Plasma Physics pp 256-281 | Cite as

Transport Processes

  • Kyoji Nishikawa
  • Masahiro Wakatani
Part of the Springer Series on Atoms+Plasmas book series (SSAOPP, volume 8)


The first and most fundamental problem in thermonuclear fusion research is to heat a plasma to the ignition temperature and to confine such a plasma such that the product of the plasma density n and the confinement time τ satisfies the Lawson criterion (9.1.12). For magnetic confinement, the confinement time τ is determined by the transport process. It is a simple problem if the magnetic field is straight and the particles can be transported across the magnetic field only by collisions. However, if one wants to confine a plasma in a reasonably sized vessel such that the MHD equilibrium and stability are guaranteed, one inevitably has to use a curved magnetic field geometry, as explained in Chap. 9, so that the transport processes have to be treated in a complex configuration such as in tokamaks. The problem then becomes extremely complicated, partly due to the geometrical effects on the particle orbits and more seriously due to electromagnetic fluctuations that result from microscopic instabilities. In this chapter, we first describe in Sects. 13.1–3 the geometrical effects, considering only the collisional displacement of the particle orbits across magnetic surfaces. We then briefly describe the so-called anomalous transport due to electromagnetic fluctuations in Sect. 13.4–6. At present, the physical mechanism of the anomalous transport as observed in tokamaks and other advanced devices is not well understood, but remarkable progress has been seen in recent years. These developments are beyond the scope of the present book. Several recent seminal papers are cited, however [13.1–5].


Field Line Magnetic Field Line Magnetic Surface Trap Particle Radial Electric Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 13.1
    S.I. Bragniskii: Transport Processes in a Plasma, in Reviews of Plasma Physics, Vol. 1 (Consultants Bureau, New York 1965) p. 205Google Scholar
  2. 13.2
    F.L. Hinton, R.D. Hazeltine: Theory of Plasma Transport in Toroidal Confinement Systems, Rev. Mod. Phys. 48, 239 (1976)MathSciNetADSCrossRefGoogle Scholar
  3. 13.3
    A.A. Galeev, R.Z. Sagdeev: “Theory of Neoclassical Diffusion”, in Reviews of Plasma Physics, Vol. 7 (Consultants Bureau, New York 1975) p. 257Google Scholar
  4. 13.4
    B.B. Kadomtsev, O.P. Pogutse: Trapped Particles in Toroidal Magnetic Systems, Nucl. Fusion 11, 67 (1971)CrossRefGoogle Scholar
  5. 13.5
    P.C. Liewer: Measurements of Microturbulence in Tokamaks and Comparison with Theories of Turbulence and Anomalous Transport, Nucl. Fusion 25, 543 (1985)CrossRefGoogle Scholar
  6. 13.6
    D. Montgomery: “Introduction to the Theory of Fluid and Magnet Fluid Turbulence”, in Nagoya Lectures in Plasma Physics and Controlled Fusion, ed. by Y.M. Ichikawa, T. Kamimura (Tokai University Press 1989) p. 207Google Scholar
  7. 13.7
    A. Hasegawa: Self-Organization Processes in Continuous Media, Adv. Phys. 34, 1 (1985)ADSCrossRefGoogle Scholar
  8. 13.8
    W.M. Tang: Microinstability Theory in Tokamaks, Nucl. Fusion 18, 1089 (1978)ADSCrossRefGoogle Scholar
  9. 13.9
    M.N. Rosenbluth, R.Z. Sagdeev, J.B. Taylor, G.M. Zaslavski: Destruction of Magnetic Surfaces by Magnetic Field Irregularities, Nucl. Fusion 6, 297 (1966)CrossRefGoogle Scholar
  10. 13.10
    A.B. Rechester, M.N. Rosenbluth: Electron Heat Transport in a Tokamak with Destroyed Magnetic Surfaces, Phys. Rev. Lett. 40, 38 (1978)ADSCrossRefGoogle Scholar
  11. 13.11
    R.E. Waltz: “Turbulent Transport in Tokamaks”, in Nagoya Lectures in Plasma Physics and Controlled Fusion, ed. by Y.H. Ichikawa, T. Kamimura (Tokai University Press 1989) p. 357Google Scholar
  12. 13.12
    R.H. Kraichnan: Inertial Range in Two-Dimensional Turbulence, Phys. Fluids 10, 1417 (1967)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kyoji Nishikawa
    • 1
  • Masahiro Wakatani
    • 2
  1. 1.Faculty of EngineeringKinki UniversityTakaya, Higashihiroshima, HiroshimaJapan
  2. 2.Graduate School of Energy ScienceKyoto UniversityGakasho, Uji, KyotoJapan

Personalised recommendations