Critical magnetic Prandtl number for small-scale dynamo

Area of Science:

• Astrophysics
• Geophysics
• Plasma Physics

Background:

• Small-scale dynamos are crucial for generating magnetic fields in various astrophysical and geophysical contexts.
• Understanding the conditions for dynamo operation is essential for explaining cosmic magnetic fields.

Purpose of the Study:

• To investigate the dependence of the critical magnetic Reynolds number (Rm(c)) for nonhelical small-scale dynamos on the Reynolds number (Re).
• To determine the influence of the magnetic Prandtl number (Pr(m)) on dynamo suppression.
• To explore the existence of finite critical values for Pr(m) and Rm(c) in the limit of infinite Re.

Main Methods:

• Numerical simulations were employed to explore the parameter space of the small-scale dynamo.
• The study systematically varied the magnetic Reynolds number (Rm) and the Reynolds number (Re).
• The magnetic Prandtl number (Pr(m) = Rm/Re) was analyzed in relation to dynamo onset and suppression.

Main Results:

• The critical magnetic Reynolds number (Rm(c)) for nonhelical small-scale dynamos is shown to be dependent on the Reynolds number (Re).
• A critical magnetic Prandtl number (Pr(m,c) < 1) was identified, below which dynamo action is suppressed, even for sufficiently large Rm.
• Two scenarios for the limit of Re → ∞ were proposed: a finite Pr(m,c) or Pr(m,c) → 0 with Rm(c) approaching a large constant.
• If Pr(m,c) is finite, dynamo sustainability requires magnetic field existence at sub-flow scales, effectively becoming a large-Pr(m) dynamo.
• A lower bound of Rm(c) ≈ 220 was established for Pr(m) ≤ 1/8, exceeding values in planets and liquid-metal experiments.

Conclusions:

• The onset and sustainability of small-scale dynamos are sensitive to the interplay between Re and Pr(m).
• Dynamo suppression at low Pr(m) suggests that certain astrophysical and geophysical environments may not sustain small-scale dynamos.
• The findings provide crucial insights into the fundamental physics of magnetic field generation and have implications for planetary magnetism and laboratory experiments.