Theory of the Fireball

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Table VI. Average Mean Free Paths (gm/cm ) 2 8,000 0 105 0.20 0.76 12,000 I. 82’2 A fair approximat ion to Table VI is Gilmore’s equation of state can be approximated near T = 1, p/po = 0.1 by Using this in (4.10) gives c . Ultraviolet The absorption in the ultraviolet is generally high at all tempera- . . tures. At lcrw temperatures, the absorption is mainly due to the Schumann- Runge bands; at higher temperature (8000°) these are replaced by NO and y, and at high temperature (12,000°) by photoelectric absorption in 0-, 40 t r
N, and 0. The Schumann-Runge bands start from the electronic ground state of 02, hence are available at law T; at higher T, the spectral region of strong absorption spreads due to excitation of vibrational states; but at still higher T, oxygen dissociates and therefore the bands die out (at &looo, they contribute less than lO$ of the absorption). The photoelectric absorption in N and 0 requires not only the presence of these atoms but also their electronic excitation, and therefore does not become importast until about 10,OOOo. Table VI1 gives, for density p = O.lpO, the spectral regions of strong absorption. In accord with Sec. 3b, we define this by p > lom3 (mean free path less than 10 meters) or I-L > lom2 (4 1 meter). The table shows that strong absorption covers a particularly wide spectral region at 4000°, shrinking substantially at 6000~. Very strong absorption, p > LOm2 m-', occurs in quite a lwge spectral. region for T = 4000° but shrinks to practically nothing at 6000~ and to nothing at 8000°. At 12,000°, very strong absorption occurs again but is now in the visible. The strong absorption in the ultraviolet (hv > 3.5 w) means first of all that the W is not emitted to large distances and can therefore 0 not be observed; e.g., at T = 4000 and hv = 3.5 ev, we have %e should also add the photoelectric absorption from excited states of NO, which should be especially noticeable at 8000°. 41 JC.
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 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

Theory of the Fireball

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