Theory of the Fireball

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Pa f(x) = - P and obtain the simple differential equation ay - - Af(x) l-l/3Y , dx- vnich yields, together witn the boundary conditions, is 1 v (6.10) (6.11) The constant A can be determined from Sec. ?e. Tne condition there dr u = - p E a where p is the density outside t'ne cooling wzve. According to (3 .!&) Tnen using (5.43) 74 R a E- a (6.12) (6.14)
which is a pure number, and small: The calculation could be improved by not neglecting 5 compared with H . a According to (6.11) t'ne fireball is used up at the time x defined X (6.16) This relation is valid (granted the approximations we have made) what- ever the relation between pressure and time, f (x) * This generality is useful for sea level explosions, where p is only 5 times ambient pressure: a The relation between p and t cm then be taken from a machine calculation ( or observation) . For higher altitude, let us say h > LO b, pa = 5( p /p )1/3 is 1 0 sufficiently above, the ambient pressure, pl/po, so that the shock is still strong and we may use f(x) = x 1.2 Tnen (6.11) becomes 75 r
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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
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 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 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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