SRX Physics

SRX Physics / 2010 / Article

Research Article | Open Access

Volume 2010 |Article ID 640826 |

Z. T. Wang, Y. X. Long, J. Q. Dong, "Relativistic Quasilinear Description of Three-Dimensional Diffusion", SRX Physics, vol. 2010, Article ID 640826, 4 pages, 2010.

Relativistic Quasilinear Description of Three-Dimensional Diffusion

Received28 Aug 2009
Revised02 Nov 2009
Accepted05 Nov 2009
Published30 Dec 2009


Quasilinear theory is developed by using canonical variables for a relativistic plasma. It is self-consistent, including momentum, pitch angle, and spatial diffusions. By assuming the wave field as a superposition of known toroidal and poloidal Fourier modes, the quasilinear diffusion coefficients are written in a form which can be directly evaluated using the output of a spectral full-wave solver of Maxwell equations in toroidal plasmas. The formalism is special for tokamas and, therefore, simple and suitable for simulations of cyclotron heating, current drive, and radio-frequency wave-induced radial transport in ITER.


  1. A. N. Kaufman, “Quasilinear diffusion of an axisymmetric toroidal plasma,” Physics of Fluids, vol. 15, no. 6, pp. 1063–1069, 1972. View at: Publisher Site | Google Scholar
  2. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion: Applied Sciences, vol. 38, Springer, New York, NY, USA, 1983.
  3. A. J. Brizard and A. A. Chan, “Relativistic quasilinear diffusion in axisymmetric magnetic geometry for arbitrary-frequency electromagnetic fluctuations,” Physics of Plasmas, vol. 11, no. 9, pp. 4220–4229, 2004. View at: Publisher Site | Google Scholar | MathSciNet
  4. L.-G. Eriksson and P. Helander, “Monte Carlo operators for orbit-averaged Fokker-Planck equations,” Physics of Plasmas, vol. 1, no. 2, pp. 308–314, 1994. View at: Google Scholar
  5. M. Brambila, Plasma Physics and Controlled Fusion, vol. 41, p. 1, 1999.
  6. A. Cardinali, L. Morini, and F. Zonca, in Proceedings of the Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas, J. Conner, O. Sauter, and E. Sindoni, Eds., vol. 871, p. 292, American Institute of Physics, Varenna, Italy, 2006.
  7. Z. Wang, “Plasma transport at magnetic axis in toroidal confinement systems,” Plasma Physics and Controlled Fusion, vol. 41, pp. A679–A686, 1999. View at: Publisher Site | Google Scholar
  8. R. D. Hazeltine, S. M. Mahajan, and D. A. Hitchcock, “Quasi-linear diffusion and radial transport in tokamaks,” Physics of Fluids, vol. 24, no. 6, pp. 1164–1179, 1981. View at: Google Scholar
  9. Z. T. Wang, Y. X. Long, J. Q. Dong, L. Wang, and F. Zonca, “Fishbone instability excited by barely trapped electrons,” Chinese Physics Letters, vol. 23, no. 1, pp. 158–160, 2006. View at: Google Scholar
  10. P. U. Lamalle, “A qualitative comparison of theoretical models of radiofrequency wave propagation and absorption in tokamak plasmas,” Plasma Physics and Controlled Fusion, vol. 40, no. 4, pp. 465–479, 1998. View at: Google Scholar
  11. B. J. Braams and C. F. F. Karney, “Conductivity of a relativistic plasma,” Physics of Fluids B, vol. 1, no. 7, pp. 1355–1368, 1989. View at: Google Scholar

Copyright © 2010 Z. T. Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

More related articles

 PDF Download Citation Citation
 Download other formatsMore
 Order printed copiesOrder

Related articles

Article of the Year Award: Outstanding research contributions of 2020, as selected by our Chief Editors. Read the winning articles.