Carl David Anderson
Carl David Anderson was an American physicist. He is best known for his discovery of the positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics, of the muon in 1936. Anderson was born in the son of Swedish immigrants, he studied engineering at Caltech. Under the supervision of Robert A. Millikan, he began investigations into cosmic rays during the course of which he encountered unexpected particle tracks in his cloud chamber photographs that he interpreted as having been created by a particle with the same mass as the electron, but with opposite electrical charge; this discovery, announced in 1932 and confirmed by others, validated Paul Dirac's theoretical prediction of the existence of the positron. Anderson first detected the particles in cosmic rays, he produced more conclusive proof by shooting gamma rays produced by the natural radioactive nuclide ThC" into other materials, resulting in the creation of positron-electron pairs. For this work, Anderson shared the 1936 Nobel Prize in Physics with Victor Hess.
Fifty years Anderson acknowledged that his discovery was inspired by the work of his Caltech classmate Chung-Yao Chao, whose research formed the foundation from which much of Anderson's work developed but was not credited at the time. In 1936, Anderson and his first graduate student, Seth Neddermeyer, discovered the muon, a subatomic particle 207 times more massive than the electron, but with the same negative electric charge and spin 1/2 as the electron, again in cosmic rays. Anderson and Neddermeyer at first believed that they had seen the pion, a particle which Hideki Yukawa had postulated in his theory of the strong interaction; when it became clear that what Anderson had seen was not the pion, the physicist I. I. Rabi, puzzled as to how the unexpected discovery could fit into any logical scheme of particle physics, quizzically asked "Who ordered that?". The muon was the first of a long list of subatomic particles whose discovery baffled theoreticians who could not make the confusing "zoo" fit into some tidy conceptual scheme.
Willis Lamb, in his 1955 Nobel Prize Lecture, joked that he had heard it said that "the finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a 10,000 dollar fine."Anderson spent all of his academic and research career at Caltech. During World War II, he conducted research in rocketry there, he was elected a Fellow of the American Academy of Arts and Sciences in 1950. He died on January 11, 1991, his remains were interred in the Forest Lawn, Hollywood Hills Cemetery in Los Angeles, California, his wife Lorraine died in 1984. Anderson, C. D.. "The Positive Electron". Physical Review. 43: 491. Bibcode:1933PhRv...43..491A. Doi:10.1103/PhysRev.43.491. Anderson, C. D.. "The Apparent Existence of Easily Deflectable Positives". Science. 76: 238–9. Bibcode:1932Sci....76..238A. Doi:10.1126/science.76.1967.238. PMID 17731542. Anderson, C. D.. The Strange Case of the Cosmic Rays; the Bell Laboratory Science Series. 1983 Audio Interview with Carl Anderson by Martin Sherwin Voices of the Manhattan Project American National Biography, vol.
1, pp. 445–446. Annotated bibliography for Carl David Anderson from the Alsos Digital Library for Nuclear Issues "Carl David Anderson". Find a Grave. Retrieved August 10, 2010. Carl Anderson and the Discovery of the Positron National Academy of Sciences Biographical Memoir Oral History interview transcript with Carl D. Anderson 30 June 1966, American Institute of Physics, Niels Bohr Library and Archives Weisstein, Eric Wolfgang. "Anderson, Carl". ScienceWorld
Paul Adrien Maurice Dirac was an English theoretical physicist, regarded as one of the most significant physicists of the 20th century. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory", he made significant contributions to the reconciliation of general relativity with quantum mechanics. Dirac was regarded by his colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "This balancing on the dizzying path between genius and madness is awful", he was the Lucasian Professor of Mathematics at the University of Cambridge, a member of the Center for Theoretical Studies, University of Miami, spent the last decade of his life at Florida State University.
Paul Adrien Maurice Dirac was born at his parents' home in Bristol, England, on 8 August 1902, grew up in the Bishopston area of the city. His father, Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice, who worked in Bristol as a French teacher, his mother, Florence Hannah Dirac, née Holten, the daughter of a ship's captain, was born in Cornwall and worked as a librarian at the Bristol Central Library. Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, an older brother, Reginald Charles Félix, known as Felix, who committed suicide in March 1925. Dirac recalled: "My parents were distressed. I didn't know they cared so much I never knew that parents were supposed to care for their children, but from on I knew."Charles and the children were Swiss nationals until they became naturalised on 22 October 1919. Dirac's father was authoritarian, although he disapproved of corporal punishment. Dirac had a strained relationship with his father, so much so that after his father's death, Dirac wrote, "I feel much freer now, I am my own man."
Charles forced his children to speak to him only in French. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent. Dirac was educated first at Bishop Road Primary School and at the all-boys Merchant Venturers' Technical College, where his father was a French teacher; the school was an institution attached to the University of Bristol. It emphasised technical subjects like bricklaying and metal work, modern languages; this was unusual at a time when secondary education in Britain was still dedicated to the classics, something for which Dirac would express his gratitude. Dirac studied electrical engineering on a City of Bristol University Scholarship at the University of Bristol's engineering faculty, co-located with the Merchant Venturers' Technical College. Shortly before he completed his degree in 1921, he sat the entrance examination for St John's College, Cambridge, he passed and was awarded a £70 scholarship, but this fell short of the amount of money required to live and study at Cambridge.
Despite his having graduated with a first class honours Bachelor of Science degree in engineering, the economic climate of the post-war depression was such that he was unable to find work as an engineer. Instead, he took up an offer to study for a Bachelor of Arts degree in mathematics at the University of Bristol free of charge, he was permitted to skip the first year of the course owing to his engineering degree. In 1923, Dirac graduated, once again with first class honours, received a £140 scholarship from the Department of Scientific and Industrial Research. Along with his £70 scholarship from St John's College, this was enough to live at Cambridge. There, Dirac pursued his interests in the theory of general relativity, an interest he had gained earlier as a student in Bristol, in the nascent field of quantum physics, under the supervision of Ralph Fowler. From 1925 to 1928 he held an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851, he completed his PhD in June 1926 with the first thesis on quantum mechanics to be submitted anywhere.
He continued his research in Copenhagen and Göttingen. Dirac married Margit Wigner, in 1937, he adopted Margit's two children and Gabriel. Paul and Margit Dirac had two children together, Mary Elizabeth and Florence Monica. Margit, known as Manci, visited her brother in 1934 in Princeton, New Jersey, from her native Hungary and, while at dinner at the Annex Restaurant met the "lonely-looking man at the next table." This account from a Korean physicist, Y. S. Kim, who met and was influenced by Dirac says: "It is quite fortunate for the physics community that Manci took good care of our respected Paul A. M. Dirac. Dirac published eleven papers during the period 1939–46.... Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else." Dirac was known among his colleagues for his taciturn nature. His colleagues in Cambridge jokingly defined a unit called a "dirac", one word per hour; when Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it."
He criticised the physicist J. Robert Oppenheimer's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way.
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1 e, a spin of 1/2, has the same mass as an electron; when a positron collides with an electron, annihilation occurs. If this collision occurs at low energies, it results in the production of two or more gamma ray photons. Positrons can be created by positron emission radioactive decay, or by pair production from a sufficiently energetic photon, interacting with an atom in a material. In 1928, Paul Dirac published a paper proposing that electrons can have both a positive and negative charge; this paper introduced the Dirac equation, a unification of quantum mechanics, special relativity, the then-new concept of electron spin to explain the Zeeman effect. The paper did not explicitly predict a new particle but did allow for electrons having either positive or negative energy as solutions. Hermann Weyl published a paper discussing the mathematical implications of the negative energy solution.
The positive-energy solution explained experimental results, but Dirac was puzzled by the valid negative-energy solution that the mathematical model allowed. Quantum mechanics did not allow the negative energy solution to be ignored, as classical mechanics did in such equations. However, no such transition had yet been observed experimentally. Dirac wrote a follow-up paper in December 1929 that attempted to explain the unavoidable negative-energy solution for the relativistic electron, he argued that "... an electron with negative energy moves in an external field as though it carries a positive charge." He further asserted that all of space could be regarded as a "sea" of negative energy states that were filled, so as to prevent electrons jumping between positive energy states and negative energy states. The paper explored the possibility of the proton being an island in this sea, that it might be a negative-energy electron. Dirac acknowledged that the proton having a much greater mass than the electron was a problem, but expressed "hope" that a future theory would resolve the issue.
Robert Oppenheimer argued against the proton being the negative-energy electron solution to Dirac's equation. He asserted that if it were, the hydrogen atom would self-destruct. Persuaded by Oppenheimer's argument, Dirac published a paper in 1931 that predicted the existence of an as-yet-unobserved particle that he called an "anti-electron" that would have the same mass and the opposite charge as an electron and that would mutually annihilate upon contact with an electron. Feynman, earlier Stueckelberg, proposed an interpretation of the positron as an electron moving backward in time, reinterpreting the negative-energy solutions of the Dirac equation. Electrons moving backward in time would have a positive electric charge. Wheeler invoked this concept to explain the identical properties shared by all electrons, suggesting that "they are all the same electron" with a complex, self-intersecting worldline. Yoichiro Nambu applied it to all production and annihilation of particle-antiparticle pairs, stating that "the eventual creation and annihilation of pairs that may occur now and is no creation or annihilation, but only a change of direction of moving particles, from the past to the future, or from the future to the past."
The backwards in time point of view is nowadays accepted as equivalent to other pictures, but it does not have anything to do with the macroscopic terms "cause" and "effect", which do not appear in a microscopic physical description. Dmitri Skobeltsyn first observed the positron in 1929. While using a Wilson cloud chamber to try to detect gamma radiation in cosmic rays, Skobeltsyn detected particles that acted like electrons but curved in the opposite direction in an applied magnetic field. In 1929 Chung-Yao Chao, a graduate student at Caltech, noticed some anomalous results that indicated particles behaving like electrons, but with a positive charge, though the results were inconclusive and the phenomenon was not pursued. Carl David Anderson discovered the positron on 2 August 1932, for which he won the Nobel Prize for Physics in 1936. Anderson did not coin the term positron, but allowed it at the suggestion of the Physical Review journal editor to whom he submitted his discovery paper in late 1932.
The positron was the first evidence of antimatter and was discovered when Anderson allowed cosmic rays to pass through a cloud chamber and a lead plate. A magnet surrounded this apparatus, causing particles to bend in different directions based on their electric charge; the ion trail left by each positron appeared on the photographic plate with a curvature matching the mass-to-charge ratio of an electron, but in a direction that showed its charge was positive. Anderson wrote in retrospect that the positron could have been discovered earlier based on Chung-Yao Chao's work, if only it had been followed up on. Frédéric and Irène Joliot-Curie in Paris had evidence of positrons in old photographs when Anderson's results came out, but they had dismissed them as protons; the positron had been contemporaneously discovered by Patrick Blackett and Giuseppe Occhialini at the Cavendish Laboratory in 1932. Blackett and Occhialini had delayed publication to obtain more solid evidence, so Anderson was able to publish the discovery first.
Positrons are produced in β+ decays of occurring radioactive isotopes and in interactions of gamma quanta with matter. Antineutrinos a
A Penning trap is a device for the storage of charged particles using a homogeneous axial magnetic field and an inhomogeneous quadrupole electric field. This kind of trap is well suited to precision measurements of properties of ions and stable subatomic particles. Geonium atoms have been studied this way, to measure the electron magnetic moment; these traps have been used in the physical realization of quantum computation and quantum information processing by trapping qubits. Penning traps are used in many laboratories worldwide, including CERN, to store antimatter like antiprotons; the Penning trap was named after F. M. Penning by Hans Georg Dehmelt. Dehmelt got inspiration from the vacuum gauge built by F. M. Penning where a current through a discharge tube in a magnetic field is proportional to the pressure. Citing from H. Dehmelt's autobiography: "I began to focus on the magnetron/Penning discharge geometry, which, in the Penning ion gauge, had caught my interest at Göttingen and at Duke.
In their 1955 cyclotron resonance work on photoelectrons in vacuum Franken and Liebes had reported undesirable frequency shifts caused by accidental electron trapping. Their analysis made me realize that in a pure electric quadrupole field the shift would not depend on the location of the electron in the trap; this is an important advantage over many other traps. A magnetron trap of this type had been discussed in J. R. Pierce's 1949 book, I developed a simple description of the axial and cyclotron motions of an electron in it. With the help of the expert glassblower of the Department, Jake Jonson, I built my first high vacuum magnetron trap in 1959 and was soon able to trap electrons for about 10 sec and to detect axial and cyclotron resonances. " – H. Dehmelt H. Dehmelt shared the Nobel Prize in Physics in 1989 for the development of the ion trap technique. Penning traps use a strong homogeneous axial magnetic field to confine particles radially and a quadrupole electric field to confine the particles axially.
The static electric potential can be generated using a set of three electrodes: a ring and two endcaps. In an ideal Penning trap the ring and endcaps are hyperboloids of revolution. For trapping of positive ions, the endcap electrodes are kept at a positive potential relative to the ring; this potential produces a saddle point in the centre of the trap, which traps ions along the axial direction. The electric field causes ions to oscillate along the trap axis; the magnetic field in combination with the electric field causes charged particles to move in the radial plane with a motion which traces out an epitrochoid. The orbital motion of ions in the radial plane is composed of two modes at frequencies which are called the magnetron ω − and the modified cyclotron ω + frequencies; these motions are similar to the deferent and epicycle of the Ptolemaic model of the solar system. The sum of these two frequencies is the cyclotron frequency, which depends only on the ratio of electric charge to mass and on the strength of the magnetic field.
This frequency can be measured accurately and can be used to measure the masses of charged particles. Many of the highest-precision mass measurements come from Penning traps. Buffer gas cooling, resistive cooling, laser cooling are techniques to remove energy from ions in a Penning trap. Buffer gas cooling relies on collisions between the ions and neutral gas molecules that bring the ion energy closer to the energy of the gas molecules. In resistive cooling, moving image charges in the electrodes are made to do work through an external resistor removing energy from the ions. Laser cooling can be used to remove energy from some kinds of ions in Penning traps; this technique requires ions with an appropriate electronic structure. Radiative cooling is the process by which the ions lose energy by creating electromagnetic waves by virtue of their acceleration in the magnetic field; this process dominates the cooling of electrons in Penning traps, but is small and negligible for heavier particles. Using the Penning trap can have advantages over the radio frequency trap.
Firstly, in the Penning trap only static fields are applied and therefore there is no micro-motion and resultant heating of the ions due to the dynamic fields for extended 2- and 3-dimensional ion Coulomb crystals. The Penning trap can be made larger whilst maintaining strong trapping; the trapped ion can be held further away from the electrode surfaces. Interaction with patch potentials on the electrode surfaces can be responsible for heating and decoherence effects and these effects scale as a high power of the inverse distance between the ion and the electrode. Fourier transform ion cyclotron resonance mass spectrometry is a type of mass spectrometry used for determining the mass-to-charge ratio of ions based on the cyclotron frequency of the ions in a fixed magnetic field; the ions are trapped in a Penning trap where they are excited to a larger cyclotron radius by an oscillating electric field perpendicular to the magnetic field. The excitation results in the ions moving in phase; the signal is detected as an image current on a pair of plates which the packet of ions passes close to as they cyclotron.
The resulting signal is called a free induction decay, transient or interferogram that consists of a superposition of sine waves. The useful sign
The Antiproton Decelerator is a storage ring at the CERN laboratory near Geneva. It was built as a successor to the Low Energy Antiproton Ring and started operation in the year 2000. Antiprotons are created by impinging a proton beam from the Proton Synchrotron on a metal target; the AD decelerates the resultant antiprotons to an energy of 5.3 MeV, which are ejected to one of several connected experiments. ELENA is a 30 m hexagonal storage ring situated inside the AD complex, it is designed to further decelerate the antiproton beam to an energy of 0.1 MeV for more precise measurements. The first beam circulated ELENA on 18 November 2016; the ring is expected to be operational in 2018. GBAR will be the first experiment to use a beam from ELENA, with the rest of the AD experiments following suit in 2019-2020. ATHENA was an antimatter research project. In August 2002, it was the first experiment to produce 50,000 low-energy antihydrogen atoms, as reported in Nature. In 2005, ATHENA was disbanded and many of the former members worked on the subsequent ALPHA experiment.
The ATHENA apparatus comprises four main subsystems: the antiproton catching trap, the positron accumulator, the antiproton/positron mixing trap, the antihydrogen annihilation detector. All traps in the experiment are variations on the Penning trap, which uses an axial magnetic field to transversely confine the charged particles, a series of hollow cylindrical electrodes to trap them axially; the catching and mixing traps are adjacent to each other, coaxial with a 3 T magnetic field from a superconducting solenoid. The positron accumulator has its own magnetic system a solenoid, of 0.14 T. A separate cryogenic heat exchanger in the bore of the superconducting magnet cools the catching and mixing traps to about 15 K; the ATHENA apparatus features an open, modular design that allows great experimental flexibility in introducing large numbers of positrons into the apparatus. The catching trap slows, traps and accumulates antiprotons. To cool antiprotons, the catching trap is first loaded with 3×108 electrons, which cool by synchrotron radiation in the 3 T magnetic field.
The AD delivers 2×107 antiprotons having kinetic energy 5.3 MeV and a pulse duration of 200 ns to the experiment at 100 s intervals. The antiprotons are trapped using a pulsed electric field; the antiprotons lose equilibrate with the cold electrons by Coulomb interaction. The electrons are ejected before mixing the antiprotons with positrons; each AD shot results in about 3×103 cold antiprotons for interaction experiments. The positron accumulator slows and accumulates positrons emitted from a radioactive source. Accumulation for 300 s yields 1.5×108 positrons, 50% of which are transferred to the mixing trap, where they cool by synchrotron radiation. The mixing trap has the axial potential configuration of a nested Penning trap, which permits two plasmas of opposite charge to come into contact. In ATHENA, the spheroidal positron cloud can be characterized by exciting and detecting axial plasma oscillations. Typical conditions are: 7×107 stored positrons, a radius of 2 – 2.5 mm, a length of 32 mm, a maximum density of 2.5×108 cm−3.
Key to the observations reported here is the antihydrogen annihilation detector, situated coaxially with the mixing region, between the trap outer radius and the magnet bore. The detector is designed to provide unambiguous evidence for antihydrogen production by detecting the temporally and spatially coincident annihilations of the antiproton and positron when a neutral antihydrogen atom escapes the electromagnetic trap and strikes the trap electrodes. An antiproton annihilates into a few charged or neutral pions; the charged pions are detected by two layers of double-sided, position sensitive, silicon microstrips. The path of a charged particle passing through both layers can be reconstructed, two or more intersecting tracks allow determination of the position, or vertex, of the antiproton annihilation; the uncertainty in vertex determination is 4 mm and is dominated by the unmeasured curvature of the charged pions’ trajectories in the magnetic field. The temporal coincidence window is 5 microseconds.
The solid angle coverage of the interaction region is about 80% of 4π. A positron annihilating with an electron yields three photons; the positron detector, comprising 16 rows each containing 12 scintillating, pure cesium-iodide-crystals, is designed to detect the two-photon events, consisting of two 511 keV photons which are always emitted back-to-back. The energy resolution of the detector is 18% FWHM at 511 keV, the photo-peak detection efficiency for single photons is about 20%; the maximum readout rate of the whole detector is about 40 Hz. Ancillary detectors include large scintillator paddles external to the magnet, a thin, position sensitive, silicon diode through which the incident antiproton beam passes before entering the catching trap. To produce antihydrogen atoms, a positron well in the mixing region is filled with about 7×107 positrons and allowed to cool to the ambient temperature; the nested trap is formed around the positron well. Next 104 antiprotons are launched into the mixing region by pulsing the trap from one potential configuration to another.
The mixing time is 190 s, after which all particles are dumped and the process repeated. Events triggering the imaging silicon detector initiate readout of both the silicon and the CsI modules. Using this method, ATHENA could produce -
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to high speeds and energies, to contain them in well-defined beams. Large accelerators are used for basic research in particle physics; the most powerful accelerator is the Large Hadron Collider near Geneva, built by the European collaboration CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5 TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV. Other powerful accelerators are KEKB at KEK in Japan, RHIC at Brookhaven National Laboratory, the Tevatron at Fermilab, Illinois. Accelerators are used as synchrotron light sources for the study of condensed matter physics. Smaller particle accelerators are used in a wide variety of applications, including particle therapy for oncological purposes, radioisotope production for medical diagnostics, ion implanters for manufacture of semiconductors, accelerator mass spectrometers for measurements of rare isotopes such as radiocarbon.
There are more than 30,000 accelerators in operation around the world. There are two basic classes of accelerators: electrodynamic accelerators. Electrostatic accelerators use static electric fields to accelerate particles; the most common types are the Cockcroft -- the Van de Graaff generator. A small-scale example of this class is the cathode ray tube in an ordinary old television set; the achievable kinetic energy for particles in these devices is determined by the accelerating voltage, limited by electrical breakdown. Electrodynamic or electromagnetic accelerators, on the other hand, use changing electromagnetic fields to accelerate particles. Since in these types the particles can pass through the same accelerating field multiple times, the output energy is not limited by the strength of the accelerating field; this class, first developed in the 1920s, is the basis for most modern large-scale accelerators. Rolf Widerøe, Gustav Ising, Leó Szilárd, Max Steenbeck, Ernest Lawrence are considered pioneers of this field and building the first operational linear particle accelerator, the betatron, the cyclotron.
Because colliders can give evidence of the structure of the subatomic world, accelerators were referred to as atom smashers in the 20th century. Despite the fact that most accelerators propel subatomic particles, the term persists in popular usage when referring to particle accelerators in general. Beams of high-energy particles are useful for fundamental and applied research in the sciences, in many technical and industrial fields unrelated to fundamental research, it has been estimated that there are 30,000 accelerators worldwide. Of these, only about 1% are research machines with energies above 1 GeV, while about 44% are for radiotherapy, 41% for ion implantation, 9% for industrial processing and research, 4% for biomedical and other low-energy research; the bar graph shows the breakdown of the number of industrial accelerators according to their applications. The numbers are based on 2012 statistics available from various sources, including production and sales data published in presentations or market surveys, data provided by a number of manufacturers.
For the most basic inquiries into the dynamics and structure of matter and time, physicists seek the simplest kinds of interactions at the highest possible energies. These entail particle energies of many GeV, the interactions of the simplest kinds of particles: leptons and quarks for the matter, or photons and gluons for the field quanta. Since isolated quarks are experimentally unavailable due to color confinement, the simplest available experiments involve the interactions of, leptons with each other, second, of leptons with nucleons, which are composed of quarks and gluons. To study the collisions of quarks with each other, scientists resort to collisions of nucleons, which at high energy may be usefully considered as 2-body interactions of the quarks and gluons of which they are composed, thus elementary particle physicists tend to use machines creating beams of electrons, positrons and antiprotons, interacting with each other or with the simplest nuclei at the highest possible energies hundreds of GeV or more.
The largest and highest energy particle accelerator used for elementary particle physics is the Large Hadron Collider at CERN, operating since 2009. Nuclear physicists and cosmologists may use beams of bare atomic nuclei, stripped of electrons, to investigate the structure and properties of the nuclei themselves, of condensed matter at high temperatures and densities, such as might have occurred in the first moments of the Big Bang; these investigations involve collisions of heavy nuclei – of atoms like iron or gold – at energies of several GeV per nucleon. The largest such particle accelerator is the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. Particle accelerators can produce proton beams, which can produce proton-rich medical or research isotopes as opposed to the neutron-rich ones made in fission reactors. An example of this type of machine is LANSCE at Los Alamos. Besides being of fundamental interest, electrons accelerated in the magnetic field causes the high energy electrons to emit extre
The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, many astronomical objects. More the term magnetic moment refers to a system's magnetic dipole moment, the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a small distance; the magnetic dipole component is sufficient for large enough distances. Higher order terms may be needed in addition to the dipole moment for extended objects; the magnetic dipole moment of an object is defined in terms of the torque that object experiences in a given magnetic field. The same applied magnetic field creates larger torques on objects with larger magnetic moments; the strength of this torque depends not only on the magnitude of the magnetic moment but on its orientation relative to the direction of the magnetic field.
The magnetic moment may be considered, therefore. The direction of the magnetic moment points from the south to north pole of the magnet; the magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, decreases as the inverse cube of the distance from the object; the magnetic moment can be defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. The relationship is given by: τ = m × B where τ is the torque acting on the dipole, B is the external magnetic field, m is the magnetic moment; this definition is based on how one could, in principle, measure the magnetic moment of an unknown sample. For a current loop, this definition leads to the magnitude of the magnetic dipole moment equaling the product of the current times the area of the loop. Further, this definition allows the calculation of the expected magnetic moment for any known macroscopic current distribution.
An alternative definition is useful for thermodynamics calculations of the magnetic moment. In this definition, the magnetic dipole moment of a system is the negative gradient of its intrinsic energy, with respect to external magnetic field: m = − x ^ ∂ U i n t ∂ B x − y ^ ∂ U i n t ∂ B y − z ^ ∂ U i n t ∂ B z. Generically, the intrinsic energy includes the self-field energy of the system plus the energy of the internal workings of the system. For example, for a hydrogen atom in a 2p state in an external field, the self-field energy is negligible, so the internal energy is the eigenenergy of the 2p state, which includes Coulomb potential energy and the kinetic energy of the electron; the interaction-field energy between the internal dipoles and external fields is not part of this internal energy. The unit for magnetic moment in International System of Units base units is A⋅m2, where A is ampere and m is meter; this unit has equivalents in other SI derived units including: A ⋅ m 2 = N ⋅ m T = J T, where N is newton, T is tesla, J is joule.
Although torque and energy are dimensionally equivalent, torques are never expressed in units of energy. In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, EMU. Among these, there are two alternative units of magnetic dipole moment: 1 statA ⋅ cm 2 = 3.33564095 × 10 − 14 A ⋅ m 2 1 erg G = 10 − 3 A ⋅ m 2,where statA is statamperes, cm is centimeters, erg is ergs, G is gauss. The ratio of these two non-equivalent CGS units is equal to the speed of light in free space, expressed in cm⋅s−1. All formula