Theory of the Fireball

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U" J, A Ho - H(T1) To determine u we therefore have to proceed as follows: 1. Find the temperature T at which the opacity K(T1) is such that there 1 is one optical mean free path outside x i.e., 1' For this purpose we must haw, of course, the temperature distribution T(x) for T < T1. 2. Determine J(Tl) from (5.9) and Knaring the internal enthalpy H(T ) from the equation of state. 1 'Ho then gives u frmn (5.10). Note that u is the Lagrangian velocity of the cooling wave. It has the cor- rect dimension. To solve problem 1, Z assume that the material which has gone through the cooling wave will expand adiabatically. We shall find that this is a reasonable assumption in most conditions (Sec. 5d) but that at early times (Sec. 5f) and in certain late stages other considerations apply (Sec. 6b) b. Inside Structure of Fireball, Blocking Layer In early stages (Stage B I), just after the shock wave is formed, the isothermal sphere expands, by radiation diffusion, into the material which has been heated by shock. This process, which w ill be treated in a subsequent report, depends on the temperature and temperature gradient 48
in the isothem. sphere. For its occurrence it is important that the opacity actually decreases with increasing T at higher temperature. Many calculations of K(T) in this temperature region have been made. Curves have been compiled, especially by Gilmore,21 and revised as more mor- mation has become available. The most recent and most extensive calculation, to my howledge, is by Stuart and matt. 22 AU. calculations agree that T 3 /K(T), which is the important quantity according to ( 5.3), has a pronounced minimum at about T ’ = 2, T = 20,000°. (The temperature of the minimum increases slightly with increasing density. ) Molecules are no longer present at these temperatures, and absorption is mainly by bound-free electron transitions in atoms and atomic ions, with some contribution from broadened atomic lines (bound- bound transitions) whose calculation is the most difficult . Radiation transport, then, is most difficult around Tb = 20,00O0, - and temperatures around Tb constitute an effective blocking layer for radiation. Until about 0.5 second, the central temperature of a 1-megaton sea level explosion is greater than T according to the calculations of b’ 0 Brode. Radiation flm can then be considered as taking place separately in an interior and an exterior region. The Stertor flaw is determined by the central temperature Tc, and this flaw generally decreases with , time because Tc decreases and with it the quantity T 3 /K. The exterior flaw is dominated by the cooling wave and increases with time because the decrease of density causes a decrease of opacity for any given T. The two flow regions are separated by a blocking layer in which the 49
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 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 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

Theory of the Fireball

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