Misplaced Pages

#13986

95-404: DIII-D was built on the basis of the earlier Doublet III, the third in a series of machines built at GA to experiment with tokamaks having non-circular plasma cross sections. This work demonstrated that certain shapes strongly suppressed a variety of instabilities in the plasma, which led to much higher plasma pressure and performance. DIII-D is so-named because the plasma is shaped like the letter D,

190-545: A β max {\displaystyle \beta _{\text{max}}} around 5%, the Troyon limit was a serious concern when it was introduced. However, it was found that β N {\displaystyle \beta _{N}} changed dramatically with the shape of the plasma, and non-circular systems would have much better performance. Experiments on the DIII-D machine (the second D referring to

285-490: A plasma , symbolized by β , is the ratio of the plasma pressure ( p = n k B T ) to the magnetic pressure ( p mag = B /2 μ 0 ). The term is commonly used in studies of the Sun and Earth's magnetic field , and in the field of fusion power designs. In the fusion power field, plasma is often confined using strong magnets. Since the temperature of the fuel scales with pressure, reactors attempt to reach

380-424: A combination of electromagnets and electrical currents running through the plasma itself. Systems using only magnets are generally built using the stellarator approach, while those using current only are the pinch machines. The most studied approach since the 1970s is the tokamak , where the fields generated by the external magnets and internal current are roughly equal in magnitude. In all of these machines,

475-400: A critical field other "high-n instabilities" will invariably appear, notably the ballooning mode . For any given fusion reactor design, there is a limit to the beta it can sustain. As beta is a measure of economic merit, a practical tokamak based fusion reactor must be able to sustain a beta above some critical value, which is calculated to be around 5%. Through the 1980s the understanding of

570-410: A cycle of states of its working body. The engine takes in a quantity of heat Q 1 from a hot reservoir and passes out a lesser quantity of waste heat Q 2 < 0 to a cold reservoir. The net heat energy absorbed by the working body is passed, as thermodynamic work, to a work reservoir, and is considered to be the output of the engine. The cycle is imagined to run so slowly that at each point of

665-402: A fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature range that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today. The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This

760-488: A gas can be calculated theoretically from the gas's molecular character, temperature, pressure, and the Boltzmann constant. For a gas of known molecular character and pressure, this provides a relation between temperature and the Boltzmann constant. Those quantities can be known or measured more precisely than can the thermodynamic variables that define the state of a sample of water at its triple point. Consequently, taking

855-406: A linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic . A definite sense of greater hotness can be had, independently of calorimetry , of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation : the temperature of a bath of thermal radiation

950-415: A loss of heat from a closed system, without phase change, without change of volume, and without a change in external force fields acting on it, decreases its temperature. While for bodies in their own thermodynamic equilibrium states, the notion of temperature requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement

1045-485: A reference temperature at the triple point of water, the numerical value of which is defined by measurements using the aforementioned internationally agreed Kelvin scale. Many scientific measurements use the Kelvin temperature scale (unit symbol: K), named in honor of the physicist who first defined it . It is an absolute scale. Its numerical zero point, 0 K , is at the absolute zero of temperature. Since May 2019,

SECTION 10

#1732776285014

1140-524: A reference temperature. It is known as the Kelvin scale , widely used in science and technology. The kelvin (the unit name is spelled with a lower-case 'k') is the unit of temperature in the International System of Units (SI). The temperature of a body in a state of thermodynamic equilibrium is always positive relative to absolute zero. Besides the internationally agreed Kelvin scale, there

1235-653: A self-sustained burning plasma that will produce 10 times as much energy from fusion reactions as it requires for heating. The DIII-D research program is a large international collaboration, with over 600 users participating from more than 100 institutions. General Atomics operates the San Diego–based facility for the Department of Energy through the Office of Fusion Energy Sciences. Research in DIII-D aims to elucidate

1330-441: A shaping that is now widely used on modern designs, and has led to the class of machines known as "advanced tokamaks." Advanced tokamaks are characterized by operation at high plasma β through strong plasma shaping , active control of various plasma instabilities, and achievement of steady-state current and pressure profiles that produce high energy confinement for high fusion gain (ratio of fusion power to heating power). DIII-D

1425-462: A spatially varying local property in that body, and this is because the temperature is an intensive variable. Temperature is a measure of a quality of a state of a material. The quality may be regarded as a more abstract entity than any particular temperature scale that measures it, and is called hotness by some writers. The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in

1520-551: A species being all alike. It explains macroscopic phenomena through the classical mechanics of the microscopic particles. The equipartition theorem of kinetic theory asserts that each classical degree of freedom of a freely moving particle has an average kinetic energy of k B T /2 where k B denotes the Boltzmann constant . The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate,

1615-415: A specific intensive variable. An example is a diathermic wall that is permeable only to heat; the intensive variable for this case is temperature. When the two bodies have been connected through the specifically permeable wall for a very long time, and have settled to a permanent steady state, the relevant intensive variables are equal in the two bodies; for a diathermal wall, this statement is sometimes called

1710-400: A steady state of thermodynamic equilibrium, hotness varies from place to place. It is not necessarily the case that a material in a particular place is in a state that is steady and nearly homogeneous enough to allow it to have a well-defined hotness or temperature. Hotness may be represented abstractly as a one-dimensional manifold . Every valid temperature scale has its own one-to-one map into

1805-524: A substance. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called centigrade ), the Fahrenheit scale (°F), and the Kelvin scale (K), with the third being used predominantly for scientific purposes. The kelvin

1900-435: A system undergoing a first-order phase change such as the melting of ice, as a closed system receives heat, without a change in its volume and without a change in external force fields acting on it, its temperature rises. For a system undergoing such a phase change so slowly that departure from thermodynamic equilibrium can be neglected, its temperature remains constant as the system is supplied with latent heat . Conversely,

1995-414: A useful figure of merit when comparing MCF designs. Plainly, the higher the beta value, the more economically viable the design is and further the higher Q value the design possibly has. In effect, the ratio illustrates how effectively a design confines its plasma. This ratio, beta, is widely used in the fusion field: β {\displaystyle \beta } is normally measured in terms of

SECTION 20

#1732776285014

2090-511: Is proportional , by a universal constant, to the frequency of the maximum of its frequency spectrum ; this frequency is always positive, but can have values that tend to zero . Thermal radiation is initially defined for a cavity in thermodynamic equilibrium. These physical facts justify a mathematical statement that hotness exists on an ordered one-dimensional manifold . This is a fundamental character of temperature and thermometers for bodies in their own thermodynamic equilibrium. Except for

2185-604: Is also a thermodynamic temperature scale , invented by Lord Kelvin , also with its numerical zero at the absolute zero of temperature, but directly relating to purely macroscopic thermodynamic concepts, including the macroscopic entropy , though microscopically referable to the Gibbs statistical mechanical definition of entropy for the canonical ensemble , that takes interparticle potential energy into account, as well as independent particle motion so that it can account for measurements of temperatures near absolute zero. This scale has

2280-469: Is also used as a test bed to investigate innovative mechanisms for plasma heating, fueling and current drive. In May 1974, AEC selected General Atomics to build the Doublet III magnetic fusion experiment based on the success of earlier Doublet I and II magnetic confinement experiments. In Feb 1978, the Doublet III fusion experiment achieved its first operation with plasma at General Atomics. The machine

2375-409: Is an intensive variable because it is equal to a differential coefficient of one extensive variable with respect to another, for a given body. It thus has the dimensions of a ratio of two extensive variables. In thermodynamics, two bodies are often considered as connected by contact with a common wall, which has some specific permeability properties. Such specific permeability can be referred to

2470-518: Is arbitrary, and an alternate, less widely used absolute temperature scale exists called the Rankine scale , made to be aligned with the Fahrenheit scale as Kelvin is with Celsius. The thermodynamic definition of temperature is due to Kelvin. It is framed in terms of an idealized device called a Carnot engine , imagined to run in a fictive continuous cycle of successive processes that traverse

2565-454: Is because the entropy of an ideal gas at its absolute zero of temperature is not a positive semi-definite quantity, which puts the gas in violation of the third law of thermodynamics. In contrast to real materials, the ideal gas does not liquefy or solidify, no matter how cold it is. Alternatively thinking, the ideal gas law, refers to the limit of infinitely high temperature and zero pressure; these conditions guarantee non-interactive motions of

2660-495: Is created by applying a voltage to generate a large electric current (more than one million amperes) in the chamber. The plasma is heated to temperatures ten times hotter than that of the sun by a combination of high-power neutral beams and microwaves. The plasma conditions are measured using instrumentation based on intense lasers, microwaves, and other precision plasma diagnostics. Experiments explore such topics as confinement, transient events, and power and particle exhaust. DIII-D

2755-547: Is directly proportional to the temperature of the black body; this is known as Wien's displacement law and has a theoretical explanation in Planck's law and the Bose–Einstein law . Measurement of the spectrum of noise-power produced by an electrical resistor can also provide accurate temperature measurement. The resistor has two terminals and is in effect a one-dimensional body. The Bose-Einstein law for this case indicates that

2850-436: Is disregarded. In an ideal gas , and in other theoretically understood bodies, the Kelvin temperature is defined to be proportional to the average kinetic energy of non-interactively moving microscopic particles, which can be measured by suitable techniques. The proportionality constant is a simple multiple of the Boltzmann constant. If molecules, atoms, or electrons are emitted from material and their velocities are measured,

2945-434: Is important in all fields of natural science , including physics , chemistry , Earth science , astronomy , medicine , biology , ecology , material science , metallurgy , mechanical engineering and geography as well as most aspects of daily life. Many physical processes are related to temperature; some of them are given below: Temperature scales need two values for definition: the point chosen as zero degrees and

DIII-D (tokamak) - Misplaced Pages Continue

3040-403: Is normally given as 0.028 if I is measured in megaamperes. However, it is also common to use 2.8 if β max {\displaystyle \beta _{\text{max}}} is expressed as a percentage. Given that the Troyon limit suggested a β max {\displaystyle \beta _{\text{max}}} around 2.5 to 4%, and a practical reactor had to have

3135-455: Is not safe for bodies that are in steady states though not in thermodynamic equilibrium. It can then well be that different empirical thermometers disagree about which is hotter, and if this is so, then at least one of the bodies does not have a well-defined absolute thermodynamic temperature. Nevertheless, any one given body and any one suitable empirical thermometer can still support notions of empirical, non-absolute, hotness, and temperature, for

3230-417: Is often known simply as the beta limit in tokamaks. The Troyon limit is given as: where I is the plasma current, B 0 {\displaystyle B_{0}} is the external magnetic field, and a is the minor radius of the tokamak (see torus for an explanation of the directions). β N {\displaystyle \beta _{N}} was determined numerically, and

3325-418: Is one of the seven base units in the International System of Units (SI). Absolute zero , i.e., zero kelvin or −273.15 °C, is the lowest point in the thermodynamic temperature scale. Experimentally, it can be approached very closely but not actually reached, as recognized in the third law of thermodynamics . It would be impossible to extract energy as heat from a body at that temperature. Temperature

3420-508: Is one of two large magnetic fusion experiments in the U.S. (the other being NSTX-U at Princeton Plasma Physics Laboratory ) supported by the U.S. Department of Energy Office of Science. The program is focusing on R&D for pursuing steady-state advanced tokamak operation and supporting design and operation of the ITER experiment now under construction in France. ITER is designed to demonstrate

3515-551: Is only one degree of freedom left to arbitrary choice, rather than two as in relative scales. For the Kelvin scale since May 2019, by international convention, the choice has been made to use knowledge of modes of operation of various thermometric devices, relying on microscopic kinetic theories about molecular motion. The numerical scale is settled by a conventional definition of the value of the Boltzmann constant , which relates macroscopic temperature to average microscopic kinetic energy of particles such as molecules. Its numerical value

3610-404: Is reached, the gas will be constantly losing energy to its surroundings (cooling off). This gives rise to the concept of the "confinement time", the amount of time the plasma is maintained at the required temperature. However, the fusion reactions might deposit their energy back into the plasma, heating it back up, which is a function of the density of the plasma. These considerations are combined in

3705-419: Is said to prevail throughout the body. It makes good sense, for example, to say of the extensive variable U , or of the extensive variable S , that it has a density per unit volume or a quantity per unit mass of the system, but it makes no sense to speak of the density of temperature per unit volume or quantity of temperature per unit mass of the system. On the other hand, it makes no sense to speak of

3800-572: The Boltzmann constant , to the Maxwell–Boltzmann distribution , and to the Boltzmann statistical mechanical definition of entropy , as distinct from the Gibbs definition, for independently moving microscopic particles, disregarding interparticle potential energy, by international agreement, a temperature scale is defined and said to be absolute because it is independent of the characteristics of particular thermometric substances and thermometer mechanisms. Apart from absolute zero, it does not have

3895-525: The Boltzmann constant . That constant refers to chosen kinds of motion of microscopic particles in the constitution of the body. In those kinds of motion, the particles move individually, without mutual interaction. Such motions are typically interrupted by inter-particle collisions, but for temperature measurement, the motions are chosen so that, between collisions, the non-interactive segments of their trajectories are known to be accessible to accurate measurement. For this purpose, interparticle potential energy

DIII-D (tokamak) - Misplaced Pages Continue

3990-489: The Lawson criterion , or its modern form, the fusion triple product. In order to be efficient, the rate of fusion energy being deposited into the reactor would ideally be greater than the rate of loss to the surroundings, a condition known as "ignition". In magnetic confinement fusion (MCF) reactor designs, the plasma is confined within a vacuum chamber using a series of magnetic fields. These fields are normally created using

4085-464: The zeroth law of thermodynamics says that they all measure the same quality. This means that for a body in its own state of internal thermodynamic equilibrium, every correctly calibrated thermometer, of whatever kind, that measures the temperature of the body, records one and the same temperature. For a body that is not in its own state of internal thermodynamic equilibrium, different thermometers can record different temperatures, depending respectively on

4180-483: The 100-degree interval. Since the standardization of the kelvin in the International System of Units, it has subsequently been redefined in terms of the equivalent fixing points on the Kelvin scale, so that a temperature increment of one degree Celsius is the same as an increment of one kelvin, though numerically the scales differ by an exact offset of 273.15. The Fahrenheit scale is in common use in

4275-506: The 1990s as well as both active and passive edge localized mode suppression mechanisms in the 2000s. In 2021, the program announced an improved boundary cooling approach, replacing a gaseous solution with a boron , boron nitride , lithium powder mixture. This dissipated the plasma's heat and protected the reactor walls. 32°53′36.46″N 117°14′4.40″W  /  32.8934611°N 117.2345556°W  / 32.8934611; -117.2345556 Beta (plasma physics) The beta of

4370-409: The Boltzmann constant. Taking the value of the Boltzmann constant as a primarily defined reference of exactly defined value, a measurement of the speed of sound can provide a more precise measurement of the temperature of the gas. It is possible to measure the average kinetic energy of constituent microscopic particles if they are allowed to escape from the bulk of the system, through a small hole in

4465-760: The International System of Units defined a scale and unit for the kelvin as a thermodynamic temperature , by using the reliably reproducible temperature of the triple point of water as a second reference point, the first reference point being 0 K at absolute zero. Historically, the temperature of the triple point of water was defined as exactly 273.16 K. Today it is an empirically measured quantity. The freezing point of water at sea-level atmospheric pressure occurs at very close to 273.15 K ( 0 °C ). There are various kinds of temperature scale. It may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in

4560-401: The Sun's corona has a beta around 1%. Active regions have much higher beta, over 1 in some cases, which makes the area unstable. Temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measured with a thermometer . It reflects the average kinetic energy of the vibrating and colliding atoms making up

4655-515: The United States. Water freezes at 32 °F and boils at 212 °F at sea-level atmospheric pressure. At the absolute zero of temperature, no energy can be removed from matter as heat, a fact expressed in the third law of thermodynamics . At this temperature, matter contains no macroscopic thermal energy, but still has quantum-mechanical zero-point energy as predicted by the uncertainty principle , although this does not enter into

4750-412: The average translational kinetic energy of a freely moving particle in a system with temperature T will be 3 k B T /2 . Molecules, such as oxygen (O 2 ), have more degrees of freedom than single spherical atoms: they undergo rotational and vibrational motions as well as translations. Heating results in an increase of temperature due to an increase in the average translational kinetic energy of

4845-406: The basic physics processes that govern the behavior of a hot magnetized plasma, and to establish a scientific basis for future burning plasma devices such as ITER. Ultimately, the goal is to use this understanding to develop an economically attractive fusion power plant. The tokamak consists of a toroidal vacuum chamber surrounded by magnetic field coils which contain and shape the plasma. The plasma

SECTION 50

#1732776285014

4940-411: The body is described by stating its entropy S as a function of its internal energy U , and other state variables V , N , with S = S ( U , V , N ) , then the reciprocal of the temperature is equal to the partial derivative of the entropy with respect to the internal energy: The above definition, equation (1), of the absolute temperature, is due to Kelvin. It refers to systems closed to

5035-483: The boiling point of mercury , a mercury-in-glass thermometer is impracticable. Most materials expand with temperature increase, but some materials, such as water, contract with temperature increase over some specific range, and then they are hardly useful as thermometric materials. A material is of no use as a thermometer near one of its phase-change temperatures, for example, its boiling-point. In spite of these limitations, most generally used practical thermometers are of

5130-408: The constituent molecules. The magnitude of the kelvin is now defined in terms of kinetic theory, derived from the value of the Boltzmann constant . Kinetic theory provides a microscopic account of temperature for some bodies of material, especially gases, based on macroscopic systems' being composed of many microscopic particles, such as molecules and ions of various species, the particles of

5225-501: The constituent particles of matter, so that they have a limiting specific heat of zero for zero temperature, according to the third law of thermodynamics. Nevertheless, a thermodynamic temperature does in fact have a definite numerical value that has been arbitrarily chosen by tradition and is dependent on the property of particular materials; it is simply less arbitrary than relative "degrees" scales such as Celsius and Fahrenheit . Being an absolute scale with one fixed point (zero), there

5320-410: The containing wall. The spectrum of velocities has to be measured, and the average calculated from that. It is not necessarily the case that the particles that escape and are measured have the same velocity distribution as the particles that remain in the bulk of the system, but sometimes a good sample is possible. Temperature is one of the principal quantities in the study of thermodynamics . Formerly,

5415-543: The cross-sectional shape of the plasma) demonstrated higher performance, and the spherical tokamak design outperformed the Troyon limit by about 10 times. Beta is also sometimes used when discussing the interaction of plasma in space with different magnetic fields. A common example is the interaction of the solar wind with the magnetic fields of the Sun or Earth . In this case, the betas of these natural phenomena are generally much smaller than those seen in reactor designs;

5510-426: The cycle the working body is in a state of thermodynamic equilibrium. The successive processes of the cycle are thus imagined to run reversibly with no entropy production . Then the quantity of entropy taken in from the hot reservoir when the working body is heated is equal to that passed to the cold reservoir when the working body is cooled. Then the absolute or thermodynamic temperatures, T 1 and T 2 , of

5605-442: The definition just stated, was printed in 1853, a paper read in 1851. Numerical details were formerly settled by making one of the heat reservoirs a cell at the triple point of water, which was defined to have an absolute temperature of 273.16 K. Nowadays, the numerical value is instead obtained from measurement through the microscopic statistical mechanical international definition, as above. In thermodynamic terms, temperature

5700-472: The definition of absolute temperature. Experimentally, absolute zero can be approached only very closely; it can never be reached (the lowest temperature attained by experiment is 38 pK). Theoretically, in a body at a temperature of absolute zero, all classical motion of its particles has ceased and they are at complete rest in this classical sense. Absolute zero, defined as 0 K , is exactly equal to −273.15 °C , or −459.67 °F . Referring to

5795-502: The density of the particles in the plasma is very low, often described as a "poor vacuum". This limits its approach to the triple product along the temperature and time axis. This requires magnetic fields on the order of tens of Teslas , currents in the megaampere, and confinement times on the order of tens of seconds. Generating currents of this magnitude is relatively simple, and a number of devices from large banks of capacitors to homopolar generators have been used. However, generating

SECTION 60

#1732776285014

5890-863: The empirically based kind. Especially, it was used for calorimetry , which contributed greatly to the discovery of thermodynamics. Nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Empirically based thermometers, beyond their base as simple direct measurements of ordinary physical properties of thermometric materials, can be re-calibrated, by use of theoretical physical reasoning, and this can extend their range of adequacy. Theoretically based temperature scales are based directly on theoretical arguments, especially those of kinetic theory and thermodynamics. They are more or less ideally realized in practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers. In physics,

5985-457: The external magnetic field is the driver of reactor cost, "beta external" is used to consider just this contribution. In a tokamak , for a stable plasma, β {\displaystyle \beta } is always much smaller than 1 (otherwise thermal pressure would cause the plasma to grow and move in the vacuum chamber until confinement is lost). Ideally, a MCF device would want to have as high beta as possible, as this would imply

6080-455: The formulation of the first law of thermodynamics. Carnot had no sound understanding of heat and no specific concept of entropy. He wrote of 'caloric' and said that all the caloric that passed from the hot reservoir was passed into the cold reservoir. Kelvin wrote in his 1848 paper that his scale was absolute in the sense that it was defined "independently of the properties of any particular kind of matter". His definitive publication, which sets out

6175-417: The high-n instabilities grew considerably. Shafranov and Yurchenko first published on the issue in 1971 in a general discussion of tokamak design, but it was the work by Wesson and Sykes in 1983 and Francis Troyon in 1984 that developed these concepts fully. Troyon's considerations, or the "Troyon limit", closely matched the real-world performance of existing machines. It has since become so widely used that it

6270-419: The highest pressures possible. The costs of large magnets roughly scales like β . Therefore, beta can be thought of as a ratio of money out to money in for a reactor, and beta can be thought of (very approximately) as an economic indicator of reactor efficiency. For tokamaks , betas of larger than 0.05 or 5% are desired for economically viable electrical production. The same term is also used when discussing

6365-494: The hotness manifold. When two systems in thermal contact are at the same temperature no heat transfers between them. When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system until they are in thermal equilibrium . Such heat transfer occurs by conduction or by thermal radiation. Experimental physicists, for example Galileo and Newton , found that there are indefinitely many empirical temperature scales . Nevertheless,

6460-409: The interactions of the solar wind with various magnetic fields. For example, beta in the corona of the Sun is about 0.01. Nuclear fusion occurs when the nuclei of two atoms approach closely enough for the nuclear force to pull them together into a single larger nucleus. The strong force is opposed by the electrostatic force created by the positive charge of the nuclei's protons , pushing

6555-419: The internal energy at a point, while when local thermodynamic equilibrium prevails, it makes good sense to speak of the temperature at a point. Consequently, the temperature can vary from point to point in a medium that is not in global thermodynamic equilibrium, but in which there is local thermodynamic equilibrium. Thus, when local thermodynamic equilibrium prevails in a body, the temperature can be regarded as

6650-409: The internationally agreed conventional temperature scale is called the Kelvin scale. It is calibrated through the internationally agreed and prescribed value of the Boltzmann constant, referring to motions of microscopic particles, such as atoms, molecules, and electrons, constituent in the body whose temperature is to be measured. In contrast with the thermodynamic temperature scale invented by Kelvin,

6745-453: The kelvin has been defined through particle kinetic theory , and statistical mechanics. In the International System of Units (SI), the magnitude of the kelvin is defined in terms of the Boltzmann constant , the value of which is defined as fixed by international convention. Since May 2019, the magnitude of the kelvin is defined in relation to microscopic phenomena, characterized in terms of statistical mechanics. Previously, but since 1954,

6840-428: The magnitude of the kelvin was defined in thermodynamic terms, but nowadays, as mentioned above, it is defined in terms of kinetic theory. The thermodynamic temperature is said to be absolute for two reasons. One is that its formal character is independent of the properties of particular materials. The other reason is that its zero is, in a sense, absolute, in that it indicates absence of microscopic classical motion of

6935-427: The magnitudes of the incremental unit of temperature. The Celsius scale (°C) is used for common temperature measurements in most of the world. It is an empirical scale that developed historically, which led to its zero point 0 °C being defined as the freezing point of water , and 100 °C as the boiling point of water, both at atmospheric pressure at sea level. It was called a centigrade scale because of

7030-419: The mechanisms of operation of the thermometers. For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria , any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature. This does not require the two thermometers to have

7125-444: The middle of the nineteenth century. Empirically based temperature scales rely directly on measurements of simple macroscopic physical properties of materials. For example, the length of a column of mercury, confined in a glass-walled capillary tube, is dependent largely on temperature and is the basis of the very useful mercury-in-glass thermometer. Such scales are valid only within convenient ranges of temperature. For example, above

7220-453: The minimum amount of magnetic force needed for confinement. In practice, most tokamaks operate at beta of order 0.01, or 1%. Spherical tokamaks typically operate at beta values an order of magnitude higher. The record was set by the START device at 0.4, or 40%. These low achievable betas are due to instabilities in the plasma generated through the interaction of the fields and the motion of

7315-435: The molecules. Heating will also cause, through equipartitioning , the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas will require more energy input to increase its temperature by a certain amount, i.e. it will have a greater heat capacity than a monatomic gas. As noted above, the speed of sound in a gas can be calculated from the gas's molecular character, temperature, pressure, and

7410-449: The nature of the fuel at high temperatures. When the fusion fuel gasses are heated to the temperatures required for rapid fusion, they will be completely ionized into a plasma, a mixture of electrons and nuclei forming a globally neutral gas. As the particles within the gas are charged, this allows them to be manipulated by electric or magnetic fields. This gives rise to the majority of controlled fusion concepts. Even if this temperature

7505-400: The noise-power is directly proportional to the temperature of the resistor and to the value of its resistance and to the noise bandwidth. In a given frequency band, the noise-power has equal contributions from every frequency and is called Johnson noise . If the value of the resistance is known then the temperature can be found. Historically, till May 2019, the definition of the Kelvin scale

7600-557: The nuclei apart. The amount of energy that is needed to overcome this repulsion is known as the Coulomb barrier . The amount of energy released by the fusion reaction when it occurs may be greater or less than the Coulomb barrier. Generally, lighter nuclei with a smaller number of protons and greater number of neutrons will have the greatest ratio of energy released to energy required, and the majority of fusion power research focusses on

7695-456: The particles due to the induced current. As the amount of current is increased in relation to the external field, these instabilities become uncontrollable. In early pinch experiments the current dominated the field components and the kink and sausage instabilities were common, today collectively referred to as "low-n instabilities". As the relative strength of the external magnetic field is increased, these simple instabilities are damped out, but at

7790-454: The presently conventional Kelvin temperature is not defined through comparison with the temperature of a reference state of a standard body, nor in terms of macroscopic thermodynamics. Apart from the absolute zero of temperature, the Kelvin temperature of a body in a state of internal thermodynamic equilibrium is defined by measurements of suitably chosen of its physical properties, such as have precisely known theoretical explanations in terms of

7885-481: The required energy even when the gas as a whole is relatively "cool" compared to the Coulomb barrier energy. In the case of the D-T mixture, rapid fusion will occur when the gas is heated to about 100 million degrees. This temperature is well beyond the physical limits of any material container that might contain the gases, which has led to a number of different approaches to solving this problem. The main approach relies on

7980-412: The required magnetic fields is another issue, generally requiring expensive superconducting magnets . For any given reactor design, the cost is generally dominated by the cost of the magnets. Given that the magnets are a dominant factor in reactor design, and that density and temperature combine to produce pressure, the ratio of the pressure of the plasma to the magnetic energy density naturally becomes

8075-403: The reservoirs are defined such that The zeroth law of thermodynamics allows this definition to be used to measure the absolute or thermodynamic temperature of an arbitrary body of interest, by making the other heat reservoir have the same temperature as the body of interest. Kelvin's original work postulating absolute temperature was published in 1848. It was based on the work of Carnot, before

8170-453: The spectrum of their velocities often nearly obeys a theoretical law called the Maxwell–Boltzmann distribution , which gives a well-founded measurement of temperatures for which the law holds. There have not yet been successful experiments of this same kind that directly use the Fermi–Dirac distribution for thermometry, but perhaps that will be achieved in the future. The speed of sound in

8265-407: The study by methods of classical irreversible thermodynamics, a body is usually spatially and temporally divided conceptually into 'cells' of small size. If classical thermodynamic equilibrium conditions for matter are fulfilled to good approximation in such a 'cell', then it is homogeneous and a temperature exists for it. If this is so for every 'cell' of the body, then local thermodynamic equilibrium

8360-432: The total magnetic field. However, in any real-world design, the strength of the field varies over the volume of the plasma, so to be specific, the average beta is sometimes referred to as the "beta toroidal". In the tokamak design the total field is a combination of the external toroidal field and the current-induced poloidal one, so the "beta poloidal" is sometimes used to compare the relative strengths of these fields. And as

8455-428: The transfer of matter and has a special emphasis on directly experimental procedures. A presentation of thermodynamics by Gibbs starts at a more abstract level and deals with systems open to the transfer of matter; in this development of thermodynamics, the equations (2) and (3) above are actually alternative definitions of temperature. Real-world bodies are often not in thermodynamic equilibrium and not homogeneous. For

8550-404: The use of deuterium and tritium , two isotopes of hydrogen . Even using these isotopes, the Coulomb barrier is large enough that the nuclei must be given great amounts of energy before they will fuse. Although there are a number of ways to do this, the simplest is to heat the gas mixture, which, according to the Maxwell–Boltzmann distribution , will result in a small number of particles with

8645-428: The value of the Boltzmann constant as a primarily defined reference of exactly defined value, a measurement of the speed of sound can provide a more precise measurement of the temperature of the gas. Measurement of the spectrum of electromagnetic radiation from an ideal three-dimensional black body can provide an accurate temperature measurement because the frequency of maximum spectral radiance of black-body radiation

8740-411: The zeroth law of thermodynamics. In particular, when the body is described by stating its internal energy U , an extensive variable, as a function of its entropy S , also an extensive variable, and other state variables V , N , with U = U ( S , V , N ), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy: Likewise, when

8835-421: Was defined to be exactly 273.16 K . Since May 2019, that value has not been fixed by definition but is to be measured through microscopic phenomena, involving the Boltzmann constant, as described above. The microscopic statistical mechanical definition does not have a reference temperature. A material on which a macroscopically defined temperature scale may be based is the ideal gas . The pressure exerted by

8930-422: Was later upgraded and renamed DIII-D in 1986. The DIII-D program achieved several milestones in fusion development, including the highest plasma β (ratio of plasma pressure to magnetic pressure) ever achieved at the time (early 1980s) and the highest neutron flux (fusion rate) ever achieved at the time (early 1990s). Major scientific discoveries include the validation of sheared flow suppression of turbulence in

9025-411: Was that invented by Kelvin, based on a ratio of quantities of energy in processes in an ideal Carnot engine, entirely in terms of macroscopic thermodynamics. That Carnot engine was to work between two temperatures, that of the body whose temperature was to be measured, and a reference, that of a body at the temperature of the triple point of water. Then the reference temperature, that of the triple point,

#13986