DE2350256A1 - METHOD AND APPARATUS FOR CONTAINING A HIGH TEMPERATURE PLASMA - Google Patents

Description

Method and apparatus for enclosing a High temperature plasma

The generation of useful energy by nuclear fusion has been the subject of greater concern for about twenty years Research in a number of countries. A recent global overview of various research projects with regard to nuclear fusion and fusion devices at research sites results from "World Survey of Major Facilities in Controlled Fusion "(Amasa S. Bishop ed. 1970). However, although many attempts and suggestions have been made, it has not yet met with success given in generating useful amounts of controlled, non-explosive energy by nuclear fusion. '

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'The investigations into the generation of energy by nuclear fusion are essentially directed towards the problem of Inclusion of a gas of relatively low density, about deuterium that is on. a temperature sufficient for fusion reactions to occur has been heated, in a vacuum. At temperatures necessary for that to take place are required by fusion reactions, such gases are fully ionized and are referred to as plasma. There is a fundamental obstacle to the useful generation of non-explosive energy by nuclear fusion currently in the lack of an opportunity to

Cessation of such high temperature plasmas for a long enough time so that one can get out. the fusion reactors gains more energy in the plasma than is supplied to the plasma.

A number of arrangements for the containment of high temperature plasmas in a vacuum have already been proposed, with most relying on the use of one or based on several magnetic fields, which exert forces on the electrically charged particles forming the plasma. Several of these magnetic containment arrangements, sometimes referred to as "magnetic bottles" are in "Progress Toward Fusion Power", Fowler and Post, 215 Scientific American 27 (1966); "The Prospects

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of Fusion Power, "Gough and Eastlund, 224 Scientific American 50 (1971);" The Road to Controlled Nuclear Fusion ", Artsimovich, 239 Nature 18 (1972) and in. U.S. Patents 3,009,080 and 3,088,894. No however, this magnetic confinement arrangement is capable of confining plasma for more than maintain short periods of time to enable usable energy generation. The inability of the known magnetic containment devices the plasma containment for more than very short periods of time sustained has been attributed to the instability of the plasma and has led to investigations of possible Instabilities of various plasma configurations as well as methods for eliminating these instabilities (compare, for example, "Elementary Plasma Physics", Arzimovich (1963, 1965), Chapter 8).

A widely used method of achieving plasma inclusions consists in the formation of the plasma in a toroidal vessel so that the plasma the Takes the form of a toroidal loop. Application examples are the "Stellarator", "Scyllac" and "Tokomak" machines, which are described in the preceding articles, as well as the devices according to the above U.S. Patents 3,009,080 and 3,088,894. Although these

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-H-

Solutions and corresponding modifications have been known and used for years, so far none has been. Plasma stability achieved over longer periods of time leading to the generation-of usable energy by means of nuclear fusion would be sufficient.

The invention relates to the generation of energy by nuclear fusion and, more particularly, to the containment of High-temperature plasmas for a sufficiently long period of time to generate energy in such a plasma by fusion reactions, the energy supplied to the plasma to compensate for the energy losses in the plasma and, if necessary, to keep the plasma at a sufficiently high temperature. - -

This is based on the assumption that there is a class of toroidal, magnetic confinement arrangements which are characterized by "structural stability". "Structural stability" is understood to mean that property of the plasmas enclosed by this class of magnetic confinement arrangements according to the invention, which make such plasmas relatively insensitive to approaches, tolerances and changes in the parameters of the shape, structure and operation of such plasmas for sufficiently long periods of time Arrangements are. . '■

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In the case of a plasma with TorusfOPm ₁ that is axially symmetrical, the class of magnetic confinement arrangements according to the invention is characterized in that magnetic field lines on the surface of the toroidal plasma meet the requirements for static structural stability. These requirements include the conditions that only a finite number of magnetic field lines are closed. It is also necessary that the magnetic field is not equal to zero everywhere in order to prevent plasma leakage. In addition, for the reasons explained later, it is necessary that the limit cycles of the magnetic field lines are even and not equal to zero and that the rotation transformation angle of the magnetic field lines is equal and permanently zero,. ·

Magnetic field lines that meet these conditions can be passed through a set of current-carrying conductors that are properly arranged with respect to the outer shape of the plasma so that the flow in the conductors on the surface of the plasma generated the resulting field lines a finite, even number of closed, Have toroidal field lines that form the plasma surface in a corresponding even number of Divide torus areas, with the poloidal field lines

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in each area are directed opposite to the poloidal field lines of the adjacent area or areas and where the rotation transformation angle of all magnetic Field lines in all areas is zero. Enclosed by such magnetic field lines toroidal plasmas form a class of plasmas in which each class member is represented by a non-convex, is characterized by a poloidal cross-section, for example by a cross-section of either a kidney, i.e. resembles an approximation of Pascal's snail, or a banana-shaped curve, and being the poloidal Cross-section of such a plasma has a finite, even number of stagnation points, which correspond in number and location to the closed magnetic field lines on the surface of the plasma.

The invention is explained in more detail below with reference to the figures.

Figure 1 shows schematically in perspective .and partly in section the various current conductors as well as other elements of an embodiment of the invention.

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Figure 2A shows in cross-section einen'Teil de-r I arrangement according to FIG. ₃ the non-convex cross-section of the plasma is required for static, structural stability.

Figure 2B shows a modification in cross section the illustration from FIG. 2A.

FIG. 3A shows a perspective representation

Partial section of the family of magnetic surfaces generated by the conductors according to FIG. 2A • will.

Figure 3B shows a pair of side views of a plasma that is included according to the invention, wherein the upper illustration is an external view of the magnetic Field lines on the outer or larger radius surface of the plasma and the lower view an interior view of the magnetic field lines and the boundary periods or closed magnetic Shows field line revolutions on the inner or smaller radius surface of the plasma.

FIG. 4a shows partially in a perspective view in section a toroidal plasma according to FIG Invention. ■. ·. '■

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Figure Hb shows a section through the toroidal plasma according to Figure 4.A. '

Figure 5 shows a section through another toroidal Plasma according to the "invention, where" the number of poloidal stagnation points is the same "four is.

FIG. 6 shows a cross section through a further toroidal plasma according to the invention.

Figures J _3, 8 and 9 show diagrams to explain the theoretical principles of the invention.

FIGS. 10, 11 and 12 show representations calculated by means of a computer specific parameter values of a preferred embodiment of the invention.

Fig. 13 shows a cross section through the toroidal plasma, with the calculation of the required Currents can be seen.

contraption

In Figures 1 and 2, a hollow, current-carrying conductor 10 is shown, which consists of either a single, one-piece conductor or a number of conductor segments

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ten can exist. This conductor 10 forms a toroidal chamber 11, in which a suitable, non-conductive, toroidal envelope 12 is attached, which on a electrically insulating, magnetically permeable material such as quartz or porcelain is arranged. Both head 10 and envelope 12 have a common axis Z, hereinafter referred to as "toroidal axis" or "axis of the toroid". The inside of the envelope 12 is through an inner wall 120 in two gas-tight chambers 121 and 122 are divided, and the chamber 121 is filled with a gas, such as deuterium, at a relatively low pressure, for example a pressure of one thousandth Atmosphere filled. "In the chamber 122 are toroidal or azimuthal current-carrying conductors 123 and 126, which also have the Z-axis as their common torus axis. The conductor 123 can either from a variety of toroidal, current-carrying Wires that are arranged around a longitudinal axis Ll and have the Z-axis as a common axis (as circles enclosing a point shown in Figures 1 and 2), or from a single toroidal, There are current-carrying conductors, which is arranged about the longitudinal axis Llj as shown in Figure 3A is. The conductor 126 is embedded in an insulator, which also serves as a carrier for the conductor 123, and conductor 126 may be in the form of a plurality of live wires as shown in the figures

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, 1, 2A and 3A.

Outside the envelope 12, a toroidal, current-carrying conductor 13 is attached, which consists of a plurality of consists of toroidal, current-carrying wires, which in Figures 1 and 2 are shown as small circles and all have the Z-axis as a common torus axis.

The gas in the chamber 121 is first ionized to obtain a toroidal plasma with the Z-axis as the toroidal axis. This can be done with any known arrangement (not shown), as described, for example, in "Controlled Thermonuclear Reactions", Glasstone & Lovberg, pages 116 to 163 (1960). After the gas has been ionized in the chamber 121 to form a plasma, the conductors 10, 123 and 13 are connected to voltage by means of the capacitor blocks 130, 131, 132, as described in US Pat. No. 3,009,080, around the toroidal plasma in the chamber 121 ″, so that it assumes the shape 14 according to FIGS. 2A, 2B, 3A, 3B and 4A. Poloidal current is supplied through the conductor 10, ie transversely around the toroidal chamber H ₃ enclosed by the conductor 10 like this 2A and 2B. At the same time, current flows through conductors 123, 126 and 13, the current through conductors 123 and 126 flowing in the opposite direction to the current through conductor 13. For example, the current in the conductor 13 flow counterclockwise around the torus axis, as indicated by the in the

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Circles that denote the wires of the conductor 13, each provided "x" is indicated while the current flows through the conductors 123 and 126 clockwise around the toroidal axis Z, which is shown in FIG. 1 by the points in the Wires of these conductors are indicated in the designating circles.

As will be explained in detail later, the generate by conductors 10, 123, 126 and 13 have currents flowing inside of wrapping 12 sets or families of toroidal magnetic field surfaces 124 and 125 - like this shown by the dashed lines provided with arrows in FIG. 2A and by the exemplary areas is indicated in Figure 3A. The presence of two Stagnation points 4 and 5 in the poloidal component of the Figure 3A shows the magnetic field by means of the arrow directions, which indicate the direction of the magnetic field lines caused by the currents in the plasma surface and the wires 123 and 126 are generated. The currents also induce magnetic field lines 19 on the surface of the Plasmas 14 (Figure 3B), the magnetic envelopes 124, 125 and the magnetic field lines 19 have certain properties which are desirable for the invention and which later explained. .

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The magnetic field contributed by the current flow through the conductor 10 tends to shift the magnetic field Field lines 19 on the surface of the plasma 1 * ί inwards to the longitudinal axis L2, thereby exerting a compressive effect on the plasma around the longitudinal axis L2 and the magnetic Field lines 19 on the surface of the plasma 1 * J be bent about the torus axis Z. The currents in lines 10, 123, 126 and 13 are corresponding to The criteria of static structural stability explained later are set to a final equilibrium configuration of the magnetic field.

The magnet generated by the current flowing through the conductors 123 and 126, which is set according to the invention,

netfeld is used to create an area on the inner Surface of the plasma 40, i.e. on that surface which. the torus axis Z and that having the smaller radius or inner wall 120 of the envelope 12 is closer, on which the magnetic field lines 19 are bent or to the longitudinal axis L2 of the plasma 14 are pressed so that a depression arises and the poloidal cross-section of the plasma 14 is not convex. This area is between the lines 15 and 16 in the lower illustration in FIG. 33 shown. The non-convex, poloidal cross-section can take one of several shapes, for example

4 0 3 8 1 9/0 B 9 2

Kidney shape L4L (Figures 2A, 2B, 3A and ¹ IB), modified form of kidney-1-42 (Figure 5) or banana shape 153 (Figure 6).

The magnetic field generated by the conductor 13 acts on the plasma 14 to cause this plasma to move outward from the torus axis Z away to the outer wall or to the larger one To prevent radius having side of the chamber 121.

The combined effect of the magnetic field formed by the currents through the conductors 10 _a 123, 126 and 13 serves to contain the plasma 14 so that the requirements for static, structural stability are met, as will be explained later.

The two families or sets' of magnetic fields or magnetic surfaces 124, 126 according to Figure 3 · ₃ in the enclosure 12 by the current in the conductors 10 ,. 123, 126 and 13 are characterized by the following properties. The group of magnetic fields 24 is arranged in a toroidal shape around the conductor 123 and the other group of magnetic fields 125 "in a toroidal shape between the envelope 12 and the outer boundaries of the group of magnetic fields 124 and the plasma. The magnetic field lines from the conductor 126 enter the plasma. 14 surrounding vacuum space and leave it.

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where the entry and exit from conductor 126 occurs, there is a discontinuity in the tangential component of the magnetic field and the size of the discontinuity is determined by the values of the currents in these conductors. It can be seen from FIGS. 3A and 3B that the poloidal component of the magnetic field on the surface of the plasma 14 does not have a uniform direction, but is characterized by two oppositely directed magnetic fields. The inner segment '4/6/5 » that consists of the arc 4 to 6 and the arc 6 to 5 of the interface Γ of the poloidal cross section of the plasma 14, ie the border area of the poloidal cross section of the plasma 14, the conductor 123 and the Torus axis Z is closer, thus has the poloidal magnetic field line, which has a direction which is opposite to the direction of the poloidal field line on the outer segment 4/7/5 (arc 4 to 7 and arc 7 to 5) of the border area Γ , which is located near the outer wall of the envelope 12 and further away from the torus axis Z of the plasma 14. As a result, the poloidal components of the magnetic field lines 19 on the surface of the plasma 14 are divided into two groups, each of which follows the direction of the next adjacent group of magnetic fields 125 and 125 that are generated in the chamber 121.

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As can be seen from Figures 3A and 3B, the
poloidal components of magnetic field lines 19
on the inner segment 4/6/5 'of the border area Γ the same. Direction like the neighboring group of magnetic surfaces 124, while the polar components of the magnetic field lines 19 on the outer segment 4/7/5 of the border area / follow the direction of the neighboring group of magnetic surfaces 125. '·

As will be explained in detail later, the rotation transformation angle of the magnetic field lines on the surface of the plasma must be l4 im axial
symmetrical case according to the invention for all sufficiently 'small deviations in the parameters of the overall system'
be identical and permanently zero. This requirement is
shown in Figures 2-A and 3B, in which the magne- ·. table field lines 19 on the plasma surface
the magnetic field lines 15 and 16 on the surface of the plasma 14 are divided into two areas. The field lines 15 and 16 are closed, ie they describe a closed, circular toroidal path on the surface of the plasma 14. According to the principles of the invention, the number N of the closed magnetic field lines, for example the field lines 15, 16, must be an even number, ie -N = 2, 4, 6,..., And

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these closed field lines divide the surface of the plasma I ¹ J into a corresponding number of N torus areas. As shown in FIG. 3B (interior view), the two closed magnetic field lines 15 and 16 thus divide the surface of the plasma 14 into a corresponding pair of torus regions. It will be explained later how the current intensities in the conductors 10, 123, 126 and 13 are to be calculated in order to obtain a magnetic field with these desired properties on the surface of the plasma 14.

In the surface areas of the plasma between the closed magnetic field lines, all other magnetic field lines describe non-closed, toroidal courses that asymptotically approach the closed field lines or move away from the inside. This results, for example, from FIG. 3B (interior view), where the non-closed magnetic field lines 19 move asymptotically away from the closed field line 15 and asymptotically approach the closed field line 16, but without intersecting one of the closed field lines 15 and 16. FIGS. 2A and 3B also show that the course of a non-closed field line 19 is offset by a finite angle cf during each path around the circumference of the plasma IH.

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With a given rotation around the circumference of the plasma Ik, this angle cannot exceed 2 "7T or 36O, since the non-closed field line 19 cannot intersect the closed field lines I5 and 16. · The total displacement angle <f after η-rotations of a magnetic one Field line 19 around the circumference of the plasma cannot exceed 2TT for the same reasons.

By definition, the rotation transformation angle of the magnetic field lines 19 is the limit of the ratio of the total displacement angle Q to 2 TTn for an arbitrarily large value of n, ie ** ^m 5

η - * <* »2irn.

Since ei can not exceed 27T, in order to comply with the structural stability principles according to the invention

S _n

agree, the limit ratio is ^ for a

arbitrarily large η = zero and remains for non-closed magnetic field lines I9 always zero. In addition, because of their closeness, all closed field lines have zero rotation transform angle, those are both closed and not closed magnetic field lines, on the surface of the plasma 14 by a rotation transformation angle marked by zero. The requirement for a finite, even number of closed field lines with respect to which all other field lines on the surface

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are asymptotic, is an essential feature of the invention. Hyperbolic stagnation points of the poloidal Field must at a described critical radius through a specific configuration of the external currents are generated, which are calculated according to "the principles to be described according to the invention"

It can be seen that a plasma characterized by the structural stability defined in the description can be obtained by generating magnetic fields which differ from those described here if only the stated principles according to the invention are followed. Thus, conductors can be arranged in the vacuum space surrounding the plasma, which conductors are provided at other locations, at the same locations or at parts of locations on the conductors 13, 123 and 126. For example, in FIG. 2B, a plurality of conductors 21, 22 and a pair of conductors 23a, 23b are provided, which represent magnetic dipoles in the poloidal field. Both known analytical and numerical methods can be used to select and arrange suitable conductors.

Although the arrangements according to Figures 1 and 2A ladder on river surfaces or in correspondence with river

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Contain singularities, for example the outer one Element of the group of surfaces 125 or the inner element of the group of surfaces 124, it is clear, the & other as the liquid surfaces can be chosen if appropriate conventional magnetic dipole means are chosen (Figure 2B), which serve to create the magnetic field that is otherwise generated by the conductors on the flux surfaces is produced.

Although a rotation transformation angle of zero is required for an axially symmetrical, toroidal plasma, it is clear that with a / topological, toroidal plasma that is not axially symmetrical, for example a toroidal plasma that is helically twisted, structural stability according to the principles of the invention is achieved in that such a plasma has a rational number of rotations and at least, but not more than a finite, even number of closed magnetic field lines on the plasma surface, the number not being equal to zero ] .

4 0 9 SI 9 / Ό 6. ¹ S 2

Theoretical foundations

The following terms are used in the following:

B vector of magnetic field

r radius vector "

J. ^c vector of electric current

β magnetic field strength (length I? or ϊ ^: ϊΓ)

α *, .magnetic permeability

B ^Z / 2f ^ magnetic pressure

ρ plasma fluid pressure

Δ ratio of plasma fluid pressure to greater

magnetic pressure

^ the boundary layer between plasma and vacuum

forming surface, i.e. plasma boundary η ■ normal vector on S * s arc length along the field line

tk denotes the positive limit theorem of a

Field line φ. denotes the negative limit theorem of a

Field line

(x., x „) spatial coordinates on Σ ¹ (X ₁ , X ₂ ) components of · B in the spatial coordinate system on Σ7 y closed field line on 57 (topological circle

4 0 9 '8 1 9 / Q 6 3

_ 21 -

/ Q _z ) cylindrical coordinates

f \ y puncture of the magnetic flux

Γ cut from J? with the plane Θ = O "

2> partial differential operator

d differential operator

V Hamiltonoperatqr "

Δ Laplace operator

A ^ Stokes operator

V volume

S surface area

rf critical radius

c indicator

In the following description of the theoretical basis on which the invention is based, only the static, structural Stability considered in detail, although there are two different phenomena of structural stability! -, -tat of a toroidal plasma there, the static and the dynamic structural stability. At one through, the static structural, stability according to the fundamentals The toroidal plasma characterized by the invention can achieve dynamic structural stability by means of known methods can be achieved, such as systematic, theoretical multi-channel design methods such as them

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be used in the design and development of stabilization systems for spacecraft. Thus becomes by using the term "structural stability" in the following, only the static structural stability unless expressly stated otherwise.

Let us consider a plasma which is enclosed in a certain, finite, limited area of space by a magnetic field B, the plasma containing no internal current conductors and wherein there is little or no magnetic field inside the plasma. At the plasma boundary or surface ^ , which forms the boundary layer between the plasma and the magnetic field B, it is necessary that the total pressure p _{T is} continuous across the plasma / vacuum boundary, where p _{T is} the sum of the plasma fluid pressure ρ and the magnetic pressure B. /2.u with, u as per-

2
meability, ie p "= ρ + B / 2, u. So the

β -η

Total pressure on each side of the surface ^, be the same. Using the index "i" for the pressure inside the plasma and the index "o" for the pressure outside the plasma results

Since the plasma fluid pressure ρ is the same outside the plasma O, the equation (2) x ^ ie follows

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to be written:

The value Δ is defined as the ratio of the plasma fluid pressure p. "Inside the" plasma to the magnetic one

Pressure B / 2, u outside the plasma, i.e. '■■

/ P-Pi / (B _o ² / 2p). (M

This definition shows that the parameter is between 0 and 1. By requiring that there is little or no magnetic field inside the plasma. is present (this can be achieved in a highly conductive plasma by inducing currents in the plasma surface that prevent the penetration of the magnetic field; this is possible by quickly switching on the currents in the outer conductors)., the equation (3) write as follows '

_: ..ρ _ί? .ψΕ , (5)

By inserting equation (5) into (4) it results that / 3 goes to one "under these conditions. Considerations of the transport processes, in particular the finite specific resistance, show that the value of Δ for the required dynamic stability of the plasma should approach 1 (high A value) as much as possible, but not necessarily.

At Δ - 1 under equilibrium conditions, the fluid pressure inside the plasma has the same value everywhere

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not equal to O, so that there is a generally continuous Pluid current in the plasma results. Then according to the equation (5) the magnetic pressure outside the plasma anywhere on the boundaries or surface of the plasma not equal to 0.

The plasma surface S should also have no turning points or edges and must be closed, ie "cannot have any topological boundaries. Furthermore, 2 * should be orientable in the sense that the surface has a clear outside and inside, ie no part of % can penetrate another part of Σ . "

Another boundary condition for Σ is that the normal component of the magnetic field outside the plasma is continuous over Σ , which implies that the magnetic field on the surface of the plasma is tangential to S and therefore forms a non-vanishing tangential vector of the magnetic field everywhere on Z * .

It can be shown by means of the fixed point theorem of Lefsehetz-Hopf (Lefsehetz-Hopf fixed point thec ^ -em) that Σ ¹ for the aforementioned flat bed'ingunnen (compact orientable 2-manifold) without fixed points and

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for a continuous course of the normal component of the magnetic field on S? outside of the plasma topologically must be a torus - i.e. the topological product of two topological circles.

The next requirement is that the confinement of a toroidal plasma should be statically "structurally stable", that is, such a plasma must have equilibrium properties that are insensitive to small changes in such system parameters, such as the qualitative or topological properties of the magnetic Form field line configuration to 5Γ so that this configuration is not changed by such changes. The necessary and required criteria for the structural stability of an arbitrary vector field on a topological torus are given by M. Peixoto (references in "Foundations of Mechanics", Abraham (1967)) and by VA Pliss (as indicated by the expression "coarseness" in " Nonlocal Problems in the Theory of Oscillations (1964, 1966). Reference is also made to "Systemes Grossiers", Andronov & Pontriagin, Ik "Dokl. Akad. Nauk. SSSR (1937). These are:. ■ - ■

(a) there are only a finite number of singularities, all genericj

(b) the Oi and W boundary sets of each orbit can only be singularities or closed revolutions; · '

(c) no track connects saddle points;

(d) there are only a finite number of closed circulationsj all of which are simple.

The term "singularities" in conditions (a) and (b) above refers to points at which the Vector field disappears. Such points are usually referred to as "stagnation points" in this context. A "saddle point" is a type of singularity also known as a "hyperbolic stagnation point".

If one applies these criteria of structural stability on a plasma in a magnetic field under the conditions mentioned above, according to which the plasma boundaries a topological torus and the magnetic field correspond to the vector field, so criteria (a) and (c) fulfilled, since the magnetic field is not equal to 0 at all points on the plasma surface 57, which means that none Singularities are present.

The terms "tracks" and "circulations" relate to

the arc-length parameterization of the magnetic field lines, which is obtained by integrating the usual non-linear vector differential equation ^ = Bo ( ^r ) ^ o ( ^r ) · on S ¹ '. The "K " or " ω " limit set of these magnetic field lines is the totality of the limit points on / the lines in the limit of the arc length parameter s_, which approaches -oo or -fco in each case. Since there are no singularities, it follows from criterion (b) that the limit sets must be closed or endless revolutions, ie the limit sets must be limit cycles or closed revolutions in the Q { or co- limit sets of other-different magnetic field lines lie.

The criterion (d) requires that the "number of closed Circulations must be both finite and "simple". In order to be "simple", the following applies

exp (fMl + 1% .W ^ 1,

; _y U.xi

where the integrand of equation (6) is the two-dimensional _r divergence 'of the magnetic field on the plasma surface S. and in which x ^ and X _{2 are} the spatial coordinates on the plasma surface, X ^. and Xp are the corresponding coordinates of the magnetic field lines at these coordinates and f is the considered closed circuit.

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By combining the criteria of 'structural stability with Maxwell's equations and the Bernoulli's theorem for a continuous fluid flow can be shown _a that, as is by considering the equation (3) clearly, the magnetic field line configuration on the surface of the plasma meet the following criteria must to achieve structural stability:

• (a) the rotation transformation angle of the magnetic field lines on the surface of the plasma is identical to zero; -

(b) the number N of closed revolutions is finite and even (N = 2,4,6, ...); and

(c) the closed circuits are not only simple, but must occur in pairs, the parts of each pair for increasing or decreasing arc lengths (after a certain assignment was made for the sense of increasing arc length) asymptotically are stable. .

An application of these criteria to the simplest case two closed magnetic field lines (this case is not redundant, since all other cases are for even-numbered N require the doubling of all elements), shows that one of the two closed field lines,

is asymptotically stable, i.e. the neighboring field lines

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approach it asymptotically, and that the other closed field line is asymptotically unstable, in the sense that neighboring field lines move asymptotically away from it ("asymptotically" here refers to parameterization by arc length, not by time) * Let it be for example the closed field lines 15 and 16 and the neighboring field lines 19 in Figure 3'B considered. It can be shown that the requirement that the two field lines are simple with closed circulation is equivalent to the requirement that the "flow" j of the on the plasma surface S by the arc length parameterization of the field lines in the immediate vicinity of the two closed field lines is induced, is on average not area-preserving. ·

It is shown below that, under the above conditions, the equations for equilibrium in magneto-fluid dynamics, a unique type of solution in ..Shape of a group of physically feasible, toroidal Have plasma configurations. This group of physically realizable, toroidal plasma configurations is characterized by the following properties :.

(1) The two closed magnetic orbital field lines are two boundary cycles on the plasma surface, one of which is asymptotically stable

«09919/0892 ■ - '' ■

and the other is asymptotically unstable.

(2). The poloidal cross-section of the plasma is characterized by two stagnation points in the poloidal magnetic field on the plasma surface, each stagnation point on the poloidal cross-section of one of the two limit cycles corresponds to the plasma surface.

(3) D & r poloidal cross-section is not convex.

No plasma confinement method used to date has this characteristic of static structural stability There is also a 'non-content-oriented river in the neighborhood of each (isolated) closed Field line, since none used the possibility of asymptotic field lines on the plasma surface ^ and in particular is none in the previous plasma containment facilities closed field line isolated. This does not contradict the content-accurate nature of the corresponding Vacuum field flux because the closest magnetic Vacuum areas neither linked with 2f nor, in a vacuum, are homologous to 5Γ. As above in context As explained with FIG. 3A, it was found that there is a group of physically realizable arrangements for the magnetic confinement of plasmas in a

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Vacuum exists that consists of at least two single parametric families nested, toroidal magnetic surfaces, each directly at least one area of the plasma are adjacent, and a third, a single element having magnetic surface family exist which forms the plasma / vacuum interface, with none of the 'first two families of surfaces being homologous to the third Is face family and where the third face family is at the same time through-a rotation transformation angle distinguished by Ö. A special group of families of nested magnetic surfaces that meet the criteria rien are shown in Figure 3A, in which the family 124 is homologous to the conductor 123 (failure to observe the Ladder 126) and family 125 homologous to both cladding 12 and to the geometric union ■ of the family 124 with the surface of the plasma 14 is ..

The terms "homologous", "union" and "homotopic" used in the description (homotopic) are in the field of mathematical topology well known. Furthermore, it should be pointed out that the ver.- in the present application. " The terms "vacuum" or "vacuum space" were used to denote the geometrical space of the plasma surrounds, regardless of the presence or absence, of magnetically permeable substances and exempted

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-3t-

the electrical conductors. In. In this space there is a magnetic field that encloses the plasma, so that this structurally according to the principles of the invention is stable.

The following properties of the practical implementation of the invention, taking into account their theoretical

The technical basics all result from a technical consideration:

(a) finite plasma volume

(b) Connection (connectedness) of the plasma volume

(c) local homotopic triviality of plasma volume (especially no inner conductors).

(d) Closure of the device

(e) the plasma surface is a compact, orientable multiple surface (manifold)

(f) Non-redundancy of the limit cycles

(g) Axial symmetry (this restriction is only used to simplify the description)

(h) static structural stability.

Under these assumptions, the standard equations have of equilibrium has a unique type of solution that is. radically different from previous considerations in this area differs. The following explanations represent essential elements of the mathematical framework for

4 0 ¹ S 8 1 9/0 6 9 2

this type of solution.

Let ζ be a coordinate on the torus symmetry axis and let (r ₃ Θ) be polar coordinates in any plane through the z-axis, ie any poloidal plane. Then (r, 0, z) forms a standard system of cylindrical coordinates, and the vector B in this coordinate system has the components (B. B ^, "B) , magne ^ (r _a χ),

tables PIUssfunktίοη t so that is applicable B- 1 9 Ψ _R C. i> p - r

The puncture " is well known, as is the fact that its gradient Vf is necessarily perpendicular to the surface 3 " The constant c is determined by the current in the outer, polOidal conductors (or equivalently along the z-axis) The constant ρ denotes the equilibrium plasma fluid pressure.

The constant c -determines the toroidal magnetic field completely. The poloidal field is unambiguously determined by the constant ρ and the puncture * Ψ . As; however, as will be shown in the following, Ύ * is uniquely determined by * the choice of e, ρ and the geometry of Z.

4 0 0819 / 06ta

-3fr--

Once s "omit c and ρ have been determined, that is Vacuum field solely through the choice of the geometry of S " clearly determined.

> Figures hA and JJB explain this state, in which 14 denotes the topological torus, which represents the plasma volume, and 2 * denotes the surface of the plasma volume. The spoiled one. Cross-section of this torus is l4l, and Γ denotes the poloidal cross-section of the surface i »and is the curve Γ: ^ (r, z) - O. (8)

On X is the pressure equilibrium state:

J2 -2, .P ₀ * ² - c ² . . (9)

V *

It can be clearly seen that for a sufficiently small r the right side of equation (9) "CO ₃ while the left side" is always ^ O. There is thus a minimum of r, namely r, which satisfies equation (9), ie there is a minimum of r, r for which a physically real solution exists. As shown in FIGS , the plasma volume must therefore always be to the left of the vertical line r = r. The critical radius r is given by! "Ι "'' f \ n \

and the boundary condition which, together with equation (8) ^{n, is} a solution of Stokes'. Equation on the exterior

409819/0692

3Γ- ■; ■■ · .. ■ ..

determined by / is

= + I vf I = π- c / if. -1 * _ ι ι JVC}

If / lies completely to the left of r, a sign must be selected in equation (11), since 'ί) ^/ γ. '- /' S cannot disappear anywhere on Λ. This implies that the vector field on Σ inevitably always has a rotation transformation angle not equal to 0, as a result of which the prerequisite (a) of the structural stability criteria according to the invention is violated.

If, moreover, as in FIG. 9 _{3 is} chosen as the limit C of an arbitrarily convex body which touches r at just one point, 18, then it follows from equation (11) that the poloidal field at this point has a Must have stagnation point, wherever it touches

there is a stagnation point. Point 18 must be a be an elliptical singularity if one assumes the presence of a solid conductor at this point, and if the plasma were to touch an outer conductor at 18, this would be the one for controlled fusion reactions destroy required thermal insulation. However, by looking to the right and left of / opposite each other generated directed current surfaces, and by taking the square root in Crleichunc (11) at a point v / o / r 'touches, lets change the sign, can

Ii 0.3 8 1 9 / 0-692

one fulfills the requirement of a rotation transformation angle of 0 by converting the elliptic singularity into a hyperbolic one. It is clear that a second point of contact with r, which requires a non-convex, poloidal cross-section, enables the sign to be changed again to the original value, which is required for equation (11) so that O * γ / Qn no discontinuities on Γ has. Otherwise Stoke's equation would not have a physically feasible solution. The resulting kidney-shaped or non-convex poloidal cross-section 1 ^ 1 (FIGS. 4a, *! B), together with the associated magnetic field, is not only a consequence of the choice of a non-convex, poloidal plasma cross-section 141, but also the choice of mutually opposite. oppositely directed, toroidal flow surfaces, which enables a change in sign of Ο'ψίΦη , as is indicated at points H and 5 in FIG. 4B.

By choosing / as the non-convex shape that touches the line r = r at two points, 4 "and 5, the requirement of two limit cycles on ^ is met. Since at H and 5 r = r _c results from equation ( 11) / ^ ⁷ V / = O and B = B = the only at H and 5 existing magnetic field component is O. thus torus *-shaped (in azimuth) and the two field lines Vj and 16 (FIG-.3B) defined by the Point H or 5 run, circles are parallel on 2 *

409819/0692

to the Γθ-plane with centers on the z-axis. On segment ¹ I / 6/5 on Γ , Q ¹ Y1-0 η> O and on segment 4/7/5 'w' / wn ^ O (or vice versa) can be assumed.

The postulated discontinuity of the normals of B over 2? \ iris achieved by surface currents on 2> . These currents in two areas on % " , which are defined by the two limit cycles according to lines 15 and 16 in FIG. 3B, are directed in opposite directions Divide the plasma surface into N neighboring torus areas or N / 2 pairs of neighboring torus areas. Correspondingly, the non-convex, poloidal cross-section of such a surface has N poloidal congestion points corresponding to the number and geometric position of the N limit cycles. In Figure 5, for example, N =. H Therefore, there are N toroidal flow areas, one at each of the N adjacent torus regions, each flow area being opposite to the flow areas of the two immediately adjacent torus regions.

The curve 20 in FIG. 4B is a “slus surface”, ie an area j = constant. Toroidal currents brought together approximately on such a surface produce together

with induced toroidal plasma surface currents the poloidal vacuum field. In addition, oppositely directed toroidal currents are required at each of the points 8 (in the following it will be shown that these points lie on a branch section). If necessary, however, the current at the points 8 can be replaced by a family of toroidal currents which lie approximately on one of the next plus surfaces, approximately 9 , which surrounds the outermost of the points 8. Outside the area generated by the axial rotation of the curve 20, strong poloidal currents (not shown) together with induced poloidal surface currents generate the toroidal magnetic field in a vacuum.

The existence of an analytical solution of Stokes equation in the neighborhood of is proved by the Cauchy-Kovalevsk theorem, provided that / is an analytic curve and that ^ dj I ^ η on Γ is analytic. The latter forms the basis of the physical feasibility of the invention.

To simplify the calculation it is assumed that / has the shape of a Pascal see screw ₃ although this may not lead to an optimal configuration, since the resulting two-cut 8 is inconveniently close to the plasma • Another possibility is to '

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to be chosen as a banana-shaped curve, as shown in Figure β. This can be done using "capcyclide" coordinates. In this case there are two possible singularities, such as S1 and 62. For the present case, namely the plasma inclusion, there is, however, no essential difference between the forms of f according to FIGS. KB and 6.

In order to confirm the "simplicity" of the limit cycles through k and 5 according to FIG. 3B (as is required for structural stability), the solution for the magnetic field in the vicinity of each limit cycle can be represented by ■ an expansion of B and / in power series, which converge near the limit cycle.

The above statements are fundamental considerations for the proof of the existence and the uniqueness of a solution that meets the latter requirements (a, b, c, d, e, f, g, h) fulfilled. Will the condition (f) the non-redundancy dropped, then solutions of the kind shown in Figure 5 are possible in which the number of limit cycles and thus the stagnation points is increased by a multiple of 2. *

09819/069

- te -

It should be noted that the vacuum volume is at least "triple-connected", that is, there are at least three independent, non-homologous geometric cycles in the volumes including one that is homotopic to a point. These cycles are, for example, ¹ H in Figure hk, ι and 42 in Figure 4B. Thus, the conditions (a, b, c, d, e) and (g, h) assume a plasma configuration, which is a topological torus, which is axially symmetrical to a non-convex, poloidal cross-section and which is connected at least three times to the associated vacuum volume (if dipoles are not used, as shown in Figure 2B).

■ When using the terminology customary in this field, after the a "Tokomak" as a toroidal plasma monopoly with low beta and a "GuIf Energy and Environmental Systems Doublet "is referred to as a low beta torus plasma monopoly doublet (see" The Tokomak Approach in Fusion Research ", Coppi and Rem, 227 Scientific American 65 (1972)), one can choose the preferred one Designate the form of the invention as high-beta toroidal plasma dipole.

Let it now be the dynamic structural stability or, equivalent to it, the (dynar-isehe) asymptotic 'stability of the plasma pseudo-equivalency, not the five great electrical ones specific resistance, heat conduction, compressive

409819/0692

bility, viscosity and Maxwell's displacement current (consequence of the finite and not infinite speed of the electromagnetic waves) simultaneously be _ -. endeavors, while so far only one or a few of these greats have been considered at the same time. The reduction of the eleven simultaneous partial differential equations of the ENTPD (electromagnetic-thermofluidic-dynamic) wave motion to a simple, static scalar equation, namely the Helmholtz equation for the geometric shapes of the standing sound waves, plus a polynomial dispersion relationship of 7 degrees. , for the complex frequencies of the normal vibration states of the plasma make the physical nature of the • macroscopic vibrations of the plasma understandable. (A special case of the above analysis results 'from the determinant of the simultaneous, homogeneous linear equations (2.60) and' (2.6l) by RJ Tayler in "Plasma Waves And Oscillations". Edited from Physics of Hot Plasmas , p. 113 » 1970 by Rye and Taylor ,,, Oliver. And Boyd). There are basically four types of three-dimensional waves inside the plasma, namely (i) Entropy waves.

(ii.) "slow" magnetoacoustic waves (iii) "fast" magnetoacoustic waves (iv) electro-r.ar-netoacoustic waves.

The -VJeIlen (ii) and (iii) are modified sound waves and modified Alfven-Uellen or vice versa (depending on

4 09819/0692

of which is slower) while the waves (iv) are modified electromagnetic waves. A new conclusion from this analysis is that of the methods for column confinement of tubular plasmas considered so far, only those which fall into the category of "infinitely long" (ie with open ends) theta pinches (ie rotational transformation of zero ) fall. Another result (Figures 7 and 8) is that it is easier for high beta (near / j- 1) than for low. Beta (close to / 3 = 0) to achieve dynamic structural stability. In particular, the following analysis and the diagrams according to FIGS. 7 and 8 show that idealized "energy basis" calculations, in which four of the aforementioned physical effects were not taken into account, only lead to physically reliable results for dynamic instability at high beta. Thus the geometrical criterion given by Teller can be used for the dynamic instability of diamagnetic plasmas. An application of this criterion in the manner indicated by Pfirsch & Wobeg (cf. Pfirsch & Wobeg, "Proceedings, Culham Conference on Nuclear Fusion", Vol. I, 1966, page 757) shows that exchange or global «channel instabilities (flute instabilities) can not occur, since the present configuration in the appropriate sense of a "minimum, average B" an optimal,

409819/0692

represents toroidal "magnetic wall". Apparently the outer area of the plasma surface (between points ^ 3 and hk in Figure ^ B) has an unfavorable curvature and can therefore, for example, lead to local wave instabilities known as "local channel instabilities" (Pfirsch & Wobeg, "Proceedings, Culhain Conference on Nuclear Fusion" , Vol. I, 1966, page 757) known type. Such instabilities increase until the linearizability assumed in their analyzes no longer applies, but increases to infinity. The infinite growth of such instabilities can be effectively suppressed in at least two independent ways:

(i) by choosing a sufficiently large one

Torus aspect ratio, i.e. the ratio of the largest to the smallest Torus radius, suppressed. The equivalent Surface tension caused by the line binding and the finite Larmor radius effects generated instabilities; (ii) through automatic feedback stabilization. So far, feedback stabilization has only been convincing for certain open ended devices (linear theta pinches and quiet or "Q-Masehinen ^" magnetic mirror devices). shown to have static structural stability. This is not surprising given the static structural stability Stability of the plasma configuration in the technical

409819/0632

Systems for the property known as identifiability is required, which in turn for the rational structure of the feedback stability enlargement or the Stabilization systems is required.

For ordinary, linear electromagnetic systems with a finite number of degrees of freedom, static structural stability is equivalent to the requirement that there are no repeated (or "degenerate") complex frequencies and that none of the complex frequencies have a vanishing real part, while dynamic, asymptotic structural stability equivalent to the requirement that all complex frequencies must have negative real parts. The simultaneous application of these two (logically independent) requirements limits the consideration to a class of systems that "behave well" enough to be accessible to the usual technical processes. A fairly general method of designing a feedback control system applicable to the present plasma configuration is, for example, in "Magnetic Feedback Stabilization in A Tokomak" by Yu.'P. Ladikov and Yu. I. Samoilenko, Zuhrnal Technicheskoi Fiziki, Vol. 42, No. 10, pp. 2062-2073, October 1972 (English translation in Soviet Physics - Technical Physics, Vol. 17, Hr. 10, pp. 161 * 1-1650, April 1973). A similar conception for non-linear systems with an infinite number of degrees of freedom is used in the principles of the invention. 4 η q Q 19/0692

The method for calculating the external currents that are required according to the invention is a standard numerical problem in the field of solving elliptical, partial differential equations, for which, for example, refer to the section "Toroidal Equilibra With Scalar Pressure" in the chapter on Computational Problems by J. Kileen, pp. 231, 232 of Physics of Hot Plasmas , edited 1970 ^by Rye and Taylor, Oliver and Boyd. Indeed, by substituting equations (7) in the vacuum magnetic field equations

the well-known Stoke equation:

~ 5 ~ p- ~~ "IF ä ~ F" ~ * ~ Z = Z * - "'■'

which is solved outside of Γ with Gauchy's data (8) and (11) in the method described above and as shown in FIG. The specific numerical examples shown in Figures 10, 11 and 12 were calculated using a standard five point difference equation approximation of equations (8), (11) and (13). '

Figures 10, 11 and 12 are drawn to scale representations of "the actually calculated curves and" are as determined of a coordinate system-al «numerical data for the construction of a special embodiment of the invention suitable.

409819/0892

Although the invention has been described above in connection with specific exemplary embodiments and specific applications has been described, it is not limited to these, but various changes and modifications are made possible, all of which fall under the invention.

The terms and expressions used were used for description and do not mean any restriction, in particular this should not exclude any equivalent characteristics. '.

09 8 19/069 2

Claims (1)

t- Expectations 1.) Device for enclosing a high-temperature plasma, characterized by a toroidal, hollow chamber forming envelope containing a plasma of a selected gas at a predetermined low atmospheric Density and a predetermined, elevated temperature, by a device for generating magnetic Field lines for the confinement of the plasma within the chamber in a smooth torus shape with no inflection points, the has a non-convex, poloidal cross-section, by means of a set of magnetic field lines that are tangential with respect to run along the surface of the plasma, the set of magnetic field lines having no field line, which has the strength zero at any point, a selected finite, even number N not equal to zero and not has more than N closed magnetic field lines, and has a rotation transformation angle of O, and wherein the device for generating magnetic field lines has a first current arrangement for producing a poloidal Current flow "across and outside of the plasma contains in order to to shift the magnetic field lines inwards to the longitudinal axis of the plasma and thereby the plasma around its To compress the longitudinal axis and to bend the magnetic field lines around the torufi-choc of the plasma, one, second Has star arrangement to a torucoidal current flow • ^ 09819/0692 lengthways and outside the plasma near the side to cause a relatively small radius compared to the diametrically opposite side of the plasma with a large radius, as a result of which selected magnetic field lines on selected surface areas of the Plasmas are curved away from the toroidal axis and towards the longitudinal axis of the plasma, so that the poloidal cross-section of the plasma is not convex, and the third has current arrangements that are outside the plasma and the second Current arrangements are located to create a toroidal current flow in the longitudinal direction of the plasma and in the opposite direction Direction to the current flow caused by the second current arrangements, whereby a movement of the plasma in a Direction to the side of the chamber having the large radius is prevented, the values of the currents in the three current arrangements are chosen so that a magnetic field with a static, structural Stability is created. 2. Apparatus for confining a toroidal high temperature plasma within a vacuum by means of a magnetic field, so that the magnetic field lines at the Boundary layer of plasma and vacuum have structural stability, characterized by a device for generating a magnetic field in the one surrounding the plasma 409819/06 9 2 Vacuum that turns the surface of the plasma into a toroidal shape expresses, the plasma having a smooth surface with no inflection points and on this- has magnetic field lines with a rotation transformation angle of O, which is at least however not contain more than two closed magnetic field lines that divide the surface into two torus regions subdivide, the plasma being a non-convex, poloidal Contains cross-section with two poloidal stagnation points corresponding to the two closed field lines, and wherein the device for generating a magnetic field comprises an arrangement for aligning a first toroidal Current surface on the first of the two torus areas on the plasma surface, an arrangement for aligning a second toroidal flow surface on the second of the Toroidal areas of the plasma surface directed opposite to the direction of the first toroidal flow surface as well as an arrangement for directing a poloidal flow surface onto the entirety of the plasma surface. 3. Device for confining a toroidal high-temperature plasma in a vacuum by means of a magnetic field, see above that the magnetic field lines at the boundary layer of Plasma and vacuum have structural stability, characterized in that a device for generating a magnetic field surrounding the plasma in a vacuum. 819/0692 • is seen that the surface of the plasma in a torus shape presses, wherein the plasma has a smooth surface with points of inflection and magnetic field lines, the one Have rotation transformation angles of O and at least contain one but no more than N closed magnetic field lines that adjoin the surface in N / 2 Subdivide pairs of toroidal regions, and the plasma has a non-convex poloidal cross-section with N poloidals Contains stagnation points corresponding to the N closed, toroidal magnetic field lines, and N is a selected one A finite even number greater than two means that the device for generating a magnetic field is an arrangement for aligning a separate toroidal flow surface to each toroidal region of the plasma surface, wherein the toroidal flow area of each toroidal area of the plasma surface opposite to the flow area of the respective immediately adjacent torus region, and that the device for generating a magnetic field is an arrangement for aligning a poloidal current surface on the entirety of the plasma surface. Device for the magnetic confinement of a toroidal high temperature plasma within a vacuum with a Magnetic field on the surface of the plasma, characterized in that to achieve structural stability 409819/0692 a device for generating a magnetic field is provided in the vacuum surrounding the plasma, which closes the plasma to a toroidal shape with a smooth surface without inflection points, whose poloidal cross-section is not convex, and that the device for generating the magnetic field is an arrangement for ZyLfuhr a set of magnetic Has field lines to the surface of the plasma, which contains at least, but not more than N closed toroidal field lines that subdivide the surface of the plasma into N toroidal areas, where N is a selected, finite, even number not equal to zero, the magnetic field lines in each area do not intersect any of the closed magnetic field lines, and wherein the poloidal component of the magnetic field lines in each torus area is directed opposite to the poloidal component of the magnetic field lines in the immediately adjacent torus area. 5 · Process for generating a high-temperature plasma in a toroidal vacuum space, which is enclosed by a magnetic field, so that the magnetic field lines have a rotation transformation angle of 0 at the interface between plasma and vacuum, thereby characterized in that a magnetic field is generated in the vacuum space, which transforms the plasma into a smooth torus shape 409819/0692 ■ -Ä- summarizes without turning points, which have a non-convex, poloidal cross-section and at least, but not more than a selected finite, even number of closed, toroidal magnetic field lines at the boundary layer of plasma and vacuum, which is not equal to zero. 6. A method for generating a high-temperature plasma, wherein a selected gas in an endless, toroidal chamber at a predetermined, relatively low density held and a high-temperature plasma is generated from the gas in the chamber, characterized in that in the Chamber a magnetic field is generated that the plasma inside the chamber to a smooth torus shape without Inflection points and with a non-convex, poloidal cross-section includes, and that at the same time applied to the surface of the plasma a set of magnetic field lines of which at least, but not more than a selected, even, finite number not equal to zero closed, has toroidal orbits, the set of magnetic field lines having a rotation transformation angle of O having. 7. Method for generating a high-temperature plasma in a toroidal vacuum space, characterized in that a magnetic field is supplied to the vacuum space, which the 409819/0692 Encloses plasma in a smooth toroidal shape without inflection points and with a non-convex, poloidal cross-section, and that at the same time magnetic field lines are induced at the boundary layer between plasma and vacuum space, the have a rotation transformation angle of. 8. Method of stable containment of a high temperature plasma in a toroidal vacuum space, characterized in that a toroidal Magnetic field is introduced, which encloses the plasma to a smooth torus shape without turning points and that at the same time a poloidal magnetic field is introduced into the vacuum space, which additionally encloses the plasma, so that it has a non-convex * poloidal cross-section has. and at least, but not more than one has selected, finite, even number of poloidal stagnation points, this number being not equal to zero. 9 · Method of generating a topologically toroidal shape High-temperature plasma in a topologically toroidal vacuum space, with the plasma being dynamically stabilized externally is, characterized in that a topologically toroidal Plasma is generated with a selected beta value and that the plasma is enclosed by means of a magnetic field so that the boundary layer of vacuum and plasma one 4098 19/0692 4 »- smooth, "magnetic surface without turning points tangential to the surface of the plasma is, being a static structural stability, a rational rotation number and at least, but not more than a chosen finite, non-zero even number of topologically circular magnetic field lines is given. 10. The method according to claim 9, characterized in that the selected beta value is of medium size. 11. The method according to claim 9 »characterized in that the selected beta value is large. 12. Method for enclosing a topologically toroidal high temperature plasma in a topologically toroidal one Vacuum space, for a period of time sufficient for usable, controlled fusion reactions, characterized in that, that a topologically toroidal plasma is generated with a selected beta value, which is a relatively contains light, fully ionized gas of low density, and that the plasma is enclosed by means of a magnetic field so that the boundary layer between plasma and vacuum is a smooth magnetic field surface without turning points, which is essentially tangential to the surface of the plasma volume, the magnetic field surface being static, 4098 1 9/0692 structural stability, a rational rotation number and at least, but not more than a chosen, finite, contains even non-zero number of topologically circular magnetic field lines. 13. The method according to claim 12, characterized in that to achieve asymptotic dynamic stability the plasma is confined to have an average local toroidal ratio of the order of 240 has. Ik, method according to claim 12, characterized in that a preprogrammed, multi-channel control with an open loop is used to achieve asymptotic dynamic stability. 15 · The method according to claim 12, characterized in that for Achieve asymptotic dynamic stability using a multichannel closed loop feedback control is used. 16. Method for the magnetic confinement of a topologically toroidal high-temperature plasma in a vacuum, see above that the magnetic surface enclosing the plasma has static structural stability, thereby ge-- 4098 19/069 indicates that in the vacuum surrounding the plasma a magnetic field is generated that affects the surface of the plasma into a smooth, topologically toroidal configuration without turning points, so that the boundary layer between plasma and vacuum is completely made up of magnetic field lines exists, which together form a magnetic surface, which has a rational rotation number and at least, however contains no more than N topologically circular magnetic field lines, where N is a chosen, finite, straight line Number is greater than zero. 17. Method for producing a topologically toroidal shape High-temperature plasma in a topologically toroidal vacuum space ·, characterized in that to achieve asymptotic dynamic stability with a topologically toroidal, smooth-surfaced plasma without inflection points high beta is generated so that an enclosing magnetic field is generated at the boundary layer between plasma and vacuum, whose total toroidal components are larger than all poloidal components, the inclusive of which Magnetic field is essentially tangential to the surface of the plasma and has a rational number of rotation as well at least, but not more than a selected, finite, even non-zero number of topologically circular ones magnetic field lines, and that the average 409819/0 692 lichen, large radii of the toroidal arched sections of the plasma on the order of 240 times larger than that corresponding average small radii. 18. High temperature plasma enclosed in a vacuum, characterized by a topologically toroidal, smooth magnetic surface with no inflection points made up of magnetic Field lines and a rational rotation number and at least, but not more than a selected, finite, even non-zero number of topologically circular ones contains magnetic field lines at the interface between plasma and vacuum. su: el: go: kö Blank page