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120-449: The name refers to the direction of the current in the devices, the Z-axis on a Cartesian three-dimensional graph . Any machine that causes a pinch effect due to current running in that direction is correctly referred to as a Z-pinch system, and this encompasses a wide variety of devices used for an equally wide variety of purposes. Early uses focused on fusion research in donut-shaped tubes with

240-429: A Cartesian coordinate system ( UK : / k ɑːr ˈ t iː zj ə n / , US : / k ɑːr ˈ t iː ʒ ə n / ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates , which are the signed distances to the point from two fixed perpendicular oriented lines , called coordinate lines , coordinate axes or just axes (plural of axis ) of

360-552: A chemical element that differ only in neutron number are called isotopes . For example, carbon , with atomic number 6, has an abundant isotope carbon-12 with 6 neutrons and a rare isotope carbon-13 with 7 neutrons. Some elements occur in nature with only one stable isotope , such as fluorine . Other elements occur with many stable isotopes, such as tin with ten stable isotopes, or with no stable isotope, such as technetium . The properties of an atomic nucleus depend on both atomic and neutron numbers. With their positive charge,

480-425: A fermion with intrinsic angular momentum equal to ⁠ 1 / 2 ⁠   ħ , where ħ is the reduced Planck constant . For many years after the discovery of the neutron, its exact spin was ambiguous. Although it was assumed to be a spin  ⁠ 1 / 2 ⁠ Dirac particle , the possibility that the neutron was a spin  ⁠ 3 / 2 ⁠ particle lingered. The interactions of

600-408: A nuclear chain reaction . These events and findings led to the first self-sustaining nuclear reactor ( Chicago Pile-1 , 1942) and the first nuclear weapon ( Trinity , 1945). Dedicated neutron sources like neutron generators , research reactors and spallation sources produce free neutrons for use in irradiation and in neutron scattering experiments. A free neutron spontaneously decays to

720-516: A , b ) to the Cartesian coordinates of every point in the set. That is, if the original coordinates of a point are ( x , y ) , after the translation they will be ( x ′ , y ′ ) = ( x + a , y + b ) . {\displaystyle (x',y')=(x+a,y+b).} To rotate a figure counterclockwise around the origin by some angle θ {\displaystyle \theta }

840-401: A bottle, while the "beam" method employs energetic neutrons in a particle beam. The measurements by the two methods have not been converging with time. The lifetime from the bottle method is presently 877.75 s which is 10 seconds below the value from the beam method of 887.7 s A small fraction (about one per thousand) of free neutrons decay with the same products, but add an extra particle in

960-606: A burned propellant mass of 350 tonnes. Although it remained relatively unknown for years, Soviet scientists used the pinch concept to develop the tokamak device. Unlike the stabilized pinch devices in the US and UK, the tokamak used considerably more energy in the stabilizing magnets, and much less in the plasma current. This reduced the instabilities due to the large currents in the plasma, and led to great improvements in stability. The results were so dramatic that other researchers were skeptical when they were first announced in 1968. Members of

1080-456: A cascade known as a nuclear chain reaction . For a given mass of fissile material, such nuclear reactions release energy that is approximately ten million times that from an equivalent mass of a conventional chemical explosive . Ultimately, the ability of the nuclear force to store energy arising from the electromagnetic repulsion of nuclear components is the basis for most of the energy that makes nuclear reactors or bombs possible; most of

1200-437: A common point (the origin ), and are pair-wise perpendicular; an orientation for each axis; and a single unit of length for all three axes. As in the two-dimensional case, each axis becomes a number line. For any point P of space, one considers a plane through P perpendicular to each coordinate axis, and interprets the point where that plane cuts the axis as a number. The Cartesian coordinates of P are those three numbers, in

1320-544: A deuteron is formed by a proton capturing a neutron (this is exothermic and happens with zero-energy neutrons). The small recoil kinetic energy ( E r d {\displaystyle E_{rd}} ) of the deuteron (about 0.06% of the total energy) must also be accounted for. The energy of the gamma ray can be measured to high precision by X-ray diffraction techniques, as was first done by Bell and Elliot in 1948. The best modern (1986) values for neutron mass by this technique are provided by Greene, et al. These give

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1440-449: A diagram ( 3D projection or 2D perspective drawing ) shows the x - and y -axis horizontally and vertically, respectively, then the z -axis should be shown pointing "out of the page" towards the viewer or camera. In such a 2D diagram of a 3D coordinate system, the z -axis would appear as a line or ray pointing down and to the left or down and to the right, depending on the presumed viewer or camera perspective . In any diagram or display,

1560-407: A division of space into eight regions or octants , according to the signs of the coordinates of the points. The convention used for naming a specific octant is to list its signs; for example, (+ + +) or (− + −) . The generalization of the quadrant and octant to an arbitrary number of dimensions is the orthant , and a similar naming system applies. The Euclidean distance between two points of

1680-650: A fusion company, Zap Energy , Inc., a spin-off from the University of Washington , and funded by strategic and financial investors and grants from the Advanced Research Projects Agency – Energy ( ARPA-E ). Flow stabilized plasma remained stable 5,000 times longer than a static plasma. A mix of 20% deuterium and 80% hydrogen by pressure, produced neutron emissions lasting approximately 5 μs with pinch currents of approximately 200 kA during an approximately 16 μs period of plasma quiescence. Average neutron yield

1800-456: A magnetic field experiences a force. One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, the wires will be pulled toward each other. In a Z-pinch machine the wires are replaced by a plasma , which can be thought of as many current-carrying wires. When a current is run through the plasma, the particles in the plasma are pulled toward each other by

1920-484: A magnetic field to separate the neutron spin states. They recorded two such spin states, consistent with a spin  ⁠ 1 / 2 ⁠ particle. As a fermion, the neutron is subject to the Pauli exclusion principle ; two neutrons cannot have the same quantum numbers. This is the source of the degeneracy pressure which counteracts gravity in neutron stars and prevents them from forming black holes. Even though

2040-417: A mass spectrometer, the mass of a neutron can be deduced by subtracting proton mass from deuteron mass, with the difference being the mass of the neutron plus the binding energy of deuterium (expressed as a positive emitted energy). The latter can be directly measured by measuring the energy ( B d {\displaystyle B_{d}} ) of the single 2.224 MeV gamma photon emitted when

2160-416: A mean-square radius of about 0.8 × 10   m , or 0.8  fm , and it is a spin-½ fermion . The neutron has no measurable electric charge. With its positive electric charge, the proton is directly influenced by electric fields , whereas the neutron is unaffected by electric fields. The neutron has a magnetic moment , however, so it is influenced by magnetic fields . The specific properties of

2280-404: A neutron by some heavy nuclides (such as uranium-235 ) can cause the nuclide to become unstable and break into lighter nuclides and additional neutrons. The positively charged light nuclides, or "fission fragments", then repel, releasing electromagnetic potential energy . If this reaction occurs within a mass of fissile material , the additional neutrons cause additional fission events, inducing

2400-445: A neutron mass of: The value for the neutron mass in MeV is less accurately known, due to less accuracy in the known conversion of Da to MeV/ c : Another method to determine the mass of a neutron starts from the beta decay of the neutron, when the momenta of the resulting proton and electron are measured. The neutron is a spin  ⁠ 1 / 2 ⁠ particle, that is, it is

2520-536: A nucleon. The discrepancy stems from the complexity of the Standard Model for nucleons, where most of their mass originates in the gluon fields, virtual particles, and their associated energy that are essential aspects of the strong force . Furthermore, the complex system of quarks and gluons that constitute a neutron requires a relativistic treatment. But the nucleon magnetic moment has been successfully computed numerically from first principles , including all of

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2640-489: A nucleus. The observed properties of atoms and molecules were inconsistent with the nuclear spin expected from the proton–electron hypothesis. Protons and electrons both carry an intrinsic spin of ⁠ 1 / 2 ⁠ ħ , and the isotopes of the same species were found to have either integer or fractional spin. By the hypothesis, isotopes would be composed of the same number of protons, but differing numbers of neutral bound proton+electron "particles". This physical picture

2760-517: A pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649 by Frans van Schooten and his students. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes's work. The development of the Cartesian coordinate system would play a fundamental role in the development of the calculus by Isaac Newton and Gottfried Wilhelm Leibniz . The two-coordinate description of

2880-417: A pair of protons, one with spin up, another with spin down. When all available proton states are filled, the Pauli exclusion principle disallows the decay of a neutron to a proton. The situation is similar to electrons of an atom, where electrons that occupy distinct atomic orbitals are prevented by the exclusion principle from decaying to lower, already-occupied, energy states. The stability of matter

3000-401: A point are usually written in parentheses and separated by commas, as in (10, 5) or (3, 5, 7) . The origin is often labelled with the capital letter O . In analytic geometry, unknown or generic coordinates are often denoted by the letters ( x , y ) in the plane, and ( x , y , z ) in three-dimensional space. This custom comes from a convention of algebra, which uses letters near the end of

3120-423: A proton, an electron , and an antineutrino , with a mean lifetime of about 15 minutes. Free neutrons do not directly ionize atoms, but they do indirectly cause ionizing radiation , so they can be a biological hazard, depending on dose. A small natural "neutron background" flux of free neutrons exists on Earth, caused by cosmic ray showers , and by the natural radioactivity of spontaneously fissionable elements in

3240-422: A real variable , for example translation of the line corresponds to addition, and scaling the line corresponds to multiplication. Any two Cartesian coordinate systems on the line can be related to each-other by a linear function (function of the form x ↦ a x + b {\displaystyle x\mapsto ax+b} ) taking a specific point's coordinate in one system to its coordinate in

3360-476: A series of experiments that showed that the new radiation consisted of uncharged particles with about the same mass as the proton. These properties matched Rutherford's hypothesized neutron. Chadwick won the 1935 Nobel Prize in Physics for this discovery. Models for an atomic nucleus consisting of protons and neutrons were quickly developed by Werner Heisenberg and others. The proton–neutron model explained

3480-404: A simple nonrelativistic , quantum mechanical wavefunction for baryons composed of three quarks. A straightforward calculation gives fairly accurate estimates for the magnetic moments of neutrons, protons, and other baryons. For a neutron, the result of this calculation is that the magnetic moment of the neutron is given by μ n = 4/3 μ d − 1/3 μ u , where μ d and μ u are

3600-503: A single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For any point P , a line is drawn through P perpendicular to each axis, and the position where it meets the axis is interpreted as a number. The two numbers, in that chosen order, are the Cartesian coordinates of P . The reverse construction allows one to determine

3720-537: Is a subatomic particle , symbol n or n , that has no electric charge, and a mass slightly greater than that of a proton . Protons and neutrons constitute the nuclei of atoms . Since protons and neutrons behave similarly within the nucleus, they are both referred to as nucleons . Nucleons have a mass of approximately one atomic mass unit, or dalton (symbol: Da). Their properties and interactions are described by nuclear physics . Protons and neutrons are not elementary particles ; each

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3840-413: Is a consequence of these constraints. The decay of a neutron within a nuclide is illustrated by the decay of the carbon isotope carbon-14 , which has 6 protons and 8 neutrons. With its excess of neutrons, this isotope decays by beta decay to nitrogen-14 (7 protons, 7 neutrons), a process with a half-life of about 5,730 years . Nitrogen-14 is stable. "Beta decay" reactions can also occur by

3960-465: Is called a Cartesian plane . In a Cartesian plane, one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at (0, 0) and (1, 1) ), the unit hyperbola , and so on. The two axes divide the plane into four right angles , called quadrants . The quadrants may be named or numbered in various ways, but

4080-411: Is composed of three quarks . The chemical properties of an atom are mostly determined by the configuration of electrons that orbit the atom's heavy nucleus. The electron configuration is determined by the charge of the nucleus, which is determined by the number of protons, or atomic number . The number of neutrons is the neutron number . Neutrons do not affect the electron configuration. Atoms of

4200-566: Is equivalent to replacing every point with coordinates ( x , y ) by the point with coordinates ( x' , y' ), where x ′ = x cos ⁡ θ − y sin ⁡ θ y ′ = x sin ⁡ θ + y cos ⁡ θ . {\displaystyle {\begin{aligned}x'&=x\cos \theta -y\sin \theta \\y'&=x\sin \theta +y\cos \theta .\end{aligned}}} Thus: Neutron The neutron

4320-403: Is essential to the production of nuclear power. In the decade after the neutron was discovered by James Chadwick in 1932, neutrons were used to induce many different types of nuclear transmutations . With the discovery of nuclear fission in 1938, it was quickly realized that, if a fission event produced neutrons, each of these neutrons might cause further fission events, in a cascade known as

4440-549: Is fairly good, about that of copper , the energy stored in the power source is quickly depleted by running through the plasma. Z-pinch devices are inherently pulsed in nature. Pinch devices were among the earliest efforts in fusion power. Research began in the UK in the immediate post-war era, but a lack of interest led to little development until the 1950s. The announcement of the Huemul Project in early 1951 led to fusion efforts around

4560-448: Is for one of the neutron's quarks to change flavour (through a Cabibbo–Kobayashi–Maskawa matrix ) via the weak interaction . The decay of one of the neutron's down quarks into a lighter up quark can be achieved by the emission of a W boson . By this process, the Standard Model description of beta decay, the neutron decays into a proton (which contains one down and two up quarks), an electron, and an electron antineutrino . The decay of

4680-508: Is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see affine plane ). The Cartesian coordinates of

4800-420: Is the nuclear magneton . The neutron's magnetic moment has a negative value, because its orientation is opposite to the neutron's spin. The magnetic moment of the neutron is an indication of its quark substructure and internal charge distribution. In the quark model for hadrons , the neutron is composed of one up quark (charge +2/3  e ) and two down quarks (charge −1/3  e ). The magnetic moment of

4920-879: Is the Cartesian version of Pythagoras's theorem . In three-dimensional space, the distance between points ( x 1 , y 1 , z 1 ) {\displaystyle (x_{1},y_{1},z_{1})} and ( x 2 , y 2 , z 2 ) {\displaystyle (x_{2},y_{2},z_{2})} is d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 , {\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}},} which can be obtained by two consecutive applications of Pythagoras' theorem. The Euclidean transformations or Euclidean motions are

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5040-551: Is the concept of the graph of a function . Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy , physics , engineering and many more. They are the most common coordinate system used in computer graphics , computer-aided geometric design and other geometry-related data processing . The adjective Cartesian refers to the French mathematician and philosopher René Descartes , who published this idea in 1637 while he

5160-454: Is the set of all real numbers. In the same way, the points in any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers; that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} . The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate

5280-501: Is usually named after the coordinate which is measured along it; so one says the x-axis , the y-axis , the t-axis , etc. Another common convention for coordinate naming is to use subscripts, as ( x 1 , x 2 , ..., x n ) for the n coordinates in an n -dimensional space, especially when n is greater than 3 or unspecified. Some authors prefer the numbering ( x 0 , x 1 , ..., x n −1 ). These notations are especially advantageous in computer programming : by storing

5400-683: The Chicago Pile-1 at the University of Chicago in 1942, the first self-sustaining nuclear reactor . Just three years later the Manhattan Project was able to test the first atomic bomb , the Trinity nuclear test in July 1945. The mass of a neutron cannot be directly determined by mass spectrometry since it has no electric charge. But since the masses of a proton and of a deuteron can be measured with

5520-599: The Earth's crust . An atomic nucleus is formed by a number of protons, Z (the atomic number ), and a number of neutrons, N (the neutron number ), bound together by the nuclear force . Protons and neutrons each have a mass of approximately one dalton . The atomic number determines the chemical properties of the atom, and the neutron number determines the isotope or nuclide . The terms isotope and nuclide are often used synonymously , but they refer to chemical and nuclear properties, respectively. Isotopes are nuclides with

5640-479: The area , the perimeter and the tangent line at any point can be computed from this equation by using integrals and derivatives , in a way that can be applied to any curve. Cartesian coordinates are the foundation of analytic geometry , and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra , complex analysis , differential geometry , multivariate calculus , group theory and more. A familiar example

5760-405: The xy -plane, yz -plane, and xz -plane. In mathematics, physics, and engineering contexts, the first two axes are often defined or depicted as horizontal, with the third axis pointing up. In that case the third coordinate may be called height or altitude . The orientation is usually chosen so that the 90-degree angle from the first axis to the second axis looks counter-clockwise when seen from

5880-416: The z -coordinate is sometimes called the applicate . The words abscissa , ordinate and applicate are sometimes used to refer to coordinate axes rather than the coordinate values. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants , each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals : I (where

6000-452: The ( bijective ) mappings of points of the Euclidean plane to themselves which preserve distances between points. There are four types of these mappings (also called isometries): translations , rotations , reflections and glide reflections . Translating a set of points of the plane, preserving the distances and directions between them, is equivalent to adding a fixed pair of numbers (

6120-480: The 1920s, physicists assumed that the atomic nucleus was composed of protons and "nuclear electrons", but this raised obvious problems. It was difficult to reconcile the proton–electron model of the nucleus with the Heisenberg uncertainty relation of quantum mechanics. The Klein paradox , discovered by Oskar Klein in 1928, presented further quantum mechanical objections to the notion of an electron confined within

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6240-507: The 1944 Nobel Prize in Chemistry "for his discovery of the fission of heavy atomic nuclei". The discovery of nuclear fission would lead to the development of nuclear power and the atomic bomb by the end of World War II. It was quickly realized that, if a fission event produced neutrons, each of these neutrons might cause further fission events, in a cascade known as a nuclear chain reaction. These events and findings led Fermi to construct

6360-545: The American chemist W. D. Harkins first named the hypothetical particle a "neutron". The name derives from the Latin root for neutralis (neuter) and the Greek suffix -on (a suffix used in the names of subatomic particles, i.e. electron and proton ). References to the word neutron in connection with the atom can be found in the literature as early as 1899, however. Throughout

6480-406: The Cartesian system, commonly learn the order to read the values before cementing the x -, y -, and z -axis concepts, by starting with 2D mnemonics (for example, 'Walk along the hall then up the stairs' akin to straight across the x -axis then up vertically along the y -axis). Computer graphics and image processing , however, often use a coordinate system with the y -axis oriented downwards on

6600-399: The Lorentz force, thus the plasma contracts. The contraction is counteracted by the increasing gas pressure of the plasma. As the plasma is electrically conductive, a magnetic field nearby will induce a current in it. This provides a way to run a current into the plasma without physical contact, which is important as a plasma can rapidly erode mechanical electrodes . In practical devices this

6720-488: The Nobel Prize in Physics "for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons". In December 1938 Otto Hahn , Lise Meitner , and Fritz Strassmann discovered nuclear fission , or the fractionation of uranium nuclei into lighter elements, induced by neutron bombardment. In 1945 Hahn received

6840-457: The Z-axis running down the inside of the tube, while modern devices are generally cylindrical and used to generate high-intensity x-ray sources for the study of nuclear weapons and other roles. It is one of the first approaches to fusion power devices, along with the stellarator and magnetic mirror . The Z-pinch is an application of the Lorentz force , in which a current-carrying conductor in

6960-469: The Z-pinch effect would accelerate lithium propellant to a high speed, resulting in a specific impulse value of 19400 s and thrust of 38 kN. A magnetic nozzle would be required to convert the released energy into a useful impulse. This propulsion method could potentially reduce interplanetary travel times. For example, a mission to Mars would take about 35 days one-way with a total burn time of 20 days and

7080-406: The alphabet for unknown values (such as the coordinates of points in many geometric problems), and letters near the beginning for given quantities. These conventional names are often used in other domains, such as physics and engineering, although other letters may be used. For example, in a graph showing how a pressure varies with time , the graph coordinates may be denoted p and t . Each axis

7200-406: The beta decay process. The neutrons and protons in a nucleus form a quantum mechanical system according to the nuclear shell model . Protons and neutrons of a nuclide are organized into discrete hierarchical energy levels with unique quantum numbers . Nucleon decay within a nucleus can occur if allowed by basic energy conservation and quantum mechanical constraints. The decay products, that is,

7320-400: The capture of a lepton by the nucleon. The transformation of a proton to a neutron inside of a nucleus is possible through electron capture : A rarer reaction, inverse beta decay , involves the capture of a neutrino by a nucleon. Rarer still, positron capture by neutrons can occur in the high-temperature environment of stars. Three types of beta decay in competition are illustrated by

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7440-1371: The chosen order. The reverse construction determines the point P given its three coordinates. Alternatively, each coordinate of a point P can be taken as the distance from P to the plane defined by the other two axes, with the sign determined by the orientation of the corresponding axis. Each pair of axes defines a coordinate plane . These planes divide space into eight octants . The octants are: ( + x , + y , + z ) ( − x , + y , + z ) ( + x , − y , + z ) ( + x , + y , − z ) ( + x , − y , − z ) ( − x , + y , − z ) ( − x , − y , + z ) ( − x , − y , − z ) {\displaystyle {\begin{aligned}(+x,+y,+z)&&(-x,+y,+z)&&(+x,-y,+z)&&(+x,+y,-z)\\(+x,-y,-z)&&(-x,+y,-z)&&(-x,-y,+z)&&(-x,-y,-z)\end{aligned}}} The coordinates are usually written as three numbers (or algebraic formulas) surrounded by parentheses and separated by commas, as in (3, −2.5, 1) or ( t , u + v , π /2) . Thus,

7560-438: The common chemical element lead , Pb, has 82 protons and 126 neutrons, for example. The table of nuclides comprises all the known nuclides. Even though it is not a chemical element, the neutron is included in this table. Protons and neutrons behave almost identically under the influence of the nuclear force within the nucleus. They are therefore both referred to collectively as nucleons . The concept of isospin , in which

7680-441: The complex behavior of quarks to be subtracted out between models, and merely exploring what the effects would be of differing quark charges (or quark type). Such calculations are enough to show that the interior of neutrons is very much like that of protons, save for the difference in quark composition with a down quark in the neutron replacing an up quark in the proton. The neutron magnetic moment can be roughly computed by assuming

7800-407: The computer display. This convention developed in the 1960s (or earlier) from the way that images were originally stored in display buffers . For three-dimensional systems, a convention is to portray the xy -plane horizontally, with the z -axis added to represent height (positive up). Furthermore, there is a convention to orient the x -axis toward the viewer, biased either to the right or left. If

7920-413: The coordinates both have positive signs), II (where the abscissa is negative − and the ordinate is positive +), III (where both the abscissa and the ordinate are −), and IV (abscissa +, ordinate −). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("north-east") quadrant. Similarly, a three-dimensional Cartesian system defines

8040-455: The coordinates of a point as an array , instead of a record , the subscript can serve to index the coordinates. In mathematical illustrations of two-dimensional Cartesian systems, the first coordinate (traditionally called the abscissa ) is measured along a horizontal axis, oriented from left to right. The second coordinate (the ordinate ) is then measured along a vertical axis, usually oriented from bottom to top. Young children learning

8160-399: The current in the transformer has to be increased over time to produce the varying magnetic field. This places a limit on the product of confinement time and magnetic field, for any given source of power. In Z-pinch machines the current is generally provided from a large bank of capacitors and triggered by a spark gap , known as a Marx Bank or Marx generator . As the conductivity of plasma

8280-399: The current. A particle near the outside of the tube that wanted to kink outward would travel along these lines until it returned to the inside of the tube, where its outward-directed motion would bring it back into the centre of the plasma. Researchers in the UK started construction of ZETA in 1954. ZETA was by far the largest fusion device of its era. At the time, almost all fusion research

8400-552: The difference in mass represents the mass equivalent to nuclear binding energy, the energy which would need to be added to take the nucleus apart. The nucleus of the most common isotope of the hydrogen atom (with the chemical symbol H) is a lone proton. The nuclei of the heavy hydrogen isotopes deuterium (D or H) and tritium (T or H) contain one proton bound to one and two neutrons, respectively. All other types of atomic nuclei are composed of two or more protons and various numbers of neutrons. The most common nuclide of

8520-459: The electron fails to gain the 13.6  eV necessary energy to escape the proton (the ionization energy of hydrogen ), and therefore simply remains bound to it, forming a neutral hydrogen atom (one of the "two bodies"). In this type of free neutron decay, almost all of the neutron decay energy is carried off by the antineutrino (the other "body"). (The hydrogen atom recoils with a speed of only about (decay energy)/(hydrogen rest energy) times

8640-405: The emitted particles, carry away the energy excess as a nucleon falls from one quantum state to one with less energy, while the neutron (or proton) changes to a proton (or neutron). For a neutron to decay, the resulting proton requires an available state at lower energy than the initial neutron state. In stable nuclei the possible lower energy states are all filled, meaning each state is occupied by

8760-593: The energy released from fission is the kinetic energy of the fission fragments. Neutrons and protons within a nucleus behave similarly and can exchange their identities by similar reactions. These reactions are a form of radioactive decay known as beta decay . Beta decay, in which neutrons decay to protons, or vice versa, is governed by the weak force , and it requires the emission or absorption of electrons and neutrinos, or their antiparticles. The neutron and proton decay reactions are: where p , e , and ν e denote

8880-425: The expression of problems of geometry in terms of algebra and calculus . Using the Cartesian coordinate system, geometric shapes (such as curves ) can be described by equations involving the coordinates of points of the shape. For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x + y = 4 ;

9000-509: The first successful step on the path to commercial fusion energy. However, further study soon demonstrated that the measurements were misleading, and none of the machines were near fusion levels. Interest in pinch devices faded, although ZETA and its cousin Sceptre served for many years as experimental devices. A concept of Z-pinch fusion propulsion system was developed through collaboration between NASA and private companies. The energy released by

9120-445: The form of an emitted gamma ray: Called a "radiative decay mode" of the neutron, the gamma ray may be thought of as resulting from an "internal bremsstrahlung " that arises from the electromagnetic interaction of the emitted beta particle with the proton. A smaller fraction (about four per million) of free neutrons decay in so-called "two-body (neutron) decays", in which a proton, electron and antineutrino are produced as usual, but

9240-400: The line can be chosen as a unit, with the orientation indicating the correspondence between directions along the line and positive or negative numbers. Each point corresponds to its signed distance from the origin (a number with an absolute value equal to the distance and a + or − sign chosen based on direction). A geometric transformation of the line can be represented by a function of

9360-486: The line. There are two degrees of freedom in the choice of Cartesian coordinate system for a line, which can be specified by choosing two distinct points along the line and assigning them to two distinct real numbers (most commonly zero and one). Other points can then be uniquely assigned to numbers by linear interpolation . Equivalently, one point can be assigned to a specific real number, for instance an origin point corresponding to zero, and an oriented length along

9480-437: The magnetic moments for the down and up quarks, respectively. This result combines the intrinsic magnetic moments of the quarks with their orbital magnetic moments, and assumes the three quarks are in a particular, dominant quantum state. The results of this calculation are encouraging, but the masses of the up or down quarks were assumed to be 1/3 the mass of a nucleon. The masses of the quarks are actually only about 1% that of

9600-406: The neutron and its magnetic moment both indicate that the neutron is a composite , rather than elementary , particle. The quarks of the neutron are held together by the strong force , mediated by gluons . The nuclear force results from secondary effects of the more fundamental strong force . The only possible decay mode for the neutron that obeys the conservation law for the baryon number

9720-401: The neutron and its properties is central to the extraordinary developments in atomic physics that occurred in the first half of the 20th century, leading ultimately to the atomic bomb in 1945. In the 1911 Rutherford model , the atom consisted of a small positively charged massive nucleus surrounded by a much larger cloud of negatively charged electrons. In 1920, Ernest Rutherford suggested that

9840-456: The neutron are described below in the Intrinsic properties section . Outside the nucleus, free neutrons undergo beta decay with a mean lifetime of about 14 minutes, 38 seconds, corresponding to a half-life of about 10 minutes, 11 s. The mass of the neutron is greater than that of the proton by 1.293 32   MeV/ c , hence the neutron's mass provides energy sufficient for the creation of

9960-401: The neutron can be modeled as a sum of the magnetic moments of the constituent quarks. The calculation assumes that the quarks behave like point-like Dirac particles, each having their own magnetic moment. Simplistically, the magnetic moment of the neutron can be viewed as resulting from the vector sum of the three quark magnetic moments, plus the orbital magnetic moments caused by the movement of

10080-434: The neutron is a neutral particle, the magnetic moment of a neutron is not zero. The neutron is not affected by electric fields, but it is affected by magnetic fields. The value for the neutron's magnetic moment was first directly measured by Luis Alvarez and Felix Bloch at Berkeley, California , in 1940. Alvarez and Bloch determined the magnetic moment of the neutron to be μ n = −1.93(2)  μ N , where μ N

10200-431: The neutron's magnetic moment with an external magnetic field were exploited to finally determine the spin of the neutron. In 1949, Hughes and Burgy measured neutrons reflected from a ferromagnetic mirror and found that the angular distribution of the reflections was consistent with spin  ⁠ 1 / 2 ⁠ . In 1954, Sherwood, Stephenson, and Bernstein employed neutrons in a Stern–Gerlach experiment that used

10320-431: The nucleus consisted of positive protons and neutrally charged particles, suggested to be a proton and an electron bound in some way. Electrons were assumed to reside within the nucleus because it was known that beta radiation consisted of electrons emitted from the nucleus. About the time Rutherford suggested the neutral proton-electron composite, several other publications appeared making similar suggestions, and in 1921

10440-420: The nucleus via the nuclear force , effectively moderating the repulsive forces between the protons and stabilizing the nucleus. Heavy nuclei carry a large positive charge, hence they require "extra" neutrons to be stable. While a free neutron is unstable and a free proton is stable, within nuclei neutrons are often stable and protons are sometimes unstable. When bound within a nucleus, nucleons can decay by

10560-412: The orientation of the three axes, as a whole, is arbitrary. However, the orientation of the axes relative to each other should always comply with the right-hand rule , unless specifically stated otherwise. All laws of physics and math assume this right-handedness , which ensures consistency. For 3D diagrams, the names "abscissa" and "ordinate" are rarely used for x and y , respectively. When they are,

10680-429: The origin has coordinates (0, 0, 0) , and the unit points on the three axes are (1, 0, 0) , (0, 1, 0) , and (0, 0, 1) . Standard names for the coordinates in the three axes are abscissa , ordinate and applicate . The coordinates are often denoted by the letters x , y , and z . The axes may then be referred to as the x -axis, y -axis, and z -axis, respectively. Then the coordinate planes can be referred to as

10800-446: The original particle is not composed of the product particles; rather, the product particles are created at the instant of the reaction. "Free" neutrons or protons are nucleons that exist independently, free of any nucleus. The free neutron has a mass of 939 565 413 .3  eV/ c , or 939.565 4133   MeV/ c . This mass is equal to 1.674 927 471 × 10   kg , or 1.008 664 915 88   Da . The neutron has

10920-424: The other system. Choosing a coordinate system for each of two different lines establishes an affine map from one line to the other taking each point on one line to the point on the other line with the same coordinate. A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system ) is defined by an ordered pair of perpendicular lines (axes),

11040-456: The plane was later generalized into the concept of vector spaces . Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space. An affine line with a chosen Cartesian coordinate system is called a number line . Every point on the line has a real-number coordinate, and every real number represents some point on

11160-520: The plane with Cartesian coordinates ( x 1 , y 1 ) {\displaystyle (x_{1},y_{1})} and ( x 2 , y 2 ) {\displaystyle (x_{2},y_{2})} is d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . {\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}.} This

11280-468: The point (0, 0, 1) ; a convention that is commonly called the right-hand rule . Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers ; that is, with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} }

11400-409: The point P given its coordinates. The first and second coordinates are called the abscissa and the ordinate of P , respectively; and the point where the axes meet is called the origin of the coordinate system. The coordinates are usually written as two numbers in parentheses, in that order, separated by a comma, as in (3, −10.5) . Thus the origin has coordinates (0, 0) , and the points on

11520-430: The point to three mutually perpendicular planes. More generally, n Cartesian coordinates specify the point in an n -dimensional Euclidean space for any dimension n . These coordinates are the signed distances from the point to n mutually perpendicular fixed hyperplanes . Cartesian coordinates are named for René Descartes , whose invention of them in the 17th century revolutionized mathematics by allowing

11640-410: The positive half-axes, one unit away from the origin, have coordinates (1, 0) and (0, 1) . In mathematics, physics, and engineering, the first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards. (However, in some computer graphics contexts, the ordinate axis may be oriented downwards.) The origin is often labeled O , and

11760-400: The problems encountered on earlier devices. Stabilized pinch machines added external magnets that created a toroidal magnetic field inside the chamber. When the device was fired, this field added to the one created by the current in the plasma. The result was that the formerly straight magnetic field was twisted into a helix, which the particles followed as they traveled around the tube driven by

11880-400: The proton and neutron are viewed as two quantum states of the same particle, is used to model the interactions of nucleons by the nuclear or weak forces. Because of the strength of the nuclear force at short distances, the nuclear energy binding nucleons is many orders of magnitude greater than the electromagnetic energy binding electrons in atoms. In nuclear fission , the absorption of

12000-406: The proton to a neutron occurs similarly through the weak force. The decay of one of the proton's up quarks into a down quark can be achieved by the emission of a W boson. The proton decays into a neutron, a positron, and an electron neutrino. This reaction can only occur within an atomic nucleus which has a quantum state at lower energy available for the created neutron. The story of the discovery of

12120-409: The proton, electron and electron anti- neutrino decay products, and where n , e , and ν e denote the neutron, positron and electron neutrino decay products. The electron and positron produced in these reactions are historically known as beta particles , denoted β or β respectively, lending the name to the decay process. In these reactions,

12240-464: The proton, electron, and anti-neutrino. In the decay process, the proton, electron, and electron anti-neutrino conserve the energy, charge, and lepton number of the neutron. The electron can acquire a kinetic energy up to 0.782 ± 0.013 MeV . Still unexplained, different experimental methods for measuring the neutron's lifetime, the "bottle" and "beam" methods, produce different values for it. The "bottle" method employs "cold" neutrons trapped in

12360-521: The protons within the nucleus are repelled by the long-range electromagnetic force , but the much stronger, but short-range, nuclear force binds the nucleons closely together. Neutrons are required for the stability of nuclei, with the exception of the single-proton hydrogen nucleus. Neutrons are produced copiously in nuclear fission and fusion . They are a primary contributor to the nucleosynthesis of chemical elements within stars through fission, fusion, and neutron capture processes. The neutron

12480-519: The puzzle of nuclear spins. The origins of beta radiation were explained by Enrico Fermi in 1934 by the process of beta decay , in which the neutron decays to a proton by creating an electron and a (at the time undiscovered) neutrino. In 1935, Chadwick and his doctoral student Maurice Goldhaber reported the first accurate measurement of the mass of the neutron. By 1934, Fermi had bombarded heavier elements with neutrons to induce radioactivity in elements of high atomic number. In 1938, Fermi received

12600-470: The quadrant where all coordinates are positive is usually called the first quadrant . If the coordinates of a point are ( x , y ) , then its distances from the X -axis and from the Y -axis are | y | and | x |, respectively; where | · | denotes the absolute value of a number. A Cartesian coordinate system for a three-dimensional space consists of an ordered triplet of lines (the axes ) that go through

12720-429: The same atomic number, but different neutron number. Nuclides with the same neutron number, but different atomic number, are called isotones . The atomic mass number , A , is equal to the sum of atomic and neutron numbers. Nuclides with the same atomic mass number, but different atomic and neutron numbers, are called isobars . The mass of a nucleus is always slightly less than the sum of its proton and neutron masses:

12840-469: The single isotope copper-64 (29 protons, 35 neutrons), which has a half-life of about 12.7 hours. This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay. This particular nuclide is almost equally likely to undergo proton decay (by positron emission , 18% or by electron capture , 43%; both forming Ni ) or neutron decay (by electron emission, 39%; forming Zn ). Within

12960-429: The speed of light, or 250  km/s .) Neutrons are a necessary constituent of any atomic nucleus that contains more than one proton. As a result of their positive charges, interacting protons have a mutual electromagnetic repulsion that is stronger than their attractive nuclear interaction , so proton-only nuclei are unstable (see diproton and neutron–proton ratio ). Neutrons bind with protons and one another in

13080-411: The still-operational ZETA team were called in to verify the results. The tokamak became the most studied approach to controlled fusion. Sheared-flow stabilizing uses one or more high speed annular flowing plasma layers, surrounding a plasma filament, to stabilize the filament against kink and pinch instabilities. In 2018, a sheared-flow stabilized Z-pinch demonstrated neutron generation. It was built by

13200-402: The system. The point where the axes meet is called the origin and has (0, 0) as coordinates. The axes directions represent an orthogonal basis . The combination of origin and basis forms a coordinate frame called the Cartesian frame . Similarly, the position of any point in three-dimensional space can be specified by three Cartesian coordinates , which are the signed distances from

13320-417: The theoretical framework of the Standard Model for particle physics, a neutron comprises two down quarks with charge − ⁠ 1 / 3 ⁠ e and one up quark with charge + ⁠ 2 / 3 ⁠ e . The neutron is therefore a composite particle classified as a hadron . The neutron is also classified as a baryon , because it is composed of three valence quarks . The finite size of

13440-435: The three charged quarks within the neutron. In one of the early successes of the Standard Model, in 1964 Mirza A.B. Beg, Benjamin W. Lee , and Abraham Pais calculated the ratio of proton to neutron magnetic moments to be −3/2 (or a ratio of −1.5), which agrees with the experimental value to within 3%. The measured value for this ratio is −1.459 898 05 (34) . The above treatment compares neutrons with protons, allowing

13560-409: The two coordinates are often denoted by the letters X and Y , or x and y . The axes may then be referred to as the X -axis and Y -axis. The choices of letters come from the original convention, which is to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values. A Euclidean plane with a chosen Cartesian coordinate system

13680-417: The world, notably in the UK and in the US (see Perhapsatron , a z-pinch machine at LANL ). Small experiments were built at labs as various practical issues were addressed, but all of these machines demonstrated unexpected instabilities of the plasma that would cause it to hit the walls of the container vessel. The problem became known as the " kink instability ". By 1953 the "stabilized pinch" seemed to solve

13800-567: Was gamma radiation . The following year Irène Joliot-Curie and Frédéric Joliot-Curie in Paris showed that if this "gamma" radiation fell on paraffin , or any other hydrogen -containing compound, it ejected protons of very high energy. Neither Rutherford nor James Chadwick at the Cavendish Laboratory in Cambridge were convinced by the gamma ray interpretation. Chadwick quickly performed

13920-418: Was a contradiction, since there is no way to arrange the spins of an electron and a proton in a bound state to get a fractional spin. In 1931, Walther Bothe and Herbert Becker found that if alpha particle radiation from polonium fell on beryllium , boron , or lithium , an unusually penetrating radiation was produced. The radiation was not influenced by an electric field, so Bothe and Becker assumed it

14040-512: Was classified, so progress on ZETA was generally unknown outside the labs working on it. However US researchers visited ZETA and realized that they were about to be outpaced. Teams on both sides of the Atlantic rushed to be the first to complete stabilized pinch machines. ZETA won the race, and by the summer of 1957 it was producing bursts of neutrons on every run. Despite the researchers' reservations, their results were released with great fanfare as

14160-688: Was estimated to be (1.25±0.45)×10 neutrons/pulse. Plasma temperatures of 1–2 keV (12–24 million °C) and densities of approximately 10 cm with 0.3 cm pinch radii were measured. Z-pinch machines can be found at University of Nevada, Reno (USA), Cornell University (USA), University of Michigan (USA), Sandia National Laboratories (USA), University of California, San Diego (USA), University of Washington (USA), Ruhr University (Germany), Imperial College (United Kingdom), École Polytechnique (France), Weizmann Institute of Science (Israel), Universidad Autónoma Metropolitana (Mexico), NSTRI (Iran). Cartesian coordinate system In geometry ,

14280-399: Was normally arranged by placing the plasma vessel inside the core of a transformer , arranged so the plasma itself would be the secondary. When current was sent into the primary side of the transformer, the magnetic field induced a current into the plasma. As induction requires a changing magnetic field, and the induced current is supposed to run in a single direction in most reactor designs,

14400-512: Was resident in the Netherlands . It was independently discovered by Pierre de Fermat , who also worked in three dimensions, although Fermat did not publish the discovery. The French cleric Nicole Oresme used constructions similar to Cartesian coordinates well before the time of Descartes and Fermat. Both Descartes and Fermat used a single axis in their treatments and have a variable length measured in reference to this axis. The concept of using

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