The nonlinear properties of a large-scale dynamo driven by helical forcing

2002 ◽  
Vol 456 ◽  
pp. 219-237 ◽  
Author(s):  
FAUSTO CATTANEO ◽  
DAVID W. HUGHES ◽  
JEAN-CLAUDE THELEN
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Mean Field ◽  
Forced Flow ◽  
Small Scale ◽  
Dynamo Action ◽  
Initial State ◽  
The Magnetic Field

By considering an idealized model of helically forced flow in an extended domain that allows scale separation, we have investigated the interaction between dynamo action on different spatial scales. The evolution of the magnetic field is studied numerically, from an initial state of weak magnetization, through the kinematic and into the dynamic regime. We show how the choice of initial conditions is a crucial factor in determining the structure of the magnetic field at subsequent times. For a simulation with initial conditions chosen to favour the growth of the small-scale field, the evolution of the large-scale magnetic field can be described in terms of the α-effect of mean field magnetohydrodynamics. We have investigated this feature further by a series of related numerical simulations in smaller domains. Of particular significance is that the results are consistent with the existence of a nonlinearly driven α-effect that becomes saturated at very small amplitudes of the mean magnetic field.

scholarly journals Mean-Field Magnetohydrodynamics as a Basis of Solar Dynamo Theory

1976 ◽  
Vol 71 ◽  
pp. 323-344 ◽  
Author(s):  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Strong Relationship ◽  
Solar Radius ◽  
Small Scale ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Complicated Situation ◽  
Insight Into

One of the most striking features of both the magnetic field and the motions observed at the Sun is their highly irregular or random character which indicates the presence of rather complicated magnetohydrodynamic processes. Of great importance in this context is a comprehension of the behaviour of the large scale components of the magnetic field; large scales are understood here as length scales in the order of the solar radius and time scales of a few years. Since there is a strong relationship between these components and the solar 22-years cycle, an insight into the mechanism controlling these components also provides for an insight into the mechanism of the cycle. The large scale components of the magnetic field are determined not only by their interaction with the large scale components of motion. On the contrary, a very important part is played also by an interaction between the large and the small scale components of magnetic field and motion so that a very complicated situation has to be considered.

scholarly journals The effect of velocity shear on dynamo action due to rotating convection

2013 ◽  
Vol 717 ◽  
pp. 395-416 ◽  
Author(s):  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Large Scale ◽  
Mean Field ◽  
Magnetic Reynolds Number ◽  
Velocity Shear ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Rotating Convection ◽  
The Magnetic Field

AbstractRecent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime. Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of significant magnetic fields on large scales. By the technique of spectral filtering, we analyse the modes in the velocity that are principally responsible for dynamo action, and show that the magnetic field resulting from the full flow relies crucially on a range of scales in the velocity field. Filtering the flow to provide a true separation of scales between the shear and the convective flow also leads to dynamo action; however, the magnetic field in this case has a very different structure from that generated by the full velocity field. We also show that the nature of the dynamo action is broadly similar irrespective of whether the flow in the absence of shear can support dynamo action.

scholarly journals Global enhancement and structure formation of the magnetic field in spiral galaxies

2018 ◽  
Vol 609 ◽  
pp. A104 ◽  
Author(s):  
Sergey A. Khoperskov ◽  
Sergey S. Khrapov
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Large Scale ◽  
Spiral Galaxies ◽  
Mean Field ◽  
Field Structure ◽  
Small Scale ◽  
Spiral Pattern ◽  
Spiral Arms ◽  
The Magnetic Field

In this paper we study numerically large-scale magnetic field evolution and its enhancement in gaseous disks of spiral galaxies. We consider a set of models with the various spiral pattern parameters and the initial magnetic field strength with taking into account gas self-gravity and cooling and heating processes. In agreement with previous studies we find out that galactic magnetic field is mostly aligned with gaseous structures, however small-scale gaseous structures (spurs and clumps) are more chaotic than the magnetic field structure. In spiral arms magnetic field often coexists with the gas distribution, in the inter-arm region we see filamentary magnetic field structure. These filaments connect several isolated gaseous clumps. Simulations reveal the presence of the small-scale irregularities of the magnetic field as well as the reversal of magnetic field at the outer edge of the large-scale spurs. We provide evidences that the magnetic field in the spiral arms has a stronger mean-field component, and there is a clear inverse correlation between gas density and plasma-beta parameter, compared to the rest of the disk with a more turbulent component of the field and an absence of correlation between gas density and plasma-beta. We show the mean field growth up to 3−10 μG in the cold gas during several rotation periods (500−800 Myr), whereas ratio between azimuthal and radial field is equal to 4/1. We find an enhancement of random and ordered components of the magnetic field. Mean field strength increases by a factor of 1.5−2.5 for models with various spiral pattern parameters. Random magnetic field component can reach up to 25% from the total strength. By making an analysis of the time-dependent evolution of the radial Poynting flux, we point out that the magnetic field strength is enhanced more strongly at the galactic outskirts which is due to the radial transfer of magnetic energy by the spiral arms pushing the magnetic field outward. Our results also support the presence of sufficient conditions for the development of magnetorotational instability at distances >11 kpc after 300 Myr of evolution.

Commission 12: Radiation and Structure of the Solar Atmosphere (Radiation et Structure De L’atmosphere Solaire)

1988 ◽  
Vol 20 (1) ◽  
pp. 91-94
Author(s):  
M. Kuperus ◽  
J. Harvey
Keyword(s):  
Magnetic Field ◽  
Solar Activity ◽  
Solar Atmosphere ◽  
Large Scale ◽  
Convection Zone ◽  
Solar Physics ◽  
Mean Field ◽  
Small Scale ◽  
Origin And Evolution ◽  
The Magnetic Field

Solar Physics has been traditionally divided into Structure and Radiation of the Solar Atmosphere (commission 12) and Solar Activity (commission 10). There has been increasing evidence that solar activity, which is basically of magnetic origin, occurs on a great variety of scales arid thus immediately touches upon the structure of the solar atmosphere as well as the structure and dynamics of the convection zone. As a consequence progress in the field of origin and evolution of solar magnetic fields from a large scale, ‘the dynamo’, to small scale is included in this report. In the past few years particular attention has been paid to the fact that the fluctuations in the magnetic field are much larger than the mean field and that the dynamo modes may be stochastically excited. The question whether there is a magnetic reservoir at the bottom of the convection zone still remains to be resolved. The interaction of the convection and the magnetic field resulting in an enhancement of the magnetic field in the intergranular lanes is studied by numerical modelling.

scholarly journals Large-scale dynamo action of magnetized Taylor–Couette flows

2020 ◽  
Vol 493 (1) ◽  
pp. 1249-1260
Author(s):  
G Rüdiger ◽  
M Schultz
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Single Mode ◽  
Eddy Diffusivity ◽  
Magnetic Reynolds Number ◽  
Dynamo Model ◽  
Turbulence Energy ◽  
Dynamo Action ◽  
Taylor Couette

ABSTRACT A conducting Taylor–Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler–Spruit type. The flows are unstable against non-axisymmetric perturbations which form electromotive forces defining α effect and eddy diffusivity. If both degenerated modes with m = ±1 are excited with the same power then the global α effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite α effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an α2 dynamo. Moreover, an αΩ dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of Rm ≃ 2000 to work. Whether it really works depends on assumptions about the turbulence energy. For a steeper-than-quadratic dependence of the turbulence intensity on the magnetic field, however, dynamos are only excited if the resulting magnetic eddy diffusivity approximates its microscopic value, ηT ≃ η. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.

scholarly journals Excitation of kinetic Alfvén turbulence by MHD waves and energization of space plasmas

2004 ◽  
Vol 11 (5/6) ◽  
pp. 535-543 ◽  
Author(s):  
Y. Voitenko ◽  
M. Goossens
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Energy Transport ◽  
Plasma Heating ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Space Plasmas ◽  
Small Scale ◽  
The Magnetic Field ◽  
Dissipation Range

Abstract. There is abundant observational evidence that the energization of plasma particles in space is correlated with an enhanced activity of large-scale MHD waves. Since these waves cannot interact with particles, we need to find ways for these MHD waves to transport energy in the dissipation range formed by small-scale or high-frequency waves, which are able to interact with particles. In this paper we consider the dissipation range formed by the kinetic Alfvén waves (KAWs) which are very short- wavelengths across the magnetic field irrespectively of their frequency. We study a nonlocal nonlinear mechanism for the excitation of KAWs by MHD waves via resonant decay AW(FW)→KAW1+KAW2, where the MHD wave can be either an Alfvén wave (AW), or a fast magneto-acoustic wave (FW). The resonant decay thus provides a non-local energy transport from large scales directly in the dissipation range. The decay is efficient at low amplitudes of the magnetic field in the MHD waves, B/B0~10-2. In turn, KAWs are very efficient in the energy exchange with plasma particles, providing plasma heating and acceleration in a variety of space plasmas. An anisotropic energy deposition in the field-aligned degree of freedom for the electrons, and in the cross-field degrees of freedom for the ions, is typical for KAWs. A few relevant examples are discussed concerning nonlinear excitation of KAWs by the MHD wave flux and consequent plasma energization in the solar corona and terrestrial magnetosphere.

scholarly journals Magnetospheric Processes Possibly Related to the Origin of Cosmic Rays

1981 ◽  
Vol 94 ◽  
pp. 373-391
Author(s):  
Gerhard Haerendel
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Small Scale ◽  
Shear Stresses ◽  
Acceleration Process ◽  
Dayside Magnetopause ◽  
Field Lines ◽  
The Magnetic Field ◽  
Auroral Particles

Two processes are discussed which violate the frozen-in condition in a highly conducting plasma, reconnection and the auroral acceleration process. The first applies to situations in which . It plays an important role in the interaction of the solar wind with the Earth's magnetic field and controls energy input into as well as energetic particle release from the magnetosphere. Detailed in situ studies of the process on the dayside magnetopause reveal its transient and small-scale nature. The auroral acceleration process occurs in the low magnetosphere (β « 1) and accompanies sudden releases of magnetic shear stresses which exist in large-scale magnetospheric-ionospheric current circuits. The process is interpreted as a kind of breaking. The movements of the magnetospheric plasma which lead to a relief of the magnetic tensions occur in thin sheets and are decoupled along the magnetic field lines by parallel electric potential drops. It is this voltage that accelerates the primary auroral particles. The visible arcs are then traces of the magnetic breaking process at several 1000 km altitude.

scholarly journals Approaching Earth’s core conditions in high-resolution geodynamo simulations

2019 ◽  
Vol 219 (Supplement_1) ◽  
pp. S137-S151 ◽  
Author(s):  
Julien Aubert
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Large Scale ◽  
Small Scale ◽  
Low Resolution ◽  
Earth’S Core ◽  
Earth's Core ◽  
Density Anomaly ◽  
Core Conditions ◽  
The Magnetic Field

SUMMARY The geodynamo features a broad separation between the large scale at which Earth’s magnetic field is sustained against ohmic dissipation and the small scales of the turbulent and electrically conducting underlying fluid flow in the outer core. Here, the properties of this scale separation are analysed using high-resolution numerical simulations that approach closer to Earth’s core conditions than earlier models. The new simulations are obtained by increasing the resolution and gradually relaxing the hyperdiffusive approximation of previously published low-resolution cases. This upsizing process does not perturb the previously obtained large-scale, leading-order quasi-geostrophic (QG) and first-order magneto-Archimedes-Coriolis (MAC) force balances. As a result, upsizing causes only weak transients typically lasting a fraction of a convective overturn time, thereby demonstrating the efficiency of this approach to reach extreme conditions at reduced computational cost. As Earth’s core conditions are approached in the upsized simulations, Ohmic losses dissipate up to 97 per cent of the injected convective power. Kinetic energy spectra feature a gradually broadening self-similar, power-law spectral range extending over more than a decade in length scale. In this range, the spectral energy density profile of vorticity is shown to be approximately flat between the large scale at which the magnetic field draws its energy from convection through the QG-MAC force balance and the small scale at which this energy is dissipated. The resulting velocity and density anomaly planforms in the physical space consist in large-scale columnar sheets and plumes, respectively, co-existing with small-scale vorticity filaments and density anomaly ramifications. In contrast, magnetic field planforms keep their large-scale structure after upsizing. The small-scale vorticity filaments are aligned with the large-scale magnetic field lines, thereby minimizing the dynamical influence of the Lorentz force. The diagnostic outputs of the upsized simulations are more consistent with the asymptotic QG-MAC theory than those of the low-resolution cases that they originate from, but still feature small residual deviations that may call for further theoretical refinements to account for the structuring constraints of the magnetic field on the flow.

scholarly journals Application of a helicity proxy to edge-on galaxies

2020 ◽  
Vol 496 (4) ◽  
pp. 4749-4759
Author(s):  
Axel Brandenburg ◽  
Ray S Furuya
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Numerical Results ◽  
Magnetic Helicity ◽  
The Galaxy ◽  
Rotationally Invariant ◽  
The Magnetic Field ◽  
Mean Field Dynamo

ABSTRACT We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the centre of the galaxy and are not a signature of magnetic helicity.

scholarly journals Large-scale dynamos in rapidly rotating plane layer convection

2018 ◽  
Vol 612 ◽  
pp. A97 ◽  
Author(s):  
P. J. Bushby ◽  
P. J. Käpylä ◽  
Y. Masada ◽  
A. Brandenburg ◽  
B. Favier ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Plane Layer ◽  
Cycle Period ◽  
Dynamo Action ◽  
Horizontal Magnetic Field ◽  
Vortex Instability ◽  
Large Scale Vortex ◽  
The Mean ◽  
The Magnetic Field

Context.Convectively driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component.Aims.Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability.Methods.The governing equations of three-dimensional non-linear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes.Results.In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, the large-scale vortex is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity (grand minima-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.

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