Vertically Stabilized Elongated Cross-Section Tokamak

In the field of plasma physics, a need exists for magnetically confining a toroidal plasma column along an endless equilibrium axis in a vacuum containment means. Various means and methods have been proposed and used for this purpose, comprising the tokamak of U.S. Pat. No. 3,663,361, wherein poloidal field coil means are combined with a toroidal field and a plasma current stably to confine the plasma column in a circular cross-section. While these arrangements have been useful and have accomplished the desired confinement, they have been expensive, since they have required large diameter plasma cross-sections. Also, it has been difficult to increase the plasma volume in an equilibrium by using elliptical plasma columns, without decreasing the vertical stability of the plasma column.

This invention overcomes the difficulties and shortcomings of the heretofore known devices by adding a specific multipole forming a poloidal coil means, which is referred to herein as an octupole, to the outside of a round cross-section toroidal current carrying plasma column in a tokamak to change the plasma column into a rectangular cross-section characterized by an external separatrix. For purposes of this invention, an octupole is defined as the number of poles present at the center of the plasma vacuum space by taking away the current carrying toroidal plasma column. By taking away the plasma, the magnetic field wouldn't be square in cross-section, as understood in more detail hereinafter, and the field lines would form loops having eight poles, as understood from the Gulf General Atomic octupole shown in "Survey of the USAEC Program in Controlled Thermo-nuclear Research" June 1971. By elongating the spacing between the octupole coil means, which comprises at least four poloidal current carrying rings that are co-axial with the plasma column equilibrium axis, the plasma column cross-section is vertically elongated while the rectangular cross-section is maintained. This maintains vertical stability efficiently to increase the poloidal flux in the plasma column in linear proportion to the plasma cross-section height to achieve a much greater plasma volume than could be achieved with the heretofore known round cross-section plasma columns. Also, plasma column stability against vertical displacement is enhanced at larger volumes over elliptical cross-section plasma columns. Additionally, in another aspect, this invention provides poloidal magnetic divertors.

In one embodiment, this invention provides in a tokamak of the type having a toroidal containment means and toroidal and poloidal current carrying magnetic field producing coil means for producing a nested set of concentric, circular cross-section, toroidal magnetic surfaces confining a plasma current carrying toroidal plasma column in the containment means so that the plasma column is stably located on a vertical axis and has equal radial axes defining an endless circular equilibrium axis around an axis of rotation in the annulus of the containment means, the improvement comprising:

octupole means along the equilibrium axis and around the outside of the plasma column in the space between the equilibrium axis and the axis of rotation for producing poloidal separatrices external to the plasma column having stagnation points that define the four corners of a rectangular magnetic surface for confining and shaping the circular cross-section magnetic surface into a rectangular cross-sectional shape inside the rectangular surface. With the proper selection of elements and steps, as described in more detail hereinafter, the desired vertical stability and elongated cross-section in a tokamak are achieved.

it is an object of this invention, therefore, to provide an elongated cross-section toroidal plasma column in an equilibrium having vertical stability.

The above and further novel features and objects of this invention will appear more fully from the following detailed description when read in connection with the attached drawings, and the novel features will be particularly pointed out in the appended claims.

In the drawings, where like elements are referenced alike:

FIG. 1 is a partial cross-section of a conventional tokamak;

FIG. 1a is a partial cross-section of FIG. 1 with an octupole added thereto;

FIG. 2 is a partial cross-section of the octupole of FIG. 1a, showing additional elements therefor;

FIG. 2a is a partial cross-section and graphic illustration of another embodiment of the apparatus of FIG. 2;

FIG. 3 is a partial cross-section of the apparatus of FIG. 1a illustrating another embodiment of the shaping means thereof;

FIG. 4 is a partial cross-section of another embodiment of the shaping means of FIG. 1a;

FIG. 5 is a partial cross-section of another embodiment of the shaping means of FIG. 1a;

FIG. 6 is a partial cross-section of another embodiment of the shaping means of FIG. 1a;

It is known that a circular cross-section plasma column can be confined along an endless circular equilibrium axis by using a tokamak. A tokamak is shown and discussed in U.S. Pat. No. 3,663,361, by Shoichi Yoshikawa. Magnetic confinement and shaping of the plasma column cross-section is based on the fact that all the particles making up a particular plasma column spiral around the axis of rotation along toroidal magnetic lines of force forming toroidal magnetic surfaces, and the particles and mathematics of such confinement and shaping systems are well known in the art. The invention hereinafter described utilizes a tokamak confinement and shaping system of the type in which the space between the equilibrium axis and the axis of rotation along radial axes above and below the equilibrium axis, and around the plasma column on a vertical axis normal to the radial axes and parallel with the axis of rotation and through which the particles spiral and in which the toroidal magnetic surfaces are arranged, are subjected to specific poloidal magnetic fields produced by specific poloidal field coils in a manner described below in connection with particular configurations of these tokamak confinement and shaping systems. A mathematical treatment of the principles involved in this invention is given in my Princeton Plasma Physics Lab. Reports MATT-999 and TM-269.

In order to explain how the method and apparatus of this invention accomplish the functions of magnetically confining and shaping the cross-section of a toroidal plasma column 11, reference is made to FIG. 1, wherein is illustrated an endless, circular, plasma column equilibrium axis 13 in a tokamak 15 around an axis of rotation 17, and the toroidal magnetic surfaces 19 representing the circular plasma column cross-section prior to alteration that are confined and shaped. Disposed along the length of axis 13 is a toroidal field coil 23, and poloidal coils 25 and 27 arranged concentrically around the axis of rotation 17 on a vertical axis normal to the radial axes of the plasma column 11, the functions of the poloidal coils, as is understood in the art, being usually divided up to produce the plasma current 33 along axis 13 and the vertical shaping field for vertically stabilizing the plasma column against tilting or from being displaced vertically, and for centering the plasma column and its equilibrium axis 13 in a vacuum containment means 35.

Consider the .PSI.=0 toroidal magnetic surface 19 shown in FIG. 1 and the path taken along this surface by a charged plasma particle in either spiraling into the plane of the paper or oppositely, depending on whether the particle is negative or positive. For ease of explanation a plus indicates a current direction into the plane of the paper, and a dot indicates an opposite direction, as understood in more detail hereinafter. It will be seen that the field lines in magnetic surface 19 would ordinarily be directed around the axis of rotation in circles by the toroidal field coil 23, so that they would return to their starting point, but the plasma current 33 causes these field lines to be twisted helically around the equilibrium axis 13. Meanwhile, the poloidal shaping field coil 27 confines and centers the magnetic surface 19 formed by these twisting field lines in containment means 35.

Magnetic surface 19 represents the outer, or .PSI.=0, one of a concentric set of toroidal nested circular cross-section magnetic surfaces, or tubes for ease of explanation, and it will be understood that the equilibrium properties of the tokamak of FIG. 1 for favorable stability are selected with a separatrix inside or outside of the plasma region in containment means 35. A separatrix, which is defined herein in accordance with the well known definition in U.S. Pat. No. 3,607,627, is a magnetic flux surface, in a set of nested magnetic surfaces, outside of which the magnetic surfaces have a different shape from those inside. The stagnation point is the point from which the separatrix takes on its different shape, as understood from the above-cited patent and "Plasma Physics", I.A.E.A., Vienna, 1965, p. 391. As understood in the art, the .PSI.=0 magnetic surface is the outer surface corresponding to the outer edge of the confined plasma region, and in accordance with this invention shell currents can occur at or near this outer edge, as described in more detail hereinafter. A theoretical discussion of the .PSI.=0 magnetic surface is provided in U.S. Pat. No. 3,278,384 to Lenard etal.

Should specific spaced apart multipolar poloidal field coil means 41, referred to hereinafter as an octupole, be added to the apparatus of FIG. 1 outside the plasma region of column 11 in containment means 35, in accordance with this invention, the magnetic surface 19 is shaped into a non-circular, non-elliptical rectangular configuration having a separatrix outside the plasma region in the containment means 35, as shown in FIG. 1a. Moreover, vertical stability is maintained although the spaces between the individual multipolar means are expanded vertically and made larger by spreading them farther apart vertically to elongate the plasma column cross-section contained in the shaped magnetic surface 19 into a truly elongated shape having a larger vertical dimension than horizontal dimension. This efficiently increases the poloidal flux in the plasma column in linear proportion to the plasma cross-section height to achieve a much greater plasma volume than could be achieved with the heretofore known round cross-section plasma columns. Also, the vertical stability is enhanced over an elliptical cross-section plasma column. Still further, the adding of the specific multipole of this invention outside the plasma column, provides poloidal divertors that are selectively arranged, shaped and/or actuated, as understood in more detail hereinafter.

Referring now to FIG. 1a for a further description of the multipole 41 of this invention, in one embodiment, it is defined herein as an octupole without magnetic levitation means or internal supports in the plasma column 11. To this end, in this embodiment, four ring-shaped, first poloidal conductor means 43 having a rectangular arrangement in cross-section, are located to extend in concentric circles around the axis of rotation 17 on the top and bottom sides of the plasma column 11 in the space between the plasma column 11 and the vacuum containment means. These coil means are energized in series in the same directions as each other and the plasma current with currents corresponding to the plasma current 33 with a current sufficient selectively to shape the round cross-section .PSI.=0 magnetic surface 19 of FIG. 1 by pulling it into the rectangular shaped .PSI.=0 magnetic surface 19 having four flats f defined by four corners c for confining the shape rectangular cross-section plasma column 11 of FIG. 1a, and to produce poloidal separtices 45 external to the shaped plasma column 11 having stagnation points 47 that define the four corners of a rectangular shaped magnetic surface 19 external to and around the .PSI.=0 surface 19, where .PSI. is the poloidal flux contained in the plasma in webers, so that the latter forms the outer edge of the confined plasma column region, and the former form poloidal diverters 49. To this end, the four ring-shaped conductor means 43, which are parallel and arranged in sets in the space between the plasma column and the vacuum containment means 35, curve the separatrices 45 around a portion of the conductor means 43 in four closed lobes from the four stagnation points 47. As shown in FIG. 1a, the containment means 35 is rectangular in cross-section, and outside the conductor means 43, but it can be any shape.

By vertically elongating the spacing between the four respective conductor means 43, the plasma column height is corresponding elongated in cross-section so that the height of the plasma column is greater than its width. To this end, the spacings between the respective conductor means 43 of FIG. 1a are expanded vertically and made larger within the stability limits of the plasma column. Thus, for example, the vertical elongated vs stability is adjusted by reference to the semi-axis ratio and the restoring force F.sub.2 /.DELTA. due to the poloidal flux per unit displacement.

It has been found that the rectangular plasma column cross-sectional shape with a uniform plasma current 33 is most advantageous since it produces the longest stable elongation, while the parabolic current for a like shape produces a slightly larger restoring force at a small elongation, and both these cases are more stable than comparable elliptical elongations. The uniform and/or parabolic plasma currents 33 are selectively chosen by a suitable control. While switches and adjustable resistances are normally used, it will be understood that a computer controlled current, and the selective arrangement of the respective windings are within the skill of the art to this end.

While the divertor 49 of FIG. 1a comprises toroidal baffles 55 connected to the inside of the containment means 35 around the top and bottom of the respective conductor means 43, a wide range of arrangements are possible, as are the cooling means therefor. Advantageously, water cooling coils 57 cool the baffles and pumps 59 remove the impurities and reaction products that follow the separatrices 45 into the divertor chambers 49. Suitable poloidal control coils 63 within the skill of the art are added as desired.

The resultant magnetic field lines and plasma parameters are determined by conventional apparatus. For example, the resultant magnetic field lines and their corresponding magnetic surfaces, comprising surfaces 19 and 19', are measured, determined, and varied with conventional controls, and probes or injected particles. One system is described in U.S. Pat. No. 3,580,802. The plasma parameters are determined by convential Thompson scattering or other probes, such as the probe described in U.S. Pat. No. 3,171,788 and/or the rf system described in U.S. Pat. No. 3,265,967.

In the modification shown in FIG. 2, poloidal rings 51 having currents opposite to the currents in rings 43 are added on either side of each of the rings 43 of FIG. 1 to push the flats f of the rectangular cross-section shown in FIG. 1a, thus to save current in conductors 43 by providing both pushing and pulling of the circular field line cross-section of FIG. 1. The rings shown, comprise divertor field DF coils having current in one direction, and limiter field LF coils having current in the opposite direction. This figure shows a general layout of the octupole 41 of this invention added to a tokamak to form an experimental reactor having toroidal field TF coils 23, and poloidal equilibrium field EF coils, corresponding to the poloidal field shaping SF coils of FIG. 1a. The individual sources A, B, C and D are conventional, as are the controls E, F, G and H. Also, induced reflector currents I for initially centering the plasma are conventional.

Advantageously, the baffles 55 are gettered by a conventional titanium getterer and evacuated by conventional vacuum pumps 59, and the individual coils are contained in coil cases so that the divertor DF coils form neutralizer plates for neutralizing the ions extracted from the outside of the plasma column 11 into the divertors 49. Also, a suitable liner formed by a fixed limiter plate attached to the vacuum containment means 35, limits the divertor aperture opening. Since the suspension means for the described coil means, baffles, and the limiter plates are equivalent and understood in the art, these are not shown for ease of explanation, particularly since they are incorporated into existing tokamaks so that use is made of the well known techniques for forming them. Also, they are described and shown in FIG. 9 of the Princeton University Report entitled "Design Considerations for the PDX", Sept. 7, 1973, in connection with the known use thereof in the FM-1 divertor at the Princeton Plasma Physics Lab.

In the modification shown in FIG. 2a, the currents and geometry of the various coil means are shown. Here a central toroidal divertor is provided, which in cross-section is inside an outer toroidal divertor forming a selected poloidal magnetic limiter around the plasma column.

In the modifications shown in FIGS. 3-6 the self consistent plasma equilibria form a "square" plasma cross-section, an intermediate elongation, a maximum elongation and a D-shaped (or mirror image) divertor, by adjusting the conductors and currents as illustrated in the respective drawings.

In operation, the multipole 41 of this invention is incorporated in the existing ST tokamak at Princeton U, so that use is made of the well known techniques for forming the plasma column energizing the windings thereof, and confining and shaping the toroidal magnetic surfaces and separatrices, as described in the above cited U.S. Patents. To this end, conventional controls E, F, G and H having conventional switches, transmit series current from separate sources A, B, C and D to the respective toroidal field coils 23, the ohmic heating poloidal field coils 25, the poloidal shaping field coils 27, and the oppositely energized poloidal octupole conductors 43 and 51 referred to in FIG. 2 as DF and LF coils. Passive inductive currents I in loops, which are known, may also be used to center the plasma columns initially. The control G for the shaping field coils, and the control for the DF and LF coils may be combined and connected to the same source, so that the shape of the current pulses therefor correspond to the EF or SF pulse, and to the TF coil pulse. It is understood, however, that the multipole 41 of this invention may be incorporated in any tokamak, such as the Princeton U. PLT Large Torus, PDX divertor experimental reactor, or the proposed two component or full scale device; also, the pulses can be of relatively long duration by suitably changing the currents in the described conductors, as described in co-pending application Ser. No. 416,902, filed Nov. 11, 1973, by Bonanos et al now abandoned. In all cases, the separatrices 45 are outside the confined plasma region of plasma column 11. Also, the described system is entirely different from the octupoles known heretofore, such as the levitated octupole described on pages 14 or 20 of "Survey of the U.S. A.E.C. Program in Controlled Thermonuclear Research" June 1971. For example, the tokamak of the invention has larger volumes leading to improved plasma parameters. Also, the octupole of this invention is not levitated or supported in the plasma.

The fact that tokamak type devices with elongated cross-sections appear to have improved plasma parameters leads to the question of the stability of these configurations against vertical translation, which can be studied and analyzed by a computer code given in Princeton U. Report TM-269. The model used for this study, is shown schematically in FIG. 1 of MATT-999, and the solution has two parts, the details of which are given in the Appendix to that report. First, an arbitrary current is distributed over the plasma region of the plasma column 11 and the external shell currents I' thereof are computed, which make the edge of the plasma region the .PSI.=0 magnetic surface 19. These shell currents are often referred to as skin currents due to vertical displacement of the plasma column, which acts like a superconductor medium with patterns frozen therein.

The second part of the solution involves translating the plasma region of plasma column 11, while holding constant the external shell currents I': A new distribution of plasma current 33 is computed which maintains constant all the flux values on the edge and inside the plasma region of plasma column 11. This new distribution of plasma current 33 interacts with the magnetic field of the external shell currents I' to give a net force on the plasma related to the displacement. This force is either in the same or the opposing direction as the translation indicating instability or stability, respectively, as understood from FIG. 2 of MATT-999.

Solutions were carried out for both elliptical and rectangular cross-section plasma regions with both uniform and parabolic current distributions, as shown in the latter above-mentioned FIG. 2, with the restoring force per unit displacement plotted against the displacement semi-axis ratio of height to width of the plasma column 11.

In the operation of one embodiment, stabilization is provided by distributing over the plasma region an arbitrary current and external shell currents computed to make the edge of the plasma region the .PSI.=0 magnetic surface. Thereupon, the plasma region is translated while maintaining the plasma current distribution in accordance with the value for maintaining all the flux values on the edge and inside of the plasma region constant for effecting a new plasma current distribution that interacts with the magnetic field of the external current shell to give a net force on the plasma related to the displacement due to said translating. Moreover, the shell and plasma currents produce an external magnetic limiter and a poloidal diverter for removing impurities and reaction products.

In one example, the described tokamak is energized to produce a plasma column major radius for toroidal equilibria of between 1.275 and 1.475 meters, and an area of plasma cross-section of 0.98 square meters. An octupole is added around the outside of the plasma column in the space between the plasma column and the vacuum containment means for the plasma column, with the octupole being supported on the inside of the containment means so that the current is fed there through with vacuum tight insulation from the same source as the poloidal field shaping coils and is in series therewith. The same computer controlled controls are also used therefor. Thus, the octupole is not levitated, is not inside the plasma column, and is completely external to the plasma column.

For a uniform plasma current, an elliptical cross-section plasma column 11 becomes unstable at a semi-axis ratio of 1.5, while the rectangular cross-section becomes unstable at 4.2. For parabolic plasma current distributions, the ellipse goes unstable at 1.6 and the rectangle at 3.2.

Two first (LF) rings and eight (DF) rings make up one poloidal conductor means at each corner of the rectangular plasma column so that four (DF) rings are inside the toroidal loop which in cross-section forms a separatrix circle from a stagnation point, and four (DF) rings are outside the loop on each side of the described circle. This configuration also produces a selected magnetic limiter, comparable to the metallic limiters known heretofore.

The steps of Example I are repeated, and the poloidal coils are energized by the described controls to produce a poloidal flux for equilibria satisfying the equation ##EQU1## where r is the minor radius of the rectangular plasma column, R is the radius of magnetic axis

r is one of the cylindrical coordinates

z is another cylindrical coordinate

a and b are constants (depending on the peculiar solution to the equation desired)

The solutions were used to generate a graph of a v s R.sup.2 b on which various constant parameter contours were plotted, comprising toroidal pressure ratio .beta. or plasma to magnetic-pressure, and safety factors q in axis, as understood from p. 65 et seq of the July 1972 Scientific-American, where the plasma current is kept below the Kruskal-Shafranov limit by a safety factor that is usually taken to be between 2.5 and 3, and while the aspect ratio R/a of major to minor plasma column radius is smaller than 1/3, where the poloidal magnetic field is weaker than the toroidal magnetic field.

Various equilibria were generated using the equations of Appendix I of TM-269 applied within the constraints shown in FIG. 1 thereof. The resulting data are tabulated in Table I.

This data includes the following quantities:

a Defined in Eq. (1)

b Defined in Eq. (1)

R radius of magnetic axis (meters)

P.sub.o Pressure at axis (Newton/Square meter)

.beta. Toroidal pressure ratio on axis

q Safety factor on axis

.PSI. Poloidal flux contained in plasma (Webers)

The tables were used to generate graphs showing how the plasma current and poloidal flux vary with semi-axis ratio for the described equilibria with axial toroidal field (TF), major radius, minor semi-axis, .beta., and safety factor q held constant. The result was that the poloidal flux was proportional to the semi-axis ratio, while the plasma current was proportional to the semi-axis ratio raised to the 1.8 power.

The steps of Example II are repeated so that the divertor controls the ion mixture in the tokamak, and so that the disadvantages of impurities and reaction product build-up are avoided. Also, the advantages of this control, comprise reducing the ion temperature required for a thermally stable, steady-state tokamak reactor, and shaping the current-density profile by appropriate distribution of mean ionic charge (Z effective) as a function of plasma radius.

In optimizing the shaping, the effect of the location of the innermost separatrix cross-over X-points for MHD stability are tested by slight variation of the poloidal field coil currents. A "D" shaped magnetic surface 19' is produced to enhance MHD-stability, while its mirror image reduces MHD-stability, and the effects on plasma confinement and divertor efficiency are optimized.

The steps of Example III are repeated at a central toroidal field strength of 24 kG, with an aspect ratio R/a=4, and a plasma current ranging from 500 kA to 1.5 MA (at q=3, depending on the degree of vertical elongation). An equivalent plasma current I* for comparison with the round cross section plasma column of FIG. 1 ranges from 500 kA to 1.0 MA.

The steps of Example IV are repeated with an initial ohmic heated plasma in the range T.sub.e .about. T.sub.i .about. 1 - 2 keV for densities of .about. 5.10.sup.13 cm .sup.-3, and neutral-beam and rf heating at powers in the range of 2-5 MW multiplied the temperature so as to approach the MHD .beta.-limits.

The steps of Example V are repeated. Following optimization, reactor-like plasma parameters: 5 .times. 10 keV temperatures at 1-2 .10.sup.14 cm .sup.-3 plasma particle number densities are employed with a central toroidal field strength of 48 kG. with corresponding doubling of the plasma currents in the configuration of FIGS. 3-6.

The steps of Example IV are repeated with poloidal-field coils of the divertor forming an integral assembly, which is displaced manually to provide increasing degrees of plasma elongation, as shown in FIGS. 3 - 6 of Princeton Report Sept. 7, 1973, on "Design and Construction of the PDX". The octupole set of poloidal (vertical) field coils is spaced to match the increasing plasma elongation. In this example, the poloidal OH air transformer coil is fully decoupled from the divertor (octupole) and poloidal (vertical) field coils (which add up to zero net ampere turns around the torus axis). It is installed outside the vacuum chamber, prior to assembly of the toroidal-field coil system.

The vacuum containment means is made of stainless steel, with poloidal breaks to permit application of the toroidal emf by the transformer. The divertor and poloidal shaping-field coils are housed individually in light-weight vacuum shells. The divertor throat is defined by moveable baffles.

The steps of Example VI are repeated using the modifications in the geometry, spacing, and currents for the multipole of this invention shown in FIGS. 3 - 6, and others for producing self-consistent plasma equilibria for the following special cases:

1. roughly "square" plasma with all cross-over points (x) on the separatrices connected to the divertor for up to 24 kG to 48 kG central toroidal fields and currents of up to 1 MA;

2. a plasma of intermediate elongation; and an equivalent plasma current I* of 750 kA at a 24 kG central toroidal field strength;

3. a plasma of maximum elongation; and an equivalent plasma current I* of up to 1 MA at 24 kG, 2 MA at 48 kG, and actual plasma currents of up to 1.5 MA at 24 kG and 3.0 MA at 48 kG.

4. D-shaped (and mirror-image D-shaped) magnetic surfaces 19 and/or 19' produced by minor adjustment of the poloidal-field coil currents connected to the outer part of the divertor.

The steps of Example VII are repeated with its currents shown in FIGS. 3 - 6 wherein various poloidal control coils 63 are located on the exterior of the toroidal field coils. Suitable coils and control currents are those shown, and those used in co-pending applications Ser. No. 379,870, filed July 16, 1973, by Uffe Christensen.

The steps of Example VIII are repeated using the relative poloidal shaping and confining coil geometry, spacing and current directions as shown in FIGS. 3 - 6, where plus is into the plane of the paper and minus is opposite.

FIG. 3 is a computer calculated self-consistent plasma equilibrium with a divertor. This is the special case of a roughly "square" plasma cross-section, with all cross over x points of the separatrix connected to the divertor. For a 24 kG - 48 kG central toroidal field, the plasma current is 1 MA. In FIG. 4 for intermediate elongation, the equivalent plasma current I* is 750 kA at 24 kG. In FIG. 5 for a plasma of maximum elongation, the equivalent plasma current I* is 1 MA at 24 kG, and 2 MA at 48 kG (actual plasma currents are 1.5 MA at 24 kG and 3.0 MA at 48 kG). FIG. 6 shows a D-shaped (cross-section) plasma produced by minor adjustment of the poloidal field currents within the skill of the art based on this disclosure, and includes a mirror-image D-plasma.

In the case shown in FIG. 2a, the respective currents correspond to the values, as illustrated: -0.05, -0.25, -3.0, -0.65, -0.05, +1.125, +0.0375, +0.0375, +0.55 and +0.5. Likewise, in FIGS. 3 - 6 the currents correspond to the values illustrated.

This invention provides a non-circular, rectangular cross-section, toroidal plasma column in a tokamak so that use is made of the well-known techniques for forming toroidal magnetic surfaces and confining and shaping them, as well as the toroidal plasma column contained therein, so as to provide external separatrices. This invention employs a specific poloidal multipole called an octupole that doesn't require levitation or plasma internal supports, and the plasma column is stably elongated in height by spreading the space between the octupole means. This has the advantage that the elongation increases the poloidal flux in the plasma columns in linear proportion to the plasma height to achieve a much greater plasma volume than an equivalent round cross-section plasma column. Also, enhanced vertical stability is achieved over elliptical plasma cross-sections.