Theory of the Fireball

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6 radiation .(Stage A of Sec. 2) is by Freeman. Brode and Gilmore 7 treat also Stage B, the rad$ation from the shock front, with particular emphasis on the dependence on altitude. The most complete numerical calculation has been done by Brode 8 on a sea level megaton explosion. We shall use his results extensively, but for convenience we shall translate them to a yield of lmegaton. Wherever the phenomena are purely hydrodynamic, we may simply scale the linear dimensions and the time by the cube root of the yield, and this is the principal. use we shall make of Brode 's results, e .g. Fn Sec. 3b. Where radiation is important, this scaling will give only a rough guide. Brode calculates pressures, temperatures, densities, etc., as functions of time and radius, for scaled (1-megaton) times of about to 10 seconds. The calculations show clearly the stages in fireball and shock development, as defined in Sec. 2, at least Stages A to C. Brode and Meyerott 9 have considered the physical phenomena involved in the optical. "opening" of the shock after the minimum of radiation, Stage C I in the nomenclature of Sec. 2, especiallythe decrease in opacity due to decreased density and to the dissociation of NO2. Zel'dovich, Kompaneets and Raizer'' have investigated haw the energy for the radiation is supplied after the radiation minimum and have intro- duced the concept of a "cooling wave" moving into the hot f irebdll. The present report is largely concerned with an extension of the ideas of 10
Much effort has been devoted to the calculation of fireballs at various altitudes. Brode'l made such calculations in 1958, in connection with the test series of that year. Gilmore12 made a prediction of the Bluegill explosion 'in 1962. of Bluegill have been made. Since then, many more ref bed calculations For any understanding of fireball phenomena it is essential to have a good equation of state for air and good tables of absorption coeffi- cients. For the equation of state, we have used Gilmore's tables, 13 14 although Hilsenrath's give more detail in some respects. The two calculations agree. Gilmore's equation was approximated analytically by Brode 8 For the absorption coefficient we have used the tables by Meyerott et al., 15'16 which extend to 12,000°. These were supplemented by the 18 work of Kivel and Bai1eyl7 and more recent work by Taylor and Kivel on the free-free electron transitions in the field of neutral atoms and molecules. At higher temperatures, there are calculations by Gilmore and Latter,I9 Karzas and LatterY2* and curves by Gilmoregl which are brought to date periodically. The most recent cdculation on the absorption of air at about 18,000' and above have been done by Stuart and Pyatt.*2 This temperature range is not of great importance for the problem of this paper, but is important for the expansion of the iso- thermal sphere inside the shock wave before it is reached by the cooling wave . 8 Brode has used the average of the absorption coefficient over
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 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 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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