Theory of the Fireball

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From y = 1.18, y=l-A Y= -1 2.2 - 0*4/y X 2.2-0.4/y 12.2 - x 1-85 11.2 and the isothermal sphere disappears for l/1 . e6 x = 12.2 = 3.811- 2 For these higher altitudes, then, the time when the isothermal sphere (6 -18) (6.20) disappears is a fixed multiple of the time when it is first reached by the cooling wave. This multiple depends only on y, and on the ratio Hc/Hl of internal to external ent'nalpy at time ta. Tne pressure at the time x is 2 1/3 -1.2 P2 = PaX2 .= 1.0 ($) (6.21) For sea level, f (x) increases more slovly (the pressure decreases more slovly) with time; hence it takes somewhat longer to use q the isotnemal sphere. Conversely, t'ne pressure at the time t = t x will have 2 aa decreased by a smaller factor from pa. For the simple case of nigher altitude, we can use (6.19) to calculate the fraction of the mass y 3 which - will still be in the isothermal
sphere, its radius R /R and other physical data. Some of these are 1 c’ given in Table M. It is seen from the table that the mass decreases, first fairly uniformly and rapidly (as if it would go to zero at x = 2.8), then more slowly (because it is proportional to y 3 ), while the radius first expands slightly, then shrinks slowly and at the end very rapidly. The latter phenomenon, the rapid shrinking of the apparent fireball, may not be observable because the bomb debris becomes visible and is laeQr -to be still opaque. But some shrinkage of the fireball should be open . to observation. Table M. Development of Isothermal Sphere and Warm Layer due to Cooling Wave x = t/ta 1.0 1.2 1.5 2.0 2 -5 3.0 3.5 3.84 C. The Warm Laver We want to assume that the outer edge of the warm layer, the 4000° temperature level, stays fixed in tine material (Sec. 6a). We wish to 2 calculate the thickness of the warm layer in gm/m , 77 *..
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, - Ip.L ,. : CIC-14 REPORT COLLECT
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LA-3064 UC-34, PHYSICS TID-4500 (30
Page 6 and 7:
i.e., the part which has not yet be
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1. INTRODUCTION 2. PHASES IN DETELO
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6 radiation .(Stage A of Sec. 2) is
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frequency, the opacity, which is su
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elations as (3.2) between shock rad
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in this case there is no Stage D 11
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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 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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