US 3141826 A
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July 21, 1964 K. o. FRIEDRICHS ETAL 3,141,326
APPARATUS AND METHOD FOR CONFINING A PLASMA Filed July 2, 1958 2 Sheets-Sheet 1 KURT O. FRIEDRICHS HAROLD GRAD July 21, 1964 K. o. FRIEDRICHS ETAL 3,141,826
APPARATUS AND msmon FOR CONFINING A PLASMA Filed July 2, 1958 2 Sheets-Sheet 2 INVENTOR. KURT O. FRIEDRICHS HAROLD GRAD 3,141,826 APPARATUS AND METHOD FOR CONFINING A PLASMA Kurt (3. Friedrichs and Harold Grad, New Rochelle, N.Y., assignors to the United States of America as represented by the United States Atomic Energy Commission Filed duly 2, 1953, Ser. No. 746,309 4- Claims. (Cl. l7d7) This invention relates generally to apparatus and method for confining a plasma, and more particularly it relates to apparatus and method for stably confining a plasma by a plasma-magnetic field configuration in which there is an interface between the plasma and the magnetic field.
Broadly, this invention involves apparatus and method for establishing a plasma-magnetic field configuration which includes a plasma separated by an interface from an electromagnetic field, the interface being everywhere convex toward the plasma and the plasma having cusps. A plasma is a fully ionized gas in which its ions and electrons are present to form a neutral matter. A plasmamagnetic field configuration is characterized by a plasma and a magnetic field in cooperative association. Plasma is confined by a magnetic field in accordance with this invention with a ratio of plasma pressure density to magnetic field pressure density at the interface equal to one. A variation of this invention involves establishing a current-carrying conductor in the plasma.
The hydromagnetic free boundary is a mathematical construct useful for theoretical treatment of a plasma in conjunction with an electromagnetic field. It involves a perfectly conducting field-free plasma separated by an interface from a vacuum electromagnetic field. The plasma pressure is balanced by the field pressure. It can be shown that any finite plasma-magnetic field configuration of the free boundary type bounded by a smooth interface is unstable for any perturbation. A perturbation of a plasma-magnetic field configuration is a change thereof from its equilibrium condition. The equilbrium condition of a plasma-magnetic field is unstable when a perturbation of the condition tends to cause the equilibrium to be lost.
This invention includes apparatus and method for establishing a finite plasma-magnetic field configuration in which the plasma is separated from the magnetic field by cusped surfaces. The configuration is stable for any perturbation. An aspect of this invention includes a magnetic field in the plasma to reduce particle losses through the cusps between the surfaces. Another aspect includes a current carrying conductor in the plasma to increase the magnetic efficiency. The magnetic efiiciency is a measure of the extent to which the magnetic field present is useful in confining the plasma.
A plasma-magnetic field configuration in accordance with this invention is especially suitable for stably confining a thermonuclear-reaction-sustaining plasma. The ions of a thermonuclear-reaction-sustaining plasma are established from low atomic number elements such as deuterium and/ or tritium.
An object of this invention is to provide apparatus and method for establishing a stable plasma-magnetic field configuration of the free boundary type.
Another object of this invention is to provide apparatus and method for establishing a plasma-magnetic field configuration for stably confining a plasma which includes a plasma separated by an interface from an electromagnetic field, the interface being everywhere convex toward the plasma and the plasma having cusps.
Still another object of this invention is to provide apparatus and method for confining a cusped plasma hav- 3,141,825 Patented July 21, 1964 ing a boundary which is everywhere convex toward he plasma and for establishing a magnetic field in the plasma.
And a further object of this invention is to provide apparatus and method for confining a cusped plasma having a boundary which is everywhere convex toward the plasma and for establishing a current carrying conductor in the plasma.
Other objects of this invention will be understood through consideration of the following discussion taken in conjunction with the drawings in which:
FIGURE 1 is a line drawing of a two-dimensional plasma-magnetic field configuration having four cusps illustrative of a field-free plasma separated by an interface from a vacuum magnetic field.
FIGURE 2 is a line drawing of three two-dimensional plasma-magnetic field configurations illustrative of the smallest and the largest plasma-confining configuration for a particular coil and current arrangement and a plasma-magnetic field configuration having an interface which is everywhere convex toward the plasma but having a plasma without cusps.
FIGURE 3 is a line drawing of a three-dimensional plasma-magnetic field configuration obtained by rotating the plasma of FIGURE 1 about an axis through two cusps. It is illustrative of a plasma-magnetic field configuration having a line cusp and two point cusps.
FIGURE 4 is a line drawing of a plasma-magnetic field configuration having three circular line cusps and two point cusps.
FIGURE 5 is a line drawing illustrative of a torus-like plasma-magnetic field configuration having a plurality of sections joined by line cusps.
FIGURE 6 is a line drawing of a torus-like plasmarnagnetic field obtained by rotating the cusped plasma of FIGURE 1 about an axis outside the plasma in the plane thereof.
FIGURE 7 is a line drawing of a plasma-magnetic field configuration obtained by translating the configuration of FIGURE 1 along the perpendicular direction to its plane illustrative of a magnetic field in the plasma.
FIGURE 8 is a line drawing illustrative of a currentcarrying conductor in the plasma-magnetic field configuration of FIGURE 3.
FIGURE 9 is a diagrammatic view showing a currentcarrying coil arrangement for establishing the plasmamagnetic field configuration of FIGURE 3.
FIGURE 10 shows diagrammatically the coils and plasma-magnetic field configuration of FIGURE 9 disposed in a structure suitable for use as a part of a reactor in which thermonuclear reactions may be produced.
Referring now to FIGURE 1, a two-dimensional plasma-magnetic field configuration is shown established by a plasma it? and direct line currents 12, 14, 16 and 18. The line currents 12, 14, 16 and 18 are alternately, respectively, out of and into the plane of the figure. Line currents 12, 14, I6 and 18 establish magnetic fields 2t 22, 24 and 26, respectively. The plasma 1t) cooperatively with magnetic fields 2t 22, 24 and 26 establishes interfaces 28, 30, 32 and 34. Interfaces 28, 30, 32 and 34 form a boundary on plasma 10 which is everywhere convex toward it. The magnetic fields 28, 30, 32 and 34 are initiated after plasma It) has been established. As plasma 10 is a highly conductive state of matter, there are currents which flow in interfaces 28, 30, 32 and 34 as a result of induction. The magnetic fields associated with these currents interact with the magnetic fields 28, 3t), 32 and 34 to compress the plasma 10 into a cusped shape with cusps 36, 38, 4t) and 42.
The higher the temperature of the plasma 10 the greater is the loss of plasma ions through the cusps 36, 38, 4t] and 42. This loss can be reduced by a magnetic field in the plasma. A magnetic field is in the plasma when the ions and electrons thereof gyrate about its lines of force. FIGURE 7 shows a three-dimensional plasmamagnetic field configuration 44 obtained by translating the configuration of FIGURE 1 perpendicularly to its plane. Magnetic field 45 is shown entering plasma 46 of configuration 44. The loss of ions through the line cusps 48, t), 52 and 54 is reduced because the ions of plasma 46 gyrate about the field lines of magnetic field 45 and thus are restricted in their movement.
The two-dimensional plasma-magnetic field configurations a, b and c of FIGURE 2 are illustrative that for a given current and coil arrangement there is a smallest configuration 56 and a largest configuration 58 which will confine the plasma. The limiting shape for small dimensions in a hypocycloid of the form,
and the largest shape for which the plasma doe not spill out is given by the equation where tan 0 is the slope and s is the arclength. The latter equation holds for the portion of the curve in the upper part of the first quadrant, the complete shape being found by symmetry. FIGURE 2c shows a plasma-magnetic field configuration larger than the largest shape 58 which does not spill out. The cusps have disappeared and the plasma is rapidly lost through openings 62, 64, 66 and 68 between interfaces 70 and '72, 72 and 74, 74 and 76, and 76 and 70, respectively.
Referring now to FIGURES 3 and 9, there is shown a plasma-magnetic field configuration 85 which has two point cusps 86 and 88 and a circular line cusp 90. It is obtained by rotation of the configuration of FIGURE 1 about an axis through cusps 38 and 42. The line cur rents 12 and 14 and 16 and 18 have become currentcarrying coils 92 and 94 in FIG. 10, respectively. Coils 92 and 94 lie in parallel planes and are coaxial with an axis through point cusps S6 and 88. They are energized from a direct voltage source, not shown, and carry current in opposite directions as indicated by arrows 96 and The structure of FIGURE is illustrative of a plasma container for a reactor in which thermonuclear reactions may be produced. Current-carrying coils 92 and 94 are mounted on plasma container 102, and the magnetic field configuration 85 is disposed within the chamber 103. Plasma container 102 is constructed of a non-magnetic material such as stainless steel and has end plates 104 and 106 and side wall 108. Tubular projections 110 and 112 on end plates 104 and 106, respectively, establish passageways 114 and 116 which join chamber 103. The container may be cooled by a suitable water jacket, when necessary. Coils 92 and 94 are mounted in insulated fashion on end plates 104 and 106, respectively, of plasma container 102.
The operation of the structure shown in FIGURE 10 is as follows: Chamber 103 is evacuated via passageways 114 and 116, and thereafter a gas is introduced through the same passages. For a thermonuclear reaction, the gas preferably comprises deuterium and/ or tritium atoms. The gas is ionized to a plasma in a conventional manner such as by a radiofrequency discharge and heated to a relatively high temperature in a conventional manner such as by ohmic losses through audiofrequency current flow as a result of magnetic induction. The requisite temperature is determined by the type of gas comprising the plasma but preferably should be high enough that the plasma approximates a perfectly conductive fluid. The conventional shock wave technique can satisfactorily be used both to ionize the gas and heat the plasma to the relatively high temperature. Once the plasma 85 has been established in chamber 103, the coils 92 and '94 are simultaneously energized with direct voltage. The magnetic fields produced by the development of the currents 96 and 955 (FIGURE 9) in coils 92 and 94 (FIGURES 9 and 10), respectively, induce surface currents in plasma 85. The surface currents cooperate with the magnetic fields produced by coils 92 and 94 to produce the line cusp 9t) and point cusps $6 and 88.
The plasma then is heated to thermonuclear-reaction-sustaining temperature by increasing the current in coils 92 and 94 rapidly. This causes an adiabatic compression of the plasma, i.e., without exchange of heat between the plasma and its surrounds, with a resultant heating effect thereon.
Advantage may be taken of the arrangement of FIG- URE 10 for obtaining directed streams of ions for use in research and industry by placing targets near the cusps. Both before and after the initiation in plasma-magnetic field configuration 85, plasma streams flow out of configuration 85 through point cusps 86 and 88 along an axis through them and through circular line cusp in all outward directions which lie in its plane. Within configuration 85 the plasma ions and electrons are in random motion. The plasma fiows through point cusps 36 and 33 and circular line cusp 90 in directed streams because the cusps restrict the motion to such streams. Accordingly, FIGURE 10 may be used to transform plasma in which the ions have random motion into plasma in which the ions have directed motion.
Essentially all of the methods of initiating and heating a plasma can be used in a cusped geometry. Four parallel discharges alternating in direction may be set up in a longitudinal magnetic field to initiate the plasmamagnetic field configuration of FIGURE 7 or the coils in any of the cusped configurations may be pulsed after preionization or after creation of the plasma by a shockwaye; or the plasma may be inserted in an already existing vacuum magnetic field of appropriate type by an arrangement of plasma guns. Alternatively, one may pulse the magnetic field in one shot with enough energy to bring the plasma to thermonuclear temperature.
A current carrying conductor is disposed in a plasma when the magnetic field resultant from the current fiow acts upon the plasma to urge it away from the conductor. FIGURE 8 shows current-carrying conductor 118 disposed in plasma-magnetic field configuration 120 in accordance with this invention. The current fiow and its direction in conductor 118 are indicated by arrow 122. Essentially, the configuration 120 is obtained from the configuration of FIGURE 3 by disposing conductor 118 axially through the cusps 86 and 88 and energizing it with direct voltage. The magnetic field resultant from current 122 is indicated by magnetic field lines 124 and 126. The resultant plasma-magnetic field configuration 120 has line cusps 132, 134 and 136. Magnetic field lines 124 and 126 cannot penetrate plasma 120 and so compress it against interface 130. A magnetic field established adjacent the surface of a perfectly conducting medium does not penetrate it because of the surface currents that result from magnetic induction.
The plasma-magnetic field configuration 120 including the outer interface 130 and inner interface 138 adjacent magnetic field lines 124 and 126 is stable for any perturbation. It is more elficient to compress adiabatically plasma 120 by increasing current 122 than by increasing the currents in the coils 92 and 94 (FIGURES 9 and 10) which establish interface 131). The plasma-magnetic field configuration of FIGURE 4 is obtained by placing two configurations of the type shown in FIGURE 3 end to end and broadening the intermediate point cusps into a line cusp. The plasma-magnetic field configuration 140 of FIGURE 4 is characterized by line cusps 142, 144 and 14-6 and point cusps 148 and 150. FIGURE 5 is representative of a plasma-magnetic field configuration obtained by bending the configuration of FIGURE 4 into a torus-like shape. The plasma-magnetic field configuration 152 of FIGURE 5 is characterized by a plurality of plasma sections 154. Two adjacent plasma sections 154 are joined by a line cusp 156. FIGURE 6 represents a section of a torus-like plasma-magnetic field configuration obtained by rotating the configuration of FIGURE 1 about an axis (outside the conductors 12, 14, 16 and 18) parallel to a line through two cusps. The plasma-magnetic field configuration 158 of FIGURE 6 is characterized by a cross section 160 similar to the two-dimensional configuration of FIGURE 1 and by four line cusps 162 to 168. The line cusps 162 to 168 are concentric circles.
It is not intended that this invention be restricted to plasma-magnetic field configurations established through the use of either straight-line or circular current-carrying conductors. The conductors shown and described above are merely illustrative of the apparatus and method of this invention. In its broader aspects the invention may be practiced through the use of any current flow pattern which cooperates with a plasma to establish a plasmamagnetic field configuration of the free boundary type in which there is an interface convex everywhere toward the plasma and the plasma having cusps.
It has been found convenient for the practice of this invention to design a current-carrying conductor pattern therefor through application of plane and solid geometry. For example, it is possible to develop suitable plasmamagnetic configurations by considering a hexagon By describing circles at each corner of the hexagon which are tangent the circle described at an adjacent corner, it is seen that cusps are formed within the hexagon. By causing line currents to flow at the corners of the hexagon, the currents being alternately into and out of the plasma of the hexagon at adjacent corners thereof, there is obtained a configuration analogous to the one of FIGURE 1, but with six cusps.
The following discussion relates to the plasma-magnetic field configuration of FIGURE 9 for producing thermonuclear reactions. The state of the plasma is given by three parameters, volume, pressure and temperature. The radius R of the circular line cusp section is in cm., the magnetic field H in in gauss, and the temperature T is in electron volts. The approximate energy loss through the cusp in watts is given by P :0.08 RTH An estimate of the ohmic losses is and the energy produced by thermonuclear reactions (energy of charged particles only) for a deuterium-tritium mixture at 20,000 e.v. is given by Clearly, P can be made to dominate P +P by making R and H large (the ratio of bremsstrahlung power losses to the power derived from the thermonuclear reactions depends on temperature alone).
The breakeven is defined by the condition T= C+ R) A possible set of breakeven figures is H=10 R=40, P =6 10 The density is about 10 ions/cm. The power output would be comparable in size to a conventional large generating station. A cycle of operation follows: Let 6 represent the original energy of the plasma. At some later time (in this example, about one millisecond) 6 has been reduced by one-half due to cusp losses. The energy from thermonuclear reactions in the plasma which is imparted to the plasma has at this time reached 35/2 bringing the total plasma energy to 2e and the plasma pressure to double its original value. An adiabatic expansion of the plasma against the magnetic field then transfers the amount 6 into the power source which supplies the field. For example, if the power source is a storage battery the adiabatic expansion of the plasma acts to charge the battery. The remaining energy (including the considerably greater energy .carried by the neutrons) is removed by a heat cycle of lower efliciency.
Reference is made to patent applications S.N. 688,089, filed October 3, 1957, and SN. 705,071, filed December 24, 1957, for Spitzer, now Patent 3,016,341, dated January 9, 1962, and Patent No. 3,022, 912, dated October 3, 1961, respectively, S.N. 443,447, filed July 14, 1954, for Post, S.N. 589,831, filed for McIntosh and Bostick, now Patent 2,900,548, dated August 18, 1959, and SN. 731,555, filed April 28, 1958, for Finkelstein, now Patent 2,929,951, dated March 22, 1960, and to the articles by A. C. Kolb in Physical Review, vol. 107, pp. 345-3 50 and 1197-1198, for techniques, apparatus and methods for producing and controlling plasmas suitable for use with this invention.
While the invention has been disclosed with respect to certain preferred embodiments, it will be apparent to those skilled in the art that numerous variations and modifications may be made within the spirit and scope of the invention, and thus it is not intended tolimit the invention except as defined in the following claims.
1. In a plasma device having a container, a gas of low atomic weight, and means for heating and ionizing said gas to form a substantially perfectly conducting plasma within the container, the improvement comprising first and second current conducting coils displaced from each other along the length of the device in parallel planes at opposite ends of the plasma, means for energizing said coils with oppositely directed equal currents for forming a convex plasma-field interface in which magnetic lines of force intersect to form a bi-conical monocusp having opposite point cusps connected to an annular line cusp midway therebetween, said current being sufficiently large such that the ratio of plasma pressure to magnetic field pressure is equal to one, and means for rapidly increasing said current for adiabatically compressing said plasma.
2'. Apparatus as in claim 1 further including a current conductor positioned in the center of the plasma along the length thereof between said point cusps, and means for rapidly increasing the current flow in said current conductor for adiabatically compressing said plasma from its center outwardly.
3. A method for forming, confining and heating a plasma having cusps in an evacuated container comprising the steps of injecting a gas of low atomic number into said container, forming an ionized plasma within said container with the external surfaces of said plasma convex towards the center of the plasma extending along the length of the container and the junction of adjacent surfaces forming cusps, said last mentioned step including the steps of a heating said gas to form a substantially perfectly conductive plasma and passing electrical current flow along at least four parallel current flow paths from one end of the container to the other with each current path equally spaced about the exterior surface of the plasma and with the direction of current flow in adjacent current flow paths being oppositely directed; introducing a confining magnetic field through the center of said plasma from one end of the container to the other, and subsequently rapidly increasing said current flow for adiabatically compressing said plasma inwardly.
4. A method of forming, confining and heating a plasma having cusps in an evacuated container comprising the steps of injecting a gas of low atomic number into said container, forming an ionized plasma within said container with the exterior surfaces of said plasma convex toward the center of the plasma and the junction of said surfaces forming a bi-conical mono-cusp having opposite point cusps connected to an annular line cusp midway therebetween, said last mentioned step including the step of heating the plasma to form a substantially perfect conductor, energizing two coils with oppositely directed current flow for forming opposing magnetic fields directed from opposite ends of the container to the center for creating plasma-field interface surfaces at which the ratio of plasma pressure to magnetic field pressure is substantially equal to one whereby the form of the plasma c0nforms substantially to the magnetic field pattern and is confined therein, and subsequently rapidly increasing the magnetic field strength for compressing said plasma.
References Cited in the file of this patent UNITED STATES PATENTS Josephson et a1. Jan. 13, 1959 OTHER REFERENCES G. Grad: Conference on Controlled Thermonuclear Reactions, TID-7520 (September 1956), page 99.
An introduction to Thermonuclear Research by Albert Simon, Pergamon Press, N.Y., 1959, pages 127-129, which