Patent Number: 046541845
Section: summary

BACKGROUND OF THE INVENTION This invention pertains to methods and arrangements for attaining high beta values in plasma confinement devices. More specifically, this invention pertains to methods for accessing the second stability region of operation in toroidal magnetic confinement devices. The performance of a magnetic confinement device can be expressed by the parameter beta .beta., the ratio of the plasma kinetic pressure to the confining pressure of the magnetic field. Beta is a direct measure of the efficiency of the magnetic confinement; that is, high-.beta. systems make better use of the confining field than do low-.beta. systems. Beta is defined as: ##EQU1## where p.sub.av =.intg.pd.tau./.intg.d.tau. and B.sub.av.sup.2 =.intg.B.sup.2 d.tau./.intg.d.tau., the integration being over the plasma volume, where p.sub.av is the average plasma pressure and B.sub.av.sup.2 /2 is the average magnetic pressure. A plasma confined in a magnetic field may be unstable. Various instabilities have been predicted based on ideal single fluid magnetohydrodynamic (MHD) equilibrium and linear stability analyses in axisymmetric toroidal configurations. Potentially unstable MHD modes include: the ballooning modes, the Mercier modes (interchange modes), and external and internal kinks. Of these modes, ballooning and internal kinks are serious obstacles to creating and maintaining stable high-.beta. plasmas. Generally, the criteria for ideal MHD instability will depend on specific plasma parameters such as .beta., the pressure and safety factor profiles, and the various geometrical shaping factors. Consequently, stable operation has been limited to low betas. This region of operation is referred to as the "first region" of stable operation. Increasing beta beyond the limit of the first region results in operation in the unstable region where deleterious effects of unstable MHD modes are present. Several studies have been carried out to find environments favorable for suppressing the ballooning instability mode (e.g., A. M. Todd et al., Nucl. Fusion 19 743 (1979)). An empirical shape-optimization by Miller and Moore (Phys. Rev. Lett. 43, 765 (1979)) has shown that a strongly modified dee shaped plasma with an indentation on the inside edge of the plasma (i.e., inwardly concave at the inner-major-radius side) can enhance achievable stable .beta. against ballooning for small aspect ratio configurations. Similarly, Mercier (in Lectures in Plasma Physics, EURATOM-CEA/CEN/EUR 5/27 e, EURATOM, Luxembourg, 1974) showed that an indented plasma enhanced plasma stability against localized interchange modes. While the majority of design studies have been performed at low .beta., it has also been known that at very large .beta., there exists a region of operation where stability to ballooning modes could be regained because of the magnetic well effects produced by the large outward Shafranov shift (e.g., Coppi et al., Nucl. Fusion 19, 715 (1979)). This stable region was called the "second region" of stability and many unsuccessful attempts were made to discover operating scenarios which would make this region accessible from the low-.beta. regime. [By accessibility, we mean a demonstration that a method of operation of the device is possible whereby the .beta. (or pressure) of the device can be increased continuously from zero to a very large .beta. value without passing through the unstable region.] For example, detailed numerical calculations (e.g., Monticello et al., Sherwood Meeting, Austin, Tex., April, 1981) demonstrated that in plasmas with nearly circular cross sections the second stable region occurred only for large aspect ratio configurations and accessibility was not possible. In addition, the internal kink has been shown to be a prime candidate responsible for enhanced fast-ion loss through "fishbone oscillations", thus limiting the ability to increase .beta.. It is therefore an object of the present invention to provide a method and apparatus for forming a magnetically confined plasma. Another object of the present invention is to provide a method and apparatus for forming a magnetically confined plasma and avoiding plasma MHD instabilities which defeat plasma confinement. Yet another object of the present invention is to provide a method and apparatus for forming a plasma with an increased beta. Another object of the present invention is to provide a method and apparatus which makes accessible the second region of stability against ballooning modes. Still another object of the present invention is to provide a method and apparatus for forming a high-beta plasma having stabilized ballooning and internal-kink modes thereby minimizing fast ion losses. Additional objects, advantages, and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. SUMMARY OF THE INVENTION The present invention is the first demonstration for toroidal magnetic confinement devices that the second region of stability against ballooning modes can be accessed with controlled operation. Indeed, under certain modes of operation, it has been found the first and second stability regions may be joined together. Accessing the second stability region is essential to obtaining the high beta necessary for commercial fusion reactors. The present invention also demonstrates the ability to simultaneously achieve complete stabilization to the internal (n=1) kink modes. For toroidal confinement devices, the second region of stability may be accessed by the following scenario: first, modifying the shape of the plasma until it has a bean-shaped poloidal cross-section (by bean-shaped we mean indented or inwardly concave at the inner-major-radius side). Second, operating the device in the first region of stability while further indenting the small-major radius side of the cross-section. When the device is being operated in the first region of stability, .beta. must be kept below the threshold for instability. There are several ways .beta. can be maintained below the threshold for instability, for example: controlling plasma pressure, p, while keeping magnetic field, B, constant; controlling magnetic field B while maintaining plasma pressure constant; or some combination of both. As the indentation is increased, a critical value is reached. This critical value indicates the point at which the second stability region is accessed. Third, after the second stability region has been accessed, .beta. can be increased significantly, to well over 20%. Another feature of the second region of stability is the fact that once large .beta.s are attained, the indentation can be relaxed. An alternate method of accessing the second region of stability is as follows. First the magnetic field would be applied to the device. Then the bean-shaped plasma would be formed. The bean-shaped cross-section would be chosen such that the indentation is at least as large as the critical value. Then the beta would be increased to the desired value for operation. Since operation is in the region where both first and second regions are joined, there are no problems with balloon instabilities. After the desired beta is attained (such as by heating the plasma) then the indentation can be relaxed. The method of the present invention has been demonstrated to provide stability against ballooning modes and against internal kink modes. A theoretical analysis of the stability against ballooning modes is contained in M. S. Chance et al., "Ballooning Mode Stability of Bean-Shaped Cross Sections for High-.beta. Tokamak Plasmas", Phys. Rev. Lett. 51 1963 (November 1983), which is incorporated herein by reference. A theoretical analysis of the stability against internal kinks is contained in J. Manickam et al., "Stability of n=1 Kink Modes in Bean-Shaped Tokamaks", Phys. Rev. Lett. 51, 1959 (November 1983), which is incorporated herein by reference. It has also been found that for the method of this invention, the Mercier modes are even more stable than in conventional tokamaks (especially with the strong minimum-B property of the bean shaping) and the gross stability of the external kink modes is similar to those of conventional tokamaks.