Theory of the Fireball

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frequency, the opacity, which is sufficient for treating the internal flaw of radiation. A realistic treatment of the flow to the outside requires the absorption coefficient as a wction of frequency; Brode merely wanted to obtain reasonable overall results for this flow. He approximated the opacity by an analytic expression. Also in most of the ot'ner work cited above an average opacity has been used. An exception is some of the recent work on the radiation flow in high altitude explo- sions (Bluegill), where the frequency dependence must be, and has been, taken into account. Gilmore21 has calculated and made available curves of effective opacity, in which the radiation mean free path was averaged (using a Rosseland weighting factor) only over those frequencies for which it is less than 1 kilometer. This list of references on work on the fireball dynamics and opacity is far from complete. The energy from a nuclear explosion is transmitted through the outer parts of the weapon, including its case, either by radiation (x-rays) or by shock or both. Whichever the mode of transmission inside the weapon, once the energy gets into the surrounding air, the energy w ill be trans- ported by x-rays. This is because the air will be heated to such a high temperature (a million degrees or more) that transport by x-rays is much faster than by hydrodynamics. This stage of energy transport (Stage A) has been extensively studied by many authors (e.g., Hirschfelder and 12
Magee in Report LA-2000) and will therefore not be further" consid,ered .. here . During Stage A, temperatures are very high. The Pianck spectrum of t the air is in the x-ray or far ultraviolet region, and hence is irmnedf- ately absorbed by the surrounding air. The very hot air is therefore surrounded by a cooler envelope, and only this envelope is visible to observers at a distance. The observable temperature therefore has little physical significance. It is observed that the size of the ltrminous sphere lncreases rapidly, and the total emission also .Increases, up to a first maximum. - When the temperature of the central sphere of air has fallen, by successive emission and re-absorption of x-rays, to about j0O,00O0, a -hydrodynamic shock forms, The shock now moves faster than the temperature could propagate by radiation transport, The shock therefore sepa- rates fromthe very hot, nearly isothenml sphere at the center. This is Stage 13 in the development. The shock mves by simple Its front obeys the Hugoniot relations, the density being Behind the front, the air expands adiabatically, and at a of the shock radius, .the density is apt to have fallen. by or mre compared to the shock density, while the temperature has risen by a comparable factor, (3.16) Thus the interior is at very low density, and hence the pressure must be neasly constant (otherwise there would be very large accelerations which soon would equalize the pressure) . This . . greatly simplifies the structure of the shock, and leads to such simple 13 ,
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 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 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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