US 3155594 A
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Nov. 3, 1964 B. P. LEHNERT ETAL 3,155,594
APPARATUS FOR CONFINING AND HEATING A PLASMA Filed June 10. 1960 in, i.
United States Patent ice 3,155,594 APPARATUS FOR CONFINING AND EEATKNG A PLASMA Bo Peter Lehnert, Sornxnarvagen 1, Stoelrsund, Sweden, and Ejirn Karl Johan Bonnevier, Kopmantorget 12, Stockholm, Sweden Filed June 10, 1960, Ser. No. 35,207 Claims priority, application Sweden, June 12, 1959, 5588/59; Dec. 10, 1959, 11,633/59 2 Claims. (Cl. 176-8) The present invention relates to plasma heating and confinement apparatus in which the plasma is confined by two substantially toroidal surfaces generated by the field lines or a magnetic field surrounding an annular electric conductor having radially inward directed current supply and mechanical support means. The apparatus also comprises means for generating an electric field perpendicular to the magnetic field so that the plasma is caused to rotate round the symmetry axis of the apparatus.
The principal object of the invention is to enhance the plasma confining properties of the magnetic field.
Another object of the invention is to reduce the loss of plasma particles caused by their collisions with material walls.
A special object of the invention is to make it possible on the one hand to utilize essentially all of the volume between the two confining surfaces as a reaction space and, on the other hand, to prevent loss of plasma particles due to collisions with the energizing and supporting means of the annular conductor which means must necessarily pass through said volume. In other words, this special object of the invention is the creation of a zone free from plasma in the region surrounding the just-mentioned means.
According to the principal characteristic of the invention the abovementioned advantageous properties and features are attained by means of two electrodes each located in one of said substantially toroidal confining members or surfaces.
It is known in the art relating to fusion reactors to make use of the combination of an electric field which is perpendicular to a plasma-confining magnetic field. Several different types of such reactors are known, e.g. one embodiment of the so-called homopolar machine and the ixion. However, in these machines there is no annular current conductor. Instead, the magnetic field is in the conventional manner generated by coils located outside the confinement volume. However, in a Report from University of California Radiation Laboratory, No. 8584, January 1959, page 14, FIGURE 6 (Anderson et al.) in Peaceful Uses of Atomic Energy, Geneva 1958, volume 32, page 127, and in Rev. Mod. Phys, 31 (1959), 1045, I. M. Wilcox, there is described an apparatus having a circular current loop the magnetic field of which is utilized to define the reaction Volume and having its plasma subjected to the influence of an electric field directed perpendicularly to the magnetic field. The space within the torus is, however, in that previously known apparatus separated into an inner and an outer chamber due to the presence of a vertical partition. The current and voltage supply means intended to generate the magnetic and the electric fields, respectively, pass through the inner chamber meaning that the reaction volume proper is formed by the outer chamber only. Such an arrangement does not only involve an incomplete utilization of the available space but, above all, it results in the most disadvantageous drawback that the difference between the radii for the starting point and the final point of a particle cannot without considerable diificulties be made very large since both of these radii naturally have to exceed the radius of curvature of the partition. The significance of that fact will be shown below in connection with the explanation of the formulas relating to the particle move- Patented Nov. 3, 1964 ments. It will then become apparent that the presence of this partition has the necessary effect of creating an inner region forbidden to the particles and that the presence of such a region results in such great particle losses that most likely the apparatus can only operate theoretically. According to the present invention it is, on the other hand, feasible to attain great differences between the two justmentioned radii. By way of example it can be mentioned that at a temperature of 5-10 K. and a particle density of 3- l0 /m. the following power losses are obtained in the prior device and in the subject of the present invention, respectively: 2-10 W./1n. and W./m. These losses have been calculated per unit of the annular area in the equatorial plane between the electrodes, the ratio r r having been 1.15 and 3, respectively.
The invention will now be described in greater detail with reference to the accompanying diagrammatical drawmg.
Reference numeral 1 designates a pillar disposed along the symmetry axis of the apparatus and having a number of spokes 2 carrying the annular conductor 3. The spokes 2 do on the one hand support the current loop and on the other they convey the current to and from said loop. Thus, these spokes constitute means extending inward from the annular conductor for supporting and for passing therethrough an electric current. The passage of current through conductor 3 sets up a magnetic field B. The electric field E is formed between two electrodes 4 and 5 positioned in the members previously mentioned as definmg between themselves the plasma reaction volume. As appears from the drawing, these electrodes are not completely closed but have openings through which the current supply and support members 2. pass. The electrode 4 is the inner electrode. The electrode 5 is the outer electrode. For reasons which will become apparent hereinafter, it is important that the maximum diameter of the outer electrode be considerably greater than the minimum diameter thereof, preferably twice as great. The rotational radius for an arbitrary particle in its starting point has been designated r and the correspondmg value in an arbitrary point under consideration is marked r. The movements of the particles will be discussed below in relation to three coordinate directions, namely z passing through the symmetry axis of the apparatus, r referring to the radius of rotation and gb related to the movement in a radial plane, i.e. a plane perpendicular to the z-axis. In particular we are later going to consider situations in which r will indicate a point in the equatorial plane; i.e., the plane of the main conductor 3, at greater distances from the axis 2 than that of the conductor 3. Further, conditions will have to be considered in WlllCh r indicates the radial distance from z, and the particle being in a corresponding point can reach a material wall when it starts from 1' and moves along a magnetic field line.
Making here the permissible approximation that the rotational movement of the particle around the z-axis occurs with constant angular velocity it can be shown that the following general equation is valid for its movement within a confinement volume subjected to the infiuence of a magnetic and an electric field:
The magnitudes and designations appearing in the "above equation and hitherto not defined have the follow- =ing significances:
In the special case here discussed when the two fields are perpendicular, 3 7p as well as r A, -rA,, will equal a zero for a particle which during its rotational movement passes along a magnetic line of force. Therefore the equation can be simplified to: im (vr 112 %mv0}m (r0 The remaining terms in the right member have the following significances:
The first term relates to the total thermal energy of the particle at its point of origin.
The second term designates the centrifugal energy that must be overcome for a transport of the particle from r to r. g
The first term within the bracket corresponds to the original thermal energy in the z -direction.
The second term within the bracket arises from the magnetic field and the third term is caused by the Coriolis force.
It is now easier to analyze the equation for the purpose of establishing under which conditions or within which portions of the confining volume, respectively, a particle can exist.
As is realized at once, the left member of the equation can never be negative. Consequently, if it is desired to create a region forbidden to the plasma particles, it will suffice to find out under which conditions the right hand side could be negative. As the first term always is positive and as the expression within the bracket is raised to the second power, the second and third terms will always have a negative sign and counteract the first one. The aim will consequently be to increase these two terms numerically. As the angular velocity is constant, an increase of the second term can apparently be attained only if r can be made considerably greater than r. As already indicated above and as clearly appears from the drawing, this is conveniently attainable according to this invention. Naturally, the above statement concerning the ratio between the two radii is applicable also to the last term within the bracket. A forbidden region is accordingly present when r exceeds r by such an amount that the second and third terms in the right member are together numerically greater than the first one.
From the equation conclusions may also be drawn concerning the plasma confinement. As long as a particle moves along a magnetic field line the middle term in the bracket will equal zero. However, should the particle deviate from that path the last-mentioned term will differ from zero by an amount which increases with the intensity of the magnetic field. It may thus be said that the particle is influenced by a force tending to maintain it centered in its rotational path along the field line.
It appears from the above description that the invention involves considerable advantages as to the plasma confinement and particularly to a very high extent renders impossible a cooling down of the plasma due to collisions between the particles thereof and material Walls, in the first place the means for supplying current to the annular conductor and for supporting it which must necessarily pass through the space between the two toroidal surfaces defining the reaction volume.
It should finally be pointed out that a gas in thermal equilibrium has a velocity spectrum containing a very small group of particles of very high initial velocities v It could for that reason occur that, as far as these particles are concerned, the first term on the right hand side of equation 2 would still exceed the sum of the two other terms on the same side. Those particles would then be able to penetrate into the region forbidden to the particles of smaller energy. However, as the members located there have a much lesser target surface than those that can be subjected to particle bombardment in the prior art devices of the same type, the total particle losses in a device designed in accordance with the present invention will still become much lesser.
What is claimed is:
1. A plasma-confining and -heating device, comprising: an annular conductor for generating a magnetic field adapted to confine plasma within a reaction volume defined by two substantially toroidal confining members each coinciding with a field line generated in said magnetic field; means extending inward from said annular conductor for supporting it and for passing therethrough the electric current necessary for the creation of said magnetic field; means for generating an electric =field perpendicular to the magnetic field, said last-mentioned means including inner and outer electrodes, each located in one of said toroidal members, and the maximum outer electrode diameter being considerably greater than the minimum diameter thereof.
2. An arrangement according to claim 1 wherein the maximum outer electrode diameter is at least twice the minimum diameter thereof.
References Cited in the file of this patent UNITED STATES PATENTS Loos Nov. 14, 1961 OTHER REFERENCES