Theory of the Fireball

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