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Stellarator and Heliotron Devices

1999; IOP Publishing; Volume: 39; Issue: 2 Linguagem: Inglês

10.1088/0029-5515/39/2/701

1741-4326

John L. Johnson,

Magnetic confinement fusion research

Stellarators and tokamaks are the most advanced devices that have been developed for magnetic fusion applications. The two approaches have much in common; tokamaks have received the most attention because their axisymmetry justifies the use of simpler models and provides a more forgiving geometry. However, recent advances in treating more complicated three dimensional systems have made it possible to design stellarators that are not susceptible to disruptions and do not need plasma current control. This has excited interest recently. The two largest new magnetic experiments in the world are the LHD device, which commenced operation in Toki, Japan, in 1998 and W7-X, which should become operational in Greifswald, Germany, in 2004. Other recently commissioned stellarators, including H-1 in Canberra, Australia, TJ-II in Madrid, Spain, and IMS in Madison, Wisconsin, have joined these in rejuvenating the stellarator programme. Thus, it is most appropriate that the author has made the lecture material that he presents to his students in the Graduate School of Energy Science at Kyoto University available to everyone. Stellarator and Heliotron Devices provides an excellent treatment of stellarator theory. It is aimed at graduate students who have a good understanding of classical mechanics and mathematical techniques. It contains good descriptions and derivations of essentially every aspect of fusion theory. The author provides an excellent qualitative introduction to each subject, pointing out the strengths and weaknesses of the models that are being used and describing our present understanding. He judiciously uses simple models which illustrate the similarities and differences between stellarators and tokamaks. To some extent the treatment is uneven, rigorous derivations starting with basic principles being given in some cases and relations and equations taken from the original papers being used as a starting point in others. This technique provides an excellent training ground for students without detracting from the usefulness of the book for knowledgeable fusion physicists. After a short, somewhat historical, introduction, Chapter 2 contains a good treatment of the basic properties of a toroidal magnetic configuration (the concepts of magnetic surfaces, rotational transform, shear and magnetic wells), averaging techniques which can often be used to simplify the calculations, helically invariant configurations, magnetic islands and line tracing techniques. Derivations and discussions of the basic tools of plasma theory, including the Vlasov equation, magnetohydrodynamic equations and their reduced form for low-β, large aspect ratio systems, properties of MHD waves, the drift kinetic equation and transport equations, are given in Chapter 3. Chapter 4 contains a good treatment of MHD equilibria, including a derivation of the three dimensional Grad-Shafranov equation, a discussion of the calculation of equilibria with a planar magnetic axis with both averaged equations and a variational approach, a comparison of the results of the two techniques, a formulation for stellarators with a helical magnetic axis and a good discussion of the Pfirsch-Schluter current. The treatment of MHD instabilities in Chapter 5 is also excellent. It starts with a good derivation and discussion of the energy principle, gives a detailed treatment of ballooning modes where the wavelengths of the perturbation perpendicular to the field are short while those along B are long and derives the Mercier criterion from the ballooning mode equation. I personally prefer to obtain this criterion by making the low mode number assumption that dξ/dΨ>>dξ/dθ dξ/dζ, since non-ideal effects such as finite gyration radius corrections may provide less stabilization to these modes. A careful treatment of the resistive interchange mode is followed by a discussion of the role of localized stability criteria in the analysis of experiment and design studies, a study of Pfirsch-Schluter current driven magnetic islands and the interpretation of sawtooth instabilities in Heliotron E. The treatment of particle orbits in Chapter 6 includes a derivation of drift equations, a discussion of the characteristics of trapped particle confinement in a heliotron and one of the Monte Carlo method for studying transport phenomena. A good treatment of neoclassical transport in a stellarator, with emphasis on the relation between parallel viscosity driven fluxes and bootstrap current, is given in Chapter 7. This is the best treatment I have found, outside of the original references, but it is still demanding. In addition, a radial electric field is introduced into the energy transport equations. The treatment of heating and confinement of heliotron plasmas in Chapter 8 is a good combination of providing results from experiments on the Heliotron E and DR heliotrons and the ATF and CHS stellarators and showing how theoretical interpretation is formulated. The discussions of ray tracing and energy absorption for both ECRH and ICRF heating techniques, as well as a treatment of neutral beam injection, are very clear. Measurements of bootstrap current and plasma rotation, as well as the density limits associated with pellet injection, are discussed. The chapter ends with a discussion of what may be the author's favourite topic, pressure gradient driven turbulence, in which he describes mixing length and scale invariance techniques. Finally, a discussion of the characteristics of a steady state fusion reactor, including a treatment of the containment, slowing down and energy transfer of the alpha particles, one of the toroidal Alfven modes driven by these particles and some physics of divertors are given in Chapter 9. A reviewer is usually expected to find some faults. I had no problem in finding one as soon as I received the book: indeed, I did not like its title. I have always maintained that Lyman Spitzer defined a stellarator as any toroidal device in which the rotational transform is generated by coils outside the plasma, either through imposition of a helical magnetic axis as in a figure-8 stellarator or a heliac, or through the generation of helical magnetic fields, as in a classical stellarator, a torsatron or a quasi-helical stellarator such as W7-X. The author notes that the heliotron (as it was invented by Uo in Japan) is the same as the torsatron (first proposed by Gourdon and his colleagues in Europe) in his introduction, but cannot bring himself to ignore Uo's desire to maintain a distinction between stellarators and heliotrons. Enough typographical errors are present to make one have to be careful before relying on the book for specific formulas. Nevertheless, it will prove to be a useful reference. I have always respected the author for the quality of students he produces. He provides a list of some of them in the preface, which justifies this opinion. These students are a good demonstration of the usefulness of this book.