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Path integrals for mean-field equations in nonlinear dynamos

Part of: 50 years of Mean Field Electrodynamics

Published online by Cambridge University Press:  14 June 2018

Dmitry Sokoloff  and
Nobumitsu Yokoi
Dmitry Sokoloff*
Affiliation:
Department of Physics, Moscow State University, Moscow, 119991, Russia IZMIRAN, Kaluzhskoe shosse, Troitsk, Moscow, 108840, Russia
Nobumitsu Yokoi
Affiliation:
Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan
*
†Email address for correspondence: sokoloff.dd@gmail.com
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Abstract

Mean-field dynamo equations are addressed with the aid of the path integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener integrals taken over all the trajectories of the fluid particles. The form of the equations is just the same as the conventional mean-field equations, but here the equations are derived with the velocity field realisation affected by the force exerted by the magnetic field. In this sense, we derive nonlinear dynamo equations.

Keywords

astrophysical plasmasspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 3 , June 2018 , 735840307
Copyright
© Cambridge University Press 2018 

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