On the role of magnetic fluctuations in low magnetic Prandtl number plasmas

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• Maarit Korpi-Lagg [Helsinki/Espoo]
• Monday 12 May 2025, 14:00-15:00
• MR14 DAMTP and online.

If you have a question about this talk, please contact Mattias Brynjell-Rahkola.

Magnetic fields on small scales are ubiquitous in the universe. For example, the fluctuating magnetic fields in star-forming regions of galaxies are more than twice the strength of the magnetic fields coherent over large scales. On the solar surface, magnetic fields are mostly concentrated in medium and small-scale structures, while the proportion comprising the mean field strength is even lower than in galaxies. The generation mechanisms of the fluctuating magnetic fields are not fully understood. One possibility is the so-called small-scale dynamo (SSD), the other is tangling of the large-scale field structures through turbulence acting on them. In the interstellar medium of galaxies, the resistivity is much lower than the viscosity, such that magnetic instabilities are easier to excite relative to the turbulence. SSD in such high magnetic Prandtl number (Pm, i.e. the ratio between viscosity and resistivity) conditions has therefore been predicted to be easily excited. In the Sun and cool stars, Pm is much lower, namely in the range of 1e-6 to 1e-3. Both theoretically and especially numerically, SSD is more difficult to excite at such very low magnetic Prandtl numbers. Indeed, some recent numerical studies has indicated that the threshold for SSD excitation should systematically increase with decreasing Pm, concluding that SSD would be impossible in the Sun and cool stars.

Accelerating the magnetohydrodynamics solvers with graphics processing units has recently opened an avenue to numerically study low-Pm flows. With these tools we have been able to perform simulations that approach the solar Pm-values, studying both kinematic and non-linear regimes. Contrary to earlier findings, the SSD turns out not only to be possible for Pms down to 0.0031, but even to become increasingly easy to excite for Pm below approximately 0.05. We relate this behaviour to the known hydrodynamic phenomenon, referred to as the bottleneck effect. Extrapolating our results to solar values of Pm indicates that an SSD would be possible under such conditions. The saturation strength of the SSD is of the order of the turbulent kinetic energy independent of the Pm, when the magnetic Reynolds number (Rm) is moderate (up to a few thousands). For higher Rm the saturation strength rapidly diminishes and reaches levels of order of magnitude lower than turbulent kinetic energy, casting a new doubt of the SSD being important in the Sun and stars. Even higher resolution studies, however, would be required to verify this robustly. For such calculations, however, extraordinary resources/quantum computers are required.

This talk is part of the DAMTP Astrophysics Seminars series.

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