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A strictly Markovian expansion for plasma turbulence theory

Published online by Cambridge University Press:  13 March 2009

Frank C. Jones
Frank C. Jones
Affiliation:
Theoretical Studies Group, NASA Goddard Space Flight Center, Greenbelt, MD 20771
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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
Information
Journal of Plasma Physics , Volume 20 , Issue 1 , August 1978 , pp. 87 - 94
Copyright
Copyright © Cambridge University Press 1978

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References

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