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Publication# Shedding light on the MRI-driven dynamo in a stratified shearing box

Abstract

We study the magneto-rotational instability (MRI) dynamo in a geometrically thin disc (H/R < 1) using stratified zero net (vertical) flux shearing box simulations. We find that mean fields and electromotive forces (EMFs) oscillate with a primary frequency f(dyn )= 0.017 Omega (approximately nine orbital period), but also have higher harmonics at 3f(dyn). Correspondingly, the current helicity has two frequencies 2f(dyn) and 4f(dyn), which appear to be the beat frequencies of mean fields and EMFs, respectively, as expected from the magnetic helicity density evolution equation. Further, we adopt a novel inversion algorithm called the 'Iterative Removal Of Sources', to extract the turbulent dynamo coefficients in the mean-field closure using the mean magnetic fields and EMFs obtained from the shearing box simulation. We show that an alpha-effect (alpha(yy)) is predominantly responsible for the creation of the poloidal field from the toroidal field, while shear generates back a toroidal field from the poloidal field, indicating that an alpha-Omega-type dynamo is operative in MRI-driven accretion discs. We also find that both strong outflow (v(z)) and turbulent pumping (gamma(z)) transport mean fields away from the mid-plane. Instead of turbulent diffusivity, they are the principal sink terms in the mean magnetic energy evolution equation. We find encouraging evidence that a generative helicity flux is responsible for the effective alpha-effect. Finally, we point out potential limitations of horizontal (x - y) averaging in defining the 'mean' on the extraction of dynamo coefficients and their physical interpretations.

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Magnetic helicity

In plasma physics, magnetic helicity is a measure of the linkage, twist, and writhe of a magnetic field. In ideal magnetohydrodynamics, magnetic helicity is conserved. When a magnetic field contains magnetic helicity, it tends to form large-scale structures from small-scale ones. This process can be referred to as an inverse transfer in Fourier space. This second property makes magnetic helicity special: three-dimensional turbulent flows tend to "destroy" structure, in the sense that large-scale vortices break up into smaller and smaller ones (a process called "direct energy cascade", described by Lewis Fry Richardson and Andrey Nikolaevich Kolmogorov).

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Magnetic reconnection is a physical process occurring in electrically conducting plasmas, in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection involves plasma flows at a substantial fraction of the Alfvén wave speed, which is the fundamental speed for mechanical information flow in a magnetized plasma. The concept of magnetic reconnection was developed in parallel by researchers working in solar physics and in the interaction between the solar wind and magnetized planets.

Toroidal and poloidal coordinates

The terms toroidal and poloidal refer to directions relative to a torus of reference. They describe a three-dimensional coordinate system in which the poloidal direction follows a small circular ring around the surface, while the toroidal direction follows a large circular ring around the torus, encircling the central void. The earliest use of these terms cited by the Oxford English Dictionary is by Walter M.

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