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Universal nonlinear small-scale dynamo.

¹Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.

Physical Review Letters

|March 10, 2012

Summary

Magnetic energy in astrophysical simulations grows at a constant fraction of turbulent dissipation. This small-scale dynamo efficiency, measured at around 0.05, is constant for high Reynolds numbers.

Area of Science:

Astrophysics
Plasma Physics
Fluid Dynamics

Background:

Nonlinear magnetohydrodynamics (MHD) describes the behavior of electrically conducting fluids, crucial for understanding astrophysical phenomena like stellar magnetic fields.
The small-scale dynamo is a process that generates magnetic fields in turbulent flows at small scales.
Understanding the efficiency of dynamo action is key to explaining the origin and evolution of cosmic magnetic fields.

Purpose of the Study:

To investigate the universality and efficiency of the nonlinear MHD dynamo at high Reynolds numbers.
To quantify the fraction of turbulent dissipation converted into magnetic energy.
To determine if this efficiency is a universal constant for large Reynolds numbers.

Main Methods:

Theoretical analysis using locality bounds.

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Numerical simulations of MHD turbulence at large Reynolds numbers.

Measurement of the magnetic energy growth rate relative to turbulent dissipation.

Main Results:

The magnetic energy growth rate is a constant fraction, C(E), of the total turbulent dissipation rate.
This efficiency C(E) appears to be a true constant for large Reynolds numbers.
Numerical simulations indicate C(E) is approximately 0.05 at the highest resolutions.

Conclusions:

The small-scale dynamo in astrophysical contexts is universal, with a constant efficiency C(E).
This efficiency is determined by nonlinear dynamics at the equipartition scale.
The observed small value of C(E) (around 0.05) is a significant finding, contrasting with the Kolmogorov constant.