19th MHD Days 2024

2 Dec 2024, 14:00 → 4 Dec 2024, 16:00 Europe/Berlin

Lecture Hall, Maria Margaretha Kirch Building (Leibniz Institute for Astrophysics Potsdam (AIP))

The German MHD Days were initiated in Potsdam in 1997 as a forum for theoretical research problems in magnetohydrodynamics, predominantly in astrophysics and geophysics. Since many of the problems are of fundamental nature, links to liquid metal phenomena, turbulence, convection and rotation of fluids have been in the scope of the meeting since.

 

Organizing Committee

 

Rainer Arlt (AIP) Katrin Böhrs (AIP) Oliver Gressel (AIP)

 

Monday, 2 December

19th MHD Days 2024: Monday afternoon session

1 Opening

Speaker: Oliver Gressel (Leibniz Institute for Astrophysics Potsdam (AIP))

2 Interplays between dynamo and magneto-rotational instabilities (invited)

An MHD solution of zero magnetic field can be unstable to the dynamo instability. It plays the perhaps most important role in virtually all of astrophysics! But it requires kinetic energy which can be tapped and converted into magnetic energy. In a rotating body, shear may sometimes be important to produce an excess of toroidal field over poloidal. In the Sun, shear is the result of turbulence, but in accretion discs, a Keplerian shear flow would be stable and would not be turbulent if there was not the magneto-rotational instability. Both dynamo and magneto-rotational instabilities can lead to a doubly-positive feedback to explain the generically magnetic nature of accretion discs. For stars, instabilities akin to the magneto-rotational one have long been applied to the radiative interior, but recently also applications to the turbulent convection zone have been discussed. It might alter the nature of the Omega effect in stellar mean-field dynamos, but this requires mean-field magnetic Reynolds numbers that are perhaps unrealistically large. In my talk, I will end with an assessment of where I believe we stand with regard to the solar dynamo after all these years.

Speaker: Axel Brandenburg (Nordita)

3 Sunspot simulations with potential field initial conditions

There are many observations of sunspots, but few attempts at sunspot simulations. Rempel (2012) presented realistic magneto-hydrodynamic (MHD) sunspot simulations. Jurčák et al. (2020) showed that the magnetic field of such simulations differs from observations; in particular, the $B_\mathrm{ver}$ at the umbral boundary is too low.
Using the MURaM MHD code and a potential field top boundary condition, we simulated a set of sunspots with different box widths and potential initial fields. The fields were defined by setting $B_\mathrm{ver}$ at the bottom boundary to a Gaussian with different parameters and subtracting uniform vertical fields. If the field subtracted is strong enough, this corresponds to embedding the spot into a region with opposite polarity flux.
Initial field strengths at the bottom of less than 160kG result in much too narrow penumbrae. Those extreme field strengths at 7.4Mm beneath the photosphere decay quickly, to below 45kG in the time range we studied. In general, the penumbra-to-spot ratios in potential field simulations are smaller than those of observed sunspots. Simulations with fluxes $>10^{22}\,$Mx in the Gaussian produce unrealistic strong magnetic fields in the umbra. Widening the box and decreasing the overall flux through the box has minimal effect on the dynamics and magnetic field distribution within the spot, but allows control over the average vertical field outside the spot. The potential field simulations do not show a pure Evershed (radially outward) flow. The $B_0=160\,$kG and $F_\mathrm{Gauss}=10^{22}\,$Mx simulations show bi-directional flows: inflows in the inner penumbra and outflows in the outer penumbra, as observed in high-resolution observations of penumbra formation by García-Rivas et al. (2024).
The potential field initialized simulations provide an excellent scenario for the little-investigated processes of penumbra formation.

Speaker: Markus Schmassmann (Institut für Sonnenphysik (KIS), Freiburg, Germany)

4 Solar magnetic tornadoes ignite ambient shock waves: The surprising story of how torsional Alfvén waves can dissipate

Early high-cadence chromospheric image sequences recorded with the recently commissioned Daniel K. Inouye Solar Telescope (DKIST) have revealed propagating arc-shaped bright fronts seen to originate from chromospheric bright grains. Prior to the appearance of the bright fronts, we observe vortical flows in the photosphere located underneath the chromospheric bright grains.
Corresponding image sequences synthesized from realistic three-dimensional magnetohydrodynamic simulations show a striking similarity with the observed phenomenon, and reveal that the arc-shaped structures are weak shock fronts triggered by the vortex dynamics of the underlying magnetic flux concentration. The latter are Alfénic pulses propagating along the small-scale magnetic flux concentrations that root in the photosphere. Here, we propose a serendipitous mechanism by which the torsional Alfvén wave excites a predominantly acoustic weak shock front in the ambient medium, capable of dissipating the torsional Alfvén wave.

Speaker: Oskar Steiner (Kiepenheuer-Institut für Sonnenphysik (KIS))

15:30 Break

5 Harmonically forced and synchronized dynamos

First, we discuss a model of the solar dynamo that explain its various periodicities on widely different time scales in a self-consistent manner. Starting with Rieger-type periodicities, we show that the two-planet spring tides of Venus, Earth and Jupiter are able to excite magneto-Rossby waves in the solar tachocline with periods between 100 and 300 days and amplitudes of m/s or even more. We show that the quadratic action of these waves contains a beat period of 11.07 years, and argue that its axisymmetric part is strong enough to synchronize the entire solar dynamo via parametric resonance. A secondary beat between the arising 22.14-year Hale cycle and the 19.86-year periodic motion of the Sun around the barycentre of the solar system may explain the longer-term Gleissberg and Suess-de Vries cycles. The spectrum emerging from this double-synchronized dynamo model is in remarkable agreement with climate-related data.

In the second part of the talk, we shortly examine the present status of the DRESDYN precession-driven dynamo experiment. We discuss the combined numerical and experimental efforts to identify dynamo-optimizing precession ratios and nutation angles, and illustrate the recent steps in finalizing and commissioning the machine.

Speaker: Frank Stefani (Helmholtz-Zentrum Dresden-Rossendorf)

6 Orbit-Spin Coupling and Variations in the Length of the Hale Cycle

The dynamo problem, in its simplest form, consists of identifying and quantifying material flows which lead to amplification of magnetic fields when inserted into the MHD induction equation [1]. In this connection, we focus on solar meridional flows and flow speeds, which may dictate the timing, amplitude, and shape of magnetic cycles in flux transport dynamo models [2]. While organized large-scale motions of solar materials have been under investigation for more than 40 years, their prognostic utility in dynamo simulations has been problematic, as the observed flow speeds and morphologies vary unpredictably from cycle to cycle. The source of this variability remains an open question. In this presentation, we introduce and briefly discuss a deterministic mechanism for exciting time-varying solar meridional flows that has not yet been incorporated in dynamo models. The orbit-spin coupling hypothesis [3] identifies a reversing torque whose axis lies in the solar equatorial plane. Pulsed intensification and relaxation of meridional flow speeds is predicted under this hypothesis [3, 4]. Global circulation model investigations for the Mars atmosphere, incorporating orbit-spin coupling [4, 5], provide proof of concept for this physics, which has enabled successful years-in-advance forecasting of global-scale weather and climate anomalies [6, 7]. The applicability of the orbit-spin coupling mechanism to the problem of solar dynamo excitation has accordingly become a question of interest. Current best estimates for the amplitude of the depth-dependent tangential orbit-spin coupling accelerations of solar materials exceed by nearly two orders of magnitude the peak accelerations of planetary tides [3, 8, 9]. We compare sunspot numbers with calculated orbit-spin coupling torques in the years 1712-2023. The comparisons yield a surprisingly simple explanation for the variability of Hale cycle period lengths and Schwabe cycle period lengths during this interval [9], if we additionally postulate a magnetic cycle time-delay mechanism associated with meridional flows, as first suggested in [10].

[1] Charbonneau, P., Ann. Rev. Astron. Astrophys. 214.52:251-290.
[2] Dikpati, M., Gilman, P. A., de Toma, G., & Ulrich, R. K. (2010), Geophys. Res. Lett. 37, L14107.
[3] Shirley, J. H. (2017), Plan. Space Sci. 141, 1-16, 10.1016/j.pss.2017.04.006
[4] Mischna, M. A. & Shirley, J. H. (2017), Plan. Space Sci. 141, 45-72, 10.1016/j.pss.2017.04.003
[5] Newman, C. E., et al. (2019), icarus 317, 649-668, https://doi.org/10.1016/j.icarus.2018.07.023
[6] Shirley, J. H., et al. (2020), J. Geophys. Res.-Planets, 125, https://doi.org/10.1029/2019JE006007
[7] Shirley, J. H. (2024), https://www.hou.usra.edu/meetings/tenthmars2024/eposter/3180.pdf
[8] Shirley, J. H. (2017b), arXiv:1706.01854 [Astro-ph.SR], https://doi.org/10.48550/arXiv.1706.01854
[9] Shirley, J. H. (2023), https://arxiv.org/abs/2309.13076
[10] Wilmot-Smith, A.L., et al. (2006), Ap. J. 652, 696-708.

Speaker: James Shirley (Torquefx)

7 Deep cyclic magnetic activity of the Sun by assimilating long-term observed photospheric magnetograms in a 3D dynamo model

Solar magnetic activity is very crucial to understand as it mediates all aspects of space weather. The most successful dynamo model to explain various features of the solar magnetic cycle (e.g., equatorward migration of sunspots and 11-year periodicity) is the Babcock-Leighton Dynamo model. In this dynamo model, we solve kinematic MHD equations by providing the observed mean flows of the Sun to understand various magnetic features including the 11-year solar cycle. However, many turbulent transport parameters inside the convection zone of the Sun are not well constrained observationally but assumed appropriately based on theoretical understanding to reproduce surface observations. In this present work, we assimilate full disc MDI and HMI daily magnetogram data observed from 1996-2024 in the 3D Flux Transport dynamo model to understand the internal dynamics of the magnetic field inside the solar convection zone. As the far side of the Sun is not visible in the magnetogram, we follow a technique where the daily emergence of sunspots near the visible side including diffuse fields are included. The assimilated surface magnetic fields are being transported to the pole by surface meridional circulation and further to the bottom of the convection zone to generate the toroidal field due to differential rotation. We are successfully able to reproduce the observed polar field and polarity reversal due to the realistic decay of surface magnetic fields. We are also able to find the correct polarity of the toroidal field and cycle reversal. The toroidal field strength computed from our model is consistent with the value of flux-emergence simulations for a specific value of turbulent diffusion which allows us to constrain its value in the convection zone. The different cyclic asymmetries including cycle strength are also reproduced. This is the first time a dynamo model is successfully able to reproduce the cyclic activity of a toroidal field deep inside the convection zone from the observed photospheric magnetogram data.

Speaker: Gopal Hazra (IIT Kanpur, India)

8 Evaluating solar-like behavior in extra-long non-kinematic flux-transport solar dynamos

In this study, we simulate 30000 years of solar activity using turbulent-alpha (TA) and Babcock-Leighton (BL) mechanisms in a non-kinematic nonlinear mean field flux-transport solar dynamo model. We evaluate their performances against observational data from proxies, like 14C, and direct solar observations. The TA and BL dynamos generate Schwabe-like variations, with the TA dynamo also generating periods related to the QBOs and the Gleissberg cycle. The TA dynamo spends 13.3% (12.2%) of its time in a grand minimum (maximum) state, closely match the historical solar activity reconstructions from proxy records, while the BL dynamo underperforms. For the TA dynamo, the Schwabe cycle length variations during grand minima and the latitudinal and radial dependencies of the amplitude of variations both in Schwabe and QBO timescales align well with 14C data and solar observations, whereas the BL dynamo fails to reproduce these features.

Speaker: Fadil Inceoglu (University of Colorado Boulder)

Tuesday, 3 December

19th MHD Days 2024: Tuesday morning session

9 Magnetic Fields and Cosmic Ray Electrons (CREs) in Halos of Star Forming Disk Galaxies

Numerical models of the multiphase interstellar medium (ISM) in disk galaxies have recently underlined the importance of cosmic rays (CRs) and magnetic fields for the physics of the ISM. Thus, magnetic fields and CRs are important contributions in order to understand the large scale distribution of the ISM and its evolution. New observational evidence from radio-continuum studies of edge-on galaxies on magnetic field strength and structure will be presented and the cosmic ray propagation in galactic halos will be discussed. Observations from the CHANG- ES (Continuum HAlos in Nearby Galaxies - an EVLA Survey; PI J. Irwin) project benefit from recent LOFAR observations of edge-on galaxies by providing additional constraints on the extent of magnetic fields in galactic halos and on the synchrotron losses of the CREs.

Speaker: Ralf-Juergen Dettmar (Ruhr-Universität Bochum)

10 Zooming-in on radio relics: How density fluctuations explain the Mach number discrepancy, microgauss magnetic fields, and spectral index variations

It is generally accepted that radio relics are the result of synchrotron emission from shock-accelerated electrons. Current models, however, are still unable to explain several aspects of their formation. In this paper, we focus on three outstanding problems: i) Mach number estimates derived from radio data do not agree with those derived from X-ray data, ii) cooling length arguments imply a magnetic field that is at least an order of magnitude larger than the surrounding intracluster medium (ICM), and iii) spectral index variations do not agree with standard cooling models. We use a hybrid approach to solve these problems; first identifying typical shock conditions in cosmological simulations and then using these to inform idealized shock-tube simulations, which can be run with substantially higher resolution. We post-process our simulations with the cosmic ray electron spectra code CREST and the emission code CRAYON+, allowing us to generate mock observables ab-initio. We identify that upon running into an accretion shock, merger shocks generate a dense, shock-compressed sheet, which, in turn, runs into upstream density fluctuations. This mechanism directly gives rise to solutions to the three aforementioned problems: density fluctuations lead to a distribution of Mach numbers forming at the shock-front. This flattens cosmic ray electron spectra, thereby biasing radio-derived Mach number estimates to higher values. We show that such estimates are particularly inaccurate in weaker shocks ($\mathcal{M} \lesssim 2$). Secondly, the density sheet becomes Rayleigh-Taylor unstable at the contact discontinuity, causing turbulence and additional compression downstream. This amplifies the magnetic field from ICM-like conditions up to $\upmu$G levels. We show that synchrotron-based measurements are strongly biased by the tail of the distribution here too. Finally, the same instability also breaks the common assumption that matter is advected at the post-shock velocity downstream, thus invalidating laminar-flow based cooling models.

Speaker: Joseph Whititngham (AIP)

11 Cosmic magnetic fields: A new window to the fundamental physics of the early Universe

Magnetic fields are observed on virtually all astrophysical scales of the modern Universe, from planets and stars to galaxies and galaxy clusters. Observations of blazars suggest that even the intergalactic medium is permeated by magnetic fields. Such large-scale fields were most likely generated very shortly after the Big Bang and therefore are a unique window into the physics of the very early Universe.
In my talk, I will review theoretical models of magnetogenesis and confront these with observational constraints. I will address the possible origin of magnetic fields in the very early Universe, during inflation and the cosmological phase transitions, as well as their pre-recombination evolution in decaying magnetohydrodynamical (MHD) turbulence. Finally, I will present results from high-resolution numerical simulations that show an efficient amplification of magnetic energy due to the so-called chiral anomaly, a standard model effect that necessarily leads to an extension of the MHD equations at high energies.

Speaker: Jennifer Schober (Argelander Institute for Astronomy)

12 Early magnetic field growth in galaxy clusters; the crucial contribution from galaxy formation physics

Observations of Faraday rotation and synchrotron emission suggest galaxy clusters harbor large-scale magnetic fields potentially extending to redshift $z=4$. Non-radiative cosmological simulations show slower magnetic growth, while our MHD simulations with galaxy formation physics reveal accelerated amplification. We identify three key phases: (1) High-redshift magnetization of the proto-cluster by the central galaxy through compressive turbulence and feedback-driven outflows; (2) Enrichment of the intracluster medium as merging galaxies transport amplified fields via ram pressure and winds; and (3) Sustained growth at low redshift as accretion and mergers drive small-scale dynamo action. Initially, this amplification occurs in the collisional interstellar medium during proto-cluster assembly and later in the ICM on the magnetic coherence scale, which exceeds the particle mean free path, validating MHD as a framework for studying the cluster dynamo.

Speaker: Larissa Tevlin (Leibniz Institute for Astrophysics Potsdam)

13 Turbulent plasma flow, its energies and structures: velocity vortices, magnetic field cocoons and plasmoids

Turbulent flows are believed to be present in the solar corona, especially in connection with solar flares and coronal mass ejections. They are supposed to be very effective processes in energy transportation and can contribute to the heating of the solar corona. We study turbulence in reconnection outflows associated with flares and CMEs. We simulate the generation and evolution of the turbulent plasma flow and investigate its energies and formed plasma velocity and magnetic field structures. For the numerical simulations, we adopt a 3D magnetohydrodynamic (MHD) model, in which we solve a full set of the 3D time-dependent resistive and compressible MHD equations using the Lare3d numerical code. We numerically study turbulence in the plasma flow in the model with the plasma parameters that could simulate processes in the magnetic reconnection outflows in solar flares. Starting from a non-turbulent plasma flow in the energetically closed system, we studied the evolution of the kinetic, internal and magnetic energies during the turbulence generation. We found that most of the kinetic energy was transformed into plasma heating (about 95 %) and only a small part of the magnetic energy (about 5 %). The turbulence in the system evolved to the saturation stage with the power-law index of the kinetic density spectrum −5/3. Magnetic energy was also saturated due to its dissipation and reconnection in small and complex magnetic field structures. We show examples of the structures formed in studied turbulent flow: velocity vortices, magnetic field cocoons and plasmoids.

Speaker: Petr Jelínek (University of South Bohemia, Faculty of Science, Department of Physics)

10:40 Break

14 Tayler Instability Revisited

Tayler instability of toroidal magnetic fields is broadly invoked as a trigger for turbulence and angular momentum transport in stars. I will discuss a recent systematic revision of the linear stability analysis. A new physical picture has merged where diffusive processes enable instability by causing the overstability of two classes of waves: inertial waves and magnetostrophic waves. The new instability criteria implemented in the 1d stellar evolution code MESA reveals that the Tayler instability is suppressed in compositionally stratified regions of low mass stars. This suggests that the possible Tayler-Spruit dynamo may not be able to explain efficient core-envelope coupling.

Speaker: Valentin Skoutnev (Columbia University)

15 Stability of toroidal magnetic fields in radiative stellar interiors

The stability of toroidal magnetic fields in radiative stellar interiors is crucial for understanding the rotational and chemical evolution of low-mass stars. This study examines the roles of gravity and thermal conductivity on Tayler instabilities within stably stratified stellar interiors. Although it is often argued that the instability is most effective at very short radial length scales due to a weakened effect of stratification, the destabilizing effects of electric currents, which drive Tayler instability, also decrease with shorter radial scales. Using a linear analysis that is global in the radial and local in the latitudinal direction, we address this limitation by moving beyond traditional fully local or radially local approaches, which often overlook gravity’s role. Our results show that Tayler instability is never entirely suppressed by gravity; instead, gravity primarily slows equatorial growth rates according the scaling law previously found by Bonanno and Urpin (2012) and recently observed in 3D direct numerical simulations, while confining outwards the instability near the axis. This analysis aims to provide a more comprehensive understanding of Tayler instability dynamics in stellar interiors, offering insights into the magnetic processes influencing the cores of red giants.

Speaker: Giovanni Licciardello (INAF OACt)

16 Stability of toroidal magnetic fields in radiative stellar interiors: insights from direct numerical simulations and stellar evolution models

The stability of toroidal magnetic fields in radiative stellar interiors is a key unresolved problem in advancing our understanding of the rotational and chemical evolution of low-mass stars. We perform 3D direct numerical simulations in a spherical geometry to examine the Tayler instability, a kink-type instability of purely toroidal fields expected to occur in stably stratified stellar interiors. The simulations are novel in that they consider a consistent background state derived from magnetohydrostatic equilibrium and explore the combined effect of gravity and thermal diffusion, as well as of fluid viscosity and magnetic resistivity. We trace the entire evolution of the instability from the linear to the nonlinear phase. Our simulations show that stable stratification tames the instability, consistent with findings from a recent global linear stability analysis extending the work of Bonanno & Urpin (2012). Using actual stellar evolution models, our results suggest that toroidal fields in radiative stellar interiors may be only partially affected by Tayler instability. We examine the implications of these findings to better understand the origin of the magnetic fields recently detected in the cores of red giants.

Speaker: Domenico G. Meduri (Leibniz-Institut für Astrophysik Potsdam (AIP))

17 MHD and the Formation of the Magnetic Solar System - A didactically oriented approach

According to current findings, the self-organized creation and development of our solar system took place under the diverse influence of magnetic (e. g. dynamo, reconnection, accretion, acceleration) processes. In the context of magnetohydrodynamics, these will be discussed initially at a glance and exemplarily for protostellar systems (protostars, protostellar/protoplanetary disks and winds as well as protoplanets), then specially for the young solar system itself.

Speaker: Ulrich von Kusserow (AG, DPG)

18 Group photo

12:30 Lunch

19th MHD Days 2024: Tuesday afternoon session

19 Liquid metal MHD flows in the water-cooled lead lithium test blanket module for ITER

Liquid metals such as lead lithium (PbLi) are foreseen in future fusion reactors as coolant, heat transfer medium, and breeder material for generation of tritium, one of the plasma fuel components. The motion of an electrically conducting fluid in the plasma-confining magnetic field gives rise to induced currents and electromagnetic forces that significantly alter the flow behavior compared to hydrodynamic conditions. In the Water-Cooled Lead-Lithium (WCLL) blanket concept, PbLi circulates slowly for tritium removal, while the heat is extracted at cooling pipes immersed in the breeding zone. The liquid metal is distributed and collected among a large number of breeder units by manifolds, and it is expected that those electrically coupled complex components cause the major fraction of magnetohydrodynamic (MHD) pressure drop.

A scaled mock-up of the WCLL test blanket module to be tested in the International Thermonuclear Experimental Reactor (ITER) has been designed and manufactured at KIT. Experiments using NaK as surrogate fluid have been performed in the MEKKA laboratory. Flows investigated for various Reynolds numbers Re and for different Hartmann numbers up to Ha=4000 reveal highest pressure drop contributions in manifolds and, for the present ITER design, an inhomogeneous flow distribution among breeder units that is unfavorable for tritium extraction. Recommendations are made for future design improvement to resolve this issue.

Acknowledgment: This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

Speaker: Leo Bühler (Karlsruhe Institute of Technology)

20 Corner-mode instability of Rayleigh-Bénard convection in a vertical magnetic field

A vertical magnetic field delays the onset of Rayleigh-Bénard convection in a conducting liquid in agreement with Lenz' law. An insulating sidewall impedes the spreading of induced eddy currents, whereby the suppression of convection becomes less effective there. This mechanism causes convection to appear near the walls of the container while it remains suppressed in the bulk. Busse developed an asymptotic theory for the critical Rayleigh number of wall-attached convection near a straight wall using a separation ansatz with sine/cosine-dependence on the vertical coordinate, i.e. free-slip boundary conditions. Busse's model can be extended to the case of a closed rectangular box. A 2d numerical stability analysis shows that the blocking effect of a corner on the currents is more effective than that of a straight wall. The analysis is based on the quasistatic approximation and assumes that the primary instability is non-oscillatory. The results will be compared with those for a straight wall.

Speaker: Thomas Boeck (TU Ilmenau)

21 Convective instabilities in liquid metal duct flow in a fringing magnetic field

In blankets for future fusion reactors, liquid metals have been chosen as breeding material, heat carrier and neutron multiplier. The use of electrically conducting fluids in a magnetic environment comes with the need of investigating their magnetohydrodynamic (MHD) interaction with the imposed magnetic field. The prediction of MHD phenomena for the development of liquid metal blankets requires validated reliable computational tools. With the purpose of obtaining benchmark data, an experimental campaign has been initiated at the Karlsruhe Institute of Technology by using the MaPLE PbLi loop. The latter is equipped with an electromagnet that can provide a magnetic field up to 1.8T and is fitted with a hydraulic system that enables tilting of the magnetic gap between ± 90°. This allows studying flows oriented at any angle with respect to gravity within a horizontal magnetic field.
Recent studies of magneto-convection in simplified geometries showed the occurrence of instabilities with high-amplitude temperature fluctuations that could lead to large thermal stresses in the wall (Zikanov et al. 2019). Moreover, the occurrence of magneto-convection can significantly affect mass (corrosion) and heat transfer in the liquid metal.
In order to improve the understanding of the effect of buoyancy on MHD flows, an experimental test section has been manufactured that features a square electrically and thermally conducting duct in which a part of the lower wall is uniformly heated. The magnetic field along the channel axis is uniform in a central portion of the duct, and it reduces gradually to zero at the entrance and exit of the magnet. With the aim of supporting the design of this experiment, identifying the best location for measurement sensors, and describing the main physical phenomena, 3D numerical simulations are performed for different flow parameters.

Speaker: Chiara Mistrangelo (Karlsruhe Institute of Technology)

22 Two-dimensional Radiative MHD Rayleigh-Bénard Convection in Molten Salts

Rayleigh-Bénard convection [1-2], i.e. heat and momentum transport driven by thermally induced buoyancy force, occurs between two horizontal parallel plates which are heated from the bottom and cooled from the top. It is deemed as a paradigmatic in the study of thermal fluid flow. In the past decades, magnetohydrodynamic RB convection [3] and radiative RB convection [4] have received a great deal of attention. A review paper about RB convection with magnetic field or radiation can be found in [5]. However, few research focus on investigating the combined effects of thermal radiation and magnetic field, namely, radiative magnetohydrodynamic RB convection [6]. Therefore, in present work, we perform numerical simulations to study the heat transfer and fluid motion in a square cavity filled with electrically conducting and radiatively participating molten salts at for under different Hartmann number Ha and Planck number Pl. Here, Ha denotes the ratio of the magnetic force over the viscous force and Pl represent the ratio of the conductive heat flux over the radiative heat flux. The magnetic field is applied from the bottom wall. The flow field and temperature field are obtained by solving Navier-Stokes equations and heat transfer equation using collocation spectral method. As for the radiation field, we adopt discrete ordinate method to solve radiative transfer equation. The numerical results show that, thermal radiation at has little effect on convection in the absence of magnetic field. However, when the magnetic field is involved, it shows an obvious difference between the case with and without radiation. The global convective heat transfer at is lower than that without radiation at a fixed Ha. Besides, we noticed that Pl has positive or negative influence on overall convective heat transfer when and 50, while the positive effect disappears at and 150, indicating the suppression of magnetic field is beyond the improvement of thermal radiation.
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft (467227170), the Natural Science Foundation of China (No. 51976021), and the China Scholarship Council (No. 202206060015).
References
[1] H. Bénard, Annales de Chimie et de Physique, 1901, 23: 62-144.
[2] L. Rayleigh, Philosophical Magazine, 1916, 32: 529-546.
[3] S. Chandrasekhar, New York: Dover publications INC, 1981.
[4] R.M. Goody, Journal of Fluid Mechanics, 1956, 1: 424-435.
[5] J.J. Song, P.X. Li, L. Chen, et al. International Communications in Heat and Mass Transfer, 2023, 144: 106784.
[6] C.G.N. Ketchate, P.T. Kapen, D. Fokwa, et al. Chinese Journal of Physics, 2022, 79: 514-530.

Speaker: Panxin Li (Technische Universität Ilmenau)

23 3D magneto-convective instabilities of liquid metal flow in a generic engineering-relevant model geometry

Magnetohydrodynamic (MHD) convective flows have been well investigated theoretically and experimentally over the past few decades. However, studies on magneto-convection in closed geometries with heat transfer at internal obstacles has found less attention. In this work, we study the convective MHD flow in an engineering-relevant model geometry featuring a long rectangular cavity with a coaxial circular cooling pipe maintained at a constant temperature, with imposed volumetric heating in the fluid, to address this gap in the existing research. Temperature gradients that develop in the liquid metal drive a buoyant motion while Lorentz-forces caused by flow-induced currents oppose the flow. The magneto-convective flow is characterized mainly by a balance between the driving buoyant force, quantified in terms of the nondimensional Grashof number Gr, and the braking Lorentz force expressed by the Hartmann number Ha.

Previous numerical simulations with assumed fully established conditions along the axial direction revealed a magneto-convective motion in transverse planes, where a cold plume “falls down” below the cooling pipe. The present work shows that such flows could become unstable at sufficiently high Grashof numbers. With increasing magnetic field, the present 3D study finds a bifurcation and transition from the formerly 2D state towards complex 3D flow patterns with convection rolls then aligned preferentially with the transverse horizontal magnetic field. This transition from 2D flow pattern to 3D instabilities affects the convective heat transfer in terms of the Nusselt number Nu that is parametrically investigated depending on Gr and Ha.

Key Words: Magnetohydrodynamics (MHD), liquid metal heat transfer, magneto-convection, volumetric heating

Acknowledgment: This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

Speaker: Biao Lyu (Karlsruher Institut für Technologie (KIT))

15:40 Break

24 The Hall Effect in Neutron Stars

Neutron stars have the strongest magnetic fields in the universe, with fields up to 10^15 G in so-called magnetars. At such field strengths the classical Hall effect becomes one of the dominant effects governing the evolution of the magnetic fields. One interesting aspect of the Hall effect is that it depends on the sign of the field, unlike virtually all of classical MHD, where the sign of B is not important. Another interesting feature -- which also makes the problem numerically challenging -- is the fact that the nonlinear Hall term has just as many derivatives as the linear Ohmic decay term, meaning that there is no guarantee that any dissipative cutoff regime exists at all.

In this talk I will summarise over a decade's worth of numerical work -- starting with a collaboration with Günther Rüdiger in 2002 -- exploring some of these issues in Hall MHD, and comparing results also with real neutron stars. I will also show how the basic Hall MHD can be extended to include a temperature equation as well, with the evolution of magnetic field B and temperature T coupled together.

Speaker: Rainer Hollerbach (University of Leeds)

25 Dynamo action in a precessing cylinder.

A magnetohydrodynamic dynamo process is believed to occur in the
interior of the Sun or stars as well as in planets and smaller
celestial bodies like the ancient Moon or the asteroid Vesta,
motivating similar studies in laboratory settings. Currently, a new
dynamo experiment is under construction at Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), in which liquid sodium will be forced by a
precessing cylindrical container.

In the present study, we conduct related numerical simulations of
precession-driven dynamo action in order to examine the interaction
between flow and field and the associated transfer of kinetic energy
into magnetic energy. We compare self-consistent simulations of the
complete set of magnetohydrodynamic equations with a simplified
kinematic approach solely based on the magnetic induction equation
with a prescribed velocity field. In both cases, we observe an
optimal parameter range for the onset of dynamo action in the
transitional regime in which the flow undergoes a radical change from
a large-scale to a smaller-scale turbulent behavior. The behavior is
in agreement with previous results by R. Gans from the 1970s, obtained
at a similar but much smaller experiment, which yields a threefold
amplification of an external magnetic field at the transition from a
laminar flow state to vigorous turbulence.

The various kinematic models reveal a strong influence of the
electromagnetic properties of outer layers resembling container walls
and/or the outer laboratory area and go along with an existence of two
different branches of dynamo action. In contrast to the kinematic
solution, the character of the dynamo is small-scale in the MHD
models, which exhibit irregular magnetic bursts with an increase in
the magnetic energy by a factor of 3 to 5 but still remaining
significantly lower than the kinetic energy. As the magnetic field is
small-scale and weak, the nonlinear feedback on the flow through the
Lorentz force remains small and arises essentially in terms of a
slight damping of the fast time-scales.

Speaker: Andre Giesecke (HZDR)

26 Nonlinear flow transition in a precessing cylinder and its potential for hydromagnetic dynamo action at the DRESDYN facility

We carried out ultrasonic Doppler and power consumption measurements in a 1:6 downscaled water experiment to analyze the potential for dynamo action in a precession driven sodium experiment [1]. The experiments are embedded in the DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) project devoted to a better understanding of the homogeneous dynamo effect in planets and stars.

First of all a non-axisymmetric Kelvin mode is growing with rising precession ratio, which alone is not suitable for dynamo action in the experiment. In a narrow region of the precession ratio a secondary axisymmetric mode arises. For even higher precession ratios, a strong shear appears at the outer rim of the cylinder and the flow in the bulk becomes completely turbulent. The appearance of the secondary axisymmetric mode promises dynamo action within the sodium experiment under construction [2].

The downscaled water experiment was operated in a wide range from Re=10000 to 1.610*6, showing a very good agreement with direct numerical simulations at their upper limit of Re=10000.

Furthermore, we give an overview of the present state and the commissioning of the DRESDYN facility which is still in progress.

Speaker: Thomas Gundrum (Helmholtz-Zentrum Dresden-Rossendorf)

27 Characterizing dynamo coefficients in accretion disk turbulence

Astrophysical outflows are seen in objects ranging from compact binaries up to active galactic nuclei, and magnetized accretion disks are the central engines behind these phenomena. Disk turbulence has a profound effect on the evolution of the large-scale magnetic field and hence on the ability of the system to power its outflows. We aim to characterize the turbulence coefficients emerging in local simulations of accretion disk turbulence. We have generalized our diagnostics to the case of novel non-local and non-instantaneous closure relations, accounting for and extended “domain of dependence” in space, and “memory effects” in time. In concrete terms, we obtain Fourier spectra of the effective turbulent transport coefficients as a function of oscillation frequency. These are well approximated by a simple response function, describing a finite-time build-up of the electromotive force (EMF) as a result of a time-variable mean magnetic field. For intermediate timescales, we observe a significant phase lag of the EMF compared to the causing field.

Speaker: Oliver Gressel (Leibniz Institute for Astrophysics Potsdam (AIP))

28 Global R-MHD simulations of Transition Disks

Transition disks (TDs) are a type of protoplanetary disk characterized by an inner dust and gas cavity. The processes behind how these cavities are formed and maintained, along with the observed high accretion rates, continue to be subjects of active research. In our work, we aim to investigate if and how the inclusion of the Hall Effect alongside Ohmic Resistivity and Ambipolar Diffusion affects the TD. Of key interest is the behavior of the cavity and whether we can produce transonic accretion, as is predicted from observations. We performed 2D axisymmetric global R-MHD simulations of TD, with all three non ideal MHD effects and the inclusion of a PDR (photon dominated regime) module which provides a more realistic temperature structure in the disk. We use the Nirvana fluid code and have imposed a disk cavity in our disk. In total we performed three runs, for each configuration of the Hall effect: Hall aligned, Hall anti-aligned and Hall free. We find that for all three runs, our models reach a semi-steady state with an intact inner cavity and an outer standard disk. MHD winds are launched both from the cavity and from the disk. We get accretion rates typical of full disks and we observe (trans)sonic accretion in the cavity. Additionally, outward magnetic flux transport occurs in all three runs. Notably, when the Hall Effect is included, ring-like structures form within the cavity.

Speaker: Eleftheria Sarafidou (Leibniz Institute for Astrophysics Potsdam)

19:00 Dinner at Piazza Toscana (not covered by conference fee)

Wednesday, 4 December

19th MHD Days 2024: Wednesday morning session

29 Model reduction for MHD turbulence

The numerical representation of fully developed high-Reynolds-
number turbulence, particularly in the magnetohydrodynamic approximation,
represents a formidable challenge. We report on an interesting modelling
approach employing a network-based representation that shares fundamental
characteristics with port-Hamiltonian structures known from model reduction.
We show that this technique is able to reproduce the basic but non-
trivial statistical properties of turbulence. This framework exhibits the
logarithmic scaling of classical shell-models without their strong constraints
regarding e.g. dimensionality or isotropy of the underlying physical system.
The model furthermore allows to study the nonlinear dynamics of turbulence on a fundamental level.

Speaker: Wolf-Christian Müller (Technische Universität Berlin)

30 Exact Nonlinear Decomposition of Ideal-MHD Waves Using Eigenenergies

We introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfvén, and fast wave eigenmodes, and the entropy and field-divergence pseudoeigenmodes. First, the mathematical formalism is introduced, where it is illustrated how the ideal-MHD eigensystem can be used to construct a decomposition of the time variation of the total energy density into contributions from the eigenmodes. The decomposition method is then demonstrated by applying it to the output of three separate nonlinear MHD simulations. The analysis of the simulations confirms that the component wave modes of a composite wavefield are uniquely identified by the method. The slow, Alfvén, and fast energy densities are shown to evolve in exactly the way expected from comparison with known linear solutions and nonlinear properties, including processes such as mode conversion. Along the way, some potential pitfalls for the numerical implementation of the decomposition method are identified and discussed. We conclude that the exact, nonlinear decomposition method introduced is a powerful and promising tool for understanding the nature of the decomposition of MHD waves as well as analyzing and interpreting the output of dynamic MHD simulations.

Speaker: Abbas Raboonik (University of Newcastle)

31 As a matter of dynamical range – scale-dependent energy dynamics in magnetized turbulence and pushing simulation limits

Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even in the simplest plasma approximation, magnetohydrodynamics (MHD), the detailed energy dynamics are still not well understood. In this talk, I present a suite of idealized MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales. From a practical point of view, I show how numerical dissipation can be estimated using an energy transfer analysis framework and that implicit large eddy simulations match direct numerical simulations. From a theoretical point of view, I use the same framework to demonstrate that – contrary to hydrodynamic turbulence – the cross-scale energy fluxes are not constant in MHD turbulence. This applies both to different mediators (such as energy cascade processes) for a given dynamical range as well as to a dependence on the dynamical range itself. Moreover, there exists no indication of convergence even at the highest resolution simulation at $2048^3$ cells. This raises the question on whether an asymptotic regime in MHD turbulence exists, and, if yes, what it looks like. Finally, to tackle this question in the future I introduce Parthenon (a performance portable adaptive mesh refinement framework to solve partial differential equations) and AthenaPK (the MHD application code on top), which recently reached 92% weak scaling parallel efficiency on 73,728 GPUs on Frontier (the first TOP500 exascale supercomputer).

Speaker: Philipp Grete (University of Hamburg)

32 Solving plasma problems using adaptive multiphysics coupling.

Astrophysical systems, such as the solar atmosphere, can be modeled using various plasma descriptions. Magnetohydrodynamics (MHD) offers a less computationally expensive approach but may fail to capture small-scale phenomena, like magnetic reconnection, that require more sophisticated kinetic models. Since the regions requiring complex models are often much smaller than the rest of the domain, a coupled multiphysics approach can significantly reduce computational cost while maintaining the necessary level of realism.

In this work, we present an easy to use simulation framework implemented in Trixi.jl that can be used to adaptively couple different plasma models within a single domain. Our method is highly flexible, allowing for the coupling of diverse systems, such as a Vlasov model with an MHD model. This approach enables more accurate and efficient simulations of complex astrophysical phenomena. In this talk I will present a test case where we couple an MHD system with an Euler system.

Speaker: Simon Candelaresi (University of Augsburg)

33 Spatio-temporal correlation in three-dimensional incompressible MHD turbulence

Plasma turbulence is a widespread phenomenon that is important in many astrophysical systems. It can be described as the superposition of Alfvén wave packets on various scales in space and time, which interact with each other non-linearly, giving rise to the direct energy cascade in 3D incompressible MHD turbulence. We study the temporal and spatial properties of the energy transfer process by computing the spatio-temporal correlation between fluctuations of the Elsässer fields. To this end, direct numerical simulations are performed, in which the fluctuations are measured in the directions parallel and perpendicular to the local magnetic field. This is done in the co-moving Quasi-Lagrangian reference frame to minimize the large-scale sweeping effect.

The single-time correlation between parallel and perpendicular fluctuations allows the measurement of spatial properties such as the elongation of the turbulent structures. The multi-time correlation, on the other hand, gives insight into the time scales involved in the cross-scale energy transfer and the propagation of Alfvén waves. First results for both are presented and compared to predictions made by phenomenological models of MHD turbulence.

Speaker: Raquel Mäusle (Technische Universität Berlin)

10:40 Break

34 tbd.

35 Capturing and modeling the launching of a jet around a forming massive star

During their early formation stages, massive stars are surrounded by accretion disks and launch powerful magnetically-driven jets and molecular outflows. Observing the innermost (embedded) material surrounding a forming massive star has only been possible recently, thanks to the use of techniques like very-long-baseline interferometry (VLBI). In this contribution, I will present a new generation of non-ideal magnetohydrodynamical simulations of the formation of a massive star starting from the collapse of a molecular cloud, and including radiation transport, Ohmic dissipation and self-gravity. I will discuss how the simulations show the magnetic field and rotation self-consistently launching protostellar outflows: a fast jet (> 100 km/s) and a magnetic tower flow (~10 km/s). Finally, I will show the how the agreement between our simulations and a new generation of VLBI water maser observations in the star-forming region IRAS 21078+5211 has allowed us to confirm with unprecedented detail that protostellar outflows are launched as MHD disk winds. I will also briefly discuss about the role of MHD jets in removing angular momentum from the disk and the forming star. This contribution is based on the following articles: Oliva & Kuiper 2023 (A&A, 669, A81), and Moscadelli et al. (2022, Nature Astron., 6, 1068).

Speaker: André Oliva (University of Duisburg-Essen)

36 Non-ideal MHD processes in astrophysical jets

Accretion disks and astrophysical jets are typically found in several sources, e.g., young stellar objects, X-ray binaries, gamma-ray bursts, or active galactic nuclei. The origin and impact of a large-scale magnetic field on the dynamical and radiative features of disks and jets is still unclear. First, I will briefly discuss dynamo processes within thin accretion disks, able to amplify the magnetic field up to the point where jet launching becomes possible, focusing on how to build a more consistent dynamo and diffusivity model. Then I will present the first numerical simulations of resistive relativistic jets and the role of magnetic reconnection and dissipation in the large-scale simulations, focusing on short gamma-ray-burst jets. Such simulations investigate different values and models for the plasma resistivity coefficient, assessing their impact on the level of turbulence, the formation of current sheets and reconnection plasmoids, and the electromagnetic energy content.

Speaker: Giancarlo Mattia (Max Planck Institute for Astronomy)

37 Impact of magnetically-driven jets and radiative feedback on the formation of massive stars

Stellar feedback shapes its environment from its local cloud to his own hosting galaxy. It combines several physical processes, such as the formation of magnetically-driven jets, irradiation and photoionization which restrain its growth and final mass. In this work, we include the MHD jet contribution self-consistently while adding radiative forces and photoionization. Our goal is to understand the role that different stellar feedback effects have on the outcome of the formation process while observing the physical mechanisms governing the disk and the low-density cavity.

To achieve this, we utilize the state-of-the-art code PLUTO, which solves the equations of non-ideal magnetohydrodynamics, with the addition of specialized modules for self-gravity, radiation transport and photoionization. These simulations start from the gravitational collapse of a molecular cloud of 100 $M_\odot$ and radius of 0.1 pc with different stellar feedback effects switched on, followed by the formation of an accretion disk and the magnetically-driven jets. The radiative feedback effects are driven according to the stellar evolution tracks by Hosokawa & Omukai (2009). These simulations were stopped when accretion becomes negligible or the disk is destroyed by radiative feedback.

Magnetically-driven outflows alone limit the stellar growth at early times, while radiation and photoionization become dominant at later times, when the star has reached the zero-age sequence. We observe that radiation forces restrain gravitational infall toward the disk, affect its gravito-centrifugal equilibrium, increase the outflow and completely halt accretion, resulting in an approximately 45 $M_\odot$ star after around 100 kyr of evolution. While photoionization shapes the bipolar outflow cavity, its addition did not significantly alter the final mass of the star. In contrast, in simulations without irradiation forces, accretion continues and the star reaches a mass of around 75 $M_\odot$.

Speaker: Joshua Barquero Alvarado (University of Duisburg-Essen)

38 Closing

Speaker: Rainer Arlt (AIP)

12:30 Lunch