Theory of the Fireball
Theory of the Fireball
Theory of the Fireball
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violet, (3.17) is not valid; <strong>the</strong>se wave lengths are strongly absorbed by<br />
cold or cool air ( Sec . kc) . For example, at p = po and T = 2000°, <strong>the</strong><br />
mean free path is less than 1 meter for all light16 <strong>of</strong> hv > 4.7 ev<br />
(A < 0.26 p). Since <strong>the</strong> emission <strong>of</strong> light <strong>of</strong> such short wave length from<br />
such cool air is negligible, <strong>the</strong> fireball will not emit such radiation at<br />
all.<br />
A detailed discussion <strong>of</strong> <strong>the</strong> absorption coefficient in <strong>the</strong> visible<br />
will be given in Sec. 4b. As can be seen from <strong>the</strong> tables <strong>of</strong> Meyerott<br />
16<br />
et al. and from our Table VI, for a density p = po <strong>the</strong> mean free path<br />
is <strong>of</strong> <strong>the</strong> order <strong>of</strong> 5 meters at about 6000~. This corresponds to a pres-<br />
sure13 <strong>of</strong> about 25 bars. For p = O.lpo <strong>the</strong> requisite mean free path <strong>of</strong><br />
a few meters is obtained for about 10,OOOo, with p M 7 bars. Thus for a<br />
J<br />
relatively modest decrease in pressure, <strong>the</strong> effective temperature <strong>of</strong><br />
radiation increases from 6000 to 10,OOOo, corresponding to a very sub-<br />
stantial increase in radiation intensity. This is <strong>the</strong> mechanism <strong>of</strong> <strong>the</strong><br />
increase in radiation tarard <strong>the</strong> second maximum. A more detailed dis-<br />
cussion w ill be given in Sec. 5f.<br />
d. Energy Supply<br />
As long as <strong>the</strong> radiating temperature is low, not much energy w ill<br />
be emitted as radiation, and this emission will only slightly modify <strong>the</strong><br />
cooling <strong>of</strong> <strong>the</strong> material due to adiabatic expansion. However, when <strong>the</strong><br />
radiating temperature increases, <strong>the</strong> radiation cooling will exceed <strong>the</strong><br />
adiabatic cooling to an increasing extent. It <strong>the</strong>n becomes necessary to<br />
supply energy from <strong>the</strong> interior to <strong>the</strong> radiating surface.