Because of the extremely high temperature, there is an emission of energy by electromagnetic radiation, covering a wide range of wavelengths, from infrared (thermal) through the visible to the ultraviolet and beyond. Much of this radiation is absorbed by the air immediately surrounding the bomb, with the result that the air itself becomes heated to incandescence. In this condition the detonated bomb begins to appear, after a few millionths of a second, as a luminous sphere called the fireball. As the energy is radiated into a greater region raising the temperature of the air through which it passes, the fireball increases in size, but the temperature, pressure and luminosity decrease correspondingly. After about 0.1 msec has elapsed, the radius of the fireball is some 14 m, and the temperature is then in the vicinity of 300,000 ° K. At this instant, the luminosity, as observed at a distance of 10,000 m, is approximately 100 times that of the sun as seen at the earth's surface.
Under the conditions just described, the temperature throughout the fireball is almost uniform; since energy, as radiation, can travel rapidly between any two points in the sphere, there are no appreciable temperature gradients. Because of the uniform temperature the system is referred to as an isothermal sphere which, at this stage, is identical with the fireball.
As the fireball grows, a shock wave develops in the air, and at first the shock front coincides with the surface of the isothermal sphere and of the fireball. Below a temperature of 300,000 ° K however, the shock wave advances more rapidly than does the isothermal sphere. In other words, transport of energy by the shock wave is faster than by radiation. Nevertheless, the luminous fireball still grows in size because the great compression of the air due to the passing of the shock wave results in an increase of temperature sufficient to render incandescence. The isothermal sphere is now a high-temperature region lying inside the larger fireball; and the shock front is coincident with the surface of the latter, which consequently becomes sharply defined. The surface of separation between the very hot inner core and the somewhat cooler shock-heated air is called the radiation front.
The phenomena described above are represented schematically in Fig 9.5; qualitative temperature gradients are shown at the left, and pressure gradients at the right, of a series of photographs of the fireball taken at various intervals after detonation of an atomic bomb. It can be seen that at first the temperature is uniform throughout the fireball, which is then an isothermal sphere. Later, two distinct temperature levels are apparent, where the fireball has moved ahead of the isothermal sphere in the interior. It may be noted that the luminosity of the outer region of the fireball (brightness of the encompassing shock front) prevents the isothermal sphere from being visible on the photograph. At this time, the rise of the pressure to a peak, followed by a shark drop at the surface of the fireball, indicates that the latter is identical with the shock wave front.
The fireball continues to grow rapidly in size for about 15 msec, by which times its radius has increased to around 90 m; the surface temperature has then dropped to around 5000 ° K, although the interior is very much hotter. The temperature and pressure of the shock wave have also decreased to such an extent that the air through which it travels is no longer rendered luminous. The faintly seen shock front moves ahead of the fireball, and the onset of this condition is referred to as the breakaway (of the shock front from the luminous sphere). The rate of propagation of the shock wave is then in the vicinity of 4500 m/sec.
Although the rate of advance of the shock front decreases with time, it continues to move forward more rapidly than the fireball. After the lapse of one second, the fireball has essentially attained its maximum radius of 140 m, and the shock front is then some 180 m further ahead. After 10 sec the fireball has risen about 450 m, the shock wave has travelled about 3700 m and has passed the region of maximum damage.
An important feature of an atomic explosion in air occurs at about the time of the breakaway of the shock front (from the luminous sphere). The surface temperature (of the luminous sphere) falls to about 2000 ° K and then commences to rise again to a second maximum around 7000 ° K. The minimum is reached approximately 15 msec after the explosion, while the maximum is attained about 0.3 sec later. Subsequently, the temperature of the fireball drops steadily due to the expansion and loss of energy.
It is of interest to note that the energy radiated in an atomic explosion appears after the point of minimum luminosity of the fireball. Only about 1% of the total is lost before this time, in spite of the much higher surface temperature. The explanation of this result lies, of course, in the fact that the duration of the latter period, i.e., about 15 msec, is very short compared with the several seconds during which radiation takes place after the minimum has been passed.
As stated above the fireball expands very rapidly to its maximum radius of 140 m, within less than a second from the explosion. Consequently, if the bomb is detonated at a height of less than 140 m, the fireball can actually touch the earth's surface, as t did in the historic "Trinity" test at Alamogordo, New Mexico. Because of its low density, the fireball rises, like a gas balloon, starting at rest and accelerating within a few seconds to its maximum rate of ascent of 90 m/s.
After about 10 sec from detonation, when the luminosity of the fireball has died out and the excess of pressure of the sock wave has decreased to virtually harmless proportions, the immediate effects of the bomb may be regarded as over.
Because of its high temperature, and consequently low density, the fireball rises, as stated above, and as it rises it is cooled. At temperatures down to about 1800 ° K the cooling is mainly due to loss of energy by thermal radiation; subsequently, the temperature is lowered as a result of adiabatic expansion of the gases and by mixing with the surrounding air through turbulent convection. When the fireball is no longer luminous, it may be regarded as a large bubble of hot gases rising in the atmosphere, its temperature falling as it ascends.
An important difference between an atomic and conventional explosion is that the energy liberated per unit mass is much greater in the former case. As a consequence, the temperature attained is much higher, with the result that a larger proportion of the energy is emitted as thermal radiation at the time of the explosion. An atomic bomb, for examples, releases roughly one third of its total energy in the form of this radiation. For the nominal atomic bomb discussed, the energy emitted in this matter would be about 6.7 · 10^12 cal, which is equivalent to about 28 · 10^20 erg.
The rate at which energy passes through the whole of the spherical surface of the fireball, that is, over a solid angle of 4 \pi, is \sigma T^4 · 4 \pi R^2, where R is the radius of the fireball (and T is the surface temperature; the dependence of R and T on time is shown in Fig 9.6). Since only the fraction f_0 of this[*] penetrates the air, the rate at which the radiant energy reaches all points on a spherical area at a moderate distance from the point of detonation is f_0 \sigma T^4 · 4 \pi R^2. The radiant energy flux \phi per unit area at a distance D is then obtained upon dividing by the total spherical area 4 \pi D^2, so that
\phi = f_0 \sigma T^4 (R/D)^2
From this equation the (radiant energy flux) at a given point, distance D, can be computed for various times after an atomic explosion, using the values of R and T from Fig 9.6 and of f_0 from Fig 9.7. In order to avoid plotting values for individual distances, the quantity \phi D^2, which is equal to f_0 \sigma T^4 R^2, is given in Fig 9.8 as a function of the time; the energy flux is in cal/cm^2 . sec, and the distance is in m. From the curve, the energy flux at any given moderate distance at a specific time can be readily determined.
In order to obtain some indication of the magnitude of the illumination, it is convenient to introduce a unit called the sun; this is defined as a flux of 0.032 cal/cm^2 · sec, and is supposed to be equivalent to the energy received from the sun at the top of the atmosphere. The ordinates at the right of Fig 9.8 give the value of \phi D^2 in suns and D in m.
At the luminosity minimum, the value of \phi D^2 is about 6.8 · 10^6 sun-m^2, so that at this point the fireball, as seen at a distance of about 2600 m, should appear about as brought as the sun. Actually, it will be somewhat less bright, to an extent depending on the clearness of the air, because of atmospheric attenuation.