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A simple non-markovian equation for a magnetoplasma

Abstract

A new kinetic equation for the velocity distribution function ƒ is proposed here, with the innovation that the term (∂ƒ/∂t)c representing the effect of particle collisions, incorporates time delays extending over the interval between successive 90° collisions. When this theory is applied to magnetoplasmas of the type found in tokamaks, it is found that the time delay has a dramatic effect on the heat flux across the magnetic field, giving results orders of magnitude larger than the classical values, and in fair agreement with observations. It appears that non-markovian effects are of great importance in magnetoplasmas, and that they provide answers to some unsolved problems in fusion research.

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References

  1. Bogoliubov, N. N. Studies in Statistical Mechanics Vol. 1 (eds Boer, J. De & Uhlenbeck, G. E.) (North-Holland, Amsterdam, 1946).

    Google Scholar 

  2. Montgomery, D. Lectures in Theoretical Physics Vol. 9C (ed. Brittin, W. E.) (Gordon and Breach, New York, 1967).

    Google Scholar 

  3. Tschen, C. M. Phys. Rev. 114, 394–411 (1959).

    Article  ADS  MathSciNet  Google Scholar 

  4. Fujita, S. Lectures in Theoretical Physics Vol. 9C (ed. Brittin, W. E.) (Gordon and Breach, New York, 1967).

    Google Scholar 

  5. Woods, L. C. J. Fluid Mech. 136, 423–433 (1983).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  6. Chapman, S. & Cowling, T. G. The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, 1970).

    MATH  Google Scholar 

  7. Bragniskii, S. I. Reviews of Plasma Physics Vol. 1 (ed. Leontovich, M. A.) (Consultants Bureau, New York, 1965).

    Google Scholar 

  8. Woods, L. C. J. Plasma Phys. 29, 143–154 (1983).

    Article  ADS  Google Scholar 

  9. Murakami, M., Callen, J. D. & Berry, L. A. Nucl. Fus. 16, 347–354 (1976).

    Article  ADS  Google Scholar 

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Woods, L. A simple non-markovian equation for a magnetoplasma. Nature 307, 614–616 (1984). https://doi.org/10.1038/307614a0

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