Theory of the Fireball

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4 dF: = - 4KaT at where a is the Stefan-Boltzmann constat and K tne opacity in cm /gm, (7.5) i.e., the absorption coefficient averaged over a PlaJnck spectrum (dis- regarding spectral regions which are still black) . Since K increases rapidly with temperature, the hottest region near the center will cool fastest, so that tne temperature tends to become more uniform. For the same reason, the radiative coolhg will effectively stop at a temperature of about 5000°. At t‘nis temperature and p = O.Olpo, it takes about 5 seconds to cool the fireball by LO$. At 4000°, this takes about 200 seconds. Gilmore2’ ‘has calculated curves of cooling times for transparent bodies at various densities as a function of tine final temperature. Depending on the ambient density, tne pressure may or may not have decreased to ambient pressure when the temperature has decreased to ‘OOOo. Even if it has not, the subsequent adiabatic expansion t rill not lower the temperature much further. (Our theory is not applicable to very lar~ ambient densities because there the isolation of isotnermal sphere from t’ne outside never takes place. Probably the limit of applicability is -2 about pl/po = 10 . Therefore, and because of the small value of y - 1, expansion cannot be large.) Therefore, after both radiation and hydro- dynamics have effectively stopped, the fireball is left at a temperature not much belov 5000°. Any furt‘ner cooling can only be achieved by the rise of the fireball 82 2 .-
due to its bouyancy, and the turbulent mixing associated with this rise. Tnis is a slow process, taking tens of 'seconds. Since tine emission is now proportional to the absorption coefficient, the molecular bands will now appear in emission while in earlier stages they appear in absorption. This has been observed. The debris, at the center of tne fireball, contains metals and therefore is likely to be opaque at lower temperatures. Therefore the debris may well be opaque after all the air has become transparent. The debris usualTy has a ragged shape due to Taylor- instability. Recently, 26 Longmire has given a tentative, quantitative theory of this instability in debris expansion. Because of its higher opacity, the debris my cool to a lower temperature than tne surrounding air.
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, - Ip.L ,. : CIC-14 REPORT COLLECT
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LA-3064 UC-34, PHYSICS TID-4500 (30
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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
Page 18 and 19:
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 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 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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