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Encyclopedia of Complexity and Systems Science pp 8009–8028Cite as

Self-Organization in Magnetohydrodynamic Turbulence

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Definition of the Subject

Plasma dynamics at low frequency, i.?e. at frequencies lower then the ion cyclotron frequency, can be described using a one-fluid modelusually called magnetohydrodynamics (MHD), where the main dynamical variables are represented by fluid velocity and magnetic field, which evolvenon-linearly being coupled to each other. This description applies both to laboratory plasma devices (tokamaks, reverse field pinch etc.), devotedto realize controlled nuclear fusion, and to space and astrophysical plasmas (Solar corona, Solar wind). Very often, when viscosity and resistivity aresufficiently small, the plasma behavior is characterized by the presence of a developed turbulence. In the last 20 years huge progress inunderstanding the properties of such turbulence has been realized, both by the use of high resolution computer simulations and by analysis of space andlaboratory data. One of the most fascinating results of these studies concerns the evidence of self...

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Abbreviations

Alfvén speed:

The Alfvén speed \( { c_{\text{A}} } \) is the propagation speed of Alfvén waves and is given by \( c_{\text{A}}=B_0/(4\pi\rho)^{1/2} \), where \( { \mathbf{B}_0 } \) is mean magnetic field and ? the plasma mass density. Alfvèn waves are transverse, incompressible magnetohydrodynamic waves that propagate along \( { \mathbf{B}_0 } \) and originate from the tension of magnetic field lines.

Elsässer variables:

Elsässer variables \( { \mathbf{z}^{\sigma} } \) are defined by \( { \mathbf{z}^{\sigma}=\mathbf{v}+\sigma \mathbf{B}/(4 \pi \rho)^{1/2} } \), with \( { \sigma=\pm 1 } \), v the velocity field, B the magnetic field and ? the plasma mass density. The equations of incompressible MHD are often written in terms of these variables in order to describe the propagation of Alfvén waves and the non-linear couplings occurring in MHD turbulence.

Magnetohydrodynamics :

Magnetohydrodynamics (abbreviated, MHD) represents a one-fluid mathematical model which describes plasma dynamics at low frequencies: The main dynamical variables are the velocity of the fluid and the magnetic field. The vector equations for these variables are the fluid momentum conservation and the induction Maxwell equation.

MHD turbulence:

MHD turbulence is that turbulence which develops inside plasmas at macroscopic level, when viscosity and resistivity are low. Apart from velocity fluctuations which are also present in ordinary fluids, it is characterized also by the presence of magnetic field fluctuations.

Reverse field pinch:

Reverse field pinch (abbreviated, RFP) are plasma fusion toroidal devices whose conception is based on the idea that non-linear interactions in plasmas spontaneously give rise to magnetic structures where the Laplace force is zero (force free structures).

Shell models :

Shell models of turbulence are dynamical systems consisting of a set of ordinary differential equations representing a simplified version of the Navier–Stokes or MHD equations in the wavevector space. These models provide the possibility to investigate turbulence at very high Reynolds number regimes at the cost of neglecting information about spatial structures.

Solar corona:

The solar corona is the region extending from the solar surface up to one million of kilometers in the space, which can be visible to the naked eye during the eclipses. It is constituted mainly by a hydrogen plasma (proton and electrons) at a temperature of about two million degrees. The corona is highly structured by the magnetic field generated at the sun surface.

Solar wind:

The solar wind is a stream of plasma mainly composed of protons and electrons (hydrogen plasma), which flows out of the sun, due to the fact that plasma pressure associated to the very high coronal temperature overcomes the sun gravity. The flow velocity ranges from 250?km/s in the equatorial plane to about 900?km/s in the polar regions. Solar wind represents an extremely efficient plasma laboratory where the turbulence associated with the supersonic flow can be studied using space experiment data.

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università della Calabria, Arcavacata di Rende, Italy

    Pierluigi Veltri, Vincenzo Carbone, Fabio Lepreti & Giusy Nigro

Authors
  1. Pierluigi Veltri
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  2. Vincenzo Carbone
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  3. Fabio Lepreti
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  4. Giusy Nigro
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Veltri, P., Carbone, V., Lepreti, F., Nigro, G. (2009). Self-Organization in Magnetohydrodynamic Turbulence. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_473

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