Magnetic dynamo action at low magnetic Prandtl numbers

Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.

💡 Research Summary

The paper investigates the kinematic turbulent dynamo in the regime of very low magnetic Prandtl number (Pm = ν/η ≪ 1), a condition that characterises the interiors of planets and stars as well as liquid‑metal laboratory experiments. Using the Kazantsev‑Kraichnan framework, the authors extend the classic Kazantsev model by incorporating kinetic helicity into the velocity correlation tensor. The velocity field is taken as a statistically homogeneous, isotropic, Gaussian white‑in‑time process with a prescribed energy spectrum E(k) that follows Kolmogorov scaling (k⁻⁵ᐟ³) in the inertial range. Helicity is introduced through a helicity spectrum H(k), and the dimensionless helicity parameter σ(k)=H(k)/