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A strictly Markovian expansion for plasma turbulence theory

Published online by Cambridge University Press:  13 March 2009

Frank C. Jones
Affiliation:
Theoretical Studies Group, NASA Goddard Space Flight Center, Greenbelt, MD 20771

Abstract

The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1978

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References

REFERENCES

Bourret, R. C. 1962 Nuovo Cimento, 26, 1.CrossRefGoogle Scholar
Jones, F. C. 1975 Proc. 14th International Cosmic Ray Conference, Munich, West Germany, 3, 856.Google Scholar
Jones, F. C. & Birmingham, T. J. 1975 Plasma Phys. 17, 15.CrossRefGoogle Scholar
Kubo, R. 1962 J. Phys. Soc. Japan, 17, 1100.CrossRefGoogle Scholar
Kubo, R. 1963 J. Math. Phys. 4, 174.CrossRefGoogle Scholar
Misguich, J. H. & Balescu, R. 1975a Physica, 79c, 373.Google Scholar
Misguich, J. H. & Balescu, R. 1975b J. Plasma Phys. 13, 385.CrossRefGoogle Scholar
Misguich, J. H. & Balescu, R. 1975c J. Plasma Phys. 13, 419.CrossRefGoogle Scholar
Misguich, J. H. & Balescu, R. 1975d J. Plasma Phys. 13, 429.CrossRefGoogle Scholar
Nishikawa, K. 1966 Progr. Theoret. Phys. 36, 193.CrossRefGoogle Scholar
Thomson, J. J. & Benford, G. 1973 J. Phys. Math. 14, 531.CrossRefGoogle Scholar
Weinstock, J. 1969 Phys. Fluids, 12, 1045.CrossRefGoogle Scholar
Weinstock, J. 1970 Phys. Fluids, 13, 2308.CrossRefGoogle Scholar