Large Magnetic Reynolds Number Research Articles

Conserving Local Magnetic Helicity in Numerical Simulations

Magnetic helicity is robustly conserved in systems with very large magnetic Reynolds numbers, including most systems of astrophysical interest, and unlike kinetic and magnetic energy, it is not dissipated at small scales. This plays a major role in suppressing the kinematic large-scale dynamo and may also be responsible for driving the large-scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. In these simulations, magnetic helicity is lost either through numerical errors or through the action of an unrealistically large resistivity. Errors in the internal distribution of magnetic helicity are equally important and typically larger. Here, we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations, so that their evolution more closely approximates that of real systems.

Reconnection-driven energy cascade in magnetohydrodynamic turbulence.

Magnetohydrodynamic turbulence regulates the transfer of energy from large to small scales in many astrophysical systems, including the solar atmosphere. We perform three-dimensional magnetohydrodynamic simulations with unprecedentedly large magnetic Reynolds number to reveal how rapid reconnection of magnetic field lines changes the classical paradigm of the turbulent energy cascade. By breaking elongated current sheets into chains of small magnetic flux ropes (or plasmoids), magnetic reconnection leads to a previously undiscovered range of energy cascade, where the rate of energy transfer is controlled by the growth rate of the plasmoids. As a consequence, the turbulent energy spectra steepen and attain a spectral index of -2.2 that is accompanied by changes in the anisotropy of turbulence eddies. The omnipresence of plasmoids and their consequences on, for example, solar coronal heating, can be further explored with current and future spacecraft and telescopes.

Fast and furious dynamo action in the anisotropic dynamo

In the limit of large magnetic Reynolds numbers, it is shown that a smooth differential rotation can lead to fast dynamo action, provided that the electrical conductivity or magnetic permeability is anisotropic. If the shear is infinite, for example between two rotating solid bodies, the anisotropic dynamo becomes furious, meaning that the magnetic growth rate increases toward infinity with an increasing magnetic Reynolds number.

Comparison of Two Methods for Calculating Magnetic Helicity in the Solar Corona

Duo to the large magnetic Reynolds number, the magnetic helicity originating from the solar interior can be carried away through the photosphere into the corona. However, the relationship between the accumulated magnetic helicity flux through the photosphere and the magnetic helicity in the corona is still unclear. By selecting 36 newly emerging active regions in the 23rd solar cycle, we apply optical flow methods to derive the accumulated magnetic helicity through the photosphere (H m p ) by using the sequential longitudinal magnetograms, we use nonlinear force-free field extrapolation to obtain the 3D coronal magnetic field, and we adopt finite volume methods to calculate the instantaneous relative magnetic helicity in the corona (H m c ) by using vector magnetograms. It is found that the local correlation tracking (LCT)–based H m p is larger than H m c in 1″, and that the Differential Affine Velocity Estimator–based H m p is more consistent with H m c than the LCT-based H m p . H m p is more consistent with H m c in evaluation from 2″ than from 1″. Moreover, systematically shows consistency with the Hemispheric Helicity Rule (over 55%), no matter which resolution and method are used. These estimations suggest that the consistency of H m c and H m p is partly dependent on the resolution of the magnetograms and the calculation methods.

Helical turbulent nonlinear dynamo at large magnetic Reynolds numbers

To investigate large-scale magnetic field generation in highly conducting magnetohydrodynamic (MHD) regimes typical of rotating astrophysical systems, we conduct high-resolution MHD simulations in the dynamical regime of large magnetic Reynolds numbers, of turbulence with an inhomogeneous kinetic helicity distribution. We obtain a nonlinear helical dynamo solution, characterized by a weak large-scale magnetic wave slowly propagating over saturated small-scale MHD turbulence, bypassing the catastrophic resistive quenching problem of homogeneous helical dynamos by developing turbulent fluxes of magnetic helicity through the system equator. Hints of fast-reconnection plasmoids are found.

Plasma Flows in Solar Filaments as Electromagnetically Driven Vortical Flows

Electromagnetic expulsion acts on a body suspended in a conducting fluid or plasma, which is subject to the influence of electric and magnetic fields. Physically, the effect is a magnetohydrodynamic analogue of the buoyancy (Archimedean) force, which is caused by the nonequal electric conductivities inside and outside the body. It is suggested that electromagnetic expulsion can drive the observed plasma counter-streaming flows in solar filaments. Exact analytical solutions and scaling arguments for a characteristic plasma flow speed are reviewed, and their applicability in the limit of large magnetic Reynolds numbers, relevant in the solar corona, is discussed.

Inefficient Magnetic-Field Amplification in Supersonic Laser-Plasma Turbulence.

We report a laser-plasma experiment that was carried out at the LMJ-PETAL facility and realized the first magnetized, turbulent, supersonic (Ma_{turb}≈2.5) plasma with a large magnetic Reynolds number (Rm≈45) in the laboratory. Initial seed magnetic fields were amplified, but only moderately so, and did not become dynamically significant. A notable absence of magnetic energy at scales smaller than the outer scale of the turbulent cascade was also observed. Our results support the notion that moderately supersonic, low-magnetic-Prandtl-number plasma turbulence is inefficient at amplifying magnetic fields compared to its subsonic, incompressible counterpart.

Entropy Generation Analysis and Radiated Heat Transfer in MHD (Al2O3-Cu/Water) Hybrid Nanofluid Flow.

This research concerns the heat transfer and entropy generation analysis in the MHD axisymmetric flow of Al2O3-Cu/H2O hybrid nanofluid. The magnetic induction effect is considered for large magnetic Reynolds number. The influences of thermal radiations, viscous dissipation and convective temperature conditions over flow are studied. The problem is modeled using boundary layer theory, Maxwell’s equations and Fourier’s conduction law along with defined physical factors. Similarity transformations are utilized for model simplification which is analytically solved with the homotopy analysis method. The h-curves up to 20th order for solutions establishes the stability and convergence of the adopted computational method. Rheological impacts of involved parameters on flow variables and entropy generation number are demonstrated via graphs and tables. The study reveals that entropy in system of hybrid nanofluid affected by magnetic induction declines for β while it enhances for Bi, R and λ. Moreover, heat transfer rate elevates for large Bi with convective conditions at surface.

Numerical Treatment for Dynamics of Second Law Analysis and Magnetic Induction Effects on Ciliary Induced Peristaltic Transport of Hybrid Nanomaterial

The presented communication provides the analysis of entropy generation and heat transport rate in peristalsis of hybrid nanofluid induced by metachronal ciliary beating under magnetic environment for sufficiently large magnetic Reynolds number. Nanoparticles of Cu and Al2O3 are suspended in water. Features of their structures are determined by using long-wavelength approximation with zero Reynolds number. Adams Bashforth method has been applied to compute the results of the flow variables as well as entropy generation number from the formulated differential system which are then interpreted graphically to establish physical significance for different values of physical interest. This investigation reveals that thermal performance of fluid can be boosted by utilizing hybrid nanomaterial about the strength of a wall for stability. Irreversibility analysis ensures that entropy reduced for strong magnetic field while thermal heat generation results in an increase in temperature causing an enhancement in entropy of the system. Error analysis has been performed with reasonably accurate tolerance level. The comparative outcomes of both numerical approaches are presented with plentiful graphical as well as numerical demonstrations which demonstrate the importance in terms of robustness, accuracy and stability.

Potential Vorticity Mixing in a Tangled Magnetic Field

Abstract A theory of potential vorticity (PV) mixing in a disordered (tangled) magnetic field is presented. The analysis is in the context of β-plane MHD, with a special focus on the physics of momentum transport in the stably stratified, quasi-2D solar tachocline. A physical picture of mean PV evolution by vorticity advection and tilting of magnetic fields is proposed. In the case of weak field perturbations, quasi-linear theory predicts that the Reynolds and magnetic stresses balance as turbulence Alfvénizes for a larger mean magnetic field. Jet formation is explored quantitatively in the mean field–resistivity parameter space. However, since even a modest mean magnetic field leads to large magnetic perturbations for large magnetic Reynolds number, the physically relevant case is that of a strong but disordered field. We show that numerical calculations indicate that the Reynolds stress is modified well before Alfvénization—i.e., before fluid and magnetic energies balance. To understand these trends, a double-average model of PV mixing in a stochastic magnetic field is developed. Calculations indicate that mean-square fields strongly modify Reynolds stress phase coherence and also induce a magnetic drag on zonal flows. The physics of transport reduction by tangled fields is elucidated and linked to the related quench of turbulent resistivity. We propose a physical picture of the system as a resisto-elastic medium threaded by a tangled magnetic network. Applications of the theory to momentum transport in the tachocline and other systems are discussed in detail.

Dynamo theories

These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in turbulent fluids and plasmas, blended with a review of current research in the field. The primary focus is on the physical and mathematical concepts underlying different (turbulent) branches of dynamo theory, with some astrophysical, geophysical and experimental contexts disseminated throughout the document. The text begins with an introduction to the rationale, observational and historical roots of the subject, and to the basic concepts of magnetohydrodynamics relevant to dynamo theory. The next two sections discuss the fundamental phenomenological and mathematical aspects of (linear and nonlinear) small- and large-scale magnetohydrodynamic (MHD) dynamos. These sections are complemented by an overview of a selection of current active research topics in the field, including the numerical modelling of the geo- and solar dynamos, shear dynamos driven by turbulence with zero net helicity and MHD-instability-driven dynamos such as the magnetorotational dynamo. The difficult problem of a unified, self-consistent statistical treatment of small- and large-scale dynamos at large magnetic Reynolds numbers is also discussed throughout the text. Finally, an excursion is made into the relatively new but increasingly popular realm of magnetic-field generation in weakly collisional plasmas. A short discussion of the outlook and challenges for the future of the field concludes the presentation.

Nonaxisymmetric magnetorotational instability in spherical Couette flow.

We investigate numerically the flow of an electrically conducting fluid in a rapidly rotating spherical shell where the inner boundary spins slightly faster than the outer one. The magnetic field evolves self-consistently from an initial dipolar configuration of weak amplitude, and a toroidal field is produced by winding this poloidal field through the internal differential rotation. First, we characterize the axisymmetric field solutions obtained at long times when the Lorentz force is negligible and the flow follows the steady, purely hydrodynamical solution. We then examine the stability of these solutions, focusing on the regime of large magnetic Reynolds numbers where the field is dominantly toroidal. When the ratio of the azimuthal Alfvén frequency to the rotation frequency exceeds a certain value, a nonaxisymmetric instability develops. We show that the instability properties are compatible with those expected for the magnetorotational instability. Finally, we compare the instability properties with predictions obtained from a local linear stability analysis. The linear analysis agrees well with the numerical simulation results, except in a number of cases where the discrepancies are attributed to shearing effects on the unstable modes.

Magneto-vortical evolution of QGP in heavy ion collisions

The interplay of magnetic field and thermal vorticity in a relativistic ideal fluid might generate fluid vorticity during the fluid evolution provided the flow fields and the entropy density of the fluid is inhomogeneous (Mahajan and Yoshida 2010 Phys. Rev. Lett. 105, 095005). Exploiting this fact and assuming a large magnetic Reynolds number we study the evolution of a generalized magnetic field () which is defined as a combination of the usual magnetic field () and relativistic thermal vorticity (ωμν), in a 2(space) + 1(time) dimensional isentropic evolution of quark–gluon plasma with longitudinal boost invariance. The temporal evolution of is found to be different than , and the evolution also depends on the position of the fluid along the beam direction (taken along the z axis) with respect to the mid-plane z = 0. Further it is observed that the transverse components () evolve differently around the mid-plane.

Magnetic helicity and fluxes in an inhomogeneous α2 dynamo

Much work on turbulent three‐dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here, we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudovacuum conditions on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable α2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur on large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains still unclear.

Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence.

The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At a sufficiently large magnetic Reynolds number (R_{m}=10^{6}), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The disruption of current sheet structures facilitates the energy cascade towards small scales, leading to the breaking and steepening of the energy spectrum. In the plasmoid-mediated regime, the energy spectrum displays a scaling that is close to the spectral index -2.2 as proposed by recent analytic theories. We also demonstrate that the scale-dependent dynamic alignment exists in 2D MHD turbulence and the corresponding slope of the alignment angle is close to 0.25.

Compressibility in turbulent magnetohydrodynamics and passive scalar transport: mean-field theory

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $\unicode[STIX]{x1D70F}$-approach. We find that compressibility decreases the $\unicode[STIX]{x1D6FC}$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, $Rm$. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Péclet numbers, $Pe$. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large $Rm$, but it decreases it for small $Rm$. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large Péclet numbers. It can be interpreted as compressible turbophoresis of non-inertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.

Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. II. Simulations

Abstract Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left- and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability, (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (α μ effect), and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The α μ effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2), during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of proto-neutron stars are discussed.

Enhancement of Small-scale Turbulent Dynamo by Large-scale Shear

Abstract Small-scale dynamos (SSDs) are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology, and structure formation. Using high-resolution direct numerical simulations, we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports SSD action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate γ of the SSD and the turbulent rms velocity with shear rate S that are independent of the magnetic Prandtl number: and . For large fluid and magnetic Reynolds numbers, γ, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the SSD exhibits the scaling, , arising solely from the induction equation for a given velocity field.

Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory

Abstract The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark–gluon plasma.

The contribution of kinetic helicity to turbulent magnetic diffusivity

Using numerical simulations of forced turbulence with and without mean kinetic helicity, we show that for magnetic Reynolds numbers larger than unity, that is, beyond the regime of quasilinear theory, the turbulent magnetic diffusivity attains an additional negative contribution that is quadratic in the kinetic helicity. In particular, for large magnetic Reynolds numbers, the turbulent magnetic diffusivity without helicity is about twice the value with helicity. Such a contribution was not previously anticipated, but, as we discuss, it turns out to be important when accurate estimates of the turbulent magnetic diffusivity are needed.