Saturation of Turbulent Helical Dynamos

Area of Science:

• Plasma Physics
• Astrophysics
• Fluid Dynamics

Background:

• Large-scale magnetic fields are often explained by turbulent helical dynamos and the inverse cascade of magnetic helicity.
• Understanding the limitations of this inverse cascade is crucial for accurate astrophysical dynamo modeling.

Purpose of the Study:

• To investigate the bounds on the inverse flux of magnetic helicity in turbulent helical dynamos.
• To determine the scaling of this inverse flux with the magnetic Reynolds number (Rm).
• To establish bounds on the saturation value of magnetic energy in these systems.

Main Methods:

• Theoretical analysis of turbulent helical dynamos.
• Direct numerical simulations of turbulent dynamos forced at intermediate scales.
• Analysis of magnetic helicity flux and magnetic energy saturation.

Main Results:

• The inverse flux of magnetic helicity (Π_{H}) is bounded by |Π_{H}|≤cεk_{η}^{-1}.
• The inverse flux scales as |Π_{H}|≤cεℓ_{f}Rm^{-3/4}max[Pm,1]^{1/4} with the magnetic Reynolds number.
• Magnetic energy saturation is bounded by E_{m}≤cL(εℓ_{f})^{2/3}Rm^{1/4}max[1,Pm]^{1/4}.

Conclusions:

• Inviscid mechanisms alone cannot account for large-scale magnetic fields.
• The findings provide critical constraints for modeling astrophysical dynamos.
• The derived bounds are independent of the specific dynamo mechanism.