Mobile phone radiation and health

From Wikipedia, the free encyclopedia

The effect of mobile phone radiation on human health is a subject of interest and study worldwide, as a result of the enormous increase in mobile phone usage throughout the world. As of 2015, there were 7.4 billion subscriptions worldwide, though the actual number of users is lower as many users own more than one mobile phone. Mobile phones use electromagnetic radiation in the microwave range (450–3800 MHz and 24–80 GHz in 5G mobile). Other digital wireless systems, such as data communication networks, produce similar radiation.

The World Health Organization states that "A large number of studies have been performed over the last two decades to assess whether mobile phones pose a potential health risk. To date, no adverse health effects have been established as being caused by mobile phone use." In a 2018 statement, the FDA said that "the current safety limits are set to include a 50-fold safety margin from observed effects of Radio-frequency energy exposure".

Exposure

A cell phone is a wireless portable telephone that connects to the telephone network by radio waves exchanged with a local antenna and automated transceiver called a cellular base station (cell site or cell tower). The service area served by each provider is divided into small geographical areas called cells, and all the cell phones in a cell communicate with that cell's antenna. Both the cell phone and the cell tower have radio transmitters which communicate with each other. Since in a cellular network the same radio channels are reused every few cells, cellular networks use low power transmitters to avoid radio waves from one cell spilling over and interfering with a nearby cell using the same frequencies. 

Cell phones are limited to a equivalent isotropic radiated power (EIRP) radiated power output of 3 watts, and the network continuously adjusts the phone transmitter to the lowest power consistent with good signal quality, reducing it to as low as one milliwatt when near the cell tower. Cell phone tower channel transmitters usually have an EIRP power output of around 50 watts. Even when it is not being used, unless it is turned off, a cell phone periodically emits radio signals on its control channel, to keep contact with its cell tower and for functions like handing off the phone to another tower if the user crosses into another cell. When the user is making a call, the cell phone transmits a signal on a second channel which carries the user's voice. Existing 2G, 3G, and 4G networks use frequencies in the UHF or low microwave bands, 600 MHz to 3.5 GHz. Many household wireless devices such as Wifi networks, garage door openers, and baby monitors use other frequencies in this same frequency range. 

Radio waves decrease rapidly in intensity by the inverse square of distance as they spread out from a transmitting antenna. So the cell phone transmitter, which is held close to the user's face when talking, is a much greater source of human exposure than the cell tower transmitter, which is typically at least hundreds of meters away from the public on a cell tower. A user can reduce their exposure by using a headset and keeping the cell phone itself further away from their body. 

Next generation 5G cellular networks, which began deploying in 2019, use higher frequencies in or near the millimeter wave band, 24 to 52 GHz. Millimeter waves are absorbed by atmospheric gases so 5G networks will use smaller cells than previous cellular networks, about the size of a city block. Instead of a cell tower, each cell will use an array of multiple small antennas mounted on existing buildings and utility poles. In general, millimeter waves penetrate less deeply into biological tissue than microwaves, and are mainly absorbed within the first centimeter of the body surface.

Effects studied

Blood–brain barrier

A 2010 review stated that "The balance of experimental evidence does not support an effect of 'non-thermal' radiofrequency fields" on the permeability of the blood-brain barrier, but noted that research on low frequency effects and effects in humans was sparse. A 2012 study of low-frequency radiation on humans found "no evidence for acute effects of short-term mobile phone radiation on cerebral blood flow".

Cancer

There is no strong or consistent evidence that mobile phone use increases the risk of getting brain cancer or other head tumors. The United States National Cancer Institute points out that "Radiofrequency energy, unlike ionizing radiation, does not cause DNA damage that can lead to cancer. Its only consistently observed biological effect in humans is tissue heating. In animal studies, it has not been found to cause cancer or to enhance the cancer-causing effects of known chemical carcinogens." The majority of human studies have failed to find a link between cell phone use and cancer. In 2011 a World Health Organization working group classified cell phone use as "possibly carcinogenic to humans". The CDC states that no scientific evidence definitively answers whether cell phone use causes cancer.

In a 2018 statement, the FDA said that "the current safety limits are set to include a 50-fold safety margin from observed effects of radiofrequency energy exposure".

An analysis of an "eagerly anticipated" study using rats and mice by the National Toxicology Program indicates that due to such issues as the inconsistent appearances of "signals for harm" within and across species and the increased chances of false positives due to the multiplicity of tests, the positive results seen are more likely due to random chance. The full results of the study were released in February 2018.

Male fertility

A decline in male sperm quality has been observed over several decades. Studies on the impact of mobile radiation on male fertility are conflicting, and the effects of the radiofrequency electromagnetic radiation (RF-EMR) emitted by these devices on the reproductive systems are currently under active debate. A 2012 review concluded that "together, the results of these studies have shown that RF-EMR decreases sperm count and motility and increases oxidative stress". A 2017 study of 153 men that attended an academic fertility clinic in Boston, Massachusetts found that self-reported mobile phone use was not related to semen quality, and that carrying a mobile phone in the pants pocket was not related to semen quality.

Electromagnetic hypersensitivity

Some users of mobile phones and similar devices have reported feeling various non-specific symptoms during and after use. Studies have failed to link any of these symptoms to electromagnetic exposure. In addition, EHS is not a recognised medical diagnosis.

Glucose metabolism

According to the National Cancer Institute, two small studies exploring whether and how cell phone radiation affects brain glucose metabolism showed inconsistent results.

Base stations

Cellular Mobile and UHF Antenna Tower with multiple Antennas

 

Experts consulted by France considered it was mandatory that the main antenna axis should not to be directly in front of a living place at a distance shorter than 100 metres. This recommendation was modified in 2003 to say that antennas located within a 100-metre radius of primary schools or childcare facilities should be better integrated into the cityscape and was not included in a 2005 expert report. The Agence française de sécurité sanitaire environnementale (fr) as of 2009, says that there is no demonstrated short-term effect of electromagnetic fields on health, but that there are open questions for long-term effects, and that it is easy to reduce exposure via technological improvements.

Safety standards and licensing

In order to protect the population living around base stations and users of mobile handsets, governments and regulatory bodies adopt safety standards, which translate to limits on exposure levels below a certain value. There are many proposed national and international standards, but that of the International Commission on Non-Ionizing Radiation Protection (ICNIRP) is the most respected one, and has been adopted so far by more than 80 countries. For radio stations, ICNIRP proposes two safety levels: one for occupational exposure, another one for the general population. Currently there are efforts underway to harmonise the different standards in existence.

Radio base licensing procedures have been established in the majority of urban spaces regulated either at municipal/county, provincial/state or national level. Mobile telephone service providers are, in many regions, required to obtain construction licenses, provide certification of antenna emission levels and assure compliance to ICNIRP standards and/or to other environmental legislation. 

Many governmental bodies also require that competing telecommunication companies try to achieve sharing of towers so as to decrease environmental and cosmetic impact. This issue is an influential factor of rejection of installation of new antennas and towers in communities. 

The safety standards in the US are set by the Federal Communications Commission (FCC). The FCC has based its standards primarily on those standards established by the National Council on Radiation Protection and Measurements (NCRP) a Congressionally chartered scientific organization located in the WDC area and the Institute of Electrical and Electronics Engineers (IEEE), specifically Subcommittee 4 of the "International Committee on Electromagnetic Safety". 

Switzerland has set safety limits lower than the ICNIRP limits for certain "sensitive areas" (classrooms, for example).

Lawsuits

In the US, personal injury lawsuits have been filed by individuals against cellphone manufacturers (including Motorola, NEC, Siemens, and Nokia) on the basis of allegations of causation of brain cancer and death. In US federal courts, expert testimony relating to science must be first evaluated by a judge, in a Daubert hearing, to be relevant and valid before it is admissible as evidence. In a 2002 case against Motorola, the plaintiffs alleged that the use of wireless handheld telephones could cause brain cancer and that the use of Motorola phones caused one plaintiff's cancer. The judge ruled that no sufficiently reliable and relevant scientific evidence in support of either general or specific causation was proffered by the plaintiffs, accepted a motion to exclude the testimony of the plaintiffs' experts, and denied a motion to exclude the testimony of the defendants' experts.

Two separate cases in Italy, in 2009 and 2017, resulted in pensions being awarded to plaintiffs who had claimed their benign brain tumors were the result of prolonged mobile phone use in professional tasks, for 5–6 hours a day, which they ruled different from non-professional use.

Precautions

Precautionary principle

In 2000, the World Health Organization (WHO) recommended that the precautionary principle could be voluntarily adopted in this case. It follows the recommendations of the European Community for environmental risks. 

According to the WHO, the "precautionary principle" is "a risk management policy applied in circumstances with a high degree of scientific uncertainty, reflecting the need to take action for a potentially serious risk without awaiting the results of scientific research." Other less stringent recommended approaches are prudent avoidance principle and as low as reasonably practicable. Although all of these are problematic in application, due to the widespread use and economic importance of wireless telecommunication systems in modern civilization, there is an increased popularity of such measures in the general public, though also evidence that such approaches may increase concern. They involve recommendations such as the minimization of cellphone usage, the limitation of use by at-risk population (e.g., children), the adoption of cellphones and microcells with as low as reasonably practicable levels of radiation, the wider use of hands-free and earphone technologies such as Bluetooth headsets, the adoption of maximal standards of exposure, RF field intensity and distance of base stations antennas from human habitations, and so forth. Overall, public information remains a challenge as various health consequences are evoked in the literature and by the media, putting populations under chronic exposure to potentially worrying information.

Precautionary measures and health advisories

In May 2011, the World Health Organization's International Agency for Research on Cancer announced it was classifying electromagnetic fields from mobile phones and other sources as "possibly carcinogenic to humans" and advised the public to adopt safety measures to reduce exposure, like use of hands-free devices or texting.

Some national radiation advisory authorities, including those of Austria, France, Germany, and Sweden, have recommended measures to minimize exposure to their citizens. Examples of the recommendations are:

• Use hands-free to decrease the radiation to the head.
• Keep the mobile phone away from the body.
• Do not use telephone in a car without an external antenna.

The use of "hands-free" was not recommended by the British Consumers' Association in a statement in November 2000, as they believed that exposure was increased. However, measurements for the (then) UK Department of Trade and Industry and others for the French Agence française de sécurité sanitaire environnementale [fr] showed substantial reductions. In 2005, Professor Lawrie Challis and others said clipping a ferrite bead onto hands-free kits stops the radio waves travelling up the wire and into the head.

Several nations have advised moderate use of mobile phones for children. A journal by Gandhi et al. in 2006 states that children receive higher levels of Specific Absorption Rate (SAR). When 5- and 10-year olds are compared to adults, they receive about 153% higher SAR levels. Also, with the permittivity of the brain decreasing as one gets older and the higher relative volume of the exposed growing brain in children, radiation penetrates far beyond the mid-brain.

Bogus products

Products have been advertised that claim to shield people from EM radiation from cell phones; in the US the Federal Trade Commission published a warning that "Scam artists follow the headlines to promote products that play off the news – and prey on concerned people."

According to the FTC, "there is no scientific proof that so-called shields significantly reduce exposure from electromagnetic emissions. Products that block only the earpiece – or another small portion of the phone – are totally ineffective because the entire phone emits electromagnetic waves." Such shields "may interfere with the phone's signal, cause it to draw even more power to communicate with the base station, and possibly emit more radiation." The FTC has enforced false advertising claims against companies that sell such products.

Non-ionizing radiation

From Wikipedia, the free encyclopedia

Different types of electromagnetic radiation

 

Non-ionizing (or non-ionising) radiation refers to any type of electromagnetic radiation that does not carry enough energy per quantum (photon energy) to ionize atoms or molecules—that is, to completely remove an electron from an atom or molecule. Instead of producing charged ions when passing through matter, non-ionizing electromagnetic radiation has sufficient energy only for excitation, the movement of an electron to a higher energy state. Ionizing radiation which has a higher frequency and shorter wavelength than nonionizing radiation, has many uses but can be a health hazard; exposure to it can cause burns, radiation sickness, cancer, and genetic damage. Using ionizing radiation requires elaborate radiological protection measures which in general are not required with nonionizing radiation.

The region at which radiation becomes considered as "ionizing" is not well defined, since different molecules and atoms ionize at different energies. The usual definitions have suggested that radiation with particle or photon energies less than 10 electronvolts (eV) be considered non-ionizing. Another suggested threshold is 33 electronvolts, which is the energy needed to ionize water molecules. The light from the Sun that reaches the earth is largely composed of non-ionizing radiation, since the ionizing far-ultraviolet rays have been filtered out by the gases in the atmosphere, particularly oxygen. The remaining ultraviolet radiation from the Sun causes molecular damage (for example, sunburn) by photochemical and free-radical-producing means.

Different biological effects are observed for different types of non-ionizing radiation. The upper frequencies of non-ionizing radiation near these energies (much of the spectrum of UV light and some visible light) are capable of non-thermal biological damage, similar to ionizing radiation. Health debate therefore centers on the non-thermal effects of radiation of much lower frequencies (microwave, millimeter and radiowave radiation). The International Agency for Research on Cancer recently stated that there could be some risk from non-ionizing radiation to humans. But a subsequent study reported that the basis of the IARC evaluation was not consistent with observed incidence trends. This and other reports suggest that there is virtually no way that results on which the IARC based its conclusions are correct. The Bioinitiative Report 2012 makes the claim that there are significant health risk associated with low frequency non-ionizing electromagnetic radiation. This report claims that statistically significant increases in cancer among those exposed to even low power levels, low frequency, non-ionizing radiation. There is considerable debate on this matter. Currently regulatory bodies around the world have not seen the need to change current safety standards.

Mechanisms of interaction with matter, including living tissue

Near ultraviolet, visible light, infrared, microwave, radio waves, and low-frequency radio frequency (longwave) are all examples of non-ionizing radiation. By contrast, far ultraviolet light, X-rays, gamma-rays, and all particle radiation from radioactive decay are ionizing. Visible and near ultraviolet electromagnetic radiation may induce photochemical reactions, or accelerate radical reactions, such as photochemical aging of varnishes or the breakdown of flavoring compounds in beer to produce the "lightstruck flavor". Near ultraviolet radiation, although technically non-ionizing, may still excite and cause photochemical reactions in some molecules. This happens because at ultraviolet photon energies, molecules may become electronically excited or promoted to free-radical form, even without ionization taking place. 

The occurrence of ionization depends on the energy of the individual particles or waves, and not on their number. An intense flood of particles or waves will not cause ionization if these particles or waves do not carry enough energy to be ionizing, unless they raise the temperature of a body to a point high enough to ionize small fractions of atoms or molecules by the process of thermal-ionization. In such cases, even "non-ionizing radiation" is capable of causing thermal-ionization if it deposits enough heat to raise temperatures to ionization energies. These reactions occur at far higher energies than with ionizing radiation, which requires only a single particle to ionize. A familiar example of thermal ionization is the flame-ionization of a common fire, and the browning reactions in common food items induced by infrared radiation, during broiling-type cooking. 

The energy of particles of non-ionizing radiation is low, and instead of producing charged ions when passing through matter, non-ionizing electromagnetic radiation has only sufficient energy to change the rotational, vibrational or electronic valence configurations of molecules and atoms. This produces thermal effects. The possible non-thermal effects of non-ionizing forms of radiation on living tissue have only recently been studied. Much of the current debate is about relatively low levels of exposure to radio frequency (RF) radiation from mobile phones and base stations producing "non-thermal" effects. Some experiments have suggested that there may be biological effects at non-thermal exposure levels, but the evidence for production of health hazard is contradictory and unproven. The scientific community and international bodies acknowledge that further research is needed to improve our understanding in some areas. Meanwhile the consensus is that there is no consistent and convincing scientific evidence of adverse health effects caused by RF radiation at powers sufficiently low that no thermal health effects are produced.

Health risks

Non-ionizing radiation hazard sign

 

Non-ionizing radiation can produce non-mutagenic effects such as inciting thermal energy in biological tissue that can lead to burns. In 2011, the International Agency for Research on Cancer (IARC) from the World Health Organization (WHO) released a statement adding radiofrequency electromagnetic fields (including microwave and millimeter waves) to their list of things which are possibly carcinogenic to humans.

In terms of potential biological effects, the non-ionizing portion of the spectrum can be subdivided into:

1. The optical radiation portion, where electron excitation can occur (visible light, infrared light)
2. The portion where the wavelength is smaller than the body. Heating via induced currents can occur. In addition there are claims of other adverse biological effects. Such effects are not well understood and even largely denied. (MW and higher-frequency RF).
3. The portion where the wavelength is much larger than the body, and heating via induced currents seldom occurs (lower-frequency RF, power frequencies, static fields).

The above effects have only been shown to be due to heating effects. At low power levels where there is no heating affect, the risk of cancer is not significant.

	Source	Wavelength	Frequency	Biological effects
UVA	Black light, Sunlight	318–400 nm	750–950 THz	Eye: photochemical cataract; skin: erythema, including pigmentation
Visible light	Sunlight, fire, LEDs, light bulbs, lasers	400–780 nm	385–750 THz	Eye: photochemical & thermal retinal injury; skin: photoaging
IR-A	Sunlight, thermal radiation, incandescent light bulbs, lasers, remote controls	780 nm – 1.4 µm	215–385 THz	Eye: thermal retinal injury, thermal cataract; skin: burn
IR-B	Sunlight, thermal radiation, incandescent light bulbs, lasers	1.4–3 µm	100–215 THz	Eye: corneal burn, cataract; skin: burn
IR-C	Sunlight, thermal radiation, incandescent light bulbs, far-infrared laser	3 µm – 1 mm	300 GHz – 100 THz	Eye: corneal burn, cataract; heating of body surface
Microwave	Mobile/cell phones, microwave ovens, cordless phones, millimeter waves, airport millimeter scanners, motion detectors, long-distance telecommunications, radar, Wi-Fi	1 mm – 33 cm	1–300 GHz	Heating of body tissue
Radio-frequency radiation	Mobile/cell phones, television, FM, AM, shortwave, CB, cordless phones	33 cm – 3 km	100 kHz – 1 GHz	Heating of body tissue, raised body temperature
Low-frequency RF	Power lines	>3 km	<100 font="" khz="" nbsp="">	Cumulation of charge on body surface; disturbance of nerve & muscle responses
Static field	Strong magnets, MRI	Infinite	0 Hz (technically static fields are not "radiation")	Electric charge on body surface

Types of non-ionizing electromagnetic radiation

Near ultraviolet radiation

Ultraviolet light can cause burns to skin and cataracts to the eyes. Ultraviolet is classified into near, medium and far UV according to energy, where near and medium ultraviolet are technically non-ionizing, but where all UV wavelengths can cause photochemical reactions that to some extent mimic ionization (including DNA damage and carcinogenesis). UV radiation above 10 eV (wavelength shorter than 125 nm) is considered ionizing. However, the rest of the UV spectrum from 3.1 eV (400 nm) to 10 eV, although technically non-ionizing, can produce photochemical reactions that are damaging to molecules by means other than simple heat. Since these reactions are often very similar to those caused by ionizing radiation, often the entire UV spectrum is considered to be equivalent to ionization radiation in its interaction with many systems (including biological systems).

For example, ultraviolet light, even in the non-ionizing range, can produce free radicals that induce cellular damage, and can be carcinogenic. Photochemistry such as pyrimidine dimer formation in DNA can happen through most of the UV band, including much of the band that is formally non-ionizing. Ultraviolet light induces melanin production from melanocyte cells to cause sun tanning of skin. Vitamin D is produced on the skin by a radical reaction initiated by UV radiation. 

Plastic (polycarbonate) sunglasses generally absorb UV radiation. UV overexposure to the eyes causes snow blindness, common to areas with reflective surfaces, such as snow or water.

Visible light

Light, or visible light, is the very narrow range of electromagnetic radiation that is visible to the human eye (about 400–700 nm), or up to 380–750 nm. More broadly, physicists refer to light as electromagnetic radiation of all wavelengths, whether visible or not.

High-energy visible light is blue-violet light with a higher damaging potential.

Infrared

Infrared (IR) light is electromagnetic radiation with a wavelength between 0.7 and 300 micrometers, which equates to a frequency range between approximately 1 and 430 THz. IR wavelengths are longer than that of visible light, but shorter than that of terahertz radiation microwaves. Bright sunlight provides an irradiance of just over 1 kilowatt per square meter at sea level. Of this energy, 527 watts is infrared radiation, 445 watts is visible light, and 32 watts is ultraviolet radiation.

Microwave

Microwaves are electromagnetic waves with wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz (0.3 GHz) and 300 GHz. This broad definition includes both UHF and EHF (millimeter waves), and various sources use different boundaries. In all cases, microwave includes the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum, with RF engineering often putting the lower boundary at 1 GHz (30 cm), and the upper around 100 GHz (3mm). Applications include cellphone (mobile) telephones, radars, airport scanners, microwave ovens, earth remote sensing satellites, and radio and satellite communications.

Radio waves

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Like all other electromagnetic waves, they travel at the speed of light. Naturally occurring radio waves are made by lightning, or by astronomical objects. Artificially generated radio waves are used for fixed and mobile radio communication, broadcasting, radar and other navigation systems, satellite communication, computer networks and innumerable other applications. Different frequencies of radio waves have different propagation characteristics in the Earth's atmosphere; long waves may cover a part of the Earth very consistently, shorter waves can reflect off the ionosphere and travel around the world, and much shorter wavelengths bend or reflect very little and travel on a line of sight.

Very low frequency (VLF)

Very low frequency or VLF is the radio frequencies (RF) in the range of 3 to 30 kHz. Since there is not much bandwidth in this band of the radio spectrum, only the very simplest signals are used, such as for radio navigation. Also known as the myriameter band or myriameter wave as the wavelengths range from ten to one myriameter (an obsolete metric unit equal to 10 kilometers).

Extremely low frequency (ELF)

Extremely low frequency (ELF) is the range of radiation frequencies from 300 Hz to 3 kHz. In atmosphere science, an alternative definition is usually given, from 3 Hz to 3 kHz. In the related magnetosphere science, the lower frequency electromagnetic oscillations (pulsations occurring below ~3 Hz) are considered to be in the ULF range, which is thus also defined differently from the ITU Radio Bands.

Thermal radiation

Thermal radiation, a common synonym for infra-red when it occurs at temperatures commonly encountered on Earth, is the process by which the surface of an object radiates its thermal energy in the form of electromagnetic waves. Infrared radiation that one can feel emanating from a household heater, infra-red heat lamp, or kitchen oven are examples of thermal radiation, as is the IR and visible light emitted by a glowing incandescent light bulb (not hot enough to emit the blue high frequencies and therefore appearing yellowish; fluorescent lamps are not thermal and can appear bluer). Thermal radiation is generated when the energy from the movement of charged particles within molecules is converted to the radiant energy of electromagnetic waves. The emitted wave frequency of the thermal radiation is a probability distribution depending only on temperature, and for a black body is given by Planck's law of radiation. Wien's displacement law gives the most likely frequency of the emitted radiation, and the Stefan–Boltzmann law gives the heat intensity (power emitted per area).

Parts of the electromagnetic spectrum of thermal radiation may be ionizing, if the object emitting the radiation is hot enough (has a high enough temperature). A common example of such radiation is sunlight, which is thermal radiation from the Sun's photosphere and which contains enough ultraviolet light to cause ionization in many molecules and atoms. An extreme example is the flash from the detonation of a nuclear weapon, which emits a large number of ionizing X-rays purely as a product of heating the atmosphere around the bomb to extremely high temperatures.

As noted above, even low-frequency thermal radiation may cause temperature-ionization whenever it deposits sufficient thermal energy to raises temperatures to a high enough level. Common examples of this are the ionization (plasma) seen in common flames, and the molecular changes caused by the "browning" in food-cooking, which is a chemical process that begins with a large component of ionization.

Black-body radiation

Black body radiation is radiation from an idealized radiator that emits at any temperature the maximum possible amount of radiation at any given wavelength. A black body will also absorb the maximum possible incident radiation at any given wavelength. The radiation emitted covers the entire electromagnetic spectrum and the intensity (power/unit-area) at a given frequency is dictated by Planck's law of radiation. A black body at temperatures at or below room temperature would thus appear absolutely black as it would not reflect any light. Theoretically a black body emits electromagnetic radiation over the entire spectrum from very low frequency radio waves to X-rays. The frequency at which the black-body radiation is at maximum is given by Wien's displacement law.

Critical mass

From Wikipedia, the free encyclopedia

A re-creation of the 1945 criticality accident using the Demon core: a plutonium pit is surrounded by blocks of neutron-reflective tungsten carbide. The original experiment was designed to measure the radiation produced when an extra block was added. The mass went supercritical when the block was placed improperly by being dropped.

 

A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, the nuclear fission cross-section), its density, its shape, its enrichment, its purity, its temperature, and its surroundings. The concept is important in nuclear weapon design.

Explanation of criticality

When a nuclear chain reaction in a mass of fissile material is self-sustaining, the mass is said to be in a critical state in which there is no increase or decrease in power, temperature, or neutron population.

A numerical measure of a critical mass is dependent on the effective neutron multiplication factor k, the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material. When k = 1, the mass is critical, and the chain reaction is self-sustaining. 

A subcritical mass is a mass of fissile material that does not have the ability to sustain a fission chain reaction. A population of neutrons introduced to a subcritical assembly will exponentially decrease. In this case, k < 1. A steady rate of spontaneous fissions causes a proportionally steady level of neutron activity. The constant of proportionality increases as k increases. 

A supercritical mass is one in which, once fission has started, it will proceed at an increasing rate. The material may settle into equilibrium (i.e. become critical again) at an elevated temperature/power level or destroy itself. In the case of supercriticality, k > 1. 

Due to spontaneous fission a supercritical mass will undergo a chain reaction. For example, a spherical critical mass of pure uranium-235 will have a mass of 52 kg and will experience around 15 spontaneous fission events per second. The probability that one such event will cause a chain reaction depends on how much the mass exceeds the critical mass. If there is uranium-238 present, the rate of spontaneous fission will be much higher. Fission can also be initiated by neutrons produced by cosmic rays.

Changing the point of criticality

The mass where criticality occurs may be changed by modifying certain attributes such as fuel, shape, temperature, density and the installation of a neutron-reflective substance. These attributes have complex interactions and interdependencies. These examples only outline the simplest ideal cases:

Varying the amount of fuel

It is possible for a fuel assembly to be critical at near zero power. If the perfect quantity of fuel were added to a slightly subcritical mass to create an "exactly critical mass", fission would be self-sustaining for only one neutron generation (fuel consumption then makes the assembly subcritical again). 

If the perfect quantity of fuel were added to a slightly subcritical mass, to create a barely supercritical mass, the temperature of the assembly would increase to an initial maximum (for example: 1 K above the ambient temperature) and then decrease back to the ambient temperature after a period of time, because fuel consumed during fission brings the assembly back to subcriticality once again.

Changing the shape

A mass may be exactly critical without being a perfect homogeneous sphere. More closely refining the shape toward a perfect sphere will make the mass supercritical. Conversely changing the shape to a less perfect sphere will decrease its reactivity and make it subcritical.

Changing the temperature

A mass may be exactly critical at a particular temperature. Fission and absorption cross-sections increase as the relative neutron velocity decreases. As fuel temperature increases, neutrons of a given energy appear faster and thus fission/absorption is less likely. This is not unrelated to Doppler broadening of the ²³⁸U resonances but is common to all fuels/absorbers/configurations. Neglecting the very important resonances, the total neutron cross-section of every material exhibits an inverse relationship with relative neutron velocity. Hot fuel is always less reactive than cold fuel (over/under moderation in LWR is a different topic). Thermal expansion associated with temperature increase also contributes a negative coefficient of reactivity since fuel atoms are moving farther apart. A mass that is exactly critical at room temperature would be sub-critical in an environment anywhere above room temperature due to thermal expansion alone.

Varying the density of the mass

The higher the density, the lower the critical mass. The density of a material at a constant temperature can be changed by varying the pressure or tension or by changing crystal structure. An ideal mass will become subcritical if allowed to expand or conversely the same mass will become supercritical if compressed. Changing the temperature may also change the density; however, the effect on critical mass is then complicated by temperature effects (see "Changing the temperature") and by whether the material expands or contracts with increased temperature. Assuming the material expands with temperature (enriched uranium-235 at room temperature for example), at an exactly critical state, it will become subcritical if warmed to lower density or become supercritical if cooled to higher density. Such a material is said to have a negative temperature coefficient of reactivity to indicate that its reactivity decreases when its temperature increases. Using such a material as fuel means fission decreases as the fuel temperature increases.

Use of a neutron reflector

Surrounding a spherical critical mass with a neutron reflector further reduces the mass needed for criticality. A common material for a neutron reflector is beryllium metal. This reduces the number of neutrons which escape the fissile material, resulting in increased reactivity.

Use of a tamper

In a bomb, a dense shell of material surrounding the fissile core will contain, via inertia, the expanding fissioning material. This increases the efficiency. A tamper also tends to act as a neutron reflector. Because a bomb relies on fast neutrons (not ones moderated by reflection with light elements, as in a reactor), the neutrons reflected by a tamper are slowed by their collisions with the tamper nuclei, and because it takes time for the reflected neutrons to return to the fissile core, they take rather longer to be absorbed by a fissile nucleus. But they do contribute to the reaction, and can decrease the critical mass by a factor of four. Also, if the tamper is (e.g. depleted) uranium, it can fission due to the high energy neutrons generated by the primary explosion. This can greatly increase yield, especially if even more neutrons are generated by fusing hydrogen isotopes, in a so-called boosted configuration.

Critical size

The critical size is the minimum size of a nuclear reactor core or nuclear weapon that can be made for a specific geometrical arrangement and material composition. The critical size must at least include enough fissionable material to reach critical mass. If the size of the reactor core is less than a certain minimum, too many fission neutrons escape through its surface and the chain reaction is not sustained.

Critical mass of a bare sphere

Top: A sphere of fissile material is too small to allow the chain reaction to become self-sustaining as neutrons generated by fissions can too easily escape.
Middle: By increasing the mass of the sphere to a critical mass, the reaction can become self-sustaining.
Bottom: Surrounding the original sphere with a neutron reflector increases the efficiency of the reactions and also allows the reaction to become self-sustaining.

 

The shape with minimal critical mass and the smallest physical dimensions is a sphere. Bare-sphere critical masses at normal density of some actinides are listed in the following table. Most information on bare sphere masses is considered classified, since it is critical to nuclear weapons design, but some documents have been declassified.

Nuclide	Half life (y)	Critical mass (kg)	Diameter (cm)
uranium-233	159,200	15	11
uranium-235	703,800,000	52	17
neptunium-236	154,000	7	8.7
neptunium-237	2,144,000	60	18
plutonium-238	87.7	9.04–10.07	9.5–9.9
plutonium-239	24,110	10	9.9
plutonium-240	6561	40	15
plutonium-241	14.3	12	10.5
plutonium-242	375,000	75–100	19–21
americium-241	432.2	55–77	20–23
americium-242m	141	9–14	11–13
americium-243	7370	180–280	30–35
curium-243	29.1	7.34–10	10–11
curium-244	18.1	13.5–30	12.4–16
curium-245	8500	9.41–12.3	11–12
curium-246	4760	39–70.1	18–21
curium-247	15,600,000	6.94–7.06	9.9
berkelium-247	1380	75.7	11.8-12.2
berkelium-249	330 days	192	16.1-16.6
californium-249	351	6	9
californium-251	900	5.46	8.5
californium-252	2.6	2.73	6.9
einsteinium-254	275.7 days	9.89	7.1

The critical mass for lower-grade uranium depends strongly on the grade: with 20% ²³⁵U it is over 400 kg; with 15% ²³⁵U, it is well over 600 kg. 

The critical mass is inversely proportional to the square of the density. If the density is 1% more and the mass 2% less, then the volume is 3% less and the diameter 1% less. The probability for a neutron per cm travelled to hit a nucleus is proportional to the density. It follows that 1% greater density means that the distance travelled before leaving the system is 1% less. This is something that must be taken into consideration when attempting more precise estimates of critical masses of plutonium isotopes than the approximate values given above, because plutonium metal has a large number of different crystal phases which can have widely varying densities. 

Note that not all neutrons contribute to the chain reaction. Some escape and others undergo radiative capture. 

Let q denote the probability that a given neutron induces fission in a nucleus. Consider only prompt neutrons, and let ν denote the number of prompt neutrons generated in a nuclear fission. For example, ν ≈ 2.5 for uranium-235. Then, criticality occurs when ν·q = 1. The dependence of this upon geometry, mass, and density appears through the factor q. 

Given a total interaction cross section σ (typically measured in barns), the mean free path of a prompt neutron is ${\displaystyle \ell ^{-1}=n\sigma }$ where n is the nuclear number density. Most interactions are scattering events, so that a given neutron obeys a random walk until it either escapes from the medium or causes a fission reaction. So long as other loss mechanisms are not significant, then, the radius of a spherical critical mass is rather roughly given by the product of the mean free path ${\displaystyle \ell }$ and the square root of one plus the number of scattering events per fission event (call this s), since the net distance travelled in a random walk is proportional to the square root of the number of steps: 

${\displaystyle R_{c}\simeq \ell {\sqrt {s}}\simeq {\frac {\sqrt {s}}{n\sigma }}}$

Note again, however, that this is only a rough estimate.

In terms of the total mass M, the nuclear mass m, the density ρ, and a fudge factor f which takes into account geometrical and other effects, criticality corresponds to 

${\displaystyle 1={\frac {f\sigma }{m{\sqrt {s}}}}\rho ^{2/3}M^{1/3}}$

which clearly recovers the aforementioned result that critical mass depends inversely on the square of the density.

Alternatively, one may restate this more succinctly in terms of the areal density of mass, Σ: 

${\displaystyle 1={\frac {f'\sigma }{m{\sqrt {s}}}}\Sigma }$

where the factor f has been rewritten as f' to account for the fact that the two values may differ depending upon geometrical effects and how one defines Σ. For example, for a bare solid sphere of ²³⁹Pu criticality is at 320 kg/m², regardless of density, and for ²³⁵U at 550 kg/m². In any case, criticality then depends upon a typical neutron "seeing" an amount of nuclei around it such that the areal density of nuclei exceeds a certain threshold.

This is applied in implosion-type nuclear weapons where a spherical mass of fissile material that is substantially less than a critical mass is made supercritical by very rapidly increasing ρ (and thus Σ as well) (see below). Indeed, sophisticated nuclear weapons programs can make a functional device from less material than more primitive weapons programs require.

Aside from the math, there is a simple physical analog that helps explain this result. Consider diesel fumes belched from an exhaust pipe. Initially the fumes appear black, then gradually you are able to see through them without any trouble. This is not because the total scattering cross section of all the soot particles has changed, but because the soot has dispersed. If we consider a transparent cube of length L on a side, filled with soot, then the optical depth of this medium is inversely proportional to the square of L, and therefore proportional to the areal density of soot particles: we can make it easier to see through the imaginary cube just by making the cube larger.

Several uncertainties contribute to the determination of a precise value for critical masses, including (1) detailed knowledge of fission cross sections, (2) calculation of geometric effects. This latter problem provided significant motivation for the development of the Monte Carlo method in computational physics by Nicholas Metropolis and Stanislaw Ulam. In fact, even for a homogeneous solid sphere, the exact calculation is by no means trivial. Finally, note that the calculation can also be performed by assuming a continuum approximation for the neutron transport. This reduces it to a diffusion problem. However, as the typical linear dimensions are not significantly larger than the mean free path, such an approximation is only marginally applicable.

Finally, note that for some idealized geometries, the critical mass might formally be infinite, and other parameters are used to describe criticality. For example, consider an infinite sheet of fissionable material. For any finite thickness, this corresponds to an infinite mass. However, criticality is only achieved once the thickness of this slab exceeds a critical value.

Criticality in nuclear weapon design

If two pieces of subcritical material are not brought together fast enough, nuclear predetonation (fizzle) can occur, whereby a very small explosion will blow the bulk of the material apart.

 

Until detonation is desired, a nuclear weapon must be kept subcritical. In the case of a uranium bomb, this can be achieved by keeping the fuel in a number of separate pieces, each below the critical size either because they are too small or unfavorably shaped. To produce detonation, the pieces of uranium are brought together rapidly. In Little Boy, this was achieved by firing a piece of uranium (a 'doughnut') down a gun barrel onto another piece (a 'spike'). This design is referred to as a gun-type fission weapon. 

A theoretical 100% pure ²³⁹Pu weapon could also be constructed as a gun-type weapon, like the Manhattan Project's proposed Thin Man design. In reality, this is impractical because even "weapons grade" ²³⁹Pu is contaminated with a small amount of ²⁴⁰Pu, which has a strong propensity toward spontaneous fission. Because of this, a reasonably sized gun-type weapon would suffer nuclear reaction (predetonation) before the masses of plutonium would be in a position for a full-fledged explosion to occur. 

Instead, the plutonium is present as a subcritical sphere (or other shape), which may or may not be hollow. Detonation is produced by exploding a shaped charge surrounding the sphere, increasing the density (and collapsing the cavity, if present) to produce a prompt critical configuration. This is known as an implosion type weapon.

Prompt criticality

The event of fission must release, on the average, more than one free neutron of the desired energy level in order to sustain a chain reaction, and each must find other nuclei and cause them to fission. Most of the neutrons released from a fission event come immediately from that event, but a fraction of them come later, when the fission products decay, which may be on the average from microseconds to minutes later. This is fortunate for atomic power generation, for without this delay "going critical" would always be an immediately catastrophic event, as it is in a nuclear bomb where upwards of 80 generations of chain reaction occur in less than a microsecond, far too fast for man, or even machine, to react. Physicists recognize two points in the gradual increase of neutron flux which are significant: critical, where the chain reaction becomes self-sustaining thanks to the contributions of both kinds of neutron generation, and prompt critical, where the immediate "prompt" neutrons alone will sustain the reaction without need for the decay neutrons. Nuclear power plants operate between these two points of reactivity, while above the prompt critical point is the domain of nuclear weapons and some nuclear power accidents, such as the Chernobyl disaster.

A convenient unit for the measurement of the reactivity is that suggested by Louis Slotin: that of the dollar and cents.