into (3.32) gives $8/3 (3.39) 1 .O, this is 40 bars. Thus for p greater than 14 to 40 bars, the radiation is ' only a fraction of the adiabatic cooling, for lower pressure radiation cooling is more important. At the lower pressures then, energy must be supplied from the inside to maintain the radiation. This gives rise to a "cooling wave" moving inwards as will be discussed in Sec. 5. It is interesting that the condition (3.38) refers to the pressure alone. Neither the local density nor the equation of state enters. The opacity of air enters only insofar as it determines the radiating temperature T ' through the condition ( 3 *21) . A more accurate expression for the limiting pressure will be derived in Sec. 5e. It will turn out to be considerably lower, about 5 bars.
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 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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