Acceleration
In physics, acceleration is the rate of change of velocity of an object with respect to time. An object's acceleration is the net result of all forces acting on the object, as described by Newton's Second Law; the SI unit for acceleration is metre per second squared. Accelerations add according to the parallelogram law; the vector of the net force acting on a body has the same direction as the vector of the body's acceleration, its magnitude is proportional to the magnitude of the acceleration, with the object's mass as proportionality constant. For example, when a car starts from a standstill and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car turns, an acceleration occurs toward the new direction; the forward acceleration of the car is called a linear acceleration, the reaction to which passengers in the car experience as a force pushing them back into their seats. When changing direction, this is called radial acceleration, the reaction to which passengers experience as a sideways force.
If the speed of the car decreases, this is an acceleration in the opposite direction of the velocity of the vehicle, sometimes called deceleration or Retrograde burning in spacecraft. Passengers experience the reaction to deceleration as a force pushing them forwards. Both acceleration and deceleration are treated the same, they are both changes in velocity; each of these accelerations is felt by passengers until their velocity matches that of the uniformly moving car. An object's average acceleration over a period of time is its change in velocity divided by the duration of the period. Mathematically, a ¯ = Δ v Δ t. Instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time. In the terms of calculus, instantaneous acceleration is the derivative of the velocity vector with respect to time: a = lim Δ t → 0 Δ v Δ t = d v d t It can be seen that the integral of the acceleration function a is the velocity function v. V = ∫ a d t As acceleration is defined as the derivative of velocity, v, with respect to time t and velocity is defined as the derivative of position, x, with respect to time, acceleration can be thought of as the second derivative of x with respect to t: a = d v d t = d 2 x d t 2 Acceleration has the dimensions of velocity divided by time, i.e. L.
T−2. The SI unit of acceleration is the metre per second squared. An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, although its speed may be constant. In this case it is said to be undergoing centripetal acceleration. Proper acceleration, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an accelerometer. In classical mechanics, for a body with constant mass, the acceleration of the body's center of mass is proportional to the net force vector acting on it: F = m a → a = F / m where F is the net force acting on the body, m is the mass of the body, a is the center-of-mass acceleration; as speeds approach the speed of light, relativistic effects become large. The velocity of a particle moving on a curved path as a function of time can be written as: v = v v v = v u t, with v equal to the speed of travel along the path, u t = v v, {\displaystyle \mathbf _=
Positron
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
Geneva
Geneva is the second-most populous city in Switzerland and the most populous city of Romandy, the French-speaking part of Switzerland. Situated where the Rhône exits Lake Geneva, it is the capital of the Canton of Geneva; the municipality has a population of 200,548, the canton has 495,249 residents. In 2014, the compact agglomération du Grand Genève had 946,000 inhabitants in 212 communities in both Switzerland and France. Within Swiss territory, the commuter area named "Métropole lémanique" contains a population of 1.26 million. This area is spread east from Geneva towards the Riviera area and north-east towards Yverdon-les-Bains, in the neighbouring canton of Vaud. Geneva is a global city, a financial centre, a worldwide centre for diplomacy due to the presence of numerous international organizations, including the headquarters of many agencies of the United Nations and the Red Cross. Geneva hosts the highest number of international organizations in the world, it is where the Geneva Conventions were signed, which chiefly concern the treatment of wartime non-combatants and prisoners of war.
In 2017, Geneva was ranked as the world's fifteenth most important financial centre for competitiveness by the Global Financial Centres Index, fifth in Europe behind London, Zürich and Luxembourg. In 2019 Geneva was ranked among the ten most liveable cities in the world by Mercer together with Zürich and Basel; the city has been referred to as the world's most compact metropolis and the "Peace Capital". In 2017, Geneva was ranked as the seventh most expensive city in the world. Geneva was ranked third in purchasing power in a global cities ranking by UBS in 2018; the city was mentioned in Latin texts, by Caesar, with the spelling Genava from the Celtic *genawa- from the stem *genu-, in the sense of a bending river or estuary. The medieval county of Geneva in Middle Latin was known as pagus major Genevensis or Comitatus Genevensis. After 1400 it became the Genevois province of Savoy; the name takes various forms in modern languages, Geneva in English, French: Genève, German: Genf, Italian: Ginevra, Romansh: Genevra.
The city shares the origin of * genawa "estuary", with the Italian port city of Genoa. Geneva was an Allobrogian border town, fortified against the Helvetii tribe, when the Romans took it in 121 BC, it became Christian under the Late Roman Empire, acquired its first bishop in the 5th century, having been connected to the Bishopric of Vienne in the 4th. In the Middle Ages, Geneva was ruled by a count under the Holy Roman Empire until the late 14th century, when it was granted a charter giving it a high degree of self-governance. Around this time, the House of Savoy came to at least nominally dominate the city. In the 15th century, an oligarchic republican government emerged with the creation of the Grand Council. In the first half of the 16th century, the Protestant Reformation reached the city, causing religious strife, during which Savoy rule was thrown off and Geneva allied itself with the Swiss Confederacy. In 1541, with Protestantism on the rise, John Calvin, the Protestant Reformer and proponent of Calvinism, became the spiritual leader of the city and established the Republic of Geneva.
By the 18th century, Geneva had come under the influence of Catholic France, which cultivated the city as its own. France tended to be at odds with the ordinary townsfolk, which inspired the failed Geneva Revolution of 1782, an attempt to win representation in the government for men of modest means. In 1798, revolutionary France under the Directory annexed Geneva. At the end of the Napoleonic Wars, on 1 June 1814, Geneva was admitted to the Swiss Confederation. In 1907, the separation of Church and State was adopted. Geneva flourished in the 19th and 20th centuries, becoming the seat of many international organizations. Geneva is located at 46°12' North, 6°09' East, at the south-western end of Lake Geneva, where the Rhône flows out, it is surrounded by three mountain chains, each belonging to the Jura: the Jura main range lies north-westward, the Vuache southward, the Salève south-eastward. The city covers an area of 15.93 km2, while the area of the canton is 282 km2, including the two small exclaves of Céligny in Vaud.
The part of the lake, attached to Geneva has an area of 38 km2 and is sometimes referred to as petit lac. The canton has only a 4.5-kilometre-long border with the rest of Switzerland. Of 107.5 km of border, 103 are shared with France, the Département de l'Ain to the north and west and the Département de la Haute-Savoie to the south and east. Of the land in the city, 0.24 km2, or 1.5%, is used for agricultural purposes, while 0.5 km2, or 3.1%, is forested. The rest of the land, 14.63 km2, or 91.8%, is built up, 0.49 km2, or 3.1%, is either rivers or lakes and 0.02 km2, or 0.1%, is wasteland. Of the built up area, industrial buildings made up 3.4%, housing and buildings made up 46.2% and transportation infrastructure 25.8%, while parks, green belts and sports fields made up 15.7%. Of the agricultural land, 0.3% is used for growing crops. Of the water in the municipality, 0.2 % is composed of lakes and 2.9 % streams. The altitude of Geneva is 373.6 metres, corresponds to the altitude of
Resonator
A resonator is a device or system that exhibits resonance or resonant behavior, that is, it oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either mechanical. Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of precise frequency. A cavity resonator is one. In electronics and radio, microwave cavities consisting of hollow metal boxes are used in microwave transmitters and test equipment to control frequency, in place of the tuned circuits which are used at lower frequencies. Acoustic cavity resonators, in which sound is produced by air vibrating in a cavity with one opening, are known as Helmholtz resonators. A physical system can have as many resonant frequencies.
Systems with one degree of freedom, such as a mass on a spring, balance wheels, LC tuned circuits have one resonant frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonant frequencies. A crystal lattice composed of N atoms bound together can have N resonant frequencies; as the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next; the term resonator is most used for a homogeneous object in which vibrations travel as waves, at an constant velocity, bouncing back and forth between the sides of the resonator. The material of the resonator, through which the waves flow, can be viewed as being made of millions of coupled moving parts. Therefore, they can have millions of resonant frequencies, although only a few may be used in practical resonators.
The oppositely moving waves interfere with each other, at its resonant frequencies reinforce each other to create a pattern of standing waves in the resonator. If the distance between the sides is d, the length of a round trip is 2 d. To cause resonance, the phase of a sinusoidal wave after a round trip must be equal to the initial phase so the waves self-reinforce; the condition for resonance in a resonator is that the round trip distance, 2 d, is equal to an integer number of wavelengths λ of the wave: 2 d = N λ, N ∈ If the velocity of a wave is c, the frequency is f = c / λ so the resonant frequencies are: f = N c 2 d N ∈ So the resonant frequencies of resonators, called normal modes, are spaced multiples of a lowest frequency called the fundamental frequency. The above analysis assumes the medium inside the resonator is homogeneous, so the waves travel at a constant speed, that the shape of the resonator is rectilinear. If the resonator is inhomogeneous or has a nonrectilinear shape, like a circular drumhead or a cylindrical microwave cavity, the resonant frequencies may not occur at spaced multiples of the fundamental frequency.
They are called overtones instead of harmonics. There may be several such series of resonant frequencies in a single resonator, corresponding to different modes of vibration. An electrical circuit composed of discrete components can act as a resonator when both an inductor and capacitor are included. Oscillations are limited by the inclusion of resistance, either via a specific resistor component, or due to resistance of the inductor windings; such resonant circuits are called RLC circuits after the circuit symbols for the components. A distributed-parameter resonator has capacitance and resistance that cannot be isolated into separate lumped capacitors, inductors, or resistors. An example of this, much used in filtering, is the helical resonator. A single layer coil, used as a secondary or tertiary winding in a Tesla coil or magnifying transmitter is a distributed resonator. A cavity resonator is a hollow closed conductor such as a metal box or a cavity within a metal block, containing electromagnetic waves reflecting back and forth between the cavity's walls.
When a source of radio waves at one of the cavity's resonant frequencies is applied, the oppositely-moving waves form standing waves, the cavity stores electromagnetic energy. Since the cavity's lowest resonant frequency, the fundamental frequency, is that at which the width of the cavity is equal to a half-wavelength, cavity resonators are only used at microwave frequencies and above, where wavelengths are short enough that the cavity is conveniently small in size. Due to the low resistance of their conductive walls, cavity resonators have very
Statistics
Statistics is a branch of mathematics dealing with data collection, analysis and presentation. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics; when census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
In contrast, an observational study does not involve experimental manipulation. Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, inferential statistics, which draw conclusions from data that are subject to random variation. Descriptive statistics are most concerned with two sets of properties of a distribution: central tendency seeks to characterize the distribution's central or typical value, while dispersion characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena. A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets.
Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors and Type II errors. Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are subject to error. Many of these errors are classified as random or systematic, but other types of errors can be important; the presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more from calculus and probability theory. In more recent years statistics has relied more on statistical software to produce tests such as descriptive analysis.
Some definitions are: Merriam-Webster dictionary defines statistics as "a branch of mathematics dealing with the collection, analysis and presentation of masses of numerical data." Statistician Arthur Lyon Bowley defines statistics as "Numerical statements of facts in any department of inquiry placed in relation to each other."Statistics is a mathematical body of science that pertains to the collection, interpretation or explanation, presentation of data, or as a branch of mathematics. Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty and decision making in the face of uncertainty. Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, measure-theoretic probability theory.
In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population; this may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data types, while frequency and percentage are more useful in terms of describing categorical data; when a census is not feasible, a chosen subset of the population called. Once a sample, representative of the population is determined, data is collected for the sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data. However, the drawing of the sample has been subject to an element of randomness, hence the established numerical descriptors from the sample are due to uncertainty.
To still draw meaningful conclusions about the entire population, in
Hamburg
Hamburg is the second-largest city in Germany with a population of over 1.8 million. One of Germany's 16 federal states, it is surrounded by Schleswig-Holstein to the north and Lower Saxony to the south; the city's metropolitan region is home to more than five million people. Hamburg lies on two of its tributaries, the River Alster and the River Bille; the official name reflects Hamburg's history as a member of the medieval Hanseatic League and a free imperial city of the Holy Roman Empire. Before the 1871 Unification of Germany, it was a sovereign city state, before 1919 formed a civic republic headed constitutionally by a class of hereditary grand burghers or Hanseaten. Beset by disasters such as the Great Fire of Hamburg, north Sea flood of 1962 and military conflicts including World War II bombing raids, the city has managed to recover and emerge wealthier after each catastrophe. Hamburg is Europe's third-largest port. Major regional broadcasting firm NDR, the printing and publishing firm Gruner + Jahr and the newspapers Der Spiegel and Die Zeit are based in the city.
Hamburg is the seat of Germany's oldest stock exchange and the world's oldest merchant bank, Berenberg Bank. Media, commercial and industrial firms with significant locations in the city include multinationals Airbus, Blohm + Voss, Aurubis and Unilever; the city hosts specialists in world economics and international law, including consular and diplomatic missions as the International Tribunal for the Law of the Sea, the EU-LAC Foundation, the UNESCO Institute for Lifelong Learning, multipartite international political conferences and summits such as Europe and China and the G20. Both the former German Chancellor Helmut Schmidt and Angela Merkel, German chancellor since 2005, come from Hamburg; the city is a major domestic tourist destination. It ranked 18th in the world for livability in 2016; the Speicherstadt and Kontorhausviertel were declared World Heritage Sites by UNESCO in 2015. Hamburg is a major European science and education hub, with several universities and institutions. Among its most notable cultural venues are the Laeiszhalle concert halls.
It paved the way for bands including The Beatles. Hamburg is known for several theatres and a variety of musical shows. St. Pauli's Reeperbahn is among the best-known European entertainment districts. Hamburg is at a sheltered natural harbour on the southern fanning-out of the Jutland Peninsula, between Continental Europe to the south and Scandinavia to the north, with the North Sea to the west and the Baltic Sea to the northeast, it is on the River Elbe at its confluence with the Bille. The city centre is around the Binnenalster and Außenalster, both formed by damming the River Alster to create lakes; the islands of Neuwerk, Scharhörn, Nigehörn, 100 kilometres away in the Hamburg Wadden Sea National Park, are part of the city of Hamburg. The neighborhoods of Neuenfelde, Cranz and Finkenwerder are part of the Altes Land region, the largest contiguous fruit-producing region in Central Europe. Neugraben-Fischbek has Hamburg's highest elevation, the Hasselbrack at 116.2 metres AMSL. Hamburg borders the states of Lower Saxony.
Hamburg has an oceanic climate, influenced by its proximity to the coast and marine air masses that originate over the Atlantic Ocean. The location north of Germany provides extremes greater than marine climates, but in the category due to the mastery of the western standards. Nearby wetlands enjoy a maritime temperate climate; the amount of snowfall has differed a lot during the past decades: while in the late 1970s and early 1980s, at times heavy snowfall occurred, the winters of recent years have been less cold, with snowfall only on a few days per year. The warmest months are June and August, with high temperatures of 20.1 to 22.5 °C. The coldest are December and February, with low temperatures of −0.3 to 1.0 °C. Claudius Ptolemy reported the first name for the vicinity as Treva; the name Hamburg comes from the first permanent building on the site, a castle which the Emperor Charlemagne ordered constructed in AD 808. It rose on rocky terrain in a marsh between the River Alster and the River Elbe as a defence against Slavic incursion, acquired the name Hammaburg, burg meaning castle or fort.
The origin of the Hamma term remains uncertain. In 834, Hamburg was designated as the seat of a bishopric; the first bishop, became known as the Apostle of the North. Two years Hamburg was united with Bremen as the Bishopric of Hamburg-Bremen. Hamburg occupied several times. In 845, 600 Viking ships sailed up the River Elbe and destroyed Hamburg, at that time a town of around 500 inhabitants. In 1030, King Mieszko II Lambert of Poland burned down the city. Valdemar II of Denmark raided and occupied Hamburg in 1201 and in 1214; the Black Death killed at least 60% of the population in 1350. Hamburg experienced several great fires in the medieval period. In 1189, by imperial charter, Frederick I "Barbarossa" granted Hamburg the status of a Free Imperial City and tax-free access up the Lower Elbe into the North Sea. In 1265, an forged letter was presented to or by the Rath of Hamburg; this charter, along with Hamburg's proximity to the main trade routes of the North Sea and Baltic Sea made it a
Particle accelerator
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
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