Fireball Physics

The fireball is the hot ball of gas created when a nuclear explosion heats the bomb itself, and the immediate surrounding environment, to very high temperatures. As this incandescent ball of hot gas expands, it radiates part of its energy away as thermal radiation (including visible and ultraviolet light), part of its energy also goes into creating a shock wave or blast wave in the surrounding environment. The generation of these two destructive effects are thus closely linked by the physics of the fireball. In the discussion below I assume the fireball is forming in open air, unless stated otherwise.

The Early Fireball

Immediately after the energy-producing nuclear reactions in the weapon are completed, the energy is concentrated in the nuclear fuels themselves. The energy is stored as (in order of importance): thermal radiation or photons; as kinetic energy of the ionized atoms and the electrons (mostly as electron kinetic energy since free electrons outnumber the atoms); and as excited atoms, which are partially or completely stripped of electrons (partially for heavy elements, completely for light ones).

Thermal (also called blackbody) radiation is emitted by all matter. The intensity and most prevalent wavelength is a function of the temperature, both increasing as temperature increases. The intensity of thermal radiation increases very rapidly - as the fourth power of the temperature. Thus at the 60-100 million degrees C of a nuclear explosion, which is some 10,000 times hotter than the surface of the sun, the brightness (per unit area) is some 10 quadrillion (10^16) times greater! Consequently about 80% of the energy in a nuclear explosion exists as photons. At these temperatures the photons are soft x-rays with energies in the range of 10-200 KeV.

The first energy to escape from the bomb are the gamma rays produced by the nuclear reactions. They have energies in the MeV range, and a significant number of them penetrate through the tampers and bomb casing and escape into the outside world at the speed of light. The gamma rays strike and ionize the surrounding air molecules, causing chemical reactions that form a dense layer of "smog" tens of meters deep around the bomb. This smog is composed primarily of ozone, and nitric and nitrous oxides.

X-rays, particularly the ones at the upper end of the energy range, have substantial penetrating power and can travel significant distances through matter at the speed of light before being absorbed. Atoms become excited when they absorb x-rays, and after a time they re-emit part of the energy as a new lower energy x-ray. By a chain of emissions and absorptions, the x-rays carry energy out of the hot center of the bomb, a process called radiative transport. Since each absorption/re-emission event takes a certain amount of time, and the direction of re-emission is random (as likely back toward the center of the bomb as away from it), the net rate of radiative transport is considerably slower than the speed of light. It is however initially much faster than the expansion of the plasma (ionized gas) making up the fireball or the velocity of the neutrons.

An expanding bubble of very high temperatures is thus formed called the "iso-thermal sphere". It is a sphere were everything has been heated by x-rays to a nearly uniform temperature, initially in the tens of millions of degrees. As soon as the sphere expands beyond the bomb casing it begins radiating light away through the air (unless the bomb is buried or underwater). Due to the still enormous temperatures, it is incredibly brilliant (surface brightness trillions of times more intense than the sun). Most of the energy being radiated is in the x-ray and far ultraviolet range to which air is not transparent. Even at the wavelengths of the near ultraviolet and visible light, the "smog" layer absorbs much of the energy. Then too, at this stage the fireball is only a few meters across. Thus the apparent surface brightness at a distance, and the output power (total brightness) is not nearly as intense as the fourth-power law would indicate.

Blast Wave Development and Thermal Radiation Emission

As the fireball expands, it cools and the wavelength of the photons transporting energy drops. Longer wavelength photons do not penetrate as far before being absorbed, so the speed of energy transport also drops. When the isothermal sphere cools to about 300,000 degrees C (and the surface brightness has dropped to being a mere 10 million times brighter than the sun), the rate of radiative growth is about equal to the speed of sound in the fireball plasma. At this point a shock wave forms at the surface of the fireball as the kinetic energy of the fast moving ions starts transferring energy to the surrounding air. This phenomenon, known as "hydrodynamic separation", occurs for a 20 kt explosion about 100 microseconds after the explosion, when the fireball is some 13 meters across. A shock wave internal to the fireball caused by the rapidly expanding bomb debris may overtake and reinforce the fireball surface shock wave a few hundred microseconds later.

The shock wave initially moves at some 30 km/sec, a hundred times the speed of sound in normal air. This compresses and heats the air enormously, up to 30,000 degrees C (some five times the sun's surface temperature). At this temperature the air becomes ionized and incandescent. Ionized gas is opaque to visible radiation, so the glowing shell created by the shock front hides the much hotter isothermal sphere inside. The shock front is many times brighter than the sun, but since it is much dimmer than the isothermal sphere it acts as an optical shutter, causing the fireball's thermal power to drop rapidly.

The fireball is at its most brilliant just as hydrodynamic separation occurs, the great intensity compensating for the small size of the fireball. The rapid drop in temperature causes the thermal power to drop ten-fold, reaching a minimum in about 10 milliseconds for a 20 kt bomb (100 milliseconds for 1 Mt bomb). This "first pulse" contains only about 1 percent of the bomb's total emitted thermal radiation. At this minimum, the fireball of a 20 kt bomb is 180 meters across.

As the shock wave expands and cools to around 3000 degrees, it stops glowing and gradually also becomes transparent. This is called "breakaway" and occurs at about 15 milliseconds for a 20 kt bomb, when the shock front has expanded to 220 meters and is travelling at 4 km/second. The isothermal sphere, at a still very luminous 8000 degrees, now becomes visible and both the apparent surface temperature and brightness of the fireball climb to form the "second pulse". The isothermal sphere has grown considerably in size and now consists almost entirely of light at wavelengths to which air is transparent, so it regains much of the total luminosity of the first peak despite its lower temperature. This second peak occurs at 150 milliseconds for a 20 kt bomb, at 900 milliseconds for a 1 Mt bomb. After breakaway, the shock (blast) wave and the fireball do not interact further.

A firm cutoff for this second pulse is impossible to provide because the emission rate gradually declines over an extended period. Some rough guidelines are that by 300 milliseconds for a 20 kt bomb (1.8 seconds for a 1 Mt) 50% of the total thermal radiation has been emitted, and the rate has dropped to 40% of the second peak. These figures become 75% total emitted and 10% peak rate by 750 milliseconds (20 kt) and 4.5 second (1 Mt). The emission time scales roughly as the 0.45 power of yield (Y^0.45).

Although this pulse never gets as bright as the first, it emits about 99% of the thermal radiation because it is so much longer.

Ionizing Radiation Physics

There are four types of ionizing radiation produced by nuclear explosions that can cause significant injury: neutrons, gamma rays, beta particles, and alpha particles. Gamma rays are energetic (short wavelength) photons (as are X-rays), beta particles are energetic (fast moving) electrons, and alpha particles are energetic helium nuclei. Neutrons are damaging whether they are energetic or not, although the faster they are, the worse their effects.

They all share the same basic mechanism for causing injury though: the creation of chemically reactive compounds called "free radicals" that disrupt the normal chemistry of living cells. These radicals are produced when the energetic radiation strikes a molecule in the living issue, and breaks it into ionized (electrically charged) fragments. Fast neutrons can do this also, but all neutrons can also transmute ordinary atoms into radioactive isotopes, creating even more ionizing radiation in the body.

The different types of radiation present different risks however. Neutrons and gamma rays are very penetrating types of radiation. They are the hardest to stop with shielding. They can travel through hundreds of meters of air and the walls of ordinary houses. They can thus deliver deadly radiation doses even if an organism is not in immediate contact with the source. Beta particles are less penetrating, they can travel through several meters of air, but not walls, and can cause serious injury to organisms that are near to the source. Alpha particles have a range of only a few centimeters in air, and cannot even penetrate skin. Alphas can only cause injury if the emitting isotope is ingested.

The shielding effect of various materials to radiation is usually expressed in half-value thickness, or tenth-value thickness: in other words, the thickness of material required to reduce the intensity of radiation by one-half or one-tenth. Successive layers of shielding each reduce the intensity by the same proportion, so three tenth-value thickness reduce the intensity to one-thousandth (a tenth-value thickness is about 3.3 half-value thicknesses). Some example tenth-value thicknesses for gamma rays are: steel 8.4-11 cm, concrete 28-41 cm, earth 41-61 cm, water 61-100 cm, and wood 100-160 cm. The thickness ranges indicate the varying shielding effect for different gamma ray energies.

Even light clothing provides substantial shielding to beta rays.

Sources of Radiation

Prompt Radiation
Radiation is produced directly by the nuclear reactions that generate the explosion, and by the decay of radioactive products left over (either fission debris, or induced radioactivity from captured neutrons).

The explosion itself emits a very brief burst (about 100 nanoseconds) of gamma rays and neutrons, before the bomb has blown itself apart. The intensity of these emissions depends very heavily on the type of weapon and the specific design. In most designs the initial gamma ray burst is almost entirely absorbed by the bomb (tamper, casing, explosives, etc.) so it contributes little to the radiation hazard. The neutrons, being more penetrating, may escape. Both fission and fusion reactions produce neutrons. Fusion produces many more of them per kiloton of yield, and they are generally more energetic than fission neutrons. Some weapons (neutron bombs) are designed specifically to emit as much energy in the form as neutrons as possible. In heavily tamped fission bombs few if any neutrons escape. It is estimated that no significant neutron exposure occurred from Fat Man, and only 2% of the total radiation dose from Little Boy was due to neutrons.

The neutron burst itself can be a significant source of radiation, depending on weapon design. As the neutrons travel through the air they are slowed by collisions with air atoms, and are eventually captured. Even this process of neutron attenuation generates hazardous radiation. Part of the kinetic energy lost by fast neutrons as they slow is converted into gamma rays, some with very high energies (for the 14.1 MeV fusion neutrons). The duration of production for these neutron scattering gammas is about 10 microseconds. The capture of neutrons by nitrogen-14 also produces gammas, a process completed by 100 milliseconds.

Immediately after the explosion, there are substantial amounts of fission products with very short half-lifes (milliseconds to minutes). The decay of these isotopes generate correspondingly intense gamma radiation that is emitted directly from the fireball. This process is essentially complete within 10 seconds.

The relative importance of these gamma ray sources depends on the size of the explosion. Small explosions (20 kt, say) can generate up to 25% of the gamma dose from the direct gammas and neutron reactions. For large explosions (1 Mt) this contribution is essentially zero. In all cases, the bulk of the gammas are produced by the rapid decay of radioactive debris.

Delayed Radiation
Radioactive decay is the sole source of beta and alpha particles. They are also emitted during the immediate decay mentioned above of course, but their range is too short to make any prompt radiation contribution. Betas and alphas become important when fallout begins settling out. Gammas remain very important at this stage as well.

Fallout is a complex mixture of different radioactive isotopes, the composition of which continually changes as each isotope decays into other isotopes. Many isotopes make significant contributions to the overall radiation level. Radiation from short lived isotopes dominates initially, and the general trend is for the intensity to continually decline as they disappear. Over time the longer lived isotopes become increasingly important, and a small number of isotopes emerge as particular long-term hazards.

Radioactive isotopes are usually measured in terms of curies. A curie is the quantity of radioactive material that undergoes 3.7x10^10 decays/sec (equal to 1 g of radium-226). More recently the SI unit bequerel has become common in scientific literature, one bequerel is 1 decay/sec . The fission of 57 grams of material produces 3x10^23 atoms of fission products (two for each atom of fissionable material). One minute after the explosion this mass is undergoing decays at a rate of 10^21 disintegrations/sec (3x10^10 curies). It is estimated that if these products were spread over 1 km^2, then at a height of 1 m above the ground one hour after the explosion the radiation intensity would be 7500 rads/hr.

Isotopes of special importance include iodine-131, strontium-90 and 89, and cesium-137. This is due to both their relative abundance in fallout, and to their special biological affinity. Isotopes that are readily absorbed by the body, and concentrated and stored in particular tissues can cause harm out of proportion to their abundance.

Iodine-131 is a beta and gamma emitter with a half-life of 8.07 days (specific activity 124,000 curies/g) Its decay energy is 970 KeV; usually divided between 606 KeV beta, 364 KeV gamma. Due to its short half-life it is most dangerous in the weeks immediately after the explosion, but hazardous amounts can persist for a few months. It constitutes some 2% of fission-produced isotopes - 1.6x10^5 curies/kt. Iodine is readily absorbed by the body and concentrated in one small gland, the thyroid.

Strontium-90 is a beta emitter (546 KeV, no gammas) with a half-life of 28.1 years (specific activity 141 curies/g), Sr-89 is a beta emitter (1.463 MeV, gammas very rarely) with a half-life of 52 days (specific activity 28,200 Ci/g). Each of these isotopes constitutes about 3% of total fission isotopes: 190 curies of Sr-90 and 3.8x10^4 curies of Sr-89 per kiloton. Due to their chemical resemblance to calcium these isotopes are absorbed fairly well, and stored in bones. Sr-89 is an important hazard for a year or two after an explosion, but Sr-90 remains a hazard for centuries. Actually most of the injury from Sr-90 is due to its daughter isotope yttrium-90. Y-90 has a half-life of only 64.2 hours, so it decays as fast as it is formed, and emits 2.27 MeV beta particles.

Cesium-137 is a beta and gamma emitter with a half-life of 30.0 years (specific activity 87 Ci/g). Its decay energy is 1.176 MeV; usually divided by 514 KeV beta, 662 KeV gamma. It comprises some 3-3.5% of total fission products - 200 curies/kt. It is the primary long-term gamma emitter hazard from fallout, and remains a hazard for centuries.

Although not important for acute radiation effects, the isotopes carbon-14 and tritium are also of interest because of possible genetic injury. These are not direct fission products. They are produced by the interaction of fission and fusion neutrons with the atmosphere and, in the case of tritium, as a direct product of fusion reactions. Most of the tritium generated by fusion is consumed in the explosion but significant amounts survive. Tritium is also formed by the capture of fast neutrons by nitrogen atoms in the air: N-14 + n -> T + C-12. Carbon-14 in also formed by neutron-nitrogen reactions: N-14 + n -> C-14 + p. Tritium is a very weak beta emitter (18.6 KeV, no gamma) with a half-life of 12.3 years (9700 Ci/g).

Carbon-14 is also a weak beta emitter (156 KeV, no gamma), with a half-life of 5730 years (4.46 Ci/g). Atmospheric testing during the fifties and early sixties produced about 3.4 g of C-14 per kiloton (15.2 curies) for a total release of 1.75 tonnes (7.75x10^6 curies). For comparison, only about 1.2 tonnes of C-14 naturally exists, divided between the atmosphere (1 tonne) and living matter (0.2 tonne). Another 50-80 tonnes is dissolved in the oceans. Due to carbon exchange between the atmosphere and oceans, the half-life of C-14 residing in the atmosphere is only about 6 years. By now the atmospheric concentration has returned to within 1% or so of normal. High levels of C-14 remain in organic material formed during the sixties (in wood, say, or DNA).

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