Einstein coefficients

From Wikipedia, the free encyclopedia

Emission lines and absorption lines compared to a continuous spectrum

 

Einstein coefficients are mathematical quantities which are a measure of the probability of absorption or emission of light by an atom or molecule. The Einstein A coefficient is related to the rate of spontaneous emission of light, and the Einstein B coefficients are related to the absorption and stimulated emission of light.

Spectral lines

In physics, one thinks of a spectral line from two viewpoints.

An emission line is formed when an atom or molecule makes a transition from a particular discrete energy level E₂ of an atom, to a lower energy level E₁, emitting a photon of a particular energy and wavelength. A spectrum of many such photons will show an emission spike at the wavelength associated with these photons.

An absorption line is formed when an atom or molecule makes a transition from a lower, E₁, to a higher discrete energy state, E₂, with a photon being absorbed in the process. These absorbed photons generally come from background continuum radiation (the full spectrum of electromagnetic radiation) and a spectrum will show a drop in the continuum radiation at the wavelength associated with the absorbed photons. 

The two states must be bound states in which the electron is bound to the atom or molecule, so the transition is sometimes referred to as a "bound–bound" transition, as opposed to a transition in which the electron is ejected out of the atom completely ("bound–free" transition) into a continuum state, leaving an ionized atom, and generating continuum radiation.

A photon with an energy equal to the difference E₂ − E₁ between the energy levels is released or absorbed in the process. The frequency ν at which the spectral line occurs is related to the photon energy by Bohr's frequency condition E₂ − E₁ = hν where h denotes Planck's constant.

Emission and absorption coefficients

An atomic spectral line refers to emission and absorption events in a gas in which ${\displaystyle n_{2}}$ is the density of atoms in the upper-energy state for the line, and ${\displaystyle n_{1}}$ is the density of atoms in the lower-energy state for the line. 

The emission of atomic line radiation at frequency ν may be described by an emission coefficient ${\displaystyle \epsilon }$ with units of energy/(time × volume × solid angle). ε dt dV dΩ is then the energy emitted by a volume element ${\displaystyle dV}$ in time ${\displaystyle dt}$ into solid angle ${\displaystyle d\Omega }$. For atomic line radiation,

${\displaystyle \epsilon ={\frac {h\nu }{4\pi }}n_{2}A_{21},}$

where ${\displaystyle A_{21}}$ is the Einstein coefficient for spontaneous emission, which is fixed by the intrinsic properties of the relevant atom for the two relevant energy levels. 

The absorption of atomic line radiation may be described by an absorption coefficient ${\displaystyle \kappa }$ with units of 1/length. The expression κ' dx gives the fraction of intensity absorbed for a light beam at frequency ν while traveling distance dx. The absorption coefficient is given by

${\displaystyle \kappa '={\frac {h\nu }{4\pi }}(n_{1}B_{12}-n_{2}B_{21}),}$

where ${\displaystyle B_{12}}$ and ${\displaystyle B_{21}}$ are the Einstein coefficients for photon absorption and induced emission respectively. Like the coefficient ${\displaystyle A_{21}}$, these are also fixed by the intrinsic properties of the relevant atom for the two relevant energy levels. For thermodynamics and for the application of Kirchhoff's law, it is necessary that the total absorption be expressed as the algebraic sum of two components, described respectively by ${\displaystyle B_{12}}$ and ${\displaystyle B_{21}}$, which may be regarded as positive and negative absorption, which are, respectively, the direct photon absorption, and what is commonly called stimulated or induced emission.

The above equations have ignored the influence of the spectroscopic line shape. To be accurate, the above equations need to be multiplied by the (normalized) spectral line shape, in which case the units will change to include a 1/Hz term. 

For conditions of thermodynamic equilibrium, together the number densities ${\displaystyle n_{2}}$ and ${\displaystyle n_{1}}$, the Einstein coefficients, and the spectral energy density provide sufficient information to determine the absorption and emission rates.

Equilibrium conditions

The number densities ${\displaystyle n_{2}}$ and ${\displaystyle n_{1}}$ are set by the physical state of the gas in which the spectral line occurs, including the local spectral radiance (or, in some presentations, the local spectral radiant energy density). When that state is either one of strict thermodynamic equilibrium, or one of so-called "local thermodynamic equilibrium", then the distribution of atomic states of excitation (which includes ${\displaystyle n_{2}}$ and ${\displaystyle n_{1}}$) determines the rates of atomic emissions and absorptions to be such that Kirchhoff's law of equality of radiative absorptivity and emissivity holds. In strict thermodynamic equilibrium, the radiation field is said to be black-body radiation and is described by Planck's law. For local thermodynamic equilibrium, the radiation field does not have to be a black-body field, but the rate of interatomic collisions must vastly exceed the rates of absorption and emission of quanta of light, so that the interatomic collisions entirely dominate the distribution of states of atomic excitation. Circumstances occur in which local thermodynamic equilibrium does not prevail, because the strong radiative effects overwhelm the tendency to the Maxwell–Boltzmann distribution of molecular velocities. For example, in the atmosphere of the Sun, the great strength of the radiation dominates. In the upper atmosphere of the Earth, at altitudes over 100 km, the rarity of intermolecular collisions is decisive. 

In the cases of thermodynamic equilibrium and of local thermodynamic equilibrium, the number densities of the atoms, both excited and unexcited, may be calculated from the Maxwell–Boltzmann distribution, but for other cases, (e.g. lasers) the calculation is more complicated.

Einstein coefficients

In 1916, Albert Einstein proposed that there are three processes occurring in the formation of an atomic spectral line. The three processes are referred to as spontaneous emission, stimulated emission, and absorption. With each is associated an Einstein coefficient, which is a measure of the probability of that particular process occurring. Einstein considered the case of isotropic radiation of frequency ν and spectral energy density ρ(ν).

Various formulations

Hilborn has compared various formulations for derivations for the Einstein coefficients, by various authors. For example, Herzberg works with irradiance and wavenumber. Yariv works with energy per unit volume per unit frequency interval; also; this is how the present account is formulated. Mihalas & Weibel-Mihalas work with radiance and frequency; also Chandrasekhar; also Goody & Yung; Loudon uses angular frequency and radiance.

Spontaneous emission

Schematic diagram of atomic spontaneous emission

 

Spontaneous emission is the process by which an electron "spontaneously" (i.e. without any outside influence) decays from a higher energy level to a lower one. The process is described by the Einstein coefficient A₂₁ (s⁻¹), which gives the probability per unit time that an electron in state 2 with energy ${\displaystyle E_{2}}$ will decay spontaneously to state 1 with energy ${\displaystyle E_{1}}$, emitting a photon with an energy E₂ − E₁ = hν. Due to the energy-time uncertainty principle, the transition actually produces photons within a narrow range of frequencies called the spectral linewidth. If ${\displaystyle n_{i}}$ is the number density of atoms in state i , then the change in the number density of atoms in state 2 per unit time due to spontaneous emission will be

${\displaystyle \left({\frac {dn_{2}}{dt}}\right)_{\text{spontaneous}}=-A_{21}n_{2}.}$

The same process results in increasing of the population of the state 1:

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{spontaneous}}=A_{21}n_{2}.}$

Stimulated emission

Schematic diagram of atomic stimulated emission

 

Stimulated emission (also known as induced emission) is the process by which an electron is induced to jump from a higher energy level to a lower one by the presence of electromagnetic radiation at (or near) the frequency of the transition. From the thermodynamic viewpoint, this process must be regarded as negative absorption. The process is described by the Einstein coefficient ${\displaystyle B_{21}}$ (J⁻¹ m³ s⁻²), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 2 with energy ${\displaystyle E_{2}}$ will decay to state 1 with energy ${\displaystyle E_{1}}$, emitting a photon with an energy E₂ − E₁ = hν. The change in the number density of atoms in state 1 per unit time due to induced emission will be

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{neg. absorb.}}=B_{21}n_{2}\rho (\nu ),}$

where ${\displaystyle \rho (\nu )}$ denotes the spectral energy density of the isotropic radiation field at the frequency of the transition.

Stimulated emission is one of the fundamental processes that led to the development of the laser. Laser radiation is, however, very far from the present case of isotropic radiation.

Photon absorption

Schematic diagram of atomic absorption

 

Absorption is the process by which a photon is absorbed by the atom, causing an electron to jump from a lower energy level to a higher one. The process is described by the Einstein coefficient ${\displaystyle B_{12}}$ (J⁻¹ m³ s⁻²), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 1 with energy ${\displaystyle E_{1}}$ will absorb a photon with an energy E₂ − E₁ = hν and jump to state 2 with energy ${\displaystyle E_{2}}$. The change in the number density of atoms in state 1 per unit time due to absorption will be

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{pos. absorb.}}=-B_{12}n_{1}\rho (\nu ).}$

Detailed balancing

The Einstein coefficients are fixed probabilities per time associated with each atom, and do not depend on the state of the gas of which the atoms are a part. Therefore, any relationship that we can derive between the coefficients at, say, thermodynamic equilibrium will be valid universally.

At thermodynamic equilibrium, we will have a simple balancing, in which the net change in the number of any excited atoms is zero, being balanced by loss and gain due to all processes. With respect to bound-bound transitions, we will have detailed balancing as well, which states that the net exchange between any two levels will be balanced. This is because the probabilities of transition cannot be affected by the presence or absence of other excited atoms. Detailed balance (valid only at equilibrium) requires that the change in time of the number of atoms in level 1 due to the above three processes be zero:

${\displaystyle 0=A_{21}n_{2}+B_{21}n_{2}\rho (\nu )-B_{12}n_{1}\rho (\nu ).}$

Along with detailed balancing, at temperature T we may use our knowledge of the equilibrium energy distribution of the atoms, as stated in the Maxwell–Boltzmann distribution, and the equilibrium distribution of the photons, as stated in Planck's law of black body radiation to derive universal relationships between the Einstein coefficients.

From Boltzmann distribution we have for the number of excited atomic species i:

${\displaystyle {\frac {n_{i}}{n}}={\frac {g_{i}e^{-E_{i}/kT}}{Z}},}$

where n is the total number density of the atomic species, excited and unexcited, k is Boltzmann's constant, T is the temperature, ${\displaystyle g_{i}}$ is the degeneracy (also called the multiplicity) of state i, and Z is the partition function. From Planck's law of black-body radiation at temperature T we have for the spectral energy density at frequency ν

${\displaystyle \rho _{\nu }(\nu ,T)=F(\nu ){\frac {1}{e^{h\nu /kT}-1}},}$

where

${\displaystyle F(\nu )={\frac {8\pi h\nu ^{3}}{c^{3}}},}$

where ${\displaystyle c}$ is the speed of light and ${\displaystyle h}$ is Planck's constant. 

Substituting these expressions into the equation of detailed balancing and remembering that E₂ − E₁ = hν yields

${\displaystyle A_{21}g_{2}e^{-h\nu /kT}+B_{21}g_{2}e^{-h\nu /kT}{\frac {F(\nu )}{e^{h\nu /kT}-1}}=B_{12}g_{1}{\frac {F(\nu )}{e^{h\nu /kT}-1}},}$

separating to

${\displaystyle A_{21}g_{2}(e^{h\nu /kT}-1)+B_{21}g_{2}F(\nu )=B_{12}g_{1}e^{h\nu /kT}F(\nu ).}$

The above equation must hold at any temperature, so

${\displaystyle B_{21}g_{2}=B_{12}g_{1},}$

and

${\displaystyle -A_{21}g_{2}+B_{21}g_{2}F(\nu )=0.}$

Therefore, the three Einstein coefficients are interrelated by

${\displaystyle {\frac {A_{21}}{B_{21}}}=F(\nu )}$

and

${\displaystyle {\frac {B_{21}}{B_{12}}}={\frac {g_{1}}{g_{2}}}.}$

When this relation is inserted into the original equation, one can also find a relation between ${\displaystyle A_{21}}$ and ${\displaystyle B_{12}}$, involving Planck's law.

Oscillator strengths

The oscillator strength ${\displaystyle f_{12}}$ is defined by the following relation to the cross section ${\displaystyle \sigma }$ for absorption:

${\displaystyle \sigma ={\frac {e^{2}}{4\varepsilon _{0}m_{e}c}}\,f_{12}\,\phi _{\nu }={\frac {\pi e^{2}}{2\varepsilon _{0}m_{e}c}}\,f_{12}\,\phi _{\omega },}$

where ${\displaystyle e}$ is the electron charge, ${\displaystyle m_{e}}$ is the electron mass, and ${\displaystyle \phi _{\nu }}$ and ${\displaystyle \phi _{\omega }}$ are normalized distribution functions in frequency and angular frequency respectively. This allows all three Einstein coefficients to be expressed in terms of the single oscillator strength associated with the particular atomic spectral line:

${\displaystyle B_{12}={\frac {e^{2}}{4\varepsilon _{0}m_{e}h\nu }}f_{12},}$

${\displaystyle B_{21}={\frac {e^{2}}{4\varepsilon _{0}m_{e}h\nu }}{\frac {g_{1}}{g_{2}}}f_{12},}$

${\displaystyle A_{21}={\frac {2\pi \nu ^{2}e^{2}}{\varepsilon _{0}m_{e}c^{3}}}{\frac {g_{1}}{g_{2}}}f_{12}.}$

Neutron bomb

From Wikipedia, the free encyclopedia

A neutron bomb, officially defined as a type of enhanced radiation weapon (ERW), is a low yield thermonuclear weapon designed to maximize lethal neutron radiation in the immediate vicinity of the blast while minimizing the physical power of the blast itself. The neutron release generated by a nuclear fusion reaction is intentionally allowed to escape the weapon, rather than being absorbed by its other components. The neutron burst, which is used as the primary destructive action of the warhead, is able to penetrate enemy armor more effectively than a conventional warhead, thus making it more lethal as a tactical weapon.

The concept was originally developed by the US in the late 1950s and early 1960s. It was seen as a "cleaner" bomb for use against massed Soviet armored divisions. As these would be used over allied nations, notably West Germany, the reduced blast damage was seen as an important advantage.

ERWs were first operationally deployed for anti-ballistic missiles (ABM). In this role the burst of neutrons would cause nearby warheads to undergo partial fission, preventing them from exploding properly. For this to work, the ABM would have to explode within ca. 100 metres (300 ft) of its target. The first example of such a system was the W66, used on the Sprint missile used in the US's Nike-X system. It is believed the Soviet equivalent, the A-135's 53T6 missile, uses a similar design.

The weapon was once again proposed for tactical use by the US in the 1970s and 1980s, and production of the W70 began for the MGM-52 Lance in 1981. This time it experienced a firestorm of protest as the growing anti-nuclear movement gained strength through this period. Opposition was so intense that European leaders refused to accept it on their territory. President Ronald Reagan bowed to pressure and the built examples of the W70-3 remained stockpiled in the US until they were retired in 1992. The last W70 was dismantled in 2011.

Basic concept

In a standard thermonuclear design, a small fission bomb is placed close to a larger mass of thermonuclear fuel. The two components are then placed within a thick radiation case, usually made from uranium, lead or steel. The case traps the energy from the fission bomb for a brief period, allowing it to heat and compress the main thermonuclear fuel. The case is normally made of depleted uranium or natural uranium metal, because the thermonuclear reactions give off massive numbers of high-energy neutrons that can cause fission reactions in the casing material. These can add considerable energy to the reaction; in a typical design as much as 50% of the total energy comes from fission events in the casing. For this reason, these weapons are technically known as fission-fusion-fission designs. 

In a neutron bomb, the casing material is selected either to be transparent to neutrons or to actively enhance their production. The burst of neutrons created in the thermonuclear reaction is then free to escape the bomb, outpacing the physical explosion. By designing the thermonuclear stage of the weapon carefully, the neutron burst can be maximized while minimizing the blast itself. This makes the lethal radius of the neutron burst greater than that of the explosion itself. Since the neutrons disappear from the environment rapidly, such a burst over an enemy column would kill the crews and leave the area able to be quickly reoccupied. 

Compared to a pure fission bomb with an identical explosive yield, a neutron bomb would emit about ten times the amount of neutron radiation. In a fission bomb, at sea level, the total radiation pulse energy which is composed of both gamma rays and neutrons is approximately 5% of the entire energy released; in neutron bombs it would be closer to 40%, with the percentage increase coming from the higher production of neutrons. Furthermore, the neutrons emitted by a neutron bomb have a much higher average energy level (close to 14 MeV) than those released during a fission reaction (1–2 MeV).

Technically speaking, every low yield nuclear weapon is a radiation weapon, including non-enhanced variants. Up to about 10 kilotons in yield, all nuclear weapons have prompt neutron radiation as their furthest-reaching lethal component, after which yield in regular nuclear weapons, the lethal blast and thermal effects radius begins to out-range the lethal ionizing radiation radius. Enhanced radiation weapons also fall into this same yield range and simply enhance the intensity and range of the neutron dose for a given yield.

History and deployment to present

The conception of neutron bombs is generally credited to Samuel T. Cohen of the Lawrence Livermore National Laboratory, who developed the concept in 1958. Initial development was carried out as part of projects Dove and Starling, and an early device was tested underground in early 1962. Designs of a "weaponized" version were carried out in 1963.

Development of two production designs for the army's MGM-52 Lance short-range missile began in July 1964, the W63 at Livermore and the W64 at Los Alamos. Both entered phase three testing in July 1964, and the W64 was cancelled in favor of the W63 in September 1964. The W63 was in turn cancelled in November 1965 in favor of the W70 (Mod 0), a conventional design. By this time, the same concepts were being used to develop warheads for the Sprint missile, an anti-ballistic missile (ABM), with Livermore designing the W65 and Los Alamos the W66. Both entered phase three testing in October 1965, but the W65 was cancelled in favor of the W66 in November 1968. Testing of the W66 was carried out in the late 1960s, and entered production in June 1974, the first neutron bomb to do so. Approximately 120 were built, with about 70 of these being on active duty during 1975 and 1976 as part of the Safeguard Program. When that program was shut down they were placed in storage, and eventually decommissioned in the early 1980s.

Development of ER warheads for Lance continued, but in the early 1970s attention had turned to using modified versions of the W70, the W70 Mod 3. Development was subsequently postponed by President Jimmy Carter in 1978 following protests against his administration's plans to deploy neutron warheads to ground forces in Europe. On November 17, 1978, in a test the USSR detonated its first similar-type bomb. President Ronald Reagan restarted production in 1981. The Soviet Union renewed a propaganda campaign against the US's neutron bomb in 1981 following Reagan's announcement. In 1983 Reagan then announced the Strategic Defense Initiative, which surpassed neutron bomb production in ambition and vision and with that, neutron bombs quickly faded from the center of the public's attention.

Three types of enhanced radiation weapons (ERW) were deployed by the United States. The W66 warhead, for the anti-ICBM Sprint missile system, was deployed in 1975 and retired the next year, along with the missile system. The W70 Mod 3 warhead was developed for the short-range, tactical MGM-52 Lance missile, and the W79 Mod 0 was developed for nuclear artillery shells. The latter two types were retired by President George H. W. Bush in 1992, following the end of the Cold War. The last W70 Mod 3 warhead was dismantled in 1996, and the last W79 Mod 0 was dismantled by 2003, when the dismantling of all W79 variants was completed.

According to the Cox Report, as of 1999 the United States had never deployed a neutron weapon. The nature of this statement is not clear; it reads "The stolen information also includes classified design information for an enhanced radiation weapon (commonly known as the "neutron bomb"), which neither the United States, nor any other nation, has ever deployed." However, the fact that neutron bombs had been produced by the US was well known at this time and part of the public record. Cohen suggests the report is playing with the definitions; while the US bombs were never deployed to Europe, they remained stockpiled in the US.

In addition to the two superpowers, France and China are known to have tested neutron or enhanced radiation bombs. France conducted an early test of the technology in 1967 and tested an "actual" neutron bomb in 1980. China conducted a successful test of neutron bomb principles in 1984 and a successful test of a neutron bomb in 1988. However, neither of those countries chose to deploy neutron bombs. Chinese nuclear scientists stated before the 1988 test that China had no need for neutron bombs, but it was developed to serve as a "technology reserve", in case the need arose in the future.

In August, 1999, the Indian government disclosed that India was capable of producing a neutron bomb.

Although no country is currently known to deploy them in an offensive manner, all thermonuclear dial-a-yield warheads that have about 10 kiloton and lower as one dial option, with a considerable fraction of that yield derived from fusion reactions, can be considered able to be neutron bombs in use, if not in name. The only country definitely known to deploy dedicated (that is, not dial-a-yield) neutron warheads for any length of time is the Soviet Union/Russia, which inherited the USSR's neutron warhead equipped ABM-3 Gazelle missile program. This ABM system contains at least 68 neutron warheads with a 10 kiloton yield each and it has been in service since 1995, with inert missile testing approximately every other year since then (2014). The system is designed to destroy incoming endoatmospheric level nuclear warheads aimed at Moscow and other targets and is the lower-tier/last umbrella of the A-135 anti-ballistic missile system (NATO reporting name: ABM-3).

By 1984, according to Mordechai Vanunu, Israel was mass-producing neutron bombs.

Considerable controversy arose in the US and Western Europe following a June 1977 Washington Post exposé describing US government plans to purchase the bomb. The article focused on the fact that it was the first weapon specifically intended to kill humans with radiation. Lawrence Livermore National Laboratory director Harold Brown and Soviet General Secretary Leonid Brezhnev both described neutron bombs as a "capitalist bomb", because it was designed to destroy people while preserving property.

Use

The 1979 Soviet/Warsaw Pact invasion plan, "Seven Days to the River Rhine" to seize West Germany. Soviet analysts had correctly assumed that the NATO response would be to use regular tactical nuclear weapons to stop such a massive Warsaw Pact invasion. According to proponents, neutron bombs would blunt an invasion by Soviet tanks and armored vehicles without causing as much damage or civilian deaths as the older nuclear weapons would. Neutron bombs would have been used if the REFORGER conventional response of NATO to the invasion was too slow or ineffective.

 

Neutron bombs are purposely designed with explosive yields lower than other nuclear weapons. Since neutrons are scattered and absorbed by air, neutron radiation effects drop off rapidly with distance in air. As such, there is a sharper distinction, relative to thermal effects, between areas of high lethality and areas with minimal radiation doses. All high yield (more than c. 10 kiloton) nuclear bombs, such as the extreme example of a device that derived 97% of its energy from fusion, the 50 megaton Tsar Bomba, are not able to radiate sufficient neutrons beyond their lethal blast range when detonated as a surface burst or low altitude air burst and so are no longer classified as neutron bombs, thus limiting the yield of neutron bombs to a maximum of about 10 kilotons. The intense pulse of high-energy neutrons generated by a neutron bomb is the principal killing mechanism, not the fallout, heat or blast. 

The inventor of the neutron bomb, Sam Cohen, criticized the description of the W70 as a neutron bomb since it could be configured to yield 100 kilotons:

the W-70 ... is not even remotely a "neutron bomb." Instead of being the type of weapon that, in the popular mind, "kills people and spares buildings" it is one that both kills and physically destroys on a massive scale. The W-70 is not a discriminate weapon, like the neutron bomb—which, incidentally, should be considered a weapon that "kills enemy personnel while sparing the physical fabric of the attacked populace, and even the populace too."

Although neutron bombs are commonly believed to "leave the infrastructure intact", with current designs that have explosive yields in the low kiloton range, detonation in (or above) a built-up area would still cause a sizable degree of building destruction, through blast and heat effects out to a moderate radius, albeit considerably less destruction, than when compared to a standard nuclear bomb of the exact same total energy release or "yield".

U.S. Army M110 howitzers in a 1984 REFORGER staging area before transport. Variants of this "dual capable" nuclear artillery howitzer would launch the W79 neutron bomb.

 

The Warsaw Pact tank strength was over twice that of NATO, and Soviet deep battle doctrine was likely to be to use this numerical advantage to rapidly sweep across continental Europe if the Cold War ever turned hot. Any weapon that could break up their intended mass tank formation deployments and force them to deploy their tanks in a thinner, more easily dividable manner, would aid ground forces in the task of hunting down solitary tanks and using anti-tank missiles against them, such as the contemporary M47 Dragon and BGM-71 TOW missiles, of which NATO had hundreds of thousands.

Rather than making extensive preparations for battlefield nuclear combat in Central Europe, "The Soviet military leadership believed that conventional superiority provided the Warsaw Pact with the means to approximate the effects of nuclear weapons and achieve victory in Europe without resort to those weapons."

Neutron bombs, or more precisely, enhanced [neutron] radiation weapons were also to find use as strategic anti-ballistic missile weapons, and in this role they are believed to remain in active service within Russia's Gazelle missile.

Effects

Wood frame house in 1953 nuclear test, 5 pounds per square inch (psi) overpressure, full collapse.

 

Upon detonation, a near-ground airburst of a 1 kiloton neutron bomb would produce a large blast wave and a powerful pulse of both thermal radiation and ionizing radiation, and non-ionizing radiation in the form of fast (14.1 MeV) neutrons. The thermal pulse would cause third degree burns to unprotected skin out to approximately 500 meters. The blast would create pressures of at least 4.6 psi out to a radius of 600 meters, which would severely damage all non-reinforced concrete structures. At the conventional effective combat range against modern main battle tanks and armored personnel carriers (< 690–900 m), the blast from a 1 kt neutron bomb would destroy or damage to the point of nonusability almost all un-reinforced civilian buildings.

Using neutron bombs to stop an enemy armored attack by rapidly incapacitating crews with a dose of 8000+ rads of radiation would require exploding large numbers of them to blanket the enemy forces, destroying all normal civilian buildings within c. 600 meters of the immediate area. Neutron activation from the explosions could make many building materials in the city radioactive, such as zinc coated steel/galvanized steel (see area denial use below). 

Because liquid-filled objects like the human body are resistant to gross overpressure, the 4–5 psi blast overpressure would cause very few direct casualties at a range of c. 600 m. The powerful winds produced by this overpressure, however, could throw bodies into objects or throw debris at high velocity, including window glass, both with potentially lethal results. Casualties would be highly variable depending on surroundings, including potential building collapses.

The pulse of neutron radiation would cause immediate and permanent incapacitation to unprotected outdoor humans in the open out to 900 meters, with death occurring in one or two days. The median lethal dose (LD₅₀) of 600 rads would extend to between 1350 and 1400 meters for those unprotected and outdoors, where approximately half of those exposed would die of radiation sickness after several weeks. 

A human residing within, or simply shielded by, at least one concrete building with walls and ceilings 30 cm (12 in) thick, or alternatively of damp soil 24 inches thick, would receive a neutron radiation exposure reduced by a factor of 10. Even near ground zero, basement sheltering or buildings with similar radiation shielding characteristics would drastically reduce the radiation dose.

Furthermore, the neutron absorption spectrum of air is disputed by some authorities, and depends in part on absorption by hydrogen from water vapor. Thus, absorption might vary exponentially with humidity, making neutron bombs far more deadly in desert climates than in humid ones.

Effectiveness in modern anti-tank role

The neutron cross section and absorption probability in barns of the two natural boron isotopes found in nature (top curve is for 10 B and bottom curve for 11 B. As neutron energy increases to 14 MeV, the absorption effectiveness, in general, decreases. Thus, for boron-containing armor to be effective, fast neutrons must first be slowed by another element by neutron scattering.

 

The questionable effectiveness of ER weapons against modern tanks is cited as one of the main reasons that these weapons are no longer fielded or stockpiled. With the increase in average tank armor thickness since the first ER weapons were fielded, it was argued in the March 13, 1986 New Scientist magazine that tank armor protection was approaching the level where tank crews would be almost fully protected from radiation effects. Thus, for an ER weapon to incapacitate a modern tank crew through irradiation, the weapon must be detonated at such proximity to the tank that the nuclear explosion's blast would now be equally effective at incapacitating it and its crew. However this assertion was regarded as dubious in the 12 June, 1986 New Scientist reply by C.S. Grace, a member of the Royal Military College of Science, as neutron radiation from a 1 kiloton neutron bomb would incapacitate the crew of a tank with a protection factor of 35 out to a range of 280 meters, but the incapacitating blast range, depending on the exact weight of the tank, is much less, from 70 to 130 meters. However although the author did note that effective neutron absorbers and neutron poisons such as boron carbide can be incorporated into conventional armor and strap-on neutron moderating hydrogenous material (substances containing hydrogen atoms), such as explosive reactive armor, can both increase the protection factor, the author holds that in practice combined with neutron scattering, the actual average total tank area protection factor is rarely higher than 15.5 to 35. According to the Federation of American Scientists, the neutron protection factor of a "tank" can be as low as 2, without qualifying whether the statement implies a light tank, medium tank, or main battle tank. 

A composite high density concrete, or alternatively, a laminated graded-Z shield, 24 units thick of which 16 units are iron and 8 units are polyethylene containing boron (BPE), and additional mass behind it to attenuate neutron capture gamma rays, is more effective than just 24 units of pure iron or BPE alone, due to the advantages of both iron and BPE in combination. During Neutron transport Iron is effective in slowing down/scattering high-energy neutrons in the 14-MeV energy range and attenuating gamma rays, while the hydrogen in polyethylene is effective in slowing down these now slower fast neutrons in the few MeV range, and boron 10 has a high absorption cross section for thermal neutrons and a low production yield of gamma rays when it absorbs a neutron. The Soviet T72 tank, in response to the neutron bomb threat, is cited as having fitted a boronated polyethylene liner, which has had its neutron shielding properties simulated.

The radiation weighting factor for neutrons of various energy has been revised over time and certain agencies have different weighting factors, however despite the variation amongst the agencies, from the graph, for a given energy, A fusion neutron (14.1 MeV) although more energetic, is less biologically harmful as rated in Sieverts, than a fission generated thermal neutron or a fusion neutron slowed to that energy, c. 0.8 MeV.

 

However, some tank armor material contains depleted uranium (DU), common in the US's M1A1 Abrams tank, which incorporates steel-encased depleted uranium armor, a substance that will fast fission when it captures a fast, fusion-generated neutron, and thus on fissioning will produce fission neutrons and fission products embedded within the armor, products which emit among other things, penetrating gamma rays. Although the neutrons emitted by the neutron bomb may not penetrate to the tank crew in lethal quantities, the fast fission of DU within the armor could still ensure a lethal environment for the crew and maintenance personnel by fission neutron and gamma ray exposure, largely depending on the exact thickness and elemental composition of the armor—information usually hard to attain. Despite this, Ducrete—which has an elemental composition similar (but not identical) to the ceramic second generation heavy metal Chobham armor of the Abrams tank—is an effective radiation shield, to both fission neutrons and gamma rays due to it being a graded Z material. Uranium, being about twice as dense as lead, is thus nearly twice as effective at shielding gamma ray radiation per unit thickness.

Use against ballistic missiles

As an anti-ballistic missile weapon, the first fielded ER warhead, the W66, was developed for the Sprint missile system as part of the Safeguard Program to protect United States cities and missile silos from incoming Soviet warheads. 

A problem faced by Sprint and similar ABMs was that the blast effects of their warheads change greatly as they climb and the atmosphere thins out. At higher altitudes, starting around 60,000 feet (18,000 m) and above, the blast effects begin to drop off rapidly as the air density becomes very low. This can be countered by using a larger warhead, but then it becomes too powerful when used at lower altitudes. An ideal system would use a mechanism that was less sensitive to changes in air density. 

Neutron-based attacks offer one solution to this problem. The burst of neutrons released by an ER weapon can induce fission in the fissile materials of primary in the target warhead. The energy released by these reactions may be enough to melt the warhead, but even at lower fission rates the "burning up" of some of the fuel in the primary can cause it to fail to explode properly, or "fizzle". Thus a small ER warhead can be effective across a wide altitude band, using blast effects at lower altitudes and the increasingly long-ranged neutrons as the engagement rises.

The use of neutron-based attacks was discussed as early as the 1950s, with the US Atomic Energy Commission mentioning weapons with a "clean, enhanced neutron output" for use as "antimissile defensive warheads." Studying, improving and defending against such attacks was a major area of research during the 1950s and 60s. A particular example of this is the US Polaris A-3 missile, which delivered three warheads travelling on roughly the same trajectory, and thus with a short distance between them. A single ABM could conceivably destroy all three through neutron flux. Developing warheads that were less sensitive to these attacks was a major area of research in the US and UK during the 1960s.

Some sources claim that the neutron flux attack was also the main design goal of the various nuclear-tipped anti-aircraft weapons like the AIM-26 Falcon and CIM-10 Bomarc. One F-102 pilot noted:

GAR-11/AIM-26 was primarily a weapon-killer. The bomber(s, if any) was collateral damage. The weapon was proximity-fused to ensure detonation close enough so an intense flood of neutrons would result in an instantaneous nuclear reaction (NOT full-scale) in the enemy weapon’s pit; rendering it incapable of functioning as designed...[O]ur first “neutron bombs” were the GAR-11 and MB-1 Genie.

It has also been suggested that neutron flux's effects on the warhead electronics are another attack vector for ER warheads in the ABM role. Ionization greater than 5,000 rads in silicon chips delivered over seconds to minutes will degrade the function of semiconductors for long periods. However, while such attacks might be useful against guidance systems which used relatively advanced electronics, in the ABM role these components have long ago separated from the warheads by the time they come within range of the interceptors. The electronics in the warheads themselves tend to be very simple, and hardening them was one of the many issues studied in the 1960s.

Lithium-6 hydride (Li6H) is cited as being used as a countermeasure to reduce the vulnerability and "harden" nuclear warheads from the effects of externally generated neutrons. Radiation hardening of the warhead's electronic components as a countermeasure to high altitude neutron warheads somewhat reduces the range that a neutron warhead could successfully cause an unrecoverable glitch by the transient radiation effects on electronics (TREE) effects.

At very high altitudes, at the edge of the atmosphere and above it, another effect comes into play. At lower altitudes, the x-rays generated by the bomb are absorbed by the air and have mean free paths on the order of meters. But as the air thins out, the x-rays can travel further, eventually outpacing the area of effect of the neutrons. In exoatmospheric explosions, this can be on the order of 10 kilometres (6.2 mi) in radius. In this sort of attack, it is the x-rays promptly delivering energy on the warhead surface that is the active mechanism; the rapid ablation (or "blow off") of the surface creates shock waves that can break up the warhead.

Use as an area denial weapon

In November 2012, during the planning stages of Operation Hammer of God, British Labour peer Lord Gilbert suggested that multiple enhanced radiation reduced blast (ERRB) warheads could be detonated in the mountain region of the Afghanistan-Pakistan border to prevent infiltration. He proposed to warn the inhabitants to evacuate, then irradiate the area, making it unusable and impassable. Used in this manner, the neutron bomb(s), regardless of burst height, would release neutron activated casing materials used in the bomb, and depending on burst height, create radioactive soil activation products. 

In much the same fashion as the area denial effect resulting from fission product (the substances that make up most fallout) contamination in an area following a conventional surface burst nuclear explosion, as considered in the Korean War by Douglas MacArthur, it would thus be a form of radiological warfare—with the difference that neutron bombs produce half, or less, of the quantity of fission products relative to the same-yield pure fission bomb. Radiological warfare with neutron bombs that rely on fission primaries would thus still produce fission fallout, albeit a comparatively cleaner and shorter lasting version of it in the area than if air bursts were used, as little to no fission products would be deposited on the direct immediate area, instead becoming diluted global fallout.

The easiest to achieve fusion reaction, of deuterium ("D) with tritium (T") creating helium-4, freeing a neutron, and releasing only 3.5 MeV in the form of kinetic energy as the charged alpha particle that will inherently generate heat(which manifests as blast and thermal effects), while the majority of the energy of the reaction(14.1 MeV) is carried away by the uncharged fast neutron. Devices with a higher proportion of yield derived from this reaction would be more efficient in the stand-off asteroid impact avoidance role, due to the penetrative depth of fast-neutrons and the resulting higher momentum transfer that is produced in this "scabbing" of a much larger mass of material free from the main body, as opposed to the shallower surface penetration and ablation of regolith, that is produced by thermal/soft X-rays.

 

However the most effective use of a neutron bomb with respect to area denial would be to encase it in a thick shell of material that could be neutron activated, and use a surface burst. In this manner the neutron bomb would be turned into a salted bomb; a case of zinc-64, produced as a byproduct of depleted zinc oxide enrichment, would for example probably be the most attractive for military use, as when activated, the zinc-65 so formed is a gamma emitter, with a half life of 244 days.

Hypothetical effects of a pure fusion bomb

With considerable overlap between the two devices, the prompt radiation effects of a pure fusion weapon would similarly be much higher than that of a pure-fission device: approximately twice the initial radiation output of current standard fission-fusion-based weapons. In common with all neutron bombs that must presently derive a small percentage of trigger energy from fission, in any given yield a 100% pure fusion bomb would likewise generate a more diminutive atmospheric blast wave than a pure-fission bomb. The latter fission device has a higher kinetic energy-ratio per unit of reaction energy released, which is most notable in the comparison with the D-T fusion reaction. A larger percentage of the energy from a D-T fusion reaction, is inherently put into uncharged neutron generation as opposed to charged particles, such as the alpha particle of the D-T reaction, the primary species, that is most responsible for the coulomb explosion/fireball.

Cobalt bomb

From Wikipedia, the free encyclopedia

A cobalt bomb is a type of "salted bomb": a nuclear weapon designed to produce enhanced amounts of radioactive fallout, intended to contaminate a large area with radioactive material. The concept of a cobalt bomb was originally described in a radio program by physicist Leó Szilárd on February 26, 1950. His intent was not to propose that such a weapon be built, but to show that nuclear weapon technology would soon reach the point where it could end human life on Earth, a doomsday device. Such "salted" weapons were requested by the U.S. Air Force and seriously investigated, but not deployed. In the 1964 edition of the U.S. Department of Defense book The Effects of Nuclear Weapons, a new section titled radiological warfare clarified the "Doomsday device" issue.

The Russian Federation has allegedly developed cobalt warheads for use with their Status-6 Oceanic Multipurpose System nuclear torpedoes. However many commentators doubt that this is a real project, and see it as more likely to be a staged leak to intimidate the United States. Amongst other comments on it, Edward Moore Geist wrote a paper in which he says that "Russian decision makers would have little confidence that these areas would be in the intended locations" and Russian military experts are cited as saying that "robotic torpedoes could have other purposes, such as delivering deep-sea equipment or installing surveillance devices."

The Operation Antler/Round 1 test by the British at the Tadje site in the Maralinga range in Australia on September 14, 1957, tested a bomb using cobalt pellets as a radiochemical tracer for estimating yield. This was considered a failure and the experiment was not repeated. In Russia, the triple "taiga" nuclear salvo test, as part of the preliminary March 1971 Pechora–Kama Canal project, produced relatively high amounts of Co-60 from the steel that surrounded the Taiga devices, with this fusion generated neutron activation product being responsible for about half of the gamma dose now (2011) at the test site. This high percentage contribution is largely because the devices did not rely much at all on fission reactions and thus the quantity of gamma emitting caesium-137 fallout, is therefore comparatively low. Photosynthesizing vegetation exists all around the lake that was formed.

Mechanism

A cobalt bomb could be made by placing a quantity of ordinary cobalt metal (⁵⁹Co) around a thermonuclear bomb. When the bomb explodes, the neutrons produced by the fusion reaction in the secondary stage of the thermonuclear bomb's explosion would transmute the cobalt to the radioactive cobalt-60 (⁶⁰Co), which would be vaporized by the explosion. The cobalt would then condense and fall back to Earth with the dust and debris from the explosion, contaminating the ground. 

The deposited cobalt-60 would have a half-life of 5.27 years, decaying into ⁶⁰Ni and emitting two gamma rays with energies of 1.17 and 1.33 MeV, hence the overall nuclear equation of the reaction is: 

⁵⁹
₂₇Co
+ n → ⁶⁰
₂₇Co
→ ⁶⁰
₂₈Ni
+ e⁻ + gamma rays.

Nickel-60 is a stable isotope and undergoes no further decays after emitting the gamma rays. 

The 5.27 year half life of the ⁶⁰Co is long enough to allow it to settle out before significant decay has occurred, and to render it impractical to wait in shelters for it to decay, yet short enough that intense radiation is produced. Many isotopes are more radioactive (gold-198, tantalum-182, zinc-65, sodium-24, and many more), but they would decay faster, possibly allowing some population to survive in shelters.

Fallout from cobalt bombs vs. other nuclear weapons

Fission products are more deadly than neutron-activated cobalt in the first few weeks following detonation. After one to six months, the fission products from even a large-yield thermonuclear weapon decay to levels tolerable by humans. The large-yield three-stage (fission–fusion–fission) thermonuclear weapon is thus automatically a weapon of radiological warfare, but its fallout decays much more rapidly than that of a cobalt bomb. A cobalt bomb's fallout on the other hand would render affected areas effectively stuck in this interim state for decades: habitable, but not safe for constant habitation.

Initially, gamma radiation from the fission products of an equivalent size fission-fusion-fission bomb are much more intense than Co-60: 15,000 times more intense at 1 hour; 35 times more intense at 1 week; 5 times more intense at 1 month; and about equal at 6 months. Thereafter fission product fallout radiation levels drop off rapidly, so that Co-60 fallout is 8 times more intense than fission at 1 year and 150 times more intense at 5 years. The very long-lived isotopes produced by fission would overtake the ⁶⁰Co again after about 75 years.

Theoretically, a device containing 510 metric tons of Co-59 can spread 1 g of the material to each square km of the Earth's surface (510,000,000 km²). If one assumes that all of the material is converted to Co-60 at 100 percent efficiency and if it is spread evenly across the Earth's surface, it is possible for a single bomb to kill every person on Earth. However, in fact, complete 100% conversion into Co-60 is unlikely; a 1957 British experiment at Maralinga showed that Co-59's neutron absorption ability was much lower than predicted, resulting in a very limited formation of Co-60 isotope in practice. 

In addition, another important point in considering the effects of cobalt bombs is that deposition of fallout is not even throughout the path downwind from a detonation, so that there are going to be areas relatively unaffected by fallout and places where there is unusually intense fallout, so that the Earth would not be universally rendered lifeless by a cobalt bomb. The fallout and devastation following a nuclear detonation does not scale upwards linearly with the explosive yield (equivalent to tons of TNT). As a result, the concept of "overkill"—the idea that one can simply estimate the destruction and fallout created by a thermonuclear weapon of the size postulated by Leo Szilard's "cobalt bomb" thought experiment by extrapolating from the effects of thermonuclear weapons of smaller yields—is fallacious.

Example of radiation levels vs. time

Assume a cobalt bomb deposits intense fallout causing a dose rate of 10 sieverts (Sv) per hour. At this dose rate, any unsheltered person exposed to the fallout would receive a lethal dose in about 30 minutes (assuming a median lethal dose of 5 Sv). People in well-built shelters would be safe due to radiation shielding. 

After one half-life of 5.27 years, only half of the cobalt-60 will have decayed, and the dose rate in the affected area would be 5 Sv/hour. At this dose rate, a person exposed to the radiation would receive a lethal dose in 1 hour. 

After 10 half-lives (about 53 years), the dose rate would have decayed to around 10 mSv/hour. At this point, a healthy person could spend 1 to 4 days exposed to the fallout with no immediate effects. 

After 20 half-lives (about 105 years), the dose rate would have decayed to around 10 μSv/hour. At this stage, humans could remain unsheltered full-time since their yearly radiation dose would be about 80 mSv. However, this yearly dose rate is on the order of 30 times greater than the peacetime exposure rate of 2.5 mSv/year. As a result, the rate of cancer incidence in the survivor population would likely increase. 

After 25 half-lives (about 130 years), the dose rate from cobalt-60 would have decayed to less than 0.4 μSv/hour (natural background radiation) and could be considered negligible.

Decontamination

In practice it is unlikely that people would simply sit and wait for nuclear decay to go to completion, as in all historical fallout cases, decontamination of valuable land has occurred. This is most commonly done with the use of simple equipment such as lead glass covered excavators and bulldozers, similar to those employed in the Lake Chagan project. By skimming off the thin layer of fallout on the topsoil surface and burying it in the likes of a deep trench along with isolating it from ground water sources, the gamma air dose is cut by orders of magnitude. The decontamination after the Goiânia accident in Brazil 1987 and the possibility of a "dirty bomb" with Co-60, which has similarities with the environment that one would be faced with after a nuclear yielding cobalt bomb's fallout had settled, has prompted the invention of "Sequestration Coatings" and cheap liquid phase sorbents for Co-60 that would further aid in decontamination, including that of water.

Russian "Status-6"

In 2015, a page from an apparent Russian nuclear-armed torpedo design was accidentally or deliberately leaked. The design was titled "Oceanic Multipurpose System Status-6". The document stated the torpedo would create "wide areas of radioactive contamination, rendering them unusable for military, economic or other activity for a long time". Its payload would be "many tens of megatons in yield". Russian government newspaper Rossiiskaya Gazeta speculated that the warhead would be a cobalt bomb. It is not known whether the Status-6 is a real project, or whether it is Russian disinformation. In 2018 the Pentagon's annual Nuclear Posture Review stated Russia is developing a system called the "Status-6 Oceanic Multipurpose System". If Status-6 does exist, it is not publicly known whether the leaked 2015 design is accurate, nor whether the 2015 claim that the torpedo might be a cobalt bomb is genuine. Status-6 was officially disclosed and confirmed by Vladimir Putin in 2018 during his display of new Russian offensive weapons, including the Satan-2, Air Launched Iskander, Nuclear cruise-missile, and hypersonic glider.

In popular culture

In the 4th act of the classic Star Trek episode "Obsession", Ensign Garrovick refers to 10,000 cobalt bombs not equaling the power of less than one ounce of antimatter. 

In Beneath the Planet of the Apes (1970) the main character, upon seeing that the underground people worship a giant bomb that can wipe out the world, comments "They finally built one with a cobalt casing" in reference to a cobalt bomb that could wipe out the world. Similarly, in the bestselling On the Beach (1957) the cobalt bomb was a symbol of man's hubris.

In the black comedy Dr. Strangelove, or: How I Learned to Stop Worrying and Love the Bomb (1964), a type of cobalt-salted bomb is employed, with a Dead Hand mechanism, by the Soviet Union as a nuclear deterrent: if the system detects any nuclear attack, the doomsday device will be automatically unleashed. With unfortunate timing, a mentally ill American officer orders an attack on the USSR. One American bomber piloted by a hapless and unknowing crew gets through to their target; the Dead Hand mechanism works as designed and initiates a worldwide nuclear holocaust. The Russian Ambassador says "If you take, say, fifty H-bombs in the hundred megaton range and jacket them with cobalt thorium G, when they are exploded they will produce a doomsday shroud. A lethal cloud of radioactivity which will encircle the earth for ninety-three years!"

In the Spectreman episodes "Smash Alien Igorl!!" and "Enigma of the Cobalt Monster", the villainous Dr. Gori and race of Igorl aliens create a cobalt bomb from a heavy amount of cobalt found beneath a small village and place it within a monster, planning for it to destroy the world due to it reacting strongly to Earth's polluted atmosphere.

In the 2019 video game Metro Exodus the player visits the Russian city of Novosibirsk which was hit with at least one cobalt warhead during a worldwide nuclear war in the year 2014, resulting in catastrophic levels of radiation, and easily the most irradiated area visited in the three Metro games. While the city is left largely standing even twenty years after the cobalt warhead's detonation, the radiation in the city is so lethal that even with lead-lined full enclosure suits, the player can only spend a few minutes on the surface before receiving lethal amounts of radiation poisoning. During their visit, the player discovers that the survivors of the attack survived underground for nineteen years, but only due to constant injections of anti-radiation medicine.