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particle accelerator, apparatus used in nuclear physics to produce beams of energetic charged particles and to direct them against various targets. Such machines, popularly called atom smashers, are needed to observe objects as small as the atomic nucleus in studies of its structure and of the forces that hold it together. Accelerators are also needed to provide enough energy to create new particles. Besides pure research, accelerators have practical applications in medicine and industry, most notably in the production of radioisotopes. A majority of the world's particle accelerators are situated in the United States, either at major universities or national laboratories. In Europe the principal facility is at CERN near Geneva, Switzerland; in Russia important installations exist at Dubna and Serpukhov.
Design of Particle Accelerators
The early linear accelerators used high voltage to produce high-energy particles; a large static electric charge was built up, which produced an electric field along the length of an evacuated tube, and the particles acquired energy as they moved through the electric field. The Cockcroft-Walton accelerator produced high voltage by charging a bank of capacitors in parallel and then connecting them in series, thereby adding up their separate voltages. The Van de Graaff accelerator achieved high voltage by using a continuously recharged moving belt to deliver charge to a high-voltage terminal consisting of a hollow metal sphere. Today these two electrostatic machines are used in low-energy studies of nuclear structure and in the injection of particles into larger, more powerful machines. Linear accelerators can be used to produce higher energies, but this requires increasing their length.
Linear accelerators, in which there is very little radiation loss, are the most powerful and efficient electron accelerators; the largest of these, the Stanford linear accelerator (SLAC), completed in 1957, is 2 mi (3.2 km) long and produces 20-GeV—in particle physics energies are commonly measured in millions (MeV) or billions (GeV) of electron-volts (eV)—electrons. SLAC is now used, however, not for particle physics but to produce a powerful X-ray laser. Modern linear machines differ from earlier electrostatic machines in that they use electric fields alternating at radio frequencies to accelerate the particles, instead of using high voltage. The acceleration tube has segments that are charged alternately positive and negative. When a group of particles passes through the tube, it is repelled by the segment it has left and is attracted by the segment it is approaching. Thus the final energy is attained by a series of pushes and pulls. Recently, linear accelerators have been used to accelerate heavy ions such as carbon, neon, and nitrogen.
In order to reach high energy without the prohibitively long paths required of linear accelerators, E. O. Lawrence proposed (1932) that particles could be accelerated to high energies in a small space by making them travel in a circular or nearly circular path. In the cyclotron, which he invented, a cylindrical magnet bends the particle trajectories into a circular path whose radius depends on the mass of the particles, their velocity, and the strength of the magnetic field. The particles are accelerated within a hollow, circular, metal box that is split in half to form two sections, each in the shape of the capital letter D. A radio-frequency electric field is impressed across the gap between the D's so that every time a particle crosses the gap, the polarity of the D's is reversed and the particle gets an accelerating “kick.” The key to the simplicity of the cyclotron is that the period of revolution of a particle remains the same as the radius of the path increases because of the increase in velocity. Thus, the alternating electric field stays in step with the particles as they spiral outward from the center of the cyclotron to its circumference. However, according to the theory of relativity the mass of a particle increases as its velocity approaches the speed of light; hence, very energetic, high-velocity particles will have greater mass and thus less acceleration, with the result that they will not remain in step with the field. For protons, the maximum energy attainable with an ordinary cyclotron is about 10 million electron-volts.
Two approaches exist for exceeding the relativistic limit for cyclotrons. In the synchrocyclotron, the frequency of the accelerating electric field steadily decreases to match the decreasing angular velocity of the protons. In the isochronous cyclotron, the magnet is constructed so the magnetic field is stronger near the circumference than at the center, thus compensating for the mass increase and maintaining a constant frequency of revolution. The first synchrocyclotron, built at the Univ. of California at Berkeley in 1946, reached energies high enough to create pions, thus inaugurating the laboratory study of the meson family of elementary particles.
Further progress in physics required energies in the GeV range, which led to the development of the synchrotron. In this device, a ring of magnets surrounds a doughnut-shaped vacuum tank. The magnetic field rises in step with the proton velocities, thus keeping them moving in a circle of nearly constant radius, instead of the widening spiral of the cyclotron. The entire center section of the magnet is eliminated, making it possible to build rings with diameters measured in miles. Particles must be injected into a synchrotron from another accelerator. The first proton synchrotron was the cosmotron at Brookhaven (N.Y.) National Laboratory, which began operation in 1952 and eventually attained an energy of 3 GeV. The 6.2-GeV synchrotron (the bevatron) at the Lawrence Berkeley National Laboratory was used to discover the antiproton (see antiparticle).
The 500-GeV synchrotron at the Fermi National Accelerator Laboratory at Batavia, Ill., was built to be the most powerful accelerator in the world in the early 1970s, with a ring circumference of approximately 4 mi (6 km). The machine was upgraded (1983) to accelerate protons and counterpropagating antiprotons to such enormous speeds that the ensuing impacts delivered energies of up to 2 trillion electron-volts (TeV)—hence the ring was been dubbed the Tevatron. The Tevatron was an example of a so-called colliding-beams machine, which is really a double accelerator that causes two separate beams to collide, either head-on or at a grazing angle. Because of relativistic effects, producing the same reactions with a conventional accelerator would require a single beam hitting a stationary target with much more than twice the energy of either of the colliding beams.
Plans were made to build a huge accelerator in Waxahachie, Tex. Called the Superconducting Supercollider (SSC), a ring 54 mi (87 km) in circumference lined with superconducting magnets (see superconductivity) was intended to produce 40 TeV particle collisions. The program was ended in 1993, however, when government funding was stopped.
In Nov., 2009, the Large Hadron Collider (LHC), a synchroton constructed by CERN, became operational, and in Mar., 2010, it accelerated protons to 3.5 TeV to produce collisions of 7 TeV, a new record. The LHC's main ring, which uses superconducting magnets, is housed in a circular tunnel some 17 mi (27 km) long on the French-Swiss border; the tunnel was originally constructed for the Large Electron Positron Collider, which operated from 1989 to 2000. The LHC was shut down in 2013–15 to make improvements designed to permit it to produce collisions involving protons that have been accelerated up to 7 TeV (and collisions of lead nuclei at lower energies), and in trials in 2015 it produced collisions of 13 TeV, a further record. A new shutdown for further improvements began in 2018. In 2012 CERN scientists announced the discovery of a new elementary particle consistent with a Higgs particle; they confirmed its discovery the following year. In addition to the Higgs particle, the LHC is being used to investigate quarks, gluons, and other particles and aspects of physics' Standard Model (see elementary particles).
The synchrotron can be used to accelerate electrons but is inefficient. An electron moves much faster than a proton of the same energy and hence loses much more energy in synchrotron radiation. A circular machine used to accelerate electrons is the betatron, invented by Donald Kerst in 1939. Electrons are injected into a doughnut-shaped vacuum chamber that surrounds a magnetic field. The magnetic field is steadily increased, inducing a tangential electric field that accelerates the electrons (see induction).
in modern bourgeois macroeconomics, the ratio of the increase in investments to the relative increment in income, consumer demand, or finished product causing this increase. The accelerator is expressed by the formula
(where I = investments, Y = income, t = time). It is used as a quantitative expression of the “acceleration principle,” according to which any increase or reduction in income, demand, or product causes (or requires) a relatively greater (percentage-wise) increase or reduction in the “induced” investments. This principle, which was proposed by A. Aftalion in 1913 and J. M. Clark in 1919, was subsequently elaborated in greater detail by the Englishmen R. Harrod and J. Hicks and the American P. Samuelson. It has been included in the neo-Keynesian models of economic growth.
The reasons for the sharper dynamics in the increments or reductions in investments, in comparison with the income or demand dynamics causing them, are to be found in the duration of the equipment manufacturing time. Therefore, in the period between the development of demand for additional equipment and its output, the unsatisfied demand impels an expansion of production beyond the limit of the initial demand. Another factor is the duration of the use of equipment. As a consequence of this, the percentage of new investments to replacement investments is greater than the percentage increase of product, the demand for which caused the new investments. For example, if, with a fixed capital of $500 million of which 10 percent wears out annually ($50 million), demand for finished goods increases by 10 percent, the investments are required to compensate not only for the wear on fixed capital but also for the additional expansion of capital to satisfy the increased demand (by $50 million). A mere 10 percent increase in the demand for finished products causes a doubling of gross investments for equipment.
In macroeconomic models, the accelerator is combined with the multiplier in the form of the Hicks national income equation:
Yt = At + (1–s)Yt−1 + v (Yt−1 – Yt−2)
where A = autonomous investments and (1–s) = the share of consumption in national income or its increase. Depending on the multiplier factor, or the coefficient of the inclination to consume, and the accelerator, the dynamics of national income (Y) or its increases can assume an even or cyclical character. Cyclical fluctuations arise with a ratio
[(1–s) + v]2 < 4v
Thus, the accelerator principle is viewed by bourgeois economists as one of the main explanations for economic cycles.
The rational elements of the accelerator concept consist of certain technical proportions between the replacement and expansion of fixed capital and the depiction of turning points in investment dynamics moving from one phase of the cycle to another. The fundamental failings of the concept are the substitution of technical dependencies in the process of fixed capital reproduction for the real causes of the capitalist cycle; the erroneous notion of investment dynamics as a function of income and consumer demand, while with capitalism these dynamics are determined by the drive for profit; the contradiction between the acceleration principle and the real process of the reduction in the capital intensiveness of product; and the rejection of opportunities to satisfy demand without additional investments by the fuller loading of equipment and the intensification of its utilization. Like all models in bourgeois macroeconomics, the accelerator model reflects only certain external functional relationships and ignores the actual cause-and-effect dependencies of the reproduction process.
REFERENCESSamuelson, P. Ekonomika: Vvodnyi kurs. Moscow, 1964. Pages 289–303. (Translated from English.)
Al’ter, L. B. “Modeli mul’tiplikatora i akseleratora v mak-roekonomicheskoi dinamike.” In the collection Kapitalisticheskoe vosproizvodstvo v sovremennvkh usloviiakh. Moscow, 1966. Pages 107–128.
Al’ter, L. B. Burzhuaznaia politicheskaia ekonomiia SShA, ch. 13, pp. 593–609. Moscow, 1961.
Hansen, A. H. Business Cycles and National Income. New York, 1951.
Clark, J. M. “Business Acceleration and the Law of Demand.” In Readings in Business Cycle Theory, part 3. Philadelphia-Toronto, 1944.
L. B. AL’TER
accelerator(1) See particle accelerator.
(2) Speeding up the retrieval of Web pages. See Web page acceleration and CDN.
(3) Speeding up file downloading. See download accelerator.
(4) Speeding up hardware. See graphics accelerator, video accelerator and accelerator card.
(5) A quick way to gain knowledge when reading text on a Web page. For example, after highlighting a word and clicking a button, an accelerator may provide a dictionary definition, a foreign language translation or the map of a street address.
(6) A key combination such as Alt-Shift-G that is used to activate a task. It provides a faster activation method than selecting from a menu. See also special function key.
(7) An incubator that expects to develop the company considerably faster than normal. See incubator.