Emergence of magnetic structure in supersonic isothermal magnetohydrodynamic turbulence

The inverse transfer of magnetic helicity is a fundamental process which may explain large scale magnetic structure formation and sustainement. Until very recently, direct numerical simulations (DNS) of the inverse transfer in magnetohydrodynamics (MHD) turbulence have been done in incompressible MHD or at low Mach numbers only. We review first results obtained through DNS of the isothermal MHD equations at Mach numbers ranging from subsonic to about 10. The spectral exponent of the magnetic helicity spectrum becomes flatter with increasing compressibility. When considering the Alfv\'en velocity in place of the magnetic field however, results found in incompressible MHD, including a dynamic balance between shear and twist, can be extended to supersonic MHD. In the global picture of an inverse transfer of magnetic helicity, three phenomena are at work: a local direct transfer mediated by the large scale velocity field, a local inverse transfer mediated by the intermediate scale velocity field and a nonlocal inverse transfer mediated by the small scale velocity field. The compressive part of the velocity field is geometrically favored in the local direct transfer and contributes to the nonlocal inverse transfer, but plays no role in the local inverse transfer.Comment: Chapter in Helicities in Geophysics, Astrophysics and Beyond (AGU Books, Wiley, 2023 or 2024

Inverse transfer of magnetic helicity in supersonic magnetohydrodynamic turbulence

The inverse transfer of magnetic helicity is studied through a fourth-order finite volume numerical scheme in the framework of compressible ideal magnetohydrodynamics (MHD), with an isothermal equation of state. Using either a purely solenoidal or purely compressive mechanical driving, a hydrodynamic turbulent steady-state is reached, to which small-scale magnetic helical fluctuations are injected. The steady-state root mean squared Mach numbers considered range from 0.1 to about 11. In all cases, a growth of magnetic structures is observed. While the measured magnetic helicity spectral scaling exponents are similar to the one measured in the incompressible case for the solenoidally-driven runs, significant deviations are observed even at relatively low Mach numbers when using a compressive driving. A tendency towards equipartition between the magnetic and kinetic fields in terms of energy and helicity is noted. The joint use of the helical decomposition in the framework of shell-to-shell transfer analysis reveals the presence of three distinct features in the global picture of a magnetic helicity inverse transfer. Those are individually associated with specific scale ranges of the advecting velocity field and commensurate helical contributions

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Implementing a numerical model for investigating topologically driven magnetic reconnection

Magnetic reconnection is an omnipresent phenomenon in plasma physics, and its understanding is therefore of major importance. Most of the models of magnetic reconnection existing nowadays are two-dimensional in space, or require at least a dependence of the magnetic field on two coordinates instead of all three. Relatively recently, three-dimensional reconnection models have begun to appear. In a recent model of three-dimensional reconnection, the process is triggered as soon as the topology of the magnetic field reaches a complexity threshold. It is suggested that at this point even an exponentionally small non-ideality in the magnetic field evolution can trigger magnetic reconnection, at way lower currents than expected in two-dimensional models. This master thesis work presents main ideas of this model and a pseudospectral numerical approach to test its predictions. A pseudospectral approach was chosen due to its high numerical precision. To simplify the verification of this model, non-periodic boundary conditions are necessary along one spatial direction. As pseudospectral approaches are mostly used with full-periodic boundary conditions, analytical work is necessary in order to find relevant boundary conditions and a way to implement them using a pseudospectral approach. In addition to the model and the underlying physics, this report presents how the use of a pseudospectral approach can be maintained with proper boundary conditions and shows first encouraging outputs of the numerical code. The numerical code, as it is today, can bring the plasma topology to a maximum number of exponentiations of about 5 (this number characterizes the topological complexity of the magnetic field). Still unresolved numerical issues prevent the code to bring the number of exponentiations to a value high enough to test the validity of the model itself, where reconnection is expected to happen starting a number of exponentiations of about 10 to 20. Nevertheless, the thesis suggests a number of possible ways to improve the numerical performance of the chosen model that can be pursued in the future

Inverser Transfer magnetischer Helizität in isothermer magnetohydrodynamischer Überschall-Turbulenz

This work deals with magnetic spectral transport and structure formation processes in statistically homogeneous plasma turbulence described in the ideal single fluid magnetohydrodynamic (MHD) approximation. Of particular interest is the influence of compressibility on these nonlinear dynamics, that is usually neglected in this context but of potential relevance for many astrophysical systems exhibiting large Mach number turbulence. The fundamental process under investigation in this respect is the inverse spectral transfer of magnetic helicity to ever larger scales. Its transport is studied through direct numerical simulations of large-scale-driven compressible isothermal plasma turbulence. To this end, the time evolution of steady-state turbulence of varying levels of compressibility is analysed in Fourier and configuration space under continuous injection of random small scale helical magnetic fluctuations. Several quantities present self-similar spectral scaling laws, which are consistent with a tendency towards equipartition in terms of magnetic and kinetic energies and helicities. When the large-scale mechanical driving is solenoidal, the scaling exponents are relatively close to those observed in previous research in incompressible MHD, even at Mach numbers of the order of ten. For a purely compressive large-scale driving however, significant deviations are already observed at relatively low Mach numbers (of the order of 3). This suggests that compressible effects in astrophysical flows may already considerably affect magnetic structure formation at relatively small Mach numbers, in situations where the turbulence drivers are rather compressive. These deviations can however be alleviated by appropriate changes of variable, hinting at some universality in the inverse transfer behaviour over a wide range of compressibility. A Fourier-space analysis of the spectral transfers reveals furthermore the presence of three phenomena in the global picture of the magnetic helicity inverse transport: a local inverse transfer, a non-local inverse transfer and a direct local transfer (where "local'' refers to the distance of the involved Fourier wavevectors). A projection on the curl operator's eigenvectors (helical decomposition) of the magnetic and velocity fields allows to assess the relative importance of the different helical contributions, including the role of the compressive part of the velocity field on these three phenomena. The latter contributes to the inverse transfer essentially through non-local transfers and takes the leading role in the direct local transfer in highly compressible flows. In addition to the physical aspects, this work presents some contributions to the development of robust higher-order numerics, beneficial to attain low numerical dissipation at acceptable computational expense.Diese Arbeit beschäftigt sich mit magnetischen spektralen Transport- und Strukturbildungsprozesse in statistisch-homogener Plasmaturbulenz im Rahmen der idealen magnetohydrodynamischen (MHD) Einflüssigkeitsnäherung. Im Fokus liegt der Einfluss der Kompressibilität auf die nichtlineare Dynamik, der in vielen astrophysikalischen Systemen mit hohen Machzahlen von potenzieller Relevanz ist, jedoch in diesem Kontext üblicherweise vernachlässigt wird. Der betrachtete grundlegende Prozess in dieser Hinsicht ist der inverse Spektraltransfer der magnetischen Helizität zu immer größeren Skalen. Dieser Transport wird durch direkte numerische Simulationen von großskalig-getriebener kompressibler isothermer Plasmaturbulenz untersucht. Zu diesem Zweck wird die Zeitentwicklung stationärer Turbulenzsysteme mit unterschiedlichen Kompressibilitätsgraden, die einer kontinuierlichen Injektion von zufälligen kleinskaligen helikalen magnetischen Fluktuationen unterliegen, in Fourier- und Konfigurationsraum analysiert. Mehrere Variablen zeigen selbstähnliche spektrale Skalierungsgesetze, die mit einer Tendenz zur Gleichverteilung zwischen magnetischen und kinetischen Energien und Helizitäten im Einklang stehen. Mit einem solenoidalen großskaligen mechanischem Antrieb werden Exponenten beobachtet, die ähnlich zu denjenigen sind, die in der bisherigen Forschung in der inkompressiblen MHD gefunden wurden. Dieses gilt selbst bei Machzahlen der Größenordnung 10. Mit einem rein kompressiven großskaligen Antrieb sind jedoch signifikante Abweichungen schon bei relativ geringen Machzahlen (der Größenordnung 3) zu sehen. Das deutet darauf hin, dass kompressible Effekte schon bei relativ geringen Machzahlen die Bildung von magnetischen Strukturen in astrophysikalischen Strömungen erheblich beeinflussen können, wenn die Turbulenzanreger eher kompressiv sind. Diese Abweichungen können jedoch durch entsprechende Variablenänderungen abgeschwächt werden, was eine gewisse Universalität des inversen Transfers über einen breiten Bereich der Kompressibilität andeutet. Eine Fourier-Analyse des Spektraltransfers zeigt ferner das Vorhandensein dreier Phänomene im Gesamtbild des inversen Transfers magnetischer Helizität: lokalen inversen Transfer, nicht lokalen inversen Transfer und lokalen direkten Transfer (wobei "lokal'' sich auf den Abstand der beteiligten Fourierwellenvektoren bezieht). Eine Projektion auf die Eigenvektoren des Rotationsoperators (helikale Zerlegung) der Magnet- und Geschwindigkeistfelder ermöglicht es, die Bedeutung der verschiedenen helikalen Beiträge sowie den Einfluss des kompressiven Teils des Geschwindigkeitsfeldes auf diese drei Phänomene zu beurteilen und zu vergleichen. Der kompressive Geschwindigkeitsanteil trägt zum inversen Transport im Wesentlichen durch nicht-lokalen Transfer bei und übernimmt in hochkompressiblen Strömungen die Hauptrolle des lokalen direkten Transfers. Neben den physikalischen Aspekten präsentiert diese Arbeit einige Beiträge zur Entwicklung von robusten numerischen Verfahren höherer Ordnung, die vorteilhaft sind, um die numerische Dissipation mit akzeptablem Rechenaufwand zu reduzieren

Inverse transfer of magnetic helicity in direct numerical simulations of compressible isothermal turbulence: scaling laws

The inverse transfer of magnetic helicity is investigated through direct numerical simulations of large-scale mechanically driven turbulent flows in the isothermal ideal magnetohydrodynamics framework. The mechanical forcing is either purely solenoidal or purely compressive and the turbulent statistically stationary states considered exhibit root mean square (RMS) Mach numbers 0.1≲M≲11 . A continuous small-scale electromotive forcing injects magnetic helical fluctuations, which lead to the build-up of ever larger magnetic structures. Spectral scaling exponents are observed which, for low Mach numbers, are consistent with previous research done in the incompressible case. Higher compressibility leads to smaller absolute values of the magnetic helicity scaling exponents. The deviations from the incompressible case are comparatively small for solenoidally driven turbulence, even at high Mach numbers, as compared with those for compressively driven turbulence, where strong deviations are already visible at relatively mild RMS Mach numbers M≳3 . Compressible effects can thus play an important role in the inverse transfer of magnetic helicity, especially when the turbulence drivers are rather compressive. Theoretical results observed in the incompressible case can, however, be transferred to supersonic turbulence by an appropriate change of variables, using the Alfvén velocity in place of the magnetic field