Nuclear physics

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nuclear_physics 

Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of nuclear matter are also studied.

Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons.

Discoveries in nuclear physics have led to applications in many fields. This includes nuclear power, nuclear weapons, nuclear medicine and magnetic resonance imaging, industrial and agricultural isotopes, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology. Such applications are studied in the field of nuclear engineering.

Particle physics evolved out of nuclear physics and the two fields are typically taught in close association. Nuclear astrophysics, the application of nuclear physics to astrophysics, is crucial in explaining the inner workings of stars and the origin of the chemical elements.

History

Henri Becquerel

 

Since 1920s cloud chambers played an important role of particle detectors and eventually lead to the discovery of positron, muon and kaon.

The history of nuclear physics as a discipline distinct from atomic physics starts with the discovery of radioactivity by Henri Becquerel in 1896 while investigating phosphorescence in uranium salts. The discovery of the electron by J. J. Thomson a year later was an indication that the atom had internal structure. At the beginning of the 20th century the accepted model of the atom was J. J. Thomson's "plum pudding" model in which the atom was a positively charged ball with smaller negatively charged electrons embedded inside it.

In the years that followed, radioactivity was extensively investigated, notably by Marie Curie, Pierre Curie, Ernest Rutherford and others. By the turn of the century, physicists had also discovered three types of radiation emanating from atoms, which they named alpha, beta, and gamma radiation. Experiments by Otto Hahn in 1911 and by James Chadwick in 1914 discovered that the beta decay spectrum was continuous rather than discrete. That is, electrons were ejected from the atom with a continuous range of energies, rather than the discrete amounts of energy that were observed in gamma and alpha decays. This was a problem for nuclear physics at the time, because it seemed to indicate that energy was not conserved in these decays.

The 1903 Nobel Prize in Physics was awarded jointly to Becquerel, for his discovery and to Marie and Pierre Curie for their subsequent research into radioactivity. Rutherford was awarded the Nobel Prize in Chemistry in 1908 for his "investigations into the disintegration of the elements and the chemistry of radioactive substances".

In 1905, Albert Einstein formulated the idea of mass–energy equivalence. While the work on radioactivity by Becquerel and Marie Curie predates this, an explanation of the source of the energy of radioactivity would have to wait for the discovery that the nucleus itself was composed of smaller constituents, the nucleons.

Rutherford's team discovers the nucleus

In 1906, Ernest Rutherford published "Retardation of the α Particle from Radium in passing through matter." Hans Geiger expanded on this work in a communication to the Royal Society with experiments he and Rutherford had done, passing alpha particles through air, aluminum foil and gold leaf. More work was published in 1909 by Geiger and Ernest Marsden, and further greatly expanded work was published in 1910 by Geiger. In 1911–1912 Rutherford went before the Royal Society to explain the experiments and propound the new theory of the atomic nucleus as we now understand it.

The key experiment behind this announcement was performed in 1910, at the University of Manchester: Ernest Rutherford's team performed a remarkable experiment in which Geiger and Marsden under Rutherford's supervision fired alpha particles (helium nuclei) at a thin film of gold foil. The plum pudding model had predicted that the alpha particles should come out of the foil with their trajectories being at most slightly bent. But Rutherford instructed his team to look for something that shocked him to observe: a few particles were scattered through large angles, even completely backwards in some cases. He likened it to firing a bullet at tissue paper and having it bounce off. The discovery, with Rutherford's analysis of the data in 1911, led to the Rutherford model of the atom, in which the atom had a very small, very dense nucleus containing most of its mass, and consisting of heavy positively charged particles with embedded electrons in order to balance out the charge (since the neutron was unknown). As an example, in this model (which is not the modern one) nitrogen-14 consisted of a nucleus with 14 protons and 7 electrons (21 total particles) and the nucleus was surrounded by 7 more orbiting electrons.

Around 1920, Arthur Eddington anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper The Internal Constitution of the Stars. At that time, the source of stellar energy was a complete mystery; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation E = mc². This was a particularly remarkable development since at that time fusion and thermonuclear energy, and even that stars are largely composed of hydrogen (see metallicity), had not yet been discovered.

The Rutherford model worked quite well until studies of nuclear spin were carried out by Franco Rasetti at the California Institute of Technology in 1929. By 1925 it was known that protons and electrons each had a spin of ​± ¹⁄₂. In the Rutherford model of nitrogen-14, 20 of the total 21 nuclear particles should have paired up to cancel each other's spin, and the final odd particle should have left the nucleus with a net spin of ​¹⁄₂. Rasetti discovered, however, that nitrogen-14 had a spin of 1.

James Chadwick discovers the neutron

In 1932 Chadwick realized that radiation that had been observed by Walther Bothe, Herbert Becker, Irène and Frédéric Joliot-Curie was actually due to a neutral particle of about the same mass as the proton, that he called the neutron (following a suggestion from Rutherford about the need for such a particle). In the same year Dmitri Ivanenko suggested that there were no electrons in the nucleus — only protons and neutrons — and that neutrons were spin ​¹⁄₂ particles, which explained the mass not due to protons. The neutron spin immediately solved the problem of the spin of nitrogen-14, as the one unpaired proton and one unpaired neutron in this model each contributed a spin of ​¹⁄₂ in the same direction, giving a final total spin of 1.

With the discovery of the neutron, scientists could at last calculate what fraction of binding energy each nucleus had, by comparing the nuclear mass with that of the protons and neutrons which composed it. Differences between nuclear masses were calculated in this way. When nuclear reactions were measured, these were found to agree with Einstein's calculation of the equivalence of mass and energy to within 1% as of 1934.

Proca's equations of the massive vector boson field

Alexandru Proca was the first to develop and report the massive vector boson field equations and a theory of the mesonic field of nuclear forces. Proca's equations were known to Wolfgang Pauli who mentioned the equations in his Nobel address, and they were also known to Yukawa, Wentzel, Taketani, Sakata, Kemmer, Heitler, and Fröhlich who appreciated the content of Proca's equations for developing a theory of the atomic nuclei in Nuclear Physics.

Yukawa's meson postulated to bind nuclei

In 1935 Hideki Yukawa proposed the first significant theory of the strong force to explain how the nucleus holds together. In the Yukawa interaction a virtual particle, later called a meson, mediated a force between all nucleons, including protons and neutrons. This force explained why nuclei did not disintegrate under the influence of proton repulsion, and it also gave an explanation of why the attractive strong force had a more limited range than the electromagnetic repulsion between protons. Later, the discovery of the pi meson showed it to have the properties of Yukawa's particle.

With Yukawa's papers, the modern model of the atom was complete. The center of the atom contains a tight ball of neutrons and protons, which is held together by the strong nuclear force, unless it is too large. Unstable nuclei may undergo alpha decay, in which they emit an energetic helium nucleus, or beta decay, in which they eject an electron (or positron). After one of these decays the resultant nucleus may be left in an excited state, and in this case it decays to its ground state by emitting high-energy photons (gamma decay).

The study of the strong and weak nuclear forces (the latter explained by Enrico Fermi via Fermi's interaction in 1934) led physicists to collide nuclei and electrons at ever higher energies. This research became the science of particle physics, the crown jewel of which is the standard model of particle physics, which describes the strong, weak, and electromagnetic forces.

Modern nuclear physics

A heavy nucleus can contain hundreds of nucleons. This means that with some approximation it can be treated as a classical system, rather than a quantum-mechanical one. In the resulting liquid-drop model, the nucleus has an energy that arises partly from surface tension and partly from electrical repulsion of the protons. The liquid-drop model is able to reproduce many features of nuclei, including the general trend of binding energy with respect to mass number, as well as the phenomenon of nuclear fission.

Superimposed on this classical picture, however, are quantum-mechanical effects, which can be described using the nuclear shell model, developed in large part by Maria Goeppert Mayer and J. Hans D. Jensen. Nuclei with certain "magic" numbers of neutrons and protons are particularly stable, because their shells are filled.

Other more complicated models for the nucleus have also been proposed, such as the interacting boson model, in which pairs of neutrons and protons interact as bosons, analogously to Cooper pairs of electrons.

Ab initio methods try to solve the nuclear many-body problem from the ground up, starting from the nucleons and their interactions.

Much of current research in nuclear physics relates to the study of nuclei under extreme conditions such as high spin and excitation energy. Nuclei may also have extreme shapes (similar to that of Rugby balls or even pears) or extreme neutron-to-proton ratios. Experimenters can create such nuclei using artificially induced fusion or nucleon transfer reactions, employing ion beams from an accelerator. Beams with even higher energies can be used to create nuclei at very high temperatures, and there are signs that these experiments have produced a phase transition from normal nuclear matter to a new state, the quark–gluon plasma, in which the quarks mingle with one another, rather than being segregated in triplets as they are in neutrons and protons.

Nuclear decay

Eighty elements have at least one stable isotope which is never observed to decay, amounting to a total of about 252 stable nuclides. However, thousands of isotopes have been characterized as unstable. These "radioisotopes" decay over time scales ranging from fractions of a second to trillions of years. Plotted on a chart as a function of atomic and neutron numbers, the binding energy of the nuclides forms what is known as the valley of stability. Stable nuclides lie along the bottom of this energy valley, while increasingly unstable nuclides lie up the valley walls, that is, have weaker binding energy.

The most stable nuclei fall within certain ranges or balances of composition of neutrons and protons: too few or too many neutrons (in relation to the number of protons) will cause it to decay. For example, in beta decay, a nitrogen-16 atom (7 protons, 9 neutrons) is converted to an oxygen-16 atom (8 protons, 8 neutrons) within a few seconds of being created. In this decay a neutron in the nitrogen nucleus is converted by the weak interaction into a proton, an electron and an antineutrino. The element is transmuted to another element, with a different number of protons.

In alpha decay, which typically occurs in the heaviest nuclei, the radioactive element decays by emitting a helium nucleus (2 protons and 2 neutrons), giving another element, plus helium-4. In many cases this process continues through several steps of this kind, including other types of decays (usually beta decay) until a stable element is formed.

In gamma decay, a nucleus decays from an excited state into a lower energy state, by emitting a gamma ray. The element is not changed to another element in the process (no nuclear transmutation is involved).

Other more exotic decays are possible (see the first main article). For example, in internal conversion decay, the energy from an excited nucleus may eject one of the inner orbital electrons from the atom, in a process which produces high speed electrons but is not beta decay and (unlike beta decay) does not transmute one element to another.

Nuclear fusion

In nuclear fusion, two low-mass nuclei come into very close contact with each other so that the strong force fuses them. It requires a large amount of energy for the strong or nuclear forces to overcome the electrical repulsion between the nuclei in order to fuse them; therefore nuclear fusion can only take place at very high temperatures or high pressures. When nuclei fuse, a very large amount of energy is released and the combined nucleus assumes a lower energy level. The binding energy per nucleon increases with mass number up to nickel-62. Stars like the Sun are powered by the fusion of four protons into a helium nucleus, two positrons, and two neutrinos. The uncontrolled fusion of hydrogen into helium is known as thermonuclear runaway. A frontier in current research at various institutions, for example the Joint European Torus (JET) and ITER, is the development of an economically viable method of using energy from a controlled fusion reaction. Nuclear fusion is the origin of the energy (including in the form of light and other electromagnetic radiation) produced by the core of all stars including our own Sun.

Nuclear fission

Nuclear fission is the reverse process to fusion. For nuclei heavier than nickel-62 the binding energy per nucleon decreases with the mass number. It is therefore possible for energy to be released if a heavy nucleus breaks apart into two lighter ones.

The process of alpha decay is in essence a special type of spontaneous nuclear fission. It is a highly asymmetrical fission because the four particles which make up the alpha particle are especially tightly bound to each other, making production of this nucleus in fission particularly likely.

From several of the heaviest nuclei whose fission produces free neutrons, and which also easily absorb neutrons to initiate fission, a self-igniting type of neutron-initiated fission can be obtained, in a chain reaction. Chain reactions were known in chemistry before physics, and in fact many familiar processes like fires and chemical explosions are chemical chain reactions. The fission or "nuclear" chain-reaction, using fission-produced neutrons, is the source of energy for nuclear power plants and fission-type nuclear bombs, such as those detonated in Hiroshima and Nagasaki, Japan, at the end of World War II. Heavy nuclei such as uranium and thorium may also undergo spontaneous fission, but they are much more likely to undergo decay by alpha decay.

For a neutron-initiated chain reaction to occur, there must be a critical mass of the relevant isotope present in a certain space under certain conditions. The conditions for the smallest critical mass require the conservation of the emitted neutrons and also their slowing or moderation so that there is a greater cross-section or probability of them initiating another fission. In two regions of Oklo, Gabon, Africa, natural nuclear fission reactors were active over 1.5 billion years ago. Measurements of natural neutrino emission have demonstrated that around half of the heat emanating from the Earth's core results from radioactive decay. However, it is not known if any of this results from fission chain reactions.

Production of "heavy" elements

According to the theory, as the Universe cooled after the Big Bang it eventually became possible for common subatomic particles as we know them (neutrons, protons and electrons) to exist. The most common particles created in the Big Bang which are still easily observable to us today were protons and electrons (in equal numbers). The protons would eventually form hydrogen atoms. Almost all the neutrons created in the Big Bang were absorbed into helium-4 in the first three minutes after the Big Bang, and this helium accounts for most of the helium in the universe today.

Some relatively small quantities of elements beyond helium (lithium, beryllium, and perhaps some boron) were created in the Big Bang, as the protons and neutrons collided with each other, but all of the "heavier elements" (carbon, element number 6, and elements of greater atomic number) that we see today, were created inside stars during a series of fusion stages, such as the proton-proton chain, the CNO cycle and the triple-alpha process. Progressively heavier elements are created during the evolution of a star.

Since the binding energy per nucleon peaks around iron (56 nucleons), energy is only released in fusion processes involving smaller atoms than that. Since the creation of heavier nuclei by fusion requires energy, nature resorts to the process of neutron capture. Neutrons (due to their lack of charge) are readily absorbed by a nucleus. The heavy elements are created by either a slow neutron capture process (the so-called s-process) or the rapid, or r-process. The s process occurs in thermally pulsing stars (called AGB, or asymptotic giant branch stars) and takes hundreds to thousands of years to reach the heaviest elements of lead and bismuth. The r-process is thought to occur in supernova explosions, which provide the necessary conditions of high temperature, high neutron flux and ejected matter. These stellar conditions make the successive neutron captures very fast, involving very neutron-rich species which then beta-decay to heavier elements, especially at the so-called waiting points that correspond to more stable nuclides with closed neutron shells (magic numbers)

Nuclear chain reaction

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nuclear_chain_reaction 

 

A possible nuclear fission chain reaction. 1. A uranium-235 atom absorbs a neutron, and fissions into two (fission fragments), releasing three new neutrons and a large amount of binding energy. 2. One of those neutrons is absorbed by an atom of uranium-238, and does not continue the reaction. Another neutron leaves the system without being absorbed. However, one neutron does collide with an atom of uranium-235, which then fissions and releases two neutrons and more binding energy. 3. Both of those neutrons collide with uranium-235 atoms, each of which fissions and releases a few neutrons, which can then continue the reaction.

A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The specific nuclear reaction may be the fission of heavy isotopes (e.g., uranium-235, ²³⁵U). The nuclear chain reaction releases several million times more energy per reaction than any chemical reaction.

History

Chemical chain reactions were first proposed by German chemist Max Bodenstein in 1913, and were reasonably well understood before nuclear chain reactions were proposed. It was understood that chemical chain reactions were responsible for exponentially increasing rates in reactions, such as produced in chemical explosions.

The concept of a nuclear chain reaction was reportedly first hypothesized by Hungarian scientist Leó Szilárd on September 12, 1933. Szilárd that morning had been reading in a London paper of an experiment in which protons from an accelerator had been used to split lithium-7 into alpha particles, and the fact that much greater amounts of energy were produced by the reaction than the proton supplied. Ernest Rutherford commented in the article that inefficiencies in the process precluded use of it for power generation. However, the neutron had been discovered in 1932, shortly before, as the product of a nuclear reaction. Szilárd, who had been trained as an engineer and physicist, put the two nuclear experimental results together in his mind and realized that if a nuclear reaction produced neutrons, which then caused further similar nuclear reactions, the process might be a self-perpetuating nuclear chain-reaction, spontaneously producing new isotopes and power without the need for protons or an accelerator. Szilárd, however, did not propose fission as the mechanism for his chain reaction, since the fission reaction was not yet discovered, or even suspected. Instead, Szilárd proposed using mixtures of lighter known isotopes which produced neutrons in copious amounts. He filed a patent for his idea of a simple nuclear reactor the following year.

In 1936, Szilárd attempted to create a chain reaction using beryllium and indium, but was unsuccessful. Nuclear fission was discovered by Otto Hahn and Fritz Strassmann in December 1938 and explained theoretically in January 1939 by Lise Meitner and her nephew Otto Robert Frisch. A few months later, Frédéric Joliot-Curie, H. Von Halban and L. Kowarski in Paris searched for, and discovered, neutron multiplication in uranium, proving that a nuclear chain reaction by this mechanism was indeed possible.

On May 4, 1939, Joliot-Curie, Halban, and Kowarski filed three patents. The first two described power production from a nuclear chain reaction, the last one called Perfectionnement aux charges explosives was the first patent for the atomic bomb and is filed as patent No. 445686 by the Caisse nationale de Recherche Scientifique.

In parallel, Szilárd and Enrico Fermi in New York made the same analysis. This discovery prompted the letter from Szilárd and signed by Albert Einstein to President Franklin D. Roosevelt, warning of the possibility that Nazi Germany might be attempting to build an atomic bomb.

On December 2, 1942, a team led by Fermi (and including Szilárd) produced the first artificial self-sustaining nuclear chain reaction with the Chicago Pile-1 (CP-1) experimental reactor in a racquets court below the bleachers of Stagg Field at the University of Chicago. Fermi's experiments at the University of Chicago were part of Arthur H. Compton's Metallurgical Laboratory of the Manhattan Project; the lab was later renamed Argonne National Laboratory, and tasked with conducting research in harnessing fission for nuclear energy.

In 1956, Paul Kuroda of the University of Arkansas postulated that a natural fission reactor may have once existed. Since nuclear chain reactions may only require natural materials (such as water and uranium, if the uranium has sufficient amounts of ²³⁵U), it was possible to have these chain reactions occur in the distant past when uranium-235 concentrations were higher than today, and where there was the right combination of materials within the Earth's crust. Kuroda's prediction was verified with the discovery of evidence of natural self-sustaining nuclear chain reactions in the past at Oklo in Gabon in September 1972.

Fission chain reaction

Fission chain reactions occur because of interactions between neutrons and fissile isotopes (such as ²³⁵U). The chain reaction requires both the release of neutrons from fissile isotopes undergoing nuclear fission and the subsequent absorption of some of these neutrons in fissile isotopes. When an atom undergoes nuclear fission, a few neutrons (the exact number depends on uncontrollable and unmeasurable factors; the expected number depends on several factors, usually between 2.5 and 3.0) are ejected from the reaction. These free neutrons will then interact with the surrounding medium, and if more fissile fuel is present, some may be absorbed and cause more fissions. Thus, the cycle repeats to give a reaction that is self-sustaining.

Nuclear power plants operate by precisely controlling the rate at which nuclear reactions occur. Nuclear weapons, on the other hand, are specifically engineered to produce a reaction that is so fast and intense it cannot be controlled after it has started. When properly designed, this uncontrolled reaction will lead to an explosive energy release.

Nuclear fission fuel

Nuclear weapons employ high quality, highly enriched fuel exceeding the critical size and geometry (critical mass) necessary in order to obtain an explosive chain reaction. The fuel for energy purposes, such as in a nuclear fission reactor, is very different, usually consisting of a low-enriched oxide material (e.g. UO₂). There are two primary isotopes used for fission reactions inside of nuclear reactors. The first and most common is U-235 or uranium-235. This is the fissile isotope of uranium and it makes up approximately 0.7% of all naturally occurring uranium. Because of the small amount of uranium-235 that exists, it is considered a non-renewable energy source despite being found in rock formations around the world. U-235 cannot be used as fuel in its base form for energy production. It must undergo a process known as refinement to produce the compound UO₂ or uranium dioxide. The uranium dioxide is then pressed and formed into ceramic pellets, which can subsequently be placed into fuel rods. This is when the compound uranium dioxide can be used for nuclear power production. The second most common isotope used in nuclear fission is Pu-239 or plutonium-239. This is due to its ability to become fissile with slow neutron interaction. This isotope is formed inside nuclear reactors through exposing U-238 to the neutrons released by the radioactive U-235 isotope. This neutron capture causes beta particle decay that enables U-238 to transform into Pu-239. Plutonium was once found naturally in the earth's crust but only trace amounts remain. The only way it is accessible in large quantities for energy production is through the neutron capture method.

Enrichment Process

The fissile isotope uranium-235 in its natural state is unfit for nuclear reactors. In order to be prepared for use as fuel in energy production, it must be enriched. The enrichment process does not apply to plutonium. Reactor-grade plutonium is created as a byproduct of neutron interaction between two different isotopes of uranium. The first step to enriching uranium begins by converting uranium oxide (created through the uranium milling process) into a gaseous form. This gas is known as uranium hexafluoride, which is created by combining hydrogen fluoride, fluorine gas, and uranium oxide. Uranium dioxide is also present in this process and it is sent off to be used in reactors not requiring enriched fuel. The remaining uranium hexafluoride compound is drained into strong metal cylinders where it solidifies. The next step is separating the uranium hexafluoride from the depleted U-235 left over. This is typically done with centrifuges that spin fast enough to allow for the 1% mass difference in uranium isotopes to separate themselves. A laser is then used to enrich the hexafluoride compound. The final step involves reconverting the now enriched compound back into uranium oxide, leaving the final product: enriched uranium oxide. This form of UO₂ can now be used in fission reactors inside power plants to produce energy.

Fission reaction products

When a fissile atom undergoes nuclear fission, it breaks into two or more fission fragments. Also, several free neutrons, gamma rays, and neutrinos are emitted, and a large amount of energy is released. The sum of the rest masses of the fission fragments and ejected neutrons is less than the sum of the rest masses of the original atom and incident neutron (of course the fission fragments are not at rest). The mass difference is accounted for in the release of energy according to the equation E=Δmc²:

mass of released energy = ${\displaystyle {\frac {E}{c^{2}}}=m_{\text{original}}-m_{\text{final}}}$

Due to the extremely large value of the speed of light, c, a small decrease in mass is associated with a tremendous release of active energy (for example, the kinetic energy of the fission fragments). This energy (in the form of radiation and heat) carries the missing mass, when it leaves the reaction system (total mass, like total energy, is always conserved). While typical chemical reactions release energies on the order of a few eVs (e.g. the binding energy of the electron to hydrogen is 13.6 eV), nuclear fission reactions typically release energies on the order of hundreds of millions of eVs.

Two typical fission reactions are shown below with average values of energy released and number of neutrons ejected:

${\displaystyle {\begin{aligned}{\ce {^{235}U + neutron ->}}&\ {\text{fission fragments}}+2.4{\text{ neutrons}}+192.9{\text{ MeV}}\\{\ce {^{239}Pu + neutron ->}}&\ {\text{fission fragments}}+2.9{\text{ neutrons}}+198.5{\text{ MeV}}\end{aligned}}}$

Note that these equations are for fissions caused by slow-moving (thermal) neutrons. The average energy released and number of neutrons ejected is a function of the incident neutron speed. Also, note that these equations exclude energy from neutrinos since these subatomic particles are extremely non-reactive and, therefore, rarely deposit their energy in the system.

Timescales of nuclear chain reactions

Prompt neutron lifetime

The prompt neutron lifetime, l, is the average time between the emission of neutrons and either their absorption in the system or their escape from the system. The neutrons that occur directly from fission are called "prompt neutrons," and the ones that are a result of radioactive decay of fission fragments are called "delayed neutrons". The term lifetime is used because the emission of a neutron is often considered its "birth," and the subsequent absorption is considered its "death". For thermal (slow-neutron) fission reactors, the typical prompt neutron lifetime is on the order of 10⁻⁴ seconds, and for fast fission reactors, the prompt neutron lifetime is on the order of 10⁻⁷ seconds. These extremely short lifetimes mean that in 1 second, 10,000 to 10,000,000 neutron lifetimes can pass. The average (also referred to as the adjoint unweighted) prompt neutron lifetime takes into account all prompt neutrons regardless of their importance in the reactor core; the effective prompt neutron lifetime (referred to as the adjoint weighted over space, energy, and angle) refers to a neutron with average importance.

Mean generation time

The mean generation time, Λ, is the average time from a neutron emission to a capture that results in fission. The mean generation time is different from the prompt neutron lifetime because the mean generation time only includes neutron absorptions that lead to fission reactions (not other absorption reactions). The two times are related by the following formula:

${\displaystyle \Lambda ={\frac {l}{k}}}$

In this formula, k is the effective neutron multiplication factor, described below.

Effective neutron multiplication factor

The six factor formula effective neutron multiplication factor, k, is the average number of neutrons from one fission that cause another fission. The remaining neutrons either are absorbed in non-fission reactions or leave the system without being absorbed. The value of k determines how a nuclear chain reaction proceeds:

• k < 1 (subcriticality): The system cannot sustain a chain reaction, and any beginning of a chain reaction dies out over time. For every fission that is induced in the system, an average total of 1/(1 − k) fissions occur.
• k = 1 (criticality): Every fission causes an average of one more fission, leading to a fission (and power) level that is constant. Nuclear power plants operate with k = 1 unless the power level is being increased or decreased.
• k > 1 (supercriticality): For every fission in the material, it is likely that there will be "k" fissions after the next mean generation time (Λ). The result is that the number of fission reactions increases exponentially, according to the equation ${\displaystyle e^{(k-1)t/\Lambda }}$, where t is the elapsed time. Nuclear weapons are designed to operate under this state. There are two subdivisions of supercriticality: prompt and delayed.

When describing kinetics and dynamics of nuclear reactors, and also in the practice of reactor operation, the concept of reactivity is used, which characterizes the deflection of reactor from the critical state: ρ = (k − 1)/k. InHour (from inverse of an hour, sometimes abbreviated ih or inhr) is a unit of reactivity of a nuclear reactor.

In a nuclear reactor, k will actually oscillate from slightly less than 1 to slightly more than 1, due primarily to thermal effects (as more power is produced, the fuel rods warm and thus expand, lowering their capture ratio, and thus driving k lower). This leaves the average value of k at exactly 1. Delayed neutrons play an important role in the timing of these oscillations.

In an infinite medium, the multiplication factor may be described by the four factor formula; in a non-infinite medium, the multiplication factor may be described by the six factor formula.

Prompt and delayed supercriticality

Not all neutrons are emitted as a direct product of fission; some are instead due to the radioactive decay of some of the fission fragments. The neutrons that occur directly from fission are called "prompt neutrons," and the ones that are a result of radioactive decay of fission fragments are called "delayed neutrons". The fraction of neutrons that are delayed is called β, and this fraction is typically less than 1% of all the neutrons in the chain reaction.

The delayed neutrons allow a nuclear reactor to respond several orders of magnitude more slowly than just prompt neutrons would alone. Without delayed neutrons, changes in reaction rates in nuclear reactors would occur at speeds that are too fast for humans to control.

The region of supercriticality between k = 1 and k = 1/(1 − β) is known as delayed supercriticality (or delayed criticality). It is in this region that all nuclear power reactors operate. The region of supercriticality for k > 1/(1 − β) is known as prompt supercriticality (or prompt criticality), which is the region in which nuclear weapons operate.

The change in k needed to go from critical to prompt critical is defined as a dollar.

Nuclear weapons application of neutron multiplication

Nuclear fission weapons require a mass of fissile fuel that is prompt supercritical.

For a given mass of fissile material the value of k can be increased by increasing the density. Since the probability per distance travelled for a neutron to collide with a nucleus is proportional to the material density, increasing the density of a fissile material can increase k. This concept is utilized in the implosion method for nuclear weapons. In these devices, the nuclear chain reaction begins after increasing the density of the fissile material with a conventional explosive.

In the gun-type fission weapon, two subcritical pieces of fuel are rapidly brought together. The value of k for a combination of two masses is always greater than that of its components. The magnitude of the difference depends on distance, as well as the physical orientation.

The value of k can also be increased by using a neutron reflector surrounding the fissile material

Once the mass of fuel is prompt supercritical, the power increases exponentially. However, the exponential power increase cannot continue for long since k decreases when the amount of fission material that is left decreases (i.e. it is consumed by fissions). Also, the geometry and density are expected to change during detonation since the remaining fission material is torn apart from the explosion.

Predetonation

If two pieces of subcritical material are not brought together fast enough, nuclear predetonation can occur, whereby a smaller explosion than expected will blow the bulk of the material apart. See Fizzle (nuclear test)

Detonation of a nuclear weapon involves bringing fissile material into its optimal supercritical state very rapidly. During part of this process, the assembly is supercritical, but not yet in an optimal state for a chain reaction. Free neutrons, in particular from spontaneous fissions, can cause the device to undergo a preliminary chain reaction that destroys the fissile material before it is ready to produce a large explosion, which is known as predetonation.

To keep the probability of predetonation low, the duration of the non-optimal assembly period is minimized and fissile and other materials are used that have low spontaneous fission rates. In fact, the combination of materials has to be such that it is unlikely that there is even a single spontaneous fission during the period of supercritical assembly. In particular, the gun method cannot be used with plutonium.

Nuclear power plants and control of chain reactions

Chain reactions naturally give rise to reaction rates that grow (or shrink) exponentially, whereas a nuclear power reactor needs to be able to hold the reaction rate reasonably constant. To maintain this control, the chain reaction criticality must have a slow enough time scale to permit intervention by additional effects (e.g., mechanical control rods or thermal expansion). Consequently, all nuclear power reactors (even fast-neutron reactors) rely on delayed neutrons for their criticality. An operating nuclear power reactor fluctuates between being slightly subcritical and slightly delayed-supercritical, but must always remain below prompt-critical.

It is impossible for a nuclear power plant to undergo a nuclear chain reaction that results in an explosion of power comparable with a nuclear weapon, but even low-powered explosions due to uncontrolled chain reactions (that would be considered "fizzles" in a bomb) may still cause considerable damage and meltdown in a reactor. For example, the Chernobyl disaster involved a runaway chain reaction but the result was a low-powered steam explosion from the relatively small release of heat, as compared with a bomb. However, the reactor complex was destroyed by the heat, as well as by ordinary burning of the graphite exposed to air. Such steam explosions would be typical of the very diffuse assembly of materials in a nuclear reactor, even under the worst conditions.

In addition, other steps can be taken for safety. For example, power plants licensed in the United States require a negative void coefficient of reactivity (this means that if water is removed from the reactor core, the nuclear reaction will tend to shut down, not increase). This eliminates the possibility of the type of accident that occurred at Chernobyl (which was due to a positive void coefficient). However, nuclear reactors are still capable of causing smaller explosions even after complete shutdown, such as was the case of the Fukushima Daiichi nuclear disaster. In such cases, residual decay heat from the core may cause high temperatures if there is loss of coolant flow, even a day after the chain reaction has been shut down (see SCRAM). This may cause a chemical reaction between water and fuel that produces hydrogen gas, which can explode after mixing with air, with severe contamination consequences, since fuel rod material may still be exposed to the atmosphere from this process. However, such explosions do not happen during a chain reaction, but rather as a result of energy from radioactive beta decay, after the fission chain reaction has been stopped.

Greenhouse and icehouse Earth

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Greenhouse_and_icehouse_Earth 

 

Timeline of the five known great glaciations, shown in blue. The periods in between depict greenhouse conditions.

Throughout the history of the Earth, the planet's climate has been fluctuating between two dominant climate states: the greenhouse Earth and the icehouse Earth. These two climate states last for millions of years and should not be confused with glacial and interglacial periods, which occur only during an icehouse period and tend to last less than 1 million years. There are five known great glaciations in Earth's climate history; the main factors involved in changes of the paleoclimate are believed to be the concentration of atmospheric carbon dioxide, changes in the Earth's orbit, long-term changes in the solar constant, and oceanic and orogenic changes due to tectonic plate dynamics. Greenhouse and icehouse periods have profoundly shaped the evolution of life on Earth.

Greenhouse Earth

Overview of greenhouse Earth

A "greenhouse Earth" is a period in which there are no continental glaciers whatsoever on the planet, the levels of carbon dioxide and other greenhouse gases (such as water vapor and methane) are high, and sea surface temperatures (SSTs) range from 28 °C (82.4 °F) in the tropics to 0 °C (32 °F) in the polar regions. The Earth has been in a greenhouse state for about 85% of its history.

This state should not be confused with a hypothetical hothouse earth, which is an irreversible tipping point corresponding to the ongoing runaway greenhouse effect on Venus. The IPCC states that "a 'runaway greenhouse effect'—analogous to [that of] Venus—appears to have virtually no chance of being induced by anthropogenic activities."

Causes of greenhouse Earth

There are several theories as to how a greenhouse Earth can come about. The geological record shows CO₂ and other greenhouse gases are abundant during this time. Tectonic movements were extremely active during the more well-known greenhouse ages (such as 368 million years ago in the Paleozoic Era). Because of continental rifting (continental plates moving away from each other) volcanic activity became more prominent, producing more CO₂ and heating up the Earth's atmosphere. Earth is more commonly placed in a greenhouse state throughout the epochs, and the Earth has been in this state for approximately 80% of the past 500 million years, which makes understanding the direct causes somewhat difficult.

Icehouse Earth

Overview of icehouse Earth

An "icehouse Earth" is a period in which the Earth has at least two ice sheets, Arctic and Antarctic (on both poles); these sheets wax and wane throughout shorter times known as glacial periods (with other ice sheets in addition to the 2 polar ones) and interglacial periods (without). During an icehouse Earth, greenhouse gases tend to be less abundant, and temperatures tend to be cooler globally. The Earth is currently in an icehouse stage, that started 34 Ma with the ongoing Late Cenozoic Ice Age. Inside it, the last glacial, Würm, recently ended (110 to 12 ka), still has remnants of non-polar ice sheets (Alps, Himalaya, Patagonia). It will likely be soon followed by another interglacial, similar to the last one, Eemian (130 to 115 ka), when there were forests in North Cape and hippopotamus in the rivers Rhine and Thames. Then glacials and interglacials, of similar lengths as the recent ones, will continue to alternate until the end of the 2 pole ice sheets, meaning the end of the current Icehouse and the start of the next Greenhouse.

Causes of icehouse Earth

The causes of an icehouse state are much debated, because not much is really known about the transitions between greenhouse and icehouse climates and what could make the climate change. One important aspect is clearly the decline of CO₂ in the atmosphere, possibly due to low volcanic activity.

Other important issues are the movement of the tectonic plates and the opening and closing of oceanic gateways. These seem to play a crucial part in icehouse Earths because they can bring cool waters from very deep water circulations that could assist in creating ice sheets or thermal isolation of areas. Examples of this occurring are the opening of the Tasmanian gateway 36.5 million years ago that separated Australia and Antarctica and which is believed to have set off the Cenozoic icehouse, and the creation of the Drake Passage 32.8 million years ago by the separation of South America and Antarctica, though it was believed by other scientists that this did not come into effect until around 23 million years ago. The closing of the Isthmus of Panama and the Indonesian seaway approximately 3 or 4 million years ago may have been a major cause for our current icehouse state. For the icehouse climate, tectonic activity also creates mountains, which are produced by one continental plate colliding with another one and continuing forward. The revealed fresh soils act as scrubbers of carbon dioxide, which can significantly affect the amount of this greenhouse gas in the atmosphere. An example of this is the collision between the Indian subcontinent and the Asian continent, which created the Himalayan Mountains about 50 million years ago.

Glacials and interglacials

Within icehouse states, there are "glacial" and "interglacial" periods that cause ice sheets to build up or retreat. The causes for these glacial and interglacial periods are mainly variations in the movement of the earth around the Sun. The astronomical components, discovered by the Serbian geophysicist Milutin Milanković and now known as Milankovitch cycles, include the axial tilt of the Earth, the orbital eccentricity (or shape of the orbit) and the precession (or wobble) of the Earth's rotation. The tilt of the axis tends to fluctuate between 21.5° to 24.5° and back every 41,000 years on the vertical axis. This change actually affects the seasonality upon the earth, since more or less solar radiation hits certain areas of the planet more often on a higher tilt, while less of a tilt would create a more even set of seasons worldwide. These changes can be seen in ice cores, which also contain information showing that during glacial times (at the maximum extension of the ice sheets), the atmosphere had lower levels of carbon dioxide. This may be caused by the increase or redistribution of the acid/base balance with bicarbonate and carbonate ions that deals with alkalinity. During an icehouse, only 20% of the time is spent in interglacial, or warmer times. Model simulations suggest that the current interglacial climate state will continue for at least another 100,000 years, due to CO
2 emissions - including complete deglaciation of the Northern Hemisphere.

Snowball earth

A "snowball earth" is the complete opposite of greenhouse Earth, in which the earth's surface is completely frozen over; however, a snowball earth technically does not have continental ice sheets like during the icehouse state. "The Great Infra-Cambrian Ice Age" has been claimed to be the host of such a world, and in 1964, the scientist W. Brian Harland brought forth his discovery of indications of glaciers in low latitudes (Harland and Rudwick). This became a problem for Harland because of the thought of the "Runaway Snowball Paradox" (a kind of Snowball effect) that, once the earth enters the route of becoming a snowball earth, it would never be able to leave that state. However, in 1992 Joseph Kirschvink [de] brought up a solution to the paradox. Since the continents at this time were huddled at the low and mid-latitudes, there was less ocean water available to absorb the higher amount solar energy hitting the tropics, and at the same time, increased rainfall due to more land mass exposed to higher solar energy might have caused chemical weathering (removing CO₂ from atmosphere). Both these conditions might have caused a substantial drop in CO₂ atmospheric levels resulting in cooling temperatures, increasing ice albedo (ice reflectivity of incoming solar radiation), further increasing global cooling (a positive feedback). This might have been the mechanism of entering Snowball Earth state. Kirschvink explained that the way to get out of Snowball Earth state could be connected again to carbon dioxide. A possible explanation is that during Snowball Earth, volcanic activity would not halt, accumulating atmospheric CO₂. At the same time, global ice cover would prevent chemical weathering (in particular hydrolysis), responsible for removal of CO₂ from the atmosphere. CO₂ was therefore accumulating in the atmosphere. Once the atmosphere accumulation of CO₂ would reach a threshold, temperature would rise enough for ice sheets to start melting. This would in turn reduce ice albedo effect which would in turn further reduce ice cover, exiting Snowball Earth state. At the end of Snowball Earth, before reinstating the equilibrium "thermostat" between volcanic activity and the by then slowly resuming chemical weathering, CO₂ in the atmosphere had accumulated enough to cause temperatures to peak to as much as 60° Celsius, before eventually settling down. Around the same geologic period of Snowball Earth (debated if caused by Snowball Earth or being the cause of Snowball Earth) the Great Oxygenation Event (GOE) was occurring. The event known as the Cambrian Explosion followed, which produced the beginnings of multi-cellular life. However some biologists claim that a complete snowball Earth could not have happened since photosynthetic life would not have survived underneath many meters of ice without sunlight. However, sunlight has been observed to penetrate meters of ice in Antarctica. Most scientists today believe that a "hard" Snowball Earth, one completely covered by ice, is probably impossible. However, a "slushball earth", with points of opening near the equator, is possible.

Recent studies may have again complicated the idea of a snowball earth. In October 2011, a team of French researchers announced that the carbon dioxide during the last speculated "snowball earth" may have been lower than originally stated, which provides a challenge in finding out how Earth was able to get out of its state and if it were a snowball or slushball.

Transitions

Causes

The Eocene, which occurred between 53 and 49 million years ago, was the Earth's warmest temperature period for 100 million years. However, this "super-greenhouse" eventually became an icehouse by the late Eocene. It is believed that the decline of CO₂ caused this change, though it is possible that positive feedbacks contributed to the cooling.

The best record we have for a transition from an icehouse to greenhouse period where that plant life existed during the Permian period that occurred around 300 million years ago. 40 million years ago, a major transition took place, causing the Earth to change from a moist, icy planet where rainforests covered the tropics, into a hot, dry and windy location where little could survive. Professor Isabel P. Montañez of University of California, Davis, who has researched this time period, found the climate to be "highly unstable" and "marked by dips and rises in carbon dioxide".

Impacts

The Eocene-Oligocene transition, the latest transition, occurred approximately 34 million years ago, resulting in a rapid global temperature decrease, the glaciation of Antarctica and a series of biotic extinction events. The most dramatic species turnover event associated with this time period is the Grande Coupure, a period which saw the replacement of European tree-dwelling and leaf-eating mammal species by migratory species from Asia.

Research

The science of paleoclimatology attempts to understand the history of greenhouse and icehouse conditions over geological time. Through the study of ice cores, dendrochronology, ocean and lake sediments (varve), palynology, (paleobotany), isotope analysis (such as Radiometric dating and stable isotope analysis), and other climate proxies, scientists can create models of Earth's past energy budgets and resulting climate. One study has shown that atmospheric carbon dioxide levels during the Permian age rocked back and forth between 250 parts per million (which is close to present-day levels) up to 2,000 parts per million. Studies on lake sediments suggest that the "Hothouse" or "super-Greenhouse" Eocene was in a "permanent El Nino state" after the 10 °C warming of the deep ocean and high latitude surface temperatures shut down the Pacific Ocean's El Nino-Southern Oscillation. A theory was suggested for the Paleocene–Eocene Thermal Maximum on the sudden decrease of the carbon isotopic composition of the global inorganic carbon pool by 2.5 parts per million. A hypothesis posed for this drop of isotopes was the increase of methane hydrates, the trigger for which remains a mystery. This increase of methane in the atmosphere, which happens to be a potent, but short-lived, greenhouse gas, increased the global temperatures by 6 °C with the assistance of the less potent carbon dioxide.

List of Icehouse and Greenhouse Periods

• A greenhouse period ran from 4.6 to 2.4 billion years ago.
• Huronian Glaciation – an icehouse period that ran from 2.4 billion years ago to 2.1 billion years ago
• A greenhouse period ran from 2.1 billion to 720 million years ago.
• Cryogenian – an icehouse period that ran from 720 to 635 million years ago, at times the entire Earth was frozen over
• A greenhouse period ran from 635 million years ago to 450 million years ago.
• Andean-Saharan glaciation – an icehouse period that ran from 450 to 420 million years ago
• A greenhouse period ran from 420 million years ago to 360 million years ago.
• Late Paleozoic Ice Age – an icehouse period that ran from 360 to 260 million years ago
• A greenhouse period ran from 260 million years ago to 33.9 million years ago
• Late Cenozoic Ice Age – the current icehouse period which began 33.9 million years ago

Modern conditions

Currently, the Earth is in an icehouse climate state. About 34 million years ago, ice sheets began to form in Antarctica; the ice sheets in the Arctic did not start forming until 2 million years ago. Some processes that may have led to our current icehouse may be connected to the development of the Himalayan Mountains and the opening of the Drake Passage between South America and Antarctica but climate model simulations suggest that the early opening of the Drake Passage played only a limited role, while the later constriction of the Tethys and Central American Seaways is more important in explaining the observed Cenozoic cooling. Scientists have been attempting to compare the past transitions between icehouse and greenhouse, and vice versa, to understand where our planet is now heading.

Without the human influence on the greenhouse gas concentration, the Earth would be heading toward a glacial period. Predicted changes in orbital forcing suggest that in absence of human-made global warming, the next glacial period would begin at least 50,000 years from now, but due to the ongoing anthropogenic greenhouse gas emissions, the Earth is heading towards a greenhouse Earth period. Permanent ice is actually a rare phenomenon in the history of the Earth, occurring only in coincidence with the icehouse effect, which has affected about 20% of Earth's history.