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The stochastic tetrad magneto-hydrodynamics via functional formalism

Part of: Complex Plasma Phenomena

Published online by Cambridge University Press:  02 October 2015

Massimo Materassi  and
Giuseppe Consolini
Massimo Materassi*
Affiliation:
Istituto dei Sistemi Complessi, CNR, via Madonna del Piano 10, Sesto Fiorentino (Fi), Italy
Giuseppe Consolini
Affiliation:
INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00133 Roma, Italy
*
†Email address for correspondence: massimo.materassi@isc.cnr.it
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Abstract

In this work we discuss an application of the Tetrad Dynamics approach, a stochastic dynamical theory already introduced in hydrodynamic turbulence, to incompressible magneto-hydrodynamics. This theoretical framework is capable of taking into account some crucial aspects of turbulent plasmas, namely, (i) its material nature, which is stressed through the adoption of Lagrangian variables, (ii) its probabilistic dynamics, which is fundamental to understand the intermittency and highly irregular nature of turbulence, and (iii) the multi-scale character of interactions, which is approached by promoting the space size of parcels to the role of a dynamical variable. In particular, here, we construct the probabilistic equations of motion for quantities describing the evolution of a turbulent plasma (a matrix ${\bf\varrho}$ describing the parcel’s shape, the plasma velocity and magnetic field coarse-grained gradient tensors, $\unicode[STIX]{x1D648}$ and $\unicode[STIX]{x1D652}$), resorting the functional formalism of classical statistical dynamics. Through the introduction of a stochastic action and using a path integral approach, the statistical properties of $({\bf\varrho},\unicode[STIX]{x1D648},\unicode[STIX]{x1D652})$ can be derived from those of noises appearing in their equations of motion, both at equilibrium and out of equilibrium.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 495810602
Copyright
© Cambridge University Press 2015 

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