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The proposal to use controlled thermonuclear fusion for industrial purposes and a specific scheme using thermal insulation of high-temperature plasma by an electric field were first formulated by the Soviet physicist O. A. Lavrentiev in a work in the mid-1950s. This work served as a catalyst for Soviet research on the problem of controlled thermonuclear fusion. A.D. Sakharov and I.E. Tamm in 1951 proposed modifying the scheme, proposing a theoretical basis for a thermonuclear reactor, where the plasma would have the shape of a torus and be contained by a magnetic field. At the same time, the same idea was proposed by American scientists, but was “forgotten” until the 1970s.
Currently, the tokamak is considered the most promising device for implementing controlled thermonuclear fusion.
Device
A tokamak is a toroidal vacuum chamber on which coils are wound to create a toroidal magnetic field. The air is first pumped out of the vacuum chamber and then filled with a mixture of deuterium and tritium. Then using inductor a vortex electric field is created in the chamber. The inductor is the primary winding of a large transformer, in which the tokamak chamber is the secondary winding. The electric field causes current to flow and ignition in the plasma chamber.
The current flowing through the plasma performs two tasks:
- heats the plasma in the same way as any other conductor would (ohmic heating);
- creates a magnetic field around itself. This magnetic field is called poloidal(that is, directed along lines passing through poles spherical coordinate system).
The magnetic field compresses the current flowing through the plasma. As a result, a configuration is formed in which helical magnetic field lines “twist” the plasma cord. In this case, the step during rotation in the toroidal direction does not coincide with the step in the poloidal direction. The magnetic lines turn out to be unclosed; they twist around the torus infinitely many times, forming the so-called “magnetic surfaces” of a toroidal shape.
The presence of a poloidal field is necessary for stable plasma confinement in such a system. Since it is created by increasing the current in the inductor, and it cannot be infinite, the time of stable existence of plasma in a classical tokamak is still limited to a few seconds. To overcome this limitation, additional methods of maintaining current have been developed. For this purpose, injection into the plasma of accelerated neutral atoms of deuterium or tritium or microwave radiation can be used.
In addition to toroidal coils, additional ones are required to control the plasma cord. poloidal field coils. They are ring turns around the vertical axis of the tokamak chamber.
Heating alone due to the flow of current is not enough to heat the plasma to the temperature required for a thermonuclear reaction. For additional heating, microwave radiation is used at so-called resonant frequencies (for example, coinciding with the cyclotron frequency of either electrons or ions) or injection of fast neutral atoms.
Tokamak (TORoidal Chamber with Magnetic Coils) is a toroidal installation for magnetic plasma confinement. The plasma is held not by the walls of the chamber, which are not able to withstand its temperature, but by a specially created magnetic field. A special feature of the tokamak is the use of electric current flowing through the plasma to create the poloidal field necessary for plasma equilibrium. This distinguishes it from a stellarator, in which both the toroidal and poloidal fields are created using magnetic coils.
Story
The term “tokamak” was coined by Russian physicists Igor Evgenievich Tamm and Andrei Dmitrievich Sakharov in the 50s as an abbreviation for the phrase “toroidal chamber with magnetic coils.” The first tokamak was developed under the leadership of Academician L.A. Artsimovich at the Institute of Atomic Energy named after. I. V. Kurchatov in Moscow and demonstrated in 1968 in Novosibirsk.
Currently, a tokamak is considered the most promising device for implementing controlled thermonuclear fusion.
Device
A tokamak is a toroidal vacuum chamber on which coils are wound to create a (toroidal) magnetic field. The air is first pumped out of the vacuum chamber and then filled with a mixture of deuterium and tritium. Then, using an inductor, a vortex electric field is created in the chamber. The inductor is the primary winding of a large transformer, in which the tokamak chamber is the secondary winding. The electric field causes current to flow and ignite the plasma chamber.
The current flowing through the plasma performs two tasks:
Heats the plasma in the same way as any other conductor would (ohmic heating).
- Creates a magnetic field around itself. This magnetic field is called poloidal (that is, directed along lines passing through the poles of the spherical coordinate system).
The magnetic field compresses the current flowing through the plasma. As a result, a configuration is formed in which helical magnetic field lines “twist” the plasma cord. In this case, the step during rotation in the toroidal direction does not coincide with the step in the poloidal direction. The magnetic lines turn out to be unclosed; they twist around the torus infinitely many times, forming the so-called. “magnetic surfaces” of toroidal shape.
The presence of a poloidal field is necessary for stable plasma confinement in such a system. Since it is created by increasing the current in the inductor, and it cannot be infinite, the time of stable existence of plasma in a classical tokamak is limited. To overcome this limitation, additional methods of maintaining current have been developed. For this purpose, injection of accelerated neutral deuterium or tritium atoms or microwave radiation into the plasma can be used.
In addition to toroidal coils, additional poloidal field coils are required to control the plasma cord. They are ring turns around the vertical axis of the tokamak chamber.
Heating alone due to the flow of current is not enough to heat the plasma to the temperature required for a thermonuclear reaction. For additional heating, microwave radiation is used on the so-called. resonant frequencies (for example, coinciding with the cyclotron frequency of either electrons or ions) or injection of fast neutral atoms.
Controlled thermonuclear fusion
The sun is a natural thermonuclear reactor
Controlled thermonuclear fusion (CTF) is the synthesis of heavier atomic nuclei from lighter ones in order to obtain energy, which is controlled in nature, in contrast to explosive thermonuclear fusion (used in thermonuclear weapons). Controlled thermonuclear fusion differs from traditional nuclear energy in that the latter uses a decay reaction, during which lighter nuclei are produced from heavy nuclei. The main nuclear reactions planned to be used to achieve controlled thermonuclear fusion will use deuterium (2H) and tritium (3H), and in the longer term, helium-3 (3He).
The fate of thermonuclear fusion
The idea of creating a fusion reactor originated in the 1950s. Then it was decided to abandon it, since scientists were not able to solve many technical problems. Several decades passed before scientists were able to “force” the reactor to produce any amount of thermonuclear energy.
Diagram of the International Thermonuclear Reactor (ITER)
The decision to design the International Thermonuclear Reactor (ITER) was made in Geneva in 1985. The project involves the USSR, Japan, the USA, united Europe and Canada. After 1991, Kazakhstan joined the participants. Over the course of 10 years, many elements of the future reactor were manufactured at military-industrial enterprises in developed countries. For example, in Japan they have developed a unique system of robots capable of working inside a reactor. In Russia they created a virtual version of the installation.
In 1998, the United States, for political reasons, stopped funding its participation in the project. After the Republicans came to power and rolling blackouts began in California, the Bush administration announced increased investment in energy. The United States did not intend to participate in the international project and was engaged in its own thermonuclear project. In early 2002, President Bush's technology adviser John Marburger III said that the United States had changed its mind and intended to return to the project.
In terms of the number of participants, the project is comparable to another major international scientific project - the International Space Station. The cost of ITER, which previously reached 8 billion dollars, then amounted to less than 4 billion. As a result of the withdrawal of the United States from participation, it was decided to reduce the reactor power from 1.5 GW to 500 MW. Accordingly, the price of the project has also decreased.
In June 2002, the symposium “ITER Days in Moscow” was held in the Russian capital. It discussed the theoretical, practical and organizational problems of reviving the project, the success of which can change the fate of humanity and give it a new type of energy, comparable in efficiency and economy only to the energy of the Sun.
If the participants agree on the location of the station and the start of its construction, then, according to the forecast of Academician Velikhov, the first plasma will be obtained by 2010. Then it will be possible to begin construction of the first thermonuclear power plant, which, under favorable circumstances, can produce the first current in 2030.
In December 2003, scientists involved in the ITER project gathered in Washington to finally determine the location of its future construction. The France-Press news agency reported, citing one of the meeting participants, that the decision was postponed to 2004. The next negotiations on this project will take place in May 2004 in Vienna. The reactor will begin to be built in 2006 and is planned to be launched in 2014.
Principle of operation
Thermonuclear fusion is a cheap and environmentally friendly way to produce energy. Uncontrolled thermonuclear fusion has been occurring on the Sun for billions of years - helium is formed from the heavy hydrogen isotope deuterium. This releases a colossal amount of energy. However, people on Earth have not yet learned to control such reactions.
Plasma in a fusion reactor
The ITER reactor will use hydrogen isotopes as fuel. During a thermonuclear reaction, energy is released when light atoms combine into heavier ones. To achieve this, the gas must be heated to a temperature of over 100 million degrees - much higher than the temperature at the center of the Sun. Gas at this temperature turns into plasma. At the same time, atoms of hydrogen isotopes merge, turning into helium atoms with the release of a large number of neutrons. A power plant operating on this principle will use the energy of neutrons slowed down by a layer of dense matter (lithium)
Construction of the station will take at least 10 years and $5 billion. France and Japan are competing for the prestigious right to be the homeland of the energy giant.
Place of construction
Canada, Japan, Spain and France made proposals to locate the reactor on their territories.
Canada justifies the need to locate the reactor on its territory by the fact that it is in this country that there are significant reserves of tritium, which is a waste product of nuclear energy. The construction of a thermonuclear reactor will allow them to be disposed of.
In Japan, according to the Kyodo Tsushin agency, three prefectures were fighting desperately for the right to build a reactor in their own country. At the same time, residents of the northern island of Hokkaido opposed its construction on their land.
In November this year, the European Union recommended the French city of Cadarache as a future site for construction. However, it is difficult to predict how the voting will go. Experts are expected to make decisions based on strictly objective scientific facts, but political overtones can also affect the vote. The United States has already spoken out against giving the construction of the reactor to France, recalling its divisive behavior during the conflict in Iraq.
“We have an existing scientific and technical structure, competence and experience, which guarantees that we will meet our deadlines,” said the French Minister of Research.
Japan also has a number of advantages - Rokkasho-mura is located next to a port and next to a US military base. In addition, the Japanese are ready to invest much more money in the project than France. “If Japan is chosen, we will cover all necessary expenses,” said the Japanese Minister of Science and Education.
A French government spokesman told reporters he had held "very intensive, high-level talks" ahead of the meeting. However, according to some data, all countries except the European Union prefer Japan to France.
Environmental Safety
The new installation, according to scientists, is environmentally safer than nuclear reactors operating today. The ITER facility produces helium as spent fuel, rather than its isotopes, which must be stored in special storage facilities for decades.
Scientists believe that fuel reserves for such power plants are practically inexhaustible - deuterium and tritium are easily extracted from sea water. A kilogram of these isotopes can release as much energy as 10 million kg of fossil fuel.
TOKAMAK(abbreviated from “toroidal chamber with magnetic coils”) - a device for holding high temperatures using a strong magnet. fields. The idea of T. was expressed in 1950 by academicians I. E. Tamm and A. D. Sakharov; first experiments Research on these systems began in 1956.
The principle of the device is clear from Fig. 1. Plasma is created in a toroidal vacuum chamber, which serves as the only closed turn of the secondary winding of the transformer. When passing a current that increases over time in the primary winding of a transformer 1
inside the vacuum chamber 5
a vortex longitudinal electric force is created. field. When the initial gas is not very large (usually hydrogen or its isotopes are used), its electric power occurs. breakdown and the vacuum chamber is filled with plasma with a subsequent increase in a large longitudinal current Ip. In modern large T. the current in the plasma is several. million amperes. This current creates its own poloidal (in the plane of the plasma cross-section) magnetic field. field IN q. In addition, a strong longitudinal magnet is used to stabilize the plasma. field B f, created using special windings of toroidal magnet. fields. It is the combination of toroidal and poloidal magnets. fields ensures stable confinement of high-temperature plasma (see. Toroidal systems),necessary for implementation controlled thermonuclear fusion.
Rice. 1. Tokamak diagram: 1
- primary winding transformatter; 2
- toroidal magnetic field coils; 3
- liner, thin-walled inner chamber for engravingreduction of the toroidal electric field; 4
- reelki poloidal magnetic field; 5
- vacuum kamera; b-iron core (magnetic core).
Operating limits. Magn. the T field holds high-temperature plasma quite well, but only within certain limits of change in its parameters. The first 2 restrictions apply to the plasma current Ip and her cf. density P, expressed in units of the number of particles (electrons or ions) per 1 m 3. It turns out that for a given value of the toroidal magnet. field, the plasma current cannot exceed a certain limiting value, otherwise the plasma cord begins to twist along a helical line and eventually collapses: the so-called. current interruption instability. To characterize the limiting current, a coefficient is used. stock q by screw instability, determined by the relation q = 5B j a 2 /RI p. Here A- small, R- large radius of the plasma cord, B j - toroidal mag. field, Ip- current in plasma (dimensions are measured in meters, magnetic field - in teslas, current - in MA). A necessary condition for the stability of a plasma column is the inequality q>], so-called. k r i t e r i m K r u-s k a la - Shafranova. Experiments show that a reliably stable holding mode is achieved only at values of .
There are 2 limits for density - lower and upper. Lower The density limit is associated with the formation of the so-called. accelerated, or runaway electrons. At low densities, the frequency of collisions of electrons with ions becomes insufficient to prevent their transition to the mode of continuous acceleration in the longitudinal electric field. field. Electrons accelerated to high energies can pose a danger to the elements of the vacuum chamber, so the plasma density is chosen so high that there are no accelerated electrons. On the other hand, at a sufficiently high density, the plasma confinement mode again becomes unstable due to radiation and atomic processes at the plasma boundary, which lead to a narrowing of the current channel and the development of helical instability of the plasma. Top. the density limit is characterized by dimensionless parameters My-crayfish M=nR/B j and hugella H=nqR/B j (here averaged across the cross section is the electron density n measured in units of 10 20 particles/m 3). For stable plasma confinement it is necessary that the numbers M And H did not exceed certain critical values.
When the plasma heats up and its pressure increases, another limit appears, characterizing the maximum stable value of the plasma pressure, p = n(T e +T i), Where T e, T i-electronic and ion temperatures. This limit is imposed on the value of b equal to the ratio cf. plasma pressure to magnetic pressure. fields; a simplified expression for the limiting value b is given by Troyon's relation b c =gI p /aB j, where g-numerical factor equal to approximately 3. 10 -2.
Thermal insulation. The possibility of heating plasma to very high temperatures is due to the fact that in a strong magnetic field. charging trajectory field particles look like spirals wound on a magnetic line. fields. Thanks to this, electrons and ions are retained inside the plasma for a long time. And only due to collisions and small electrical fluctuations. and mag. fields, the energy of these particles can be transferred to the walls in the form of a heat flow. These same mechanisms determine the magnitude of diffusion fluxes. Magnetic efficiency thermal insulation of plasma is characterized by energy. lifetime t E = W/P, Where W-total energy content of plasma, a P- plasma heating power required to maintain it in a stationary state. Value t E can also be considered as the characteristic cooling time of the plasma if the heating power is suddenly turned off. In a quiet plasma, flows of particles and heat to the walls of the chamber are created due to pairwise collisions of electrons and ions. These flows are calculated theoretically taking into account real charge trajectories. particles per mag. field T. The corresponding theory of diffusion processes is called. neoclassical (see Migration processes). In real plasma T. there are always small fluctuations of fields and particle fluxes, therefore the real levels of heat and particle fluxes usually significantly exceed the predictions of neoclassical ones. theories.
Experiments carried out on many T. decomp. shapes and sizes, made it possible to summarize the results of studies of transfer mechanisms in the form of corresponding empirical studies. dependencies. In particular, energy dependences were found. lifetime t E from main plasma parameters for decomp. hold mod. These dependencies are called s k e l i n g a m i; they are successfully used to predict plasma parameters in newly commissioned installations.
Self-organization of plasma. In plasma T. there are always weakly nonlinear ones, which influence the profiles of the distribution of temperature, particle density and current density along the radius, as if they control them. In particular, to the center. areas of the plasma cord are very often present so-called. sawtooth oscillations reflecting a periodically repeating process of gradual exacerbation and then a sharp flattening of the temperature profile. Ramp-shaped oscillations prevent contraction of current to the magnet. torus axis (see Gas discharge contraction). In addition, in T. from time to time, helical modes are excited (the so-called t i r i n g modes), which are observed outside the cord in the form of low-frequency magnetic waves. hesitation. Tiring modes contribute to the establishment of a more stable distribution of current density along the radius. If the plasma is handled insufficiently carefully, tearing modes can grow so strong that the magnetic disturbances they cause can fields destroy magnets. surfaces throughout the entire volume of the plasma cord, magnetic. the configuration is destroyed, the plasma energy is released to the walls and the current in the plasma stops due to its strong cooling (see. Tearing instability).
In addition to these volumetric oscillations, there are oscillation modes localized at the boundary of the plasma column. These modes are very sensitive to the state of the plasma at the very periphery; their behavior is complicated by atomic processes. Ext. and internal vibration modes can strongly influence the processes of heat and particle transfer; they lead to the possibility of plasma transition from one magnetic mode. thermal insulation to another and back. If in plasma T. the particle velocity distribution is very different from , then the possibility arises for the development of kinetic. instabilities. For example, with the birth of a large number of runaway electrons, the so-called fan instability, leading to the transformation of longitudinal electron energy into transverse energy. Kinetic. instabilities also develop in the presence of high-energy ions that arise when complementary. heating the plasma.
Plasma heating. The plasma of any T. is automatically heated due to Joule heat from the current flowing through it. The Joule energy release is sufficient to obtain a temperature of several. million degrees For the purposes of controlled thermonuclear fusion, temperatures >10 8 K are needed, therefore all large T. are supplemented with powerful systems plasma heating. For this purpose, either electric magnets are used. waves decomposed ranges, or direct fast particles into plasma. For high-frequency plasma heating, it is convenient to use resonances, which correspond to internal. oscillate processes in plasma. For example, it is convenient to heat the ion component in the range of harmonics of cyclotron frequencies or basic. plasma ions, or specially selected additive ions. Electrons are heated by electron cyclotron resonance.
When heating ions with fast particles, powerful beams of neutral atoms are usually used. Such beams do not interact with magnetism. field and penetrate deep into the plasma, where they are ionized and captured by magnetism. field T.
With the help of additional heating methods, it is possible to raise the plasma temperature T. to >3·10 8 K, which is quite sufficient for a powerful thermonuclear reaction to occur. In future T.-reactors being developed, plasma heating will be carried out by high-energy alpha particles arising from the fusion reaction of deuterium and tritium nuclei.
Stationary tokamak. Typically, current flows in plasma only in the presence of an eddy electric current. field created by increasing the magnetic field. flow in the inductor. The inductive mechanism for maintaining current is limited in time, so the corresponding mode of plasma confinement is pulsed. However, the pulsed mode is not the only possible one; heating the plasma can also be used to maintain the current if, along with energy, a pulse that is different for different components of the plasma is also transferred to the plasma. Non-inductive current maintenance is facilitated due to the generation of current by the plasma itself during its diffusion expansion towards the walls (bootstrap effect). The bootstrap effect was predicted by neoclassical scientists. theory and then confirmed experimentally. Experiments show that T. plasma can be held stationary, and Ch. efforts to practically development of the stationary mode are aimed at increasing the efficiency of current maintenance.
Diverter, impurity control. For the purposes of controlled thermonuclear fusion, very pure plasma based on hydrogen isotopes is required. To limit the admixture of other ions in the plasma, in early T. the plasma was limited to the so-called. l i m i t e r o m (Fig. 2, A), i.e., a diaphragm that prevents the plasma from coming into contact with the large surface of the chamber. In modern T. a much more complex divertor configuration is used (Fig. 2, b), created by poloidal magnet coils. fields. These coils are necessary even for plasma with a round cross-section: with their help, the vertical magnetic component is created. fields, edges when interacting with the main. plasma current does not allow the plasma coil to be thrown onto the wall in the direction of a large radius. In the divertor configuration, the turns of the poloidal magnet. the fields are located so that the plasma cross section is elongated in the vertical direction. At the same time, closed magnetic surfaces are preserved only inside; outside, its lines of force go inside the divertor chambers, where the plasma flows flowing from the main surface are neutralized. volume. In divertor chambers, it is possible to soften the load from the plasma on the divertor plates due to the addition. plasma cooling during atomic interactions.
Rice. 2. Cross section of plasma with a circular cross-section ( A) and vertically elongated to form a divertor configuration ( 6):
1-plasma; 2- limiter; 3 - chamber wall; 4 - separatrix; 5-divertor chamber; 6 - divertor plates.
Tokamak reactor. Ch. The goal of research on T. installations is to master the concept of magnetic. Plasma Containment for Creatures fusion reactor. On T. it is possible to create a stable high-temperature plasma with a temperature and density sufficient for a thermonuclear reactor; laws have been established for thermal insulation of plasma; methods of maintaining current and controlling the level of impurities are mastered. Work on T. is moving from the purely physical phase. research in the phase of creating experiments. .
Lit.: Artsimovich L. A., Managed, 2nd ed., M., 1963; Lukyanov S. Yu., Hot plasma and controlled nuclear fusion, M., 1975; Kadomtsev B.V., Tokamak plasma a complex physical system, L., 1992. B. B. Kadomtsev.
DEVICE AND OPERATION OF TOKAMAK
Operating principle, tokamak circuit diagram, installation parameters, stability of the toroidal plasma cord, retention parameter
b, energy lifetime.
Operating principle. Schematic diagram
In the final chapter, we will take a closer look at the design and operating features of the tokamak - the most complex, but perhaps the most important plasma installation. It is with the tokamak that hopes are now pinned for the practical implementation of controlled thermonuclear fusion. The ITER thermonuclear tokamak reactor currently being built by the international community is a decisive step towards creating thermonuclear energy by the middle of the century. Tokamak is the name of the CURRENT CHAMBER installation with MAGNETIC coils created in accordance with the proposal in the middle of the last century at the Kurchatov Institute (G was transformed into K with the characteristic softening of consonants in the Russian language).
A tokamak is a transformer whose secondary “winding” is the current created in the plasma. Magnetic thermal insulation is provided by a strong toroidal magnetic field Bjº
Bt, which together with the poloidal field Bqº
Bp current IP creates the helical configuration of magnetic field lines necessary to suppress the toroidal drift of the plasma and maintain the stability of the cord (Fig. 13.1a). The conductive shell (casing) shown in Fig. 13.1 also serves for passive stabilization plasma cord during its short-term disturbances.
Relationship between casing thickness and characteristic disturbance time t 1/2, which is damped by the Foucault currents arising in the casing with such a change in the magnetic flux, is determined by the depth of the skin layer, which in practical units can be presented in the form of a very useful formula: https://pandia.ru/text/79/389/images/image002_55 .gif" width="69" height="25 src="> - resistivity of the casing material, related to the resistivity of copper at 200C, t 1/2– half-period of disturbance.
The generation and maintenance of current in the plasma is carried out using inductor, which, when the current changes in it, creates an emf on the toroidal axis ε = -
dY/dt, where Y is the magnetic flux inside the plasma ring with current. For electrical breakdown of the gas filling the chamber, a value that is significantly greater than to maintain the current is required. ε,
therefore, when creating plasma, the current in the inductor windings changes significantly
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faster than in the phase of its long-term maintenance. To ensure that the inductor field does not distort the toroidal field during breakdown, as well as the helical magnetic configuration necessary to contain the plasma, magnetic cores made of a material with high magnetic permeability (soft magnetic iron) are used, which close the magnetic flux outside the inductor. The inductor can be with an iron core or an air core - without the use of iron at all. In the latter case, poloidal coils are installed, which compensate for the inductor field in the plasma region. The equilibrium of the circular current in the longitudinal (in relation to it) magnetic field is achieved by applying an additional vertical magnetic field Bz, creating a force directed towards the axis of the system. Field Bz created by poloidal control windings(Fig.9.1b). Figure 9.2 shows the main elements of the tokamak electromagnetic system and a cyclogram of its operation. In addition to the indicated windings, tokamaks additionally install coils to ensure vertical plasma balance and magnetic field correction.
Stability of a toroidal plasma filament
Stability of a toroidal plasma column is possible only if the Kruskal-Shafranov criterion is met q = (a/R)(Bt/Bp ) >1, what is the plasma current for? IP should not exceed a certain value. Indeed, the connection between field and current
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Fig. 13.2a Electromagnetic system of a tokamak.
Where , l And I expressed respectively in oersteds, centimeters and amperes, in the case of axial symmetry ( H∙2pr =0.4pI) gives for the field H =0.2I/r. If the tokamak has a large aspect ratio A=R/a, then to a first approximation the poloidal field at the boundary of the plasma column Bp» 0.2Ip/a, And q =(5a 2/R)(Bp/Ip) >1
Thus, there is a limitation on the amount of current in the plasma.
n. At small values n in a vortex field E = ε/2pR
ne£0.07jp, where the plasma density is in [m-3], and the current density is in [MA/m2].
Fig. 13.2b Cyclogram of tokamak operation (qualitatively):JT
– current in the coils of the toroidal solenoid,J
And
- current in the inductor winding,Jp
- plasma current, J
u. To.
current in the control coils (increases with increasingT
plasma).
Other limitations are related to plasma density n. At small values n in a vortex field E = ε/2pR
electrons can go into acceleration mode (“go into whistling”). The plasma concentration critical for such a regime is determined by the Razumova criterion ne£0.07jp, where the plasma density is in [m-3], and the current density is in [MA/m2]. That is, the plasma current limit depends linearly on its concentration IP ³
( pka 2/0.07)ne. At large n there is also a density limit nMH£2Bt/qR(Murakami-Hughell limit), associated with the power balance in the peripheral plasma. At high densities, when plasma losses due to radiation and thermal conductivity begin to exceed the energy released in it due to the current flowing through the plasma, contraction (compression) of the plasma cord occurs.
It is convenient to visually illustrate the area of tokamak operating modes with the so-called Hugell-Murakami diagram (Fig. 13.3). On it, instead of density, a value proportional to it is plotted along the abscissa axis for a tokamak with a given large plasma radius and the value of the toroidal field M = (R/Bt)n(Murakami number). Region 1-2 corresponds to the Razumova limit associated with runaway electrons, region 2-3 is determined by MHD stability in accordance with the Kruskal-Shafranov criterion,
Fig. 13.3 Hugell-Murakami diagram of stable modes of a tokamak.
region 3-4 is the Murakami density limit. The energy release in plasma when current flows in it is proportional to QOHµ
IP 2, and radiation losses Qrµ
n 2e. From (13.1) it follows that QOHµ
[ (Bt/R)q]2, and the ratio Qr/QOHµ
n 2 (R/Bt )2q 2º
H 2. Number H called the Hugell number, while maintaining proportionality between energy release and radiation ( H=cons t) q -1 proportional to the Murakami number M. Section 4-1 of the diagram reflects this proportionality.
When heating the plasma, problems arise related to the MHD equilibrium of the plasma column in the tokamak. From the condition of plasma equilibrium in the MHD approximation, the total pressure of the plasma and magnetic field in the column must be balanced by the pressure of the magnetic field outside the plasma column. With increasing temperature, plasma pressure <
P>=nkT grows and, accordingly, strength grows FRpl, necessary to hold in place this plasma “balloon” inflating under internal pressure. Roughly this force can be estimated from the work of “stretching the balloon” W»
<
P >2pRpa 2, FRpl = -dW/dR = =2p2a 2<
P>. Consequently, with increasing plasma pressure, it is necessary to increase the confinement of the plasma at the radius R vertical field Bz. Let's see what happens to the total poloidal field, which consists of the current field and the external vertical field Bz. Let's assume that the field Bz homogeneous in R, then in order to ensure equilibrium it must coincide with the current field on its outer side, enhancing this field. On the inside there is a field BZ weakens the current field and with increasing plasma pressure a situation is possible when, at some distance from the center of the tokamak, it compensates for the latter with the formation of the so-called x – points. The power lines outside it are open. With increasing pressure and, accordingly, the field required to contain the plasma Bz x-the point approaches the plasma filament and when bq =<
p>/(B 2q /8p )=R/a touches it, which allows it to freely “flow” from the installation.
That is, when bq<
R/a (13.2)
retention is not possible.
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Hold optionb.
The limitation on poloidal beta also leads to limitations on the full value of this parameter in the tokamak. Complete b is found from the addition of the vectors of the toroidal and poloidal fields and is equal to
Expressing the toroidal field in terms of the poloidal field and the stability margin q =(a/R)(Bt/Bq) we get
Taking into account (13.2) we finally have:
Because A And q greater than one, then the value b limited from above, for example, when A= 3 and q=2, which approximately corresponds to the values assumed in the designs of a tokamak-based thermonuclear reactor, according to (13.3) bmax» 0.08.
We considered a tokamak with a circular plasma cross-section, however, in the ITER reactor design, the plasma cross-section is elongated along the vertical axis (Fig. 13.5). There are several reasons for this. The first, in a toroidal solenoid D-shaped with the same winding length and, accordingly, power supply, it is possible to store significantly more magnetic field energy; in addition, such a solenoid can withstand significantly greater mechanical loads that arise in strong magnetic fields than a solenoid with round coils. Suffice it to mention that with a field of 0.5 Tesla, the internal pressure from the field on the coils is one excess atmosphere. Considering that magnetic pressure depends quadratically on the field, for a field of 5 T, which is necessary for the reactor, we obtain a pressure 100 times greater. The force acting per unit length of a conductor is, in a practical system of units, equal to:
https://pandia.ru/text/79/389/images/image043_4.gif" width="184" height="45 src=">
Due to the fact that the field in a toroidal solenoid increases towards the center µ 1/
Bt, different parts of the coil are subject to different forces, creating a bending moment relative to the support point of the coil. The total force acting on the coil (see Fig. 13.5) is directed towards the center, it is easy to estimate from the amount stored in the volume V total energy W magician magnetic field: FR = -dW mag/dR »
- (B 02/8p)V»
(B 02/8p )4p2a 2. (The coil of a toroidal solenoid can be thought of as a thin hoop pressed against an internal support.) So, the fulfillment of the condition grc =const, Where r– variable radius of curvature of the coil, allows you to create the so-called torqueless coil, which dramatically increases its strength properties. At the same time the condition g (R,z)rc(R,z )=const determines the shape of such a coil, which has D- figurative appearance.
Energy life time
But besides the “engineering” ones, the plasma cross-section elongated along the vertical axis has significant physical advantages for increasing the parameters of the confined plasma. With increasing elongation k =b/a(see Fig. 13.5) at the same large radius, the plasma current and its confinement time increase. https://pandia.ru/text/79/389/images/image046_4.jpg" align="left" width="225" height="263 src=">Stability margin for non-circular plasma q (k)»
q (1+k 2)/2, which, in accordance with (13.1), with the same stability margin allows us to obtain large values IP. Scaling or similarity law, obtained from measurements at many installations, for the energy lifetime tE gives the following dependence on the current and plasma elongation tEµ
IP 0.9k 0.8. Thus, the increase k taking into account q (k) leads to a significant increase tE.
How much the value of beta will increase during the transition to an elongated section can be estimated if R/a replaced by 2
pR/l, Where l is the length of the perimeter of the elongated plasma section, which is approximately ( 1+
k )/2 times the length of a circle with radius a.
