Theory of the Fireball

More documents

Recommendations

Info

esult of the three-dimensional considerations, the one-dimensional for- . mda (5 -35 yields a decrease of p/p as t -'. Using (5.33), a constant mass absorption coefficient requires -1/3n 4/20 T; - P "P (6.28) Thus in three dimensions, the temperature continues to increase slowly after the cooling wave reaches the isothermal sphere. If we assume tinat times up to x = 2.5 in Table IX are significant, tne pressure decreases by about a factor of 3 in Stage C 11, and the temperature of the radiating d layer increases by about 513 according to (6.28). The radiated power, 2 14 being proportional to R1 T1 , may increase by about 10:'. up to x = 2, and then decreases due to the shrinkage of the radiating surface. One prediction of this theory is that the temperature,as well as the radiated power. has a rather flat second maximum while the isothermal sphere radiates treatment of J1 I - away its energy. The slaw vwiation of T justifies the 1 as constant in Sec. 6b . 7. TRANSPARENT FIREBALL ( Stage D) After the isothermal sphere has been eliminated by the cooling wave, the fireball is transparent if we neglect the effect of toe bomb debris. At this time the pressure is given by (6.21), the average temperature of the 'barn" region is about 70Oo0, and the corresponding density is about 80
If we assume that the radius Ra of the isothermal sphere scales with 4 3 p1 (which may be wrong) the radius of the warm sphere is now where Y is in megatons. Therefore, along a radius, the mount of warn material is about almost independent of ambient air density. Taking pb/po = 10 -2 (which corresponds to pl/po = 10") and an average temperature of 7000°, Meyerott's tables give for the visible: so that the radius represents 0.7 optical mean free path at 1 megaton. Tnis is nearly transparent, and the fireball becomes rapidly more transparent as it cools dawn by further emission of radiation. The emission of radiation is then proportional to the opacity; for each material element, 81
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 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 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
show all

Theory of the Fireball

Create successful ePaper yourself

Delete template?

Save as template?