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Laboratory Experiments on Magnetic Phenomena in Geo- and Astrophysics

Periodic Reporting for period 4 - LEMAP (Laboratory Experiments on Magnetic Phenomena in Geo- and Astrophysics)

Reporting period: 2023-05-01 to 2023-10-31

How is the geodynamo powered, what drove the ancient lunar dynamo? How do central objects, like protostars or supermassive black holes in the centres of galaxies, form from the gas discs surrounding them? For which disk parameters does the magnetorotational instability (MRI) enable angular momentum transport and allow for mass accretion, and where does the destabilizing field actually come from? Are there non-linear dynamos in accretion disks in which MRI and dynamo effect bootstrap each other? And, closely related to this: is the solar magnetic field really produced by a classical flux-transport dynamo, or is it also non-linear from the very outset, as proposed in the Tayler-Spruit dynamo model? Why is the butterfly diagram of sun-spots restricted to the equator-near strip around the solar equator, where the angular velocity at the tachocline just increases outward? Is that region indeed as stable as it has long been thought
to be?

The goal of the project was to gain a deeper insight into those questions related to generation and action of cosmic magnetic fields. A particular focus of the project laid on preparing and performing paradigmatic liquid-metal experiments related to both fundamental effects of geo- and astrophysical magnetohydrodynamics.

On the dynamo side, our main interest was dedicated to the question of whether precession driven flows can be considered as complementary power sources of the dynamos of the Earth, the ancient Moon, and other cosmic bodies. Our massive numerical simulations and comprehensive experiments in cylindrical geometry have lead to the identification of optimal dynamo conditions in terms of precession ratio and nutation angle.

Generalizing this concept to other astronomical forcings, like tides or libration, we have established a realistic model of planetary synchronization of the solar dynamo which seems particularly suited to explain short-, medium- and long-term cycles of the solar magnetic field in a self-consistent manner. Again, this theoretical model was underpinned by a liquid-metal experiment revealing how the helicity of a convection-driven flow (which is a key dynamo ingredient) can be synchronized by tide-like forces.

On the MRI-side, we have carried out fundamental liquid-metal experiments in a spherical shell under the influence of an axial magnetic field. Their main goal was to assess the validity of previous claims that MRI had been found in this geometry. In good agreement with theoretical predictions we were able to identify the observed patterns as the radial-jet and return-flow instabilities. Meticulous numerical simulations allowed to study these instabilities in more detail and to predict modulated waves, three- and four-torus solutions, and the transition to chaos.

An interesting outcome of our MRI-experiments in cylindrical geometry was the first characterization of the influence of convection on the MRI-wave, inducing a symmetry breaking between upward or downward traveling waves for positive or negative radial temperature gradients. This first-of-a-kind experiment on the combined action of azimuthal MRI and convection may open up new avenues for understanding similar combinations in accretion disks and stellar interiors. For the case of standard MRI, we have explained the saturation mechanism in terms of magnetic reconnection and found self-consistent scaling laws for the magnetic energy and the angular momentum transport. With the quite unexpected discovery of "Super-HMRI" we have overthrown the long-held belief that positive-shear flows, such as in the near-equator regions of the solar tachocline, are not susceptible to MRI.
As for the precession-driven dynamo, the combination of massive numerical simulations and laboratory experiments has lead to a clear identification of those precession ratios and nutation angles that are optimal for dynamo action [1].

Our work on the of tidal synchronization of the solar dynamo has regularly received a lot of public attention. The paper [2], in which we set-up a self-cosinstent model of the Schwabe cylce and the Suess-de Vries and Gleissberg cycles, has reached an Altmetric attention score of 232.

Among the numerous results on instabilities in a magnetised spherical Couette flow, the identificion of a four-frequency solutions was one of the most surprising ones [3]. It showed that in a system with symmetry, more symmetry breaking bifurcations may be required in the Ruelle-Takens scenario until a flow can become chaotic.

The rather unexpcted finding of Super-HMRI [3], i.e. the magnetic destabilization of positive-shear flows that were deemed insusceptible to MRI for over six decades, received an Altmetric attention score of 93. Its consequences for the stability of the near-equator parts of the solar tachocline are still to be elaborated.

Alfvén waves, which present a fundamental paradigm of magnetohydrodynamics, had been studied in liquid metal and plasma experiments for over seven decades. Our liquid-rubidium experiment [5], carried out at the Dresden High Magnetic Field Laboratory, has opened up a very new perspective in this field by reaching, for the very forst time, the "magic" point at which the Alfvén speed becomes equal to the sound speed. The observed parametric resonance between these two waves might be an essential mechanism for heating up the solar corona. The paper received an Altmetric attention score of 268.

[1] V. Kumar et al., Phys. Fluids 35, 014114 (2023)

[2] F. Stefani, R. Stepanov, T. Weier, Solar Phys. 296, 88 (2021)

[3] F. Garcia et al., Phys. Rev. Lett. 125, 264501 (2020)

[4] G. Mamatsashvili et al., Phys. Rev. Fluids 4, 103905 (2019)

[5] F. Stefani et al, Phys. Rev. Lett. 127, 275001 (2021)
The DRESDYN precession driven dynamo experiment: some impressions from the construction