Patent Number: 042630975
Section: description

Generally, the present invention is directed to methods and apparatus for driving a toroidal plasma current by asymmetrically altering the magnetically trapped particle population of the plasma. In connection with various of the apparatus aspects of the present invention, there is provided an improvement in toroidal plasma confinement systems comprising means for assymmetrically altering the trapped particle population of a plasma confined by the system to provide ohmic current in the plasma. Generally, conventional component elements of such toroidal plasma systems are well-known. For example, toroidal plasma confinement systems for the generation and containment of high-temperature plasmas may comprise means for providing a strong, toroidal magnetic field in a toroidal plasma zone in which the plasma is to be embedded, and which may be provided by passage of electrical current through one or more conductive coils encircling the minor toroidal axis. Such systems also comprise means for generating a plasma in the plasma zone, which may include means for providing at least an initial toroidal plasma current which current in turn generates a poloidal magnetic field component. The combination of the poloidal magnetic field and the toroidal magnetic field produces resultant magnetic field lines that lie on closed, nested surfaces, and the plasma is subjected to confining, constricting forces generated by the current flowing in it. Such conventional aspects of toroidal plasma systems are known to the art and need not be described in detail herein. As indicated, the apparatus of the present invention, in addition to conventional toroidal plasma elements, further comprises means for asymmetrically altering the trapped plasma particle population to produce a plasma current. Such asymmetric, trapped particle population altering means preferably comprises means for selectively trapping plasma electrons in a predetermined direction with respect to the minor toroidal axis. Such selective trapping means may comprise means for providing a radio frequency field (including resolvable components of such field) which propagates in a direction parallel to the plasma-confining magnetic field, which has its electric field vector perpendicular to the magnetic field, and which is at resonance with a plasma resonance frequency to increase electron perpendicular velocity to asymmetrically trap plasma electrons. The apparatus may further include means for asymmetrically trapping plasma ions in a manner which is current-complementary to the electron trapping. As indicated, a preferred aspect of the present invention involves asymmetrical trapping of charged particles in the toroidal plasma. In a high temperature toroidally confined plasma, there is a population distribution with respect to the energy of the plasma particles, and with respect to the velocity vectors of the particles. If a charged particle such as an electron has a velocity component which is perpendicular to the magnetic field, it will describe a generally circular orbit in a magnetic field of constant strength. If in addition to the perpendicular velocity component, the particle further has a velocity component parallel to the constant magnetic field, the particle will generally describe a simple spiral path in motion through the constant magnetic field. However, in a toroidal magnetic confinement system, the magnetic field is not of uniform strength, and this non-uniformity affects the plasma particle paths in a relatively complicated manner. Because of the variation of magnetic field strength with respect to the radial distance from the major axis, with the field strength being greater at shorter radii, the existence of a parallel velocity component in the particle motion results in particles travelling into increasing, or decreasing magnetic fields. As the particle moves into a magnetic field which is increasing in strength, the parallel velocity decreases in the stronger field. For a combination of parallel and perpendicular velocity components of charged particle motion in a confining toroidal magnetic field, there is a magnetic field strength for which a particle having such velocity components will stop moving in a direction parallel to the magnetic field, and will reflect back in the opposite direction. For a given parallel velocity component, moreover, it is found that the larger the perpendicular velocity component of a given charged particle with respect to the magnetic field, the sooner the particle stops and is reflected. In a tokamak system, under given conditions of operation, there is a statistical population with respect to particle velocity components. Some of the particles in the distribution spectrum will have a parallel velocity which is large enough (with respect to their respective perpendicular velocity components) so that the particles will slow down but will pass through the high magnetic field region. These particles are not trapped and continue to propagate around the toroidal system in the same general direction with a velocity component parallel to the magnetic field. However, there are statistically also a number of particles for which the parallel velocity is not sufficiently large (with respect to their respective perpendicular velocity components) to permit the particles to pass through the high magnetic field. These particles are "trapped, " and reflect back and forth with respect to the minor axial direction. These "trapped" particles do not contribute to the net toroidal current. The velocity distribution of particles is a dynamic coulomb collisional process so that trapped plasma particles may, through collision or other interaction, be changed in respect of their velocity components so that they have sufficient parallel velocity to pass through the high magnetic field region of the toroidal magnetic field. Such particles thus become detrapped. In the conventional operation of a toroidal plasma component system this detrapping is statistically symmetrical in respect of the minor toroidal axis, and makes no net contribution to plasma current. Similarly and concomitantly with the normal particle detrapping, charged particles which are not trapped may acquire velocity components which are insufficient to pass through the high magnetic field regions, and accordingly become trapped. This charged particle trapping rate is also statistically symmetrical with respect to the minor toroidal axis in conventional toroidal plasma system, and also does not have a net effect on the plasma current. Such toroidal magnetic confinement systems may be considered to be a magnetic mirror with symmetrical mirror strength. However, if an effectively asymmetrical toroidal mirror could be provided, the net ohmic current can be affected. Asymmetrical mirror systems will now be generally discussed prior to describing a specific embodiment of apparatus of the present invention. In a simple magnetic mirror confinement system with asymmetric mirror strength, charged particles trapped initially between mirrors will escape due to Coulomb collisions. Since the Coulomb collisions are predominantly small angle scattering, over a period of time, substantially all particles trapped in the asymmetrical magnetic mirror will eventually escape through the weak mirror as Coulomb collisions redistribute the particle energy distribution, thus producing mechanical momentum. In accordance with the present invention, an asymmetric magnetic mirror is effectively provided by the interaction of a specified radio frequency field with the symmetrical magnetic mirror of a toroidal magnetic confinement system. The theoretical aspects of this interaction are discussed in the following description with respect to the asymmetrical trapping of plasma electrons. If initially empty magnetic mirrors are placed in a plasma where particles are all initially untrapped, a radio frequency field may be applied to increase the perpendicular energy of particles and to cause a selective trapping of particles. The radio frequency field is a travelling wave and the heating rate is larger for particles travelling in one direction. This will result in asymmetric trapping, thereby producing an increase in momentum (and thus temperature) in the over-all particle ensemble of the confined plasma. As indicated previously in an axisymmetric torus configuration, such as the magnetic confinement configuration of tokamak and doublet plasma systems, electrons are trapped in a magnetic mirror produced by a toroidal magnetic field. For purposes of illustration, a simple plasma of unifrom density and temperature will be utilized in the following discussion which in the absence of any electric field, has an isotropic and Maxwellian particle velocity distribution. In sphereical coordinates in velocity space, the velocity components of such a simple plasma in directions parallel to the confining magnetic field and perpendicular to the confining magnetic field may be represented as follows: ##EQU3## where suffixes .perp. and .parallel. denote components perpendicular and parallel to the magnetic field, respectively. The distribution function, f, of particles may be defined at the minimum of magnetic field strength on a flux surface, since all orbits pass through the minimum field. The undisturbed distribution function, f.sub.o, is a Maxwellian function and may be given by: ##EQU4## The trapped particles of the toroidally confined plasma are in the region EQU .theta..sub.c &lt;.theta.&lt;.pi.-.theta..sub.c (3) where sin .theta..sub.c =(B.sub.min /B.sub.max).sup.1/2, B.sub.min and B.sub.max are the minimum and the maximum field strength of a toroidal system. When a radio frequency electric field is provided which propagates parallel to the lines of flux of the magnetic field, and which is oriented such that the electric field plane of the radio frequency wave is perpendicular to the magnetic field, selective interaction with the parallel velocity of charged particles such as electrons may be provided. The frequency and the wave number of the field may, for example, be chosen such that the Doppler-shifted frequency is at resonance with a particle resonance frequency, such as the cyclotron resonance frequency. EQU .omega.-k.sub..parallel. v.sub..parallel.=.OMEGA. (4) where .omega. and k.sub..parallel. are the frequency and the wave number of the radio frequency field and .OMEGA. is the particle frequency. The acceleration or heating of particles may be regarded as stochastic (i.e., after a particle passes through a region of radio frequency field with a length l, the phase relation is substantially lost before the next passage), such that the heating process may be described as a diffusion in velocity space. For the case of the cyclotron heating, the equation of motion may be represented as follows: ##EQU5## where E.sub.195 is the radio frequency field and .OMEGA..sub.e is the electron cyclotron frequency. The perpendicular velocity gain .DELTA.v.perp. per pass through the radio frequency field (such as provided by appropriate antenna elements) is roughly given by ##EQU6## The number of passages per unit time may be represented by v.sub..parallel. /L where L is the length of the system and is equal to 2.OMEGA.R.sub.o q for a circular cross-section tokamak plasma confinement system. R.sub.o is the major radius and q is the safety factor in the preceding equation. Then the diffusion coefficient, D.perp., may be represented by the following relationship: ##EQU7## For the case of resonance occuring at v.sub..parallel. =v.sub..parallel.o, the following further relationship may be provided. EQU .omega.=.OMEGA..sub.e +k.sub..parallel. v.sub..parallel.o (8) The diffusion coefficient, D.perp., may then be considered to be: ##EQU8## For the resonance to be reasonably sharp, the following condition should be substantially observed: EQU k.sub..parallel. l&gt;&gt;1 (10) For electron cyclotron resonance heating, k.sub.81 .congruent..omega./c and Equation (10) becomes ##EQU9## This condition may be readily satisfied. However, in a toroidal plasma confinement system, the magnetic field strength is not uniform, and the resonance condition is satisfied with different values of undisturbed parallel velocity v.sub..parallel.o on different flux surfaces of the confining magnetic field. By rewriting Equation (8) the following relationship may be obtained: EQU v.sub..parallel.o =c(1-.OMEGA..sub.e /.omega.) (12) Therefore, in order that the undisturbed parallel velocity v.sub..parallel.o at the minimum region of magnetic field strength, be undirectional, the variation .alpha..OMEGA..sub.e in the cyclotron frequency should not exceed .sqroot.2T/m.sub.e c.sup.2 .OMEGA..sub.e. The equation for the electron distribution function is given by ##EQU10## The righthand side of the preceding equation contains the terms responsible for electron-ion collisional drag and for the cooling of electrons by either transport of collisions. Equation (13) may be linearized with the substitutions f=f.sub.o +f.sub.1 and f.sub.1 .ltoreq..ltoreq.f.sub.o, to provide the following relationship: ##EQU11## The heating rate, W, may be represented by: ##EQU12## The preceding relationship may be used in the calculation of the heating rate, W, as follows. By partial integration, Equation (15) becomes: ##EQU13## The heating rate solution of this equation may be approximated by ##EQU14## where .DELTA.v.sub..parallel. =.vertline.v.sub..parallel. o.vertline./k.sub..parallel. l and .DELTA.v.sub..parallel. &lt;&lt;.vertline.v.sub..parallel.o .vertline.. Then we have ##EQU15## In steady state operation of a toroidal plasma system, the heating due to the application of a radio frequency trapping (or detrapping) field is balanced by energy loss of the plasma represented by the root mean square of Equation (14). By representing the loss term by 3nT/.tau..sub.E is the energy confinement time, the following relationship may be provided: EQU W.ltoreq.3nT/.tau..sub.E. (19) The preceding inequality is used to account for cases in which additional heating methods are used in the system, and the present invention does contemplate embodiments including additional or auxiliary heating means. The trapping rate may now be discussed in view of the preceding disclosure. In this connection, the particle flux .GAMMA. across the .theta.=.theta..sub.c boundary of a toroidal plasma system may be represented by: ##EQU16## By using Equation (17), the following additional relationship for the particle trapping flux, .GAMMA., may be obtained. ##EQU17## This asymmetrical particle trapping flux is balanced by collisional detrapping in a steady state operation of the system after equilibrium is reached. Since the trapping is asymmetrical with respect to the parallel velocity component v.sub..parallel., and detrapping is symmetric, the untrapped population will gain a net momentum. The change in trapped population n.sub.1 may be calculated by equating the flux .GAMMA. with the collisional detrapping flux as follows: EQU .GAMMA..apprxeq..nu.n.sub.1 (.pi.-.theta..sub.c).sup.-2 (22) where .nu. is the collision frequency. In a steady state, this momentun gain is balanced by the collision between plasma electrons and plasma ions. The current density, j, generated may be represented by ##EQU18## where .sigma. is electrical conductivity. By combining Equations (22) and (23), the following ratio relationship may be provided: EQU n.sub.1 /n.sub.o .apprxeq.(.pi.-.theta..sub.c).sup.2 j/(ev.sub..parallel.o n.sub.o). (24) For typical tokamak operating parameters, the current density j is much less than the total current flux at the minimum (i.e., j&lt;&lt;ev.sub..parallel.o n.sub.o) and therefore EQU n.sub.1 /n.sub.o &lt;&lt;1 (25) Accodingly, the linearization of Equation (13) is justified. By using Equation (18), the flux .GAMMA. may be represented in terms of the heating rate, W, as follows: ##EQU19## The appropriate combination of Equations (19), (23) and (26) results in the following relationship: ##EQU20## In a typical tokamak system, .theta.c is given by EQU cos.theta..sub.c =.sqroot..epsilon. (28) where .epsilon. is the inverse aspect ratio. For a tokamak plasma system, Equation (24) becomes approximately: ##EQU21## The magnetohydrodynamic stability condition limits the current density to a value given by ##EQU22## where R is the major radius, B.sub.t is the toroidal magnetic field, and q is the safety factor. Typically, the valve of j for a large tokamak plasma system may be 5.times.10.sup.5 amp/m.sup.2. Since the right-hand side of Equation (29) is proportional to T.sup.2, it may be considered to represent the condition for the lower limit on temperature. ##EQU23## For j=5.times.10.sup.5 amp/m.sup.2, .tau..sub.E =1 sec, and .epsilon.=1/3 we obtain EQU T.gtoreq.1.4.times.10.sup.4 eV (32) It should be noted that the indicated temperature value is not far from the optimum operating temperature of a tokamak fusion reactor in accordance with known principles. In steady state radio frequency trapping (or detrapping) heating, over an extended time period the plasma ions will gain momentum due to the friction with electrons. The ion momentum may be cancelled, for example, bt applying counter-current radio frequency ion cyclotron resonance energy, at an appropriately much lower power level, in accordance with principles previously set forth herein. It has been shown that a plasma current in a toroidal plasma system such as a tokamak system may be sustained by using a radio-frequency heating induced, asymmetrical trapping (or detrapping) phenomenon. Although electron cyclotron resonance frequencies are used in the preceding description for discussion purposes, other resonances such as the lower hybrid wave may be utilized, and may be preferred inpractice. Electron cyclotron resonance has the disadvantage of requiring a very short wave length microwave generator, and also the wave will not penetrate the plasma if the plasma frequency is larger than the cyclotron frequency. In the selection of other suitable wave resonances, it should be recognized that the wave utilized should have a resonance and should heat the electron perpendicular energy for asymmetrical trapping, and should heat the electron parallel energy for asymmetrical detrapping. Turning now to the drawings, the invention will now be more particularly described with respect to the embodiment of apparatus illustrated in FIG. 1. Illustrated in FIG. 1 is a toroidal plasma confinement apparatus 10 of the tokamak type which is adapted for providing a plasma 12 of circular cross section. The boundary 14 of the plasma 12 is schematically represented by a closed, equidensity surface, in terms of mass density, which encloses substantially all of the plasma (e.g., 95% or more of the plasma mass). The plasma 12 is contained in a toroidal zone 16 defined by a toroidal conducting shell 18 of circular cross section and which is generally radially symmetrical about the longitudinal major toroidal axis 20 of the apparatus 10. It will be appreciated that while the illustrated plasma 12 boundary 14 toroidal zone 16 and conducting shell 18 are of circular cross section, they may have other shapes such as a doublet shape (or higher multiplet). The conducting shell 18 is provided with appropriate access ports for vacuum and gas supply, in accordance with known construction. The interior walls of the shell 18 may be protected by a liner (not shown) fabricated of graphite, silicon carbide, or some other suitable low atomic number material which minimizes the impurity effects of wall material sputtered back into the plasma as a result of charged particle bombardment of the liner. External of the shell 18 is the vacuum chamber 30, which is made of an electrically insulating material and which may have a thin metallic coating to avoid introduction of an excessive amount of impurities into the plasma zone. The vacuum chamber is hermetically sealed, and is provided with conduits 32 as an access port. Surrounding the vacuum chamber 30 are toroidal field producing coils 31 which produce the toroidal magnetic field in the plasma zone within the conducting shell 18. The toroidal coils 31 may be supplied current from a suitable d-c power source (not shown) such as a lead acid battery bank. Externally of the vacuum chamber 30, but internally of the toroidal coils 31, is an additional set of magnetic coils 34 which may be driven by an appropriate capacitor bank power system (not shown). The coils 34 are electric field induction coils, which function to ionize the plasma 12 and induce an initial plasma current. A radially symmetrical manifold array 36, which may be connected to a vacuum system (not shown) via outlet ports and piping 38, communicates with the interior of the vacuum chamber 30 by means of ports 32. Associated piping and ports for hydrogen (e.g. deuterium-tritium mixtures) supply for plasma generators are also provided. These previously described elements or toroidal apparatus 10 are conventional in the plasma art and need not be further described in detail. The embodiment of apparatus 10 further includes means 40 for selectively trapping electrons in the toroidal magnetic field. In the embodiment illustrated in FIG. 1 this selective trapping is carried out by each of a plurality of substantially identical antenna elements 42, 43, 44, 45 which are vertically oriented with respect to the major axis of the toroidal system and located adjacent to the interior surface of the shell 18 in the region of higher magnetic field strength. The four antenna elements 42, 43, 44, 45 are regularly spaced at equidistant intervals about the interior wall of the plasma confinement zone such that the antenna elements are spaced at successive 90.degree. intervals in a plane perpendicular to the major axis of the apparatus 10. The antenna elements each comprise a plurality of substantially identical waveguide units 50 which are more fully illustrated in FIGS. 2 and 3. As shown in FIGS. 2 and 3, the waveguide units 50 of each antenna element are disposed in uniform, vertically oriented array in adjacent relationship conforming to the toroidal interior surface of the plasma zone. Each of the waveguide units 50 is provided with a waveguide channel 52 communicating with a suitable radio frequency generator (not shown) and transmission line (not shown). The radio frequency generators may comprise a plurality of amplifiers driven by a single source, to produce the desired output power. The radio frequency generator supplies r-f energy at a predetermined wavelength adapted to increase the perpendicular velocity component of plasma electrons in accordance with previously discussed principles. In order to provide the appropriate r-f field within the plasma zone, each of the waveguide units is provided with a plurality of slot radiators 54 having a length dimension of approximately half the free space wave length, .lambda., of the r-f output of the radio frequency generators. The slot radiators as shown in FIG. 3 are spaced at one wave length, .lambda., intervals along the longitudinal direction of each of the waveguide units 50, and the slot radiators of each of the waveguide units 50 are adjacently disposed to form radiating surfaces of the respective antenna elements 42, 43, 44, 45 having a regular array of slot radiators thereon. The antenna enters at the top of the shell 18 and is confined to the higher field strength region to provide for entry of r-f energy to the system. As indicated, the waveguide units 50 are each provided with a suitable transmission line and radio frequency power source. In this connection, the waveguide units 50 of an antenna element 42, 43, 44, or 45 may be supplied with radio frequency energy in particular phase relationship with respect to the other units 50 or the antenna element, such that the antenna element may provide a relatively narrow r-f beam which may be adjusted in propagation angle with respect to the toroidal magnetic field. The desired phase relationship may be provided by appropriately phased individual r-f power sources for each waveguide unit, such as by inserting an appropriate phase shifting array between an r-f source and the r-f power amplifiers in a known manner. The electric field component of the r-f beam is vertical with respect to the illustration of FIG. 1 (i.e., in a plane passing through or parallel to major axis 20). The provision of a propagation angle which may be shallow with respect to the minor axis provides for increasing damping at the cyclotron layer, and accordingly increases absorption efficiency. The electric field component is thus also perpendicular to the toroidal field, and the full, confining magnetic field (because the poloidal field is relatively weak with respect to the toroidal field). In operation of the illustrated embodiment, a toroidal magnetic field is provided, and plasma is created in a conventional manner in the toroidal plasma zone with capacitor bank discharge through the inductive coils to provide an initial pulsed ohmic flow in the plasma and an initial poloidal field. This produces a plasma population with trapped and untrapped electrons. The trapping means is then operated to asymmetrically trap plasma electrons to provide for continuation of the ohmic current in the original direction of the initial plasma current flow and maintenance of the initial poloidal field. Thus, through the operation of the selective trapping means 40, electrons are selectively detrapped in one direction, and an enormous current flow resulting from the selective asymmetric detrapping of electrons is produced to provide for a continuous current in the plasma. Since the resulting current flow is along the minor axial direction, the current flow produces the poloidal confining field for continuous compression and confinement of the plasma and accomodates steady-state operation of the plasma system. The ions, which in a hydrogen plasma will be protons, may be similarly trapped in a current complementary direction by a similar antenna radiator system and radio frequency generator source operating at an appropriate wavelength for interaction with the proton particles. Apparatus and methods in accordance with the present invention have particular utility in the study and analysis of the properties and behavior of plasmas, and in particular, the study of analysis of toroidal plasmas which are magnetically confined under prolonged or steady-state conditions. The systems may also be used as auxiliary toroidal plasma heating systems in conjunction with other heating systems. The illustrated embodiment is particularly adapted for use in the generation, confinement, study and analysis of hydrogen plasmas (i.e., hydrogen, deuterium, tritium and mixtures thereof such as deuterium-tritium mixtures) at high temperatures, although the invention may also be used in the production of plasmas containing highly stripped elements of higher atomic number. Accordingly, the methods and apparatus of the present invention find utility as analytical techniques and instrumentation in respect of matter in the plasma state. In this connection, the apparatus may be provided with conventional diagnostic and measurement elements including magnetic probes, inductive pickup loops, particle detectors, photographic and spectrographic systems, microwave and infra-red detection systems and other appropriate elements, the data outputs of which may be utilized directly or recorded, such as by transient data recorders. The various aspects of the invention may also find utility as, or in the design or development of, fusion systems, which of course, need not necessarily be net power producers in order to be utilizable as neutron or other particle or fusion product generators, isotope generators, etc. It is of course further understood that although a specific embodiment of the present invention is illustrated and described, various modifications thereof will be apparent to those skilled in the art and, accordingly, the scope of the present invention should be defined only by the appended claims and equivalents thereof. For example, the invention may be utilized in toroidal plasma systems with elongated plasma cross section such as doublet or higher multiplet cross section produced by suitably shaped conducting shells or by appropriately designed field shaping coils. Various features of the invention are set forth in the following claims.