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116-540: The TFTR never achieved this goal, but it did produce major advances in confinement time and energy density. It was the world's first magnetic fusion device to perform extensive scientific experiments with plasmas composed of 50/50 deuterium/tritium (D-T), the fuel mix required for practical fusion power production, and also the first to produce more than 10 MW of fusion power. It set several records for power output, maximum temperature, and fusion triple product . TFTR shut down in 1997 after fifteen years of operation. PPPL used

232-416: A fusion triple product of 1.5 x 10 Kelvin seconds per cubic centimeter, which is close to the goal for a practical reactor and five to seven times what is needed for breakeven. However, this occurred at a temperature that was far below what would be required. In July 1986, TFTR achieved a plasma temperature of 200 million kelvin (200 MK), at that time the highest ever reached in a laboratory. The temperature

348-411: A klystron and a complex bending magnet arrangement which produces a beam of energy 6–30  MeV . The electrons can be used directly or they can be collided with a target to produce a beam of X-rays . The reliability, flexibility and accuracy of the radiation beam produced has largely supplanted the older use of cobalt-60 therapy as a treatment tool. In the circular accelerator, particles move in

464-402: A circle until they reach enough energy. The particle track is typically bent into a circle using electromagnets . The advantage of circular accelerators over linear accelerators ( linacs ) is that the ring topology allows continuous acceleration, as the particle can transit indefinitely. Another advantage is that a circular accelerator is smaller than a linear accelerator of comparable power (i.e.

580-458: A commercial system followed, that could be built at Oak Ridge. They gave the project the name TFTR and went to Congress for funding, which was granted in January 1975. Conceptual design work was carried out throughout 1975, and detailed design began the next year. TFTR would be the largest tokamak in the world; for comparison, the original ST had a plasma diameter of 12 inches (300 mm), while

696-553: A constant frequency by a RF accelerating power source, as the beam spirals outwards continuously. The particles are injected in the center of the magnet and are extracted at the outer edge at their maximum energy. Cyclotrons reach an energy limit because of relativistic effects whereby the particles effectively become more massive, so that their cyclotron frequency drops out of sync with the accelerating RF. Therefore, simple cyclotrons can accelerate protons only to an energy of around 15 million electron volts (15 MeV, corresponding to

812-696: A hole in the plate, the polarity is switched so that the plate now repels them and they are now accelerated by it towards the next plate. Normally a stream of "bunches" of particles are accelerated, so a carefully controlled AC voltage is applied to each plate to continuously repeat this process for each bunch. As the particles approach the speed of light the switching rate of the electric fields becomes so high that they operate at radio frequencies , and so microwave cavities are used in higher energy machines instead of simple plates. Linear accelerators are also widely used in medicine , for radiotherapy and radiosurgery . Medical grade linacs accelerate electrons using

928-427: A linac would have to be extremely long to have the equivalent power of a circular accelerator). Depending on the energy and the particle being accelerated, circular accelerators suffer a disadvantage in that the particles emit synchrotron radiation . When any charged particle is accelerated, it emits electromagnetic radiation and secondary emissions . As a particle traveling in a circle is always accelerating towards

1044-514: A magnetic field which is fixed in time, but with a radial variation to achieve strong focusing , allows the beam to be accelerated with a high repetition rate but in a much smaller radial spread than in the cyclotron case. Isochronous FFAs, like isochronous cyclotrons, achieve continuous beam operation, but without the need for a huge dipole bending magnet covering the entire radius of the orbits. Some new developments in FFAs are covered in. A Rhodotron

1160-526: A minimum required value, and the name "Lawson criterion" may refer to this value. On August 8, 2021, researchers at Lawrence Livermore National Laboratory's National Ignition Facility in California confirmed to have produced the first-ever successful ignition of a nuclear fusion reaction surpassing the Lawson's criteria in the experiment. The central concept of the Lawson criterion is an examination of

1276-556: A new fundamental mode of plasma confinement -- enhanced reversed shear , to reduce plasma turbulence. TFTR remained in use until 1997. It was dismantled in September 2002, after 15 years of operation. It was followed by the NSTX spherical tokamak. Fusion triple product The Lawson criterion is a figure of merit used in nuclear fusion research. It compares the rate of energy being generated by fusion reactions within

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1392-519: A particle and an atomic nucleus. Beams of high-energy particles are useful for fundamental and applied research in the sciences and also in many technical and industrial fields unrelated to fundamental research. There are approximately 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, and 4% for biomedical and other low-energy research. For

1508-432: A reactor to produce tritium . An example of this type of machine is LANSCE at Los Alamos National Laboratory . Electrons propagating through a magnetic field emit very bright and coherent photon beams via synchrotron radiation . It has numerous uses in the study of atomic structure, chemistry, condensed matter physics, biology, and technology. A large number of synchrotron light sources exist worldwide. Examples in

1624-426: A shorter distance in each orbit than they would in a classical cyclotron, thus remaining in phase with the accelerating field. The advantage of the isochronous cyclotron is that it can deliver continuous beams of higher average intensity, which is useful for some applications. The main disadvantages are the size and cost of the large magnet needed, and the difficulty in achieving the high magnetic field values required at

1740-904: A special class of light sources based on synchrotron radiation that provides shorter pulses with higher temporal coherence . A specially designed FEL is the most brilliant source of x-rays in the observable universe. The most prominent examples are the LCLS in the U.S. and European XFEL in Germany. More attention is being drawn towards soft x-ray lasers, which together with pulse shortening opens up new methods for attosecond science . Apart from x-rays, FELs are used to emit terahertz light , e.g. FELIX in Nijmegen, Netherlands, TELBE in Dresden, Germany and NovoFEL in Novosibirsk, Russia. Thus there

1856-474: A speed of roughly 10% of c ), because the protons get out of phase with the driving electric field. If accelerated further, the beam would continue to spiral outward to a larger radius but the particles would no longer gain enough speed to complete the larger circle in step with the accelerating RF. To accommodate relativistic effects the magnetic field needs to be increased to higher radii as is done in isochronous cyclotrons . An example of an isochronous cyclotron

1972-649: A straight line, or circular , using magnetic fields to bend particles in a roughly circular orbit. Magnetic induction accelerators accelerate particles by induction from an increasing magnetic field, as if the particles were the secondary winding in a transformer. The increasing magnetic field creates a circulating electric field which can be configured to accelerate the particles. Induction accelerators can be either linear or circular. Linear induction accelerators utilize ferrite-loaded, non-resonant induction cavities. Each cavity can be thought of as two large washer-shaped disks connected by an outer cylindrical tube. Between

2088-452: A target or an external beam in beam "spills" typically every few seconds. Since high energy synchrotrons do most of their work on particles that are already traveling at nearly the speed of light c , the time to complete one orbit of the ring is nearly constant, as is the frequency of the RF cavity resonators used to drive the acceleration. In modern synchrotrons, the beam aperture is small and

2204-537: Is 10 times greater than the center of the Sun, and more than enough for breakeven. Unfortunately, to reach these temperatures the triple product had been greatly reduced to 10 , two or three times too small for break-even. Major efforts to reach these conditions simultaneously continued. Donald Grove, TFTR project manager, said they expected to achieve that goal in 1987. This would be followed with D-T tests that would actually produce breakeven, beginning in 1989. Unfortunately,

2320-402: Is 3 km (1.9 mi) long. SLAC was originally an electron – positron collider but is now a X-ray Free-electron laser . Linear high-energy accelerators use a linear array of plates (or drift tubes) to which an alternating high-energy field is applied. As the particles approach a plate they are accelerated towards it by an opposite polarity charge applied to the plate. As they pass through

2436-405: Is a circular magnetic induction accelerator, invented by Donald Kerst in 1940 for accelerating electrons . The concept originates ultimately from Norwegian-German scientist Rolf Widerøe . These machines, like synchrotrons, use a donut-shaped ring magnet (see below) with a cyclically increasing B field, but accelerate the particles by induction from the increasing magnetic field, as if they were

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2552-413: Is a great demand for electron accelerators of moderate ( GeV ) energy, high intensity and high beam quality to drive light sources. Everyday examples of particle accelerators are cathode ray tubes found in television sets and X-ray generators. These low-energy accelerators use a single pair of electrodes with a DC voltage of a few thousand volts between them. In an X-ray generator, the target itself

2668-509: Is an industrial electron accelerator first proposed in 1987 by J. Pottier of the French Atomic Energy Agency (CEA) , manufactured by Belgian company Ion Beam Applications . It accelerates electrons by recirculating them across the diameter of a cylinder-shaped radiofrequency cavity. A Rhodotron has an electron gun, which emits an electron beam that is attracted to a pillar in the center of the cavity. The pillar has holes

2784-422: Is commonly used for sterilization. Electron beams are an on-off technology that provide a much higher dose rate than gamma or X-rays emitted by radioisotopes like cobalt-60 ( Co) or caesium-137 ( Cs). Due to the higher dose rate, less exposure time is required and polymer degradation is reduced. Because electrons carry a charge, electron beams are less penetrating than both gamma and X-rays. Historically,

2900-404: Is determined by the accelerating voltage , which is limited by electrical breakdown . Electrodynamic or electromagnetic accelerators, on the other hand, use changing electromagnetic fields (either magnetic induction or oscillating radio frequency fields) to accelerate particles. Since in these types the particles can pass through the same accelerating field multiple times, the output energy

3016-607: Is easy to show that the fusion power is maximized by a fuel mix given by n 1 / n 2 = ( 1 + Z 2 T e / T i ) / ( 1 + Z 1 T e / T i ) {\displaystyle n_{1}/n_{2}=(1+Z_{2}T_{\mathrm {e} }/T_{\mathrm {i} })/(1+Z_{1}T_{\mathrm {e} }/T_{\mathrm {i} })} . The values for n τ {\displaystyle n\tau } , n T τ {\displaystyle nT\tau } , and

3132-560: Is more often used for accelerators that employ oscillating rather than static electric fields. Due to the high voltage ceiling imposed by electrical discharge, in order to accelerate particles to higher energies, techniques involving dynamic fields rather than static fields are used. Electrodynamic acceleration can arise from either of two mechanisms: non-resonant magnetic induction , or resonant circuits or cavities excited by oscillating radio frequency (RF) fields. Electrodynamic accelerators can be linear , with particles accelerating in

3248-399: Is not limited by the strength of the accelerating field. This class, which was first developed in the 1920s, is the basis for most modern large-scale accelerators. Rolf Widerøe , Gustav Ising , Leó Szilárd , Max Steenbeck , and Ernest Lawrence are considered pioneers of this field, having conceived and built the first operational linear particle accelerator , the betatron , as well as

3364-571: Is one of the electrodes. A low-energy particle accelerator called an ion implanter is used in the manufacture of integrated circuits . At lower energies, beams of accelerated nuclei are also used in medicine as particle therapy , for the treatment of cancer. DC accelerator types capable of accelerating particles to speeds sufficient to cause nuclear reactions are Cockcroft–Walton generators or voltage multipliers , which convert AC to high voltage DC, or Van de Graaff generators that use static electricity carried by belts. Electron beam processing

3480-431: Is readily obtained: The quantity T 2 ⟨ σ v ⟩ {\displaystyle {\frac {T^{2}}{\langle \sigma v\rangle }}} is also a function of temperature with an absolute minimum at a slightly lower temperature than T ⟨ σ v ⟩ {\displaystyle {\frac {T}{\langle \sigma v\rangle }}} . For

3596-402: Is still extremely popular today, with the electrostatic accelerators greatly out-numbering any other type, they are more suited to lower energy studies owing to the practical voltage limit of about 1 MV for air insulated machines, or 30 MV when the accelerator is operated in a tank of pressurized gas with high dielectric strength , such as sulfur hexafluoride . In a tandem accelerator

Tokamak Fusion Test Reactor - Misplaced Pages Continue

3712-468: Is that the curvature of the particle trajectory is proportional to the particle charge and to the magnetic field, but inversely proportional to the (typically relativistic ) momentum . The earliest operational circular accelerators were cyclotrons , invented in 1929 by Ernest Lawrence at the University of California, Berkeley . Cyclotrons have a single pair of hollow D-shaped plates to accelerate

3828-682: Is that the magnetic field need only be present over the actual region of the particle orbits, which is much narrower than that of the ring. (The largest cyclotron built in the US had a 184-inch-diameter (4.7 m) magnet pole, whereas the diameter of synchrotrons such as the LEP and LHC is nearly 10 km. The aperture of the two beams of the LHC is of the order of a centimeter.) The LHC contains 16 RF cavities, 1232 superconducting dipole magnets for beam steering, and 24 quadrupoles for beam focusing. Even at this size,

3944-604: Is the PSI Ring cyclotron in Switzerland, which provides protons at the energy of 590 MeV which corresponds to roughly 80% of the speed of light. The advantage of such a cyclotron is the maximum achievable extracted proton current which is currently 2.2 mA. The energy and current correspond to 1.3 MW beam power which is the highest of any accelerator currently existing. A classic cyclotron can be modified to increase its energy limit. The historically first approach

4060-501: Is the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory . Particle accelerators can also produce proton beams, which can produce proton-rich medical or research isotopes as opposed to the neutron-rich ones made in fission reactors ; however, recent work has shown how to make Mo , usually made in reactors, by accelerating isotopes of hydrogen, although this method still requires

4176-456: Is the Lawson criterion. For the deuterium – tritium reaction, the physical value is at least The minimum of the product occurs near T = 26 k e V {\displaystyle T=26\,\mathrm {keV} } . A still more useful figure of merit is the "triple product" of density, temperature, and confinement time, nTτ E . For most confinement concepts, whether inertial , mirror , or toroidal confinement,

4292-428: Is the particle density. The volume rate f {\displaystyle f} (reactions per volume per time) of fusion reactions is where σ {\displaystyle \sigma } is the fusion cross section , v {\displaystyle v} is the relative velocity , and ⟨ ⟩ {\displaystyle \langle \rangle } denotes an average over

4408-485: The Department of Energy (DOE) held a large meeting that was attended by all the major fusion labs. Notable among the attendees was Marshall Rosenbluth , a theorist who had a habit of studying machines and finding a variety of new instabilities that would ruin confinement. To everyone's surprise, at this meeting he failed to raise any new concerns. It appeared that the path to break-even was clear. The last step before

4524-946: The Diamond Light Source which has been built at the Rutherford Appleton Laboratory in England or the Advanced Photon Source at Argonne National Laboratory in Illinois , USA. High-energy X-rays are useful for X-ray spectroscopy of proteins or X-ray absorption fine structure (XAFS), for example. Synchrotron radiation is more powerfully emitted by lighter particles, so these accelerators are invariably electron accelerators. Synchrotron radiation allows for better imaging as researched and developed at SLAC's SPEAR . Fixed-Field Alternating Gradient accelerators (FFA)s , in which

4640-710: The Maxwellian velocity distribution at the temperature T {\displaystyle T} . The volume rate of heating by fusion is f {\displaystyle f} times E c h {\displaystyle E_{\mathrm {ch} }} , the energy of the charged fusion products (the neutrons cannot help to heat the plasma). In the case of the D-T reaction, E c h = 3.5 M e V {\displaystyle E_{\mathrm {ch} }=3.5\,\mathrm {MeV} } . The Lawson criterion requires that fusion heating exceeds

4756-565: The Relativistic Heavy Ion Collider at Brookhaven National Laboratory in New York and the largest accelerator, the Large Hadron Collider near Geneva, Switzerland, operated by 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. There are more than 30,000 accelerators in operation around

Tokamak Fusion Test Reactor - Misplaced Pages Continue

4872-463: The TFTR has achieved the densities and energy lifetimes needed to achieve Lawson at the temperatures it can create, but it cannot create those temperatures at the same time. ITER aims to do both. As for tokamaks , there is a special motivation for using the triple product. Empirically, the energy confinement time τ E is found to be nearly proportional to n / P . In an ignited plasma near

4988-435: The cyclotron . Because the target of the particle beams of early accelerators was usually the atoms of a piece of matter, with the goal being to create collisions with their nuclei in order to investigate nuclear structure, accelerators were commonly referred to as atom smashers in the 20th century. The term persists despite the fact that many modern accelerators create collisions between two subatomic particles , rather than

5104-404: The D-T reaction, the minimum occurs at T  = 14 keV. The average <σ v > in this temperature region can be approximated as so the minimum value of the triple product value at T  = 14 keV is about This number has not yet been achieved in any reactor, although the latest generations of machines have come close. JT-60 reported 1.53x10 keV.s.m . For instance,

5220-484: The LHC is limited by its ability to steer the particles without them going adrift. This limit is theorized to occur at 14 TeV. However, since the particle momentum increases during acceleration, it is necessary to turn up the magnetic field B in proportion to maintain constant curvature of the orbit. In consequence, synchrotrons cannot accelerate particles continuously, as cyclotrons can, but must operate cyclically, supplying particles in bunches, which are delivered to

5336-425: The Lawson criterion gives a minimum required value for the product of the plasma (electron) density n e and the " energy confinement time " τ E {\displaystyle \tau _{E}} that leads to net energy output. Later analysis suggested that a more useful figure of merit is the triple product of density, confinement time, and plasma temperature T . The triple product also has

5452-609: The Tevatron, LEP , and LHC may deliver the particle bunches into storage rings of magnets with a constant magnetic field, where they can continue to orbit for long periods for experimentation or further acceleration. The highest-energy machines such as the Tevatron and LHC are actually accelerator complexes, with a cascade of specialized elements in series, including linear accelerators for initial beam creation, one or more low energy synchrotrons to reach intermediate energy, storage rings where beams can be accumulated or "cooled" (reducing

5568-687: The U.S. are SSRL at SLAC National Accelerator Laboratory , APS at Argonne National Laboratory, ALS at Lawrence Berkeley National Laboratory , and NSLS-II at Brookhaven National Laboratory . In Europe, there are MAX IV in Lund, Sweden, BESSY in Berlin, Germany, Diamond in Oxfordshire, UK, ESRF in Grenoble , France, the latter has been used to extract detailed 3-dimensional images of insects trapped in amber. Free-electron lasers (FELs) are

5684-472: The above expression into relationship ( 1 ), we obtain This product must be greater than a value related to the minimum of T /<σv>. The same requirement is traditionally expressed in terms of mass density ρ  = < nm i >: Satisfaction of this criterion at the density of solid D-T (0.2 g/cm ) would require a laser pulse of implausibly large energy. Assuming the energy required scales with

5800-510: The alpha particles produced in the deuterium-tritium reactions, which are important for self-heating of the plasma and an important part of any operational design. In 1995, TFTR attained a world-record temperature of 510 million °C - more than 25 times that at the center of the sun. This later was beaten the following year by the JT-60 Tokamak which achieved an ion temperature of 522 million °C (45 keV). Also In 1995, TFTR scientists explored

5916-491: The attack on break-even would be to make a reactor that ran on a mixture of deuterium and tritium , as opposed to earlier machines which ran on deuterium alone. This was because tritium was both radioactive and easily absorbed in the body, presenting safety issues that made it expensive to use. It was widely believed that the performance of a machine running on deuterium alone would be basically identical to one running on D-T, but this assumption needed to be tested. Looking over

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6032-494: The beam is handled independently by specialized quadrupole magnets , while the acceleration itself is accomplished in separate RF sections, rather similar to short linear accelerators. Also, there is no necessity that cyclic machines be circular, but rather the beam pipe may have straight sections between magnets where beams may collide, be cooled, etc. This has developed into an entire separate subject, called "beam physics" or "beam optics". More complex modern synchrotrons such as

6148-460: The center of the circle, it continuously radiates towards the tangent of the circle. This radiation is called synchrotron light and depends highly on the mass of the accelerating particle. For this reason, many high energy electron accelerators are linacs. Certain accelerators ( synchrotrons ) are however built specially for producing synchrotron light ( X-rays ). Since the special theory of relativity requires that matter always travels slower than

6264-443: The cloud and T is the temperature. For his analysis, Lawson ignores conduction losses. In reality this is nearly impossible; practically all systems lose energy through mass leaving the plasma and carrying away its energy. By equating radiation losses and the volumetric fusion rates, Lawson estimated the minimum temperature for the fusion for the deuterium – tritium (D-T) reaction to be 30 million degrees (2.6 keV), and for

6380-653: The confirmation of the Novosibirsk results, they immediately began converting the Model C to a tokamak layout, known as the Symmetrical Tokamak (ST). This was completed in the short time of only eight months, entering service in May 1970. ST's computerized diagnostics allowed it to quickly match the Soviet results, and from that point, the entire fusion world was increasingly focused on this design over any other. During

6496-416: The density and temperature can be varied over a fairly wide range, but the maximum attainable pressure p is a constant. When such is the case, the fusion power density is proportional to p <σ v >/ T . The maximum fusion power available from a given machine is therefore reached at the temperature T where <σ v >/ T is a maximum. By continuation of the above derivation, the following inequality

6612-526: The density of the electrons alone, but p {\displaystyle p} here refers to the total pressure. Given two species with ion densities n 1 , 2 {\displaystyle n_{1,2}} , atomic numbers Z 1 , 2 {\displaystyle Z_{1,2}} , ion temperature T i {\displaystyle T_{\mathrm {i} }} , and electron temperature T e {\displaystyle T_{\mathrm {e} }} , it

6728-550: The designs presented at the meeting, the DOE team chose the Princeton design. Bob Hirsch , who recently took over the DOE steering committee, wanted to build the test machine at Oak Ridge National Laboratory (ORNL), but others in the department convinced him it would make more sense to do so at PPPL. They argued that a Princeton team would be more involved than an ORNL team running someone else's design. If an engineering prototype of

6844-404: The deuterium–deuterium (D-D) reaction to be 150 million degrees (12.9 keV). The confinement time τ E {\displaystyle \tau _{E}} measures the rate at which a system loses energy to its environment. The faster the rate of loss of energy, P l o s s {\displaystyle P_{\mathrm {loss} }} , the shorter

6960-613: The disks is a ferrite toroid. A voltage pulse applied between the two disks causes an increasing magnetic field which inductively couples power into the charged particle beam. The linear induction accelerator was invented by Christofilos in the 1960s. Linear induction accelerators are capable of accelerating very high beam currents (>1000 A) in a single short pulse. They have been used to generate X-rays for flash radiography (e.g. DARHT at LANL ), and have been considered as particle injectors for magnetic confinement fusion and as drivers for free electron lasers . The Betatron

7076-412: The early 1970s, Shoichi Yoshikawa was looking over the tokamak concept. He noted that as the size of the reactor's minor axis (the diameter of the tube) increased compared to its major axis (the diameter of the entire system) the system became more efficient. An added benefit was that as the minor axis increased, confinement time improved for the simple reason that it took longer for the fuel ions to reach

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7192-435: The electrons can pass through. The electron beam passes through the pillar via one of these holes and then travels through a hole in the wall of the cavity, and meets a bending magnet, the beam is then bent and sent back into the cavity, to another hole in the pillar, the electrons then again go across the pillar and pass though another part of the wall of the cavity and into another bending magnet, and so on, gradually increasing

7308-499: The electrons moving at nearly the speed of light in a relatively small radius orbit. In a linear particle accelerator (linac), particles are accelerated in a straight line with a target of interest at one end. They are often used to provide an initial low-energy kick to particles before they are injected into circular accelerators. The longest linac in the world is the Stanford Linear Accelerator , SLAC, which

7424-438: The energy balance for any fusion power plant using a hot plasma. This is shown below: Net power = Efficiency × (Fusion − Radiation loss − Conduction loss) Lawson calculated the fusion rate by assuming that the fusion reactor contains a hot plasma cloud which has a Gaussian curve of individual particle energies, a Maxwell–Boltzmann distribution characterized by the plasma's temperature. Based on that assumption, he estimated

7540-458: The energy confinement time. It is the energy density W {\displaystyle W} (energy content per unit volume) divided by the power loss density P l o s s {\displaystyle P_{\mathrm {loss} }} (rate of energy loss per unit volume): For a fusion reactor to operate in steady state, the fusion plasma must be maintained at a constant temperature. Thermal energy must therefore be added at

7656-445: The energy in the heating systems, this represented a Q of about 0.2, or about only 20% of the requirement for break-even. Further testing revealed significant problems, however. To reach break-even, the system would have to meet several goals at the same time, a combination of temperature, density and the length of time the fuel is confined. In April 1986, TFTR experiments demonstrated the last two of these requirements when it produced

7772-461: The energy of the beam until it is allowed to exit the cavity for use. The cylinder and pillar may be lined with copper on the inside. Ernest Lawrence's first cyclotron was a mere 4 inches (100 mm) in diameter. Later, in 1939, he built a machine with a 60-inch diameter pole face, and planned one with a 184-inch diameter in 1942, which was, however, taken over for World War II -related work connected with uranium isotope separation ; after

7888-530: The field. Although it became clear that TFTR would not reach break-even, experiments using tritium began in earnest in December 1993, the first such device to move primarily to this fuel. In 1994 it produced a then world-record of 10.7 megawatts of fusion power from a 50-50 D-T plasma (exceeded at JET in the UK, which generated 16MW from 24MW of injected thermal power input in 1997). The two experiments had emphasized

8004-409: The first accelerators used simple technology of a single static high voltage to accelerate charged particles. The charged particle was accelerated through an evacuated tube with an electrode at either end, with the static potential across it. Since the particle passed only once through the potential difference, the output energy was limited to the accelerating voltage of the machine. While this method

8120-414: The first term, the fusion energy being produced, using the volumetric fusion equation. Fusion = Number density of fuel A × Number density of fuel B × Cross section(Temperature) × Energy per reaction This equation is typically averaged over a population of ions which has a normal distribution . The result is the amount of energy being created by the plasma at any instant in time. Lawson then estimated

8236-475: The follow-on PLT design was 36 inches (910 mm), and the TFTR was designed to be 86 inches (2,200 mm). This made it roughly double the size of other large-scale machines of the era; the 1978 Joint European Torus and roughly concurrent JT-60 were both about half the diameter. As PLT continued to generate better and better results, in 1978 and 79, additional funding was added and the design amended to reach

8352-582: The formulas. On the other hand, for cold electrons, the formulas must all be divided by 4 {\displaystyle 4} (with no additional factor for Z > 1 {\displaystyle Z>1} ). Particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies to contain them in well-defined beams . Small accelerators are used for fundamental research in particle physics . Accelerators are also used as synchrotron light sources for

8468-433: The fusion fuel to the rate of energy losses to the environment. When the rate of production is higher than the rate of loss, the system will produce net energy. If enough of that energy is captured by the fuel, the system will become self-sustaining and is said to be ignited . The concept was first developed by John D. Lawson in a classified 1955 paper that was declassified and published in 1957. As originally formulated,

8584-401: The high temperatures of nuclear fusion reactions. The heating current is induced by the changing magnetic fields in central induction coils and exceeds a million amperes. Magnetic fusion devices keep the hot plasma out of contact with the walls of its container by keeping it moving in circular or helical paths by means of the magnetic force on charged particles and by a centripetal force acting on

8700-486: The idea of neutral beam injection . This used small particle accelerators to inject fuel atoms directly into the plasma, both heating it and providing fresh fuel. After a number of modifications to the beam injection system, the newly equipped PLT began setting records and eventually made several test runs at 60 million K, more than enough for a fusion reactor. To reach the Lawson criterion for ignition, all that

8816-483: The inertial case it is more usefully expressed in a different form. A good approximation for the inertial confinement time τ E {\displaystyle \tau _{E}} is the time that it takes an ion to travel over a distance R at its thermal speed where m i denotes mean ionic mass. The inertial confinement time τ E {\displaystyle \tau _{E}} can thus be approximated as By substitution of

8932-508: The knowledge from TFTR to begin studying another approach, the spherical tokamak , in their National Spherical Torus Experiment . The Japanese JT-60 is very similar to the TFTR, both tracing their design to key innovations introduced by Shoichi Yoshikawa (1934-2010) during his time at PPPL in the 1970s. In nuclear fusion, there are two types of reactors stable enough to conduct fusion: magnetic confinement reactors and inertial confinement reactors. The former method of fusion seeks to lengthen

9048-529: The long-sought goal of "scientific breakeven" when the amount of power produced by the fusion reactions in the plasma was equal to the amount of power being fed into it to heat it to operating temperatures. Also known as Q = 1, this is an important step on the road to useful power-producing designs. To meet this requirement, the heating system was upgraded to 50 MW, and finally to 80 MW. Construction began in 1980 and TFTR began initial operations in 1982. A lengthy period of break-in and testing followed. By

9164-467: The losses: Substituting in known quantities yields: Rearranging the equation produces: The quantity T / ⟨ σ v ⟩ {\displaystyle T/\langle \sigma v\rangle } is a function of temperature with an absolute minimum. Replacing the function with its minimum value provides an absolute lower limit for the product n τ E {\displaystyle n\tau _{E}} . This

9280-411: The magnet aperture required and permitting tighter focusing; see beam cooling ), and a last large ring for final acceleration and experimentation. Circular electron accelerators fell somewhat out of favor for particle physics around the time that SLAC 's linear particle accelerator was constructed, because their synchrotron losses were considered economically prohibitive and because their beam intensity

9396-412: The magnetic field does not cover the entire area of the particle orbit as it does for a cyclotron, so several necessary functions can be separated. Instead of one huge magnet, one has a line of hundreds of bending magnets, enclosing (or enclosed by) vacuum connecting pipes. The design of synchrotrons was revolutionized in the early 1950s with the discovery of the strong focusing concept. The focusing of

9512-468: The mass of the fusion plasma ( E laser ~ ρR ~ ρ ), compressing the fuel to 10 or 10 times solid density would reduce the energy required by a factor of 10 or 10 , bringing it into a realistic range. With a compression by 10 , the compressed density will be 200 g/cm , and the compressed radius can be as small as 0.05 mm. The radius of the fuel before compression would be 0.5 mm. The initial pellet will be perhaps twice as large since most of

9628-406: The mass will be ablated during the compression. The fusion power times density is a good figure of merit to determine the optimum temperature for magnetic confinement, but for inertial confinement the fractional burn-up of the fuel is probably more useful. The burn-up should be proportional to the specific reaction rate ( n < σv >) times the confinement time (which scales as T ) divided by

9744-407: The mid-1980s, tests with deuterium began in earnest in order to understand its performance. In 1986 it produced the first 'supershots' which produced many fusion neutrons. These demonstrated that the system could reach the goals of the initial 1976 design; the performance when running on deuterium was such that if tritium was introduced it was expected to produce about 3.5 MW of fusion power. Given

9860-481: The most basic inquiries into the dynamics and structure of matter, space, and time, physicists seek the simplest kinds of interactions at the highest possible energies. These typically entail particle energies of many GeV , and interactions of the simplest kinds of particles: leptons (e.g. electrons and positrons ) and quarks for the matter, or photons and gluons for the field quanta . Since isolated quarks are experimentally unavailable due to color confinement ,

9976-558: The moving particles. By the early 1960s, the fusion power field had grown large enough that the researchers began organizing semi-annual meetings that rotated around the various research establishments. In 1968, the now-annual meeting was held in Novosibirsk , where the Soviet delegation surprised everyone by claiming their tokamak designs had reached performance levels at least an order of magnitude better than any other device. The claims were initially met with skepticism, but when

10092-517: The need for a huge magnet of large radius and constant field over the larger orbit demanded by high energy. The second approach to the problem of accelerating relativistic particles is the isochronous cyclotron . In such a structure, the accelerating field's frequency (and the cyclotron resonance frequency) is kept constant for all energies by shaping the magnet poles so to increase magnetic field with radius. Thus, all particles get accelerated in isochronous time intervals. Higher energy particles travel

10208-430: The optimum temperature, the heating power P equals fusion power and therefore is proportional to n T . The triple product scales as The triple product is only weakly dependent on temperature as T . This makes the triple product an adequate measure of the efficiency of the confinement scheme. The Lawson criterion applies to inertial confinement fusion (ICF) as well as to magnetic confinement fusion (MCF) but in

10324-455: The outer edge of the structure. Synchrocyclotrons have not been built since the isochronous cyclotron was developed. To reach still higher energies, with relativistic mass approaching or exceeding the rest mass of the particles (for protons, billions of electron volts or GeV ), it is necessary to use a synchrotron . This is an accelerator in which the particles are accelerated in a ring of constant radius. An immediate advantage over cyclotrons

10440-577: The outside of the reactor. This led to widespread acceptance that designs with lower aspect ratios were a key advance over earlier models. This led to the Princeton Large Torus (PLT), which was completed in 1975. This system was successful to the point where it quickly reached the limits of its Ohmic heating system, the system that passed current through the plasma to heat it. Among the many ideas proposed for further heating, in cooperation with Oak Ridge National Laboratory , PPPL developed

10556-413: The particle density n : Thus the optimum temperature for inertial confinement fusion maximises <σv>/ T , which is slightly higher than the optimum temperature for magnetic confinement. Lawson's analysis is based on the rate of fusion and loss of energy in a thermalized plasma. There is a class of fusion machines that do not use thermalized plasmas but instead directly accelerate individual ions to

10672-412: The particles and a single large dipole magnet to bend their path into a circular orbit. It is a characteristic property of charged particles in a uniform and constant magnetic field B that they orbit with a constant period, at a frequency called the cyclotron frequency , so long as their speed is small compared to the speed of light c . This means that the accelerating D's of a cyclotron can be driven at

10788-449: The potential is used twice to accelerate the particles, by reversing the charge of the particles while they are inside the terminal. This is possible with the acceleration of atomic nuclei by using anions (negatively charged ions ), and then passing the beam through a thin foil to strip electrons off the anions inside the high voltage terminal, converting them to cations (positively charged ions), which are accelerated again as they leave

10904-581: The power density must be multiplied by the factor ( 1 + Z 1 T e / T i ) ⋅ ( 1 + Z 2 T e / T i ) / 4 {\displaystyle (1+Z_{1}T_{\mathrm {e} }/T_{\mathrm {i} })\cdot (1+Z_{2}T_{\mathrm {e} }/T_{\mathrm {i} })/4} . For example, with protons and boron ( Z = 5 {\displaystyle Z=5} ) as fuel, another factor of 3 {\displaystyle 3} must be included in

11020-479: The pressure forces of the plasma, it seems appropriate to define the effective (electron) density n {\displaystyle n} through the (total) pressure p {\displaystyle p} as n = p / 2 T i {\displaystyle n=p/2T_{\mathrm {i} }} . The factor of 2 {\displaystyle 2} is included because n {\displaystyle n} usually refers to

11136-413: The radiation losses using the following equation: P B = 1.4 ⋅ 10 − 34 ⋅ N 2 ⋅ T 1 / 2 W c m 3 {\displaystyle P_{B}=1.4\cdot 10^{-34}\cdot N^{2}\cdot T^{1/2}{\frac {\mathrm {W} }{\mathrm {cm} ^{3}}}} where N is the number density of

11252-503: The required energies. The best-known examples are the migma , fusor and polywell . When applied to the fusor, Lawson's analysis is used as an argument that conduction and radiation losses are the key impediments to reaching net power. Fusors use a voltage drop to accelerate and collide ions, resulting in fusion. The voltage drop is generated by wire cages, and these cages conduct away particles. Polywells are improvements on this design, designed to reduce conduction losses by removing

11368-493: The results were confirmed by a UK team the next year, this huge advance led to a "virtual stampede" of tokamak construction. In the US, one of the major approaches being studied up to this point was the stellarator , whose development was limited almost entirely to the PPPL. Their latest design, the Model C, had recently gone into operation and demonstrated performance well below theoretical calculations, far from useful figures. With

11484-433: The same rate the plasma loses energy in order to maintain the fusion conditions. This energy can be supplied by the fusion reactions themselves, depending on the reaction type, or by supplying additional heating through a variety of methods. For illustration, the Lawson criterion for the D-T reaction will be derived here, but the same principle can be applied to other fusion fuels. It will also be assumed that all species have

11600-451: The same temperature, that there are no ions present other than fuel ions (no impurities and no helium ash), and that D and T are present in the optimal 50-50 mixture. Ion density then equals electron density and the energy density of both electrons and ions together is given, according to the ideal gas law , by where T {\displaystyle T} is the temperature in electronvolt (eV) and n {\displaystyle n}

11716-434: The secondary winding in a transformer, due to the changing magnetic flux through the orbit. Achieving constant orbital radius while supplying the proper accelerating electric field requires that the magnetic flux linking the orbit be somewhat independent of the magnetic field on the orbit, bending the particles into a constant radius curve. These machines have in practice been limited by the large radiative losses suffered by

11832-571: The simplest available experiments involve the interactions of, first, leptons with each other, and 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 essentially 2-body interactions of the quarks and gluons of which they are composed. This elementary particle physicists tend to use machines creating beams of electrons, positrons, protons, and antiprotons , interacting with each other or with

11948-405: The simplest nuclei (e.g., hydrogen or deuterium ) at the highest possible energies, generally hundreds of GeV or more. The largest and highest-energy particle accelerator used for elementary particle physics is the Large Hadron Collider (LHC) at CERN , operating since 2009. Nuclear physicists and cosmologists may use beams of bare atomic nuclei , stripped of electrons, to investigate

12064-426: The speed of light in vacuum , in high-energy accelerators, as the energy increases the particle speed approaches the speed of light as a limit, but never attains it. Therefore, particle physicists do not generally think in terms of speed, but rather in terms of a particle's energy or momentum , usually measured in electron volts (eV). An important principle for circular accelerators, and particle beams in general,

12180-471: The structure, interactions, and properties of the nuclei themselves, and of condensed matter at extremely high temperatures and densities, such as might have occurred in the first moments of the Big Bang . These investigations often involve collisions of heavy nuclei – of atoms like iron or gold  – at energies of several GeV per nucleon . The largest such particle accelerator

12296-403: 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 the manufacture of semiconductors , and accelerator mass spectrometers for measurements of rare isotopes such as radiocarbon . Large accelerators include

12412-458: The system was unable to meet any of these goals. The reasons for these problems were intensively studied over the following years, leading to a new understanding of the instabilities of high-performance plasmas that had not been seen in smaller machines. A major outcome of TFTR's troubles was the development of highly non-uniform plasma cross-sections, notably the D-shaped plasmas that now dominate

12528-507: The terminal. The two main types of electrostatic accelerator are the Cockcroft–Walton accelerator , which uses a diode-capacitor voltage multiplier to produce high voltage, and the Van de Graaff accelerator , which uses a moving fabric belt to carry charge to the high voltage electrode. Although electrostatic accelerators accelerate particles along a straight line, the term linear accelerator

12644-408: The time that ions spend close together in order to fuse them together, while the latter aims to fuse the ions so fast that they do not have time to move apart. Inertial confinement reactors, unlike magnetic confinement reactors, use laser fusion and ion-beam fusion in order to conduct fusion. However, with magnetic confinement reactors you avoid the problem of having to find a material that can withstand

12760-573: The war it continued in service for research and medicine over many years. The first large proton synchrotron was the Cosmotron at Brookhaven National Laboratory , which accelerated protons to about 3  GeV (1953–1968). The Bevatron at Berkeley, completed in 1954, was specifically designed to accelerate protons to enough energy to create antiprotons , and verify the particle–antiparticle symmetry of nature, then only theorized. The Alternating Gradient Synchrotron (AGS) at Brookhaven (1960–)

12876-450: The wire cages which cause them. Regardless, it is argued that radiation is still a major impediment. ^a It is straightforward to relax these assumptions. The most difficult question is how to define n {\displaystyle n} when the ion and electrons differ in density and temperature. Considering that this is a calculation of energy production and loss by ions, and that any plasma confinement concept must contain

12992-476: The world. There are two basic classes of accelerators: electrostatic and electrodynamic (or electromagnetic) accelerators. Electrostatic particle accelerators use static electric fields to accelerate particles. The most common types are the Cockcroft–Walton generator and 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

13108-648: Was lower than for the unpulsed linear machines. The Cornell Electron Synchrotron , built at low cost in the late 1970s, was the first in a series of high-energy circular electron accelerators built for fundamental particle physics, the last being LEP , built at CERN, which was used from 1989 until 2000. A large number of electron synchrotrons have been built in the past two decades, as part of synchrotron light sources that emit ultraviolet light and X rays; see below. Some circular accelerators have been built to deliberately generate radiation (called synchrotron light ) as X-rays also called synchrotron radiation, for example

13224-434: Was needed was higher plasma density, and there seemed to be no reason this would not be possible in a larger machine. There was widespread belief that break-even would be reached during the 1970s. After the success of PLT and other follow-on designs, the basic concept was considered well understood. PPPL began the design of a much larger successor to PLT that would demonstrate plasma burning in pulsed operation. In July 1974,

13340-414: Was the synchrocyclotron , which accelerates the particles in bunches. It uses a constant magnetic field B {\displaystyle B} , but reduces the accelerating field's frequency so as to keep the particles in step as they spiral outward, matching their mass-dependent cyclotron resonance frequency. This approach suffers from low average beam intensity due to the bunching, and again from

13456-502: Was the first large synchrotron with alternating gradient, " strong focusing " magnets, which greatly reduced the required aperture of the beam, and correspondingly the size and cost of the bending magnets. The Proton Synchrotron , built at CERN (1959–), was the first major European particle accelerator and generally similar to the AGS. The Stanford Linear Accelerator , SLAC, became operational in 1966, accelerating electrons to 30 GeV in

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