110 results on '"Brandenburg, Axel"'
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2. Advances in Theory and Simulations of Large-Scale Dynamos
- Author
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Brandenburg, Axel, Thompson, M. J., editor, Balogh, A., editor, Culhane, J. L., editor, Nordlund, Å., editor, Solanki, S. K., editor, and Zahn, J.-P., editor
- Published
- 2009
- Full Text
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3. Application of a helicity proxy to edge-on galaxies
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Brandenburg, Axel and Furuya, Ray S.
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Astrophysics::Cosmology and Extragalactic Astrophysics ,individual ,NGC 891 – galaxies ,magnetic fields ,Astrophysics::Galaxy Astrophysics ,dynamo –MHD– polarization – turbulence – galaxies - 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.
- Published
- 2020
4. Towards The Magnetic Field of M81
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Moss, David, Brandenburg, Axel, Donner, Karl Johan, Thomasson, Magnus, Krause, F., editor, Rädler, K.-H., editor, and Rüdiger, G., editor
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- 1993
- Full Text
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5. Current Status of Turbulent Dynamo Theory: From Large-Scale to Small-Scale Dynamos
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Brandenburg, Axel, Sokoloff, Dmitry, and Subramanian, Kandaswamy
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- 2012
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6. Self-Regulating Supernova Heating in Interstellar Medium Simulations
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Sarson, Graeme R., Shukurov, Anvar, Nordlund, Åke, Gudiksen, Boris, and Brandenburg, Axel
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- 2004
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7. Magnetic Mysteries
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Brandenburg, Axel
- Published
- 2001
8. Relic Gravitational Waves from the Chiral Magnetic Effect.
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Brandenburg, Axel, He, Yutong, Kahniashvili, Tina, Rheinhardt, Matthias, and Schober, Jennifer
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CORONAL mass ejections , *MAGNETIC flux density , *WHITE noise , *MAGNETIC fields , *GRAVITATIONAL waves , *RELICS , *MONOCHROMATIC light , *WAVENUMBER - Abstract
Relic gravitational waves (GWs) can be produced by primordial magnetic fields. However, not much is known about the resulting GW amplitudes and their dependence on the details of the generation mechanism. Here we treat magnetic field generation through the chiral magnetic effect (CME) as a generic mechanism and explore its dependence on the speed of generation (the product of magnetic diffusivity and characteristic wavenumber) and the speed characterizing the maximum magnetic field strength expected from the CME. When the latter exceeds the former (regime I), which is the regime applicable to the early universe, we obtain an inverse cascade with moderate GW energy that scales with the third power of the magnetic energy. When the generation speed exceeds the CME limit (regime II), the GW energy continues to increase without a corresponding increase of magnetic energy. In the early kinematic phase, the GW energy spectrum (per linear wavenumber interval) has opposite slopes in both regimes and is characterized by an inertial range spectrum in regime I and a white noise spectrum in regime II. The occurrence of these two slopes is shown to be a generic consequence of a nearly monochromatic exponential growth of the magnetic field. The resulting GW energy is found to be proportional to the fifth power of the limiting CME speed and the first power of the generation speed. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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9. Hall Cascade with Fractional Magnetic Helicity in Neutron Star Crusts.
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Brandenburg, Axel
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NEUTRON stars , *MAGNETIC fields , *ENERGY dissipation - Abstract
The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift, which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time t: instead of ∝t−2/3 in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber k is compatible with earlier findings for the forced Hall cascade, i.e., proportional to k−7/3, but in the decaying cases, the subinertial range spectrum steepens to a novel k5 slope instead of the k4 slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the rms magnetic field. For neutron star conditions with an rms magnetic field of a few times , the large-scale magnetic field might only be , while still producing magnetic dissipation of for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries. [ABSTRACT FROM AUTHOR]
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- 2020
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10. The nature of mean-field generation in three classes of optimal dynamos.
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Brandenburg, Axel and Chen, Long
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ELECTRIC generators , *MEAN field theory , *REYNOLDS number , *ENERGY dissipation , *FIXED interest rates , *MAGNETIC fields - Abstract
In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an $\unicode[STIX]{x1D6FC}^{2}$ dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23–45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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11. f-mode strengthening from a localised bipolar subsurface magnetic field.
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Singh, Nishant K., Raichur, Harsha, Käpylä, Maarit J., Rheinhardt, Matthias, Brandenburg, Axel, and Käpylä, Petri J.
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MAGNETIC fields ,SOLAR magnetic fields ,MAGNETIC structure ,MAGNETIC flux density ,SOLAR cycle - Abstract
Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the f-mode, which emerges from a density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localised bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the f-mode is significantly larger at high horizontal wavenumbers k, but the fanning is weaker for the localised subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the f-mode in the k ω diagram increases proportionally in such a way that the normalised f-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localised magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the f-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of f-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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12. Strong nonlocality variations in a spherical mean‐field dynamo.
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Brandenburg, Axel and Chatterjee, Piyali
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COSMIC magnetic fields , *MEAN field theory , *EDDIES , *ELECTRIC potential , *DIFFERENTIAL equations - Abstract
To explain the large‐scale magnetic field of the sun and other bodies, the mean‐field dynamo theory is commonly applied, where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the convection zone where the size of the turbulent eddies is comparable to the depth of the convection zone itself. We approximate the underlying integro‐differential equation using a partial differential equation corresponding to a reaction–diffusion‐type equation for the mean electromotive force, making an approach that is nonlocal in space and time feasible under conditions where spherical geometry and nonlinearity are included. In agreement with earlier findings, spatiotemporal nonlocality lowers the excitation conditions of the dynamo. Sharp structures are now found to be absent. However, in the surface layers, the field remains similar to before. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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13. Sharp magnetic structures from dynamos with density stratification.
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Jabbari, Sarah, Brandenburg, Axel, Kleeorin, Nathan, and Rogachevskii, Igor
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ELECTRIC generators , *MAGNETIC fields , *TURBULENCE , *LORENTZ force , *COMPUTER simulation - Abstract
Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here, we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in non-linear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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14. Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field.
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Brandenburg, Axel, Kahniashvili, Tina, and Tevzadze, Alexander G.
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MAGNETIC fields , *ELECTROMAGNETIC fields , *HELICAL structure , *INVERSE functions , *WEAK interactions (Nuclear physics) , *BETA decay - Abstract
In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower k2 subinertial range spectrum of kinetic energy forcing the magnetic field with a k4 subinertial range to attain larger-scale coherence. The inertial range shows a clear k-2 spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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15. Traces of large-scale dynamo action in the kinematic stage.
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Subramanian, Kandaswamy and Brandenburg, Axel
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COSMIC magnetic fields , *COMPUTER simulation , *KINEMATICS , *SPECTRUM analysis , *TURBULENCE , *MAGNETOHYDRODYNAMICS , *ELECTRIC generators - Abstract
Using direct numerical simulations (DNS), we verify that in the kinematic regime, a turbulent helical dynamo grows in such a way that the magnetic energy spectrum remains to high-precision shape-invariant, i.e. at each wavenumber k the spectrum grows with the same growth rate. Signatures of large-scale dynamo action can be identified through the excess of magnetic energy at small k, of one of the two oppositely polarized constituents. Also a suitably defined planar average of the magnetic field can be chosen such that its rms value isolates the strength of the mean field. However, these different means of analysis suggest that the strength of the large-scale field diminishes with increasing magnetic Reynolds number ReM like ${\rm Re}_{\rm M}^{-1/2}$ for intermediate values and like ${\rm Re}_{\rm M}^{-3/4}$ for larger ones. Both an analysis from the Kazantsev model including helicity and the DNS show that this arises due to the magnetic energy spectrum still peaking at resistive scales, even when helicity is present. As expected, the amplitude of the large-scale field increases with increasing fractional helicity, enabling us to determine the onset of large-scale dynamo action and distinguishing it from that of the small-scale dynamo. Our DNS show that, contrary to earlier results for smaller scale separation (only 1.5 instead of now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers of 0.1 and only moderate values of the magnetic Reynolds numbers (∼160). [ABSTRACT FROM AUTHOR]
- Published
- 2014
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16. Mean-field dynamo action from delayed transport.
- Author
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Rheinhardt, Matthias, Devlen, Ebru, Rädler, Karl-Heinz, and Brandenburg, Axel
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COSMIC magnetic fields ,TURBULENCE ,REYNOLDS number ,DIFFUSION ,ELECTRIC potential ,ASTROPHYSICS ,COMPUTER simulation - Published
- 2014
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17. Particle energization through time-periodic helical magnetic fields.
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Mitra, Dhrubaditya, Brandenburg, Axel, Dasgupta, Brahmananda, Niklasson, Eyvind, and Ram, Abhay
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MAGNETIC fields , *CHARGED particle accelerators , *LYAPUNOV exponents , *KINETIC energy , *POWER law (Mathematics) , *GAUSSIAN processes - Abstract
We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients A = B = C = 1 are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the probability density function of kinetic energy is, at late times, close to a Gaussian but with steeper tails. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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18. Spontaneous Formation of Magnetic Flux Concentrations in Stratified Turbulence.
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Kemel, Koen, Brandenburg, Axel, Kleeorin, Nathan, Mitra, Dhrubaditya, and Rogachevskii, Igor
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MAGNETIC flux , *TURBULENCE , *PLASMA instabilities , *MAGNETIC fields , *NUMERICAL analysis , *SIMULATION methods & models , *SOLAR activity , *LORENTZ force , *SOLAR active regions , *SUN - Abstract
The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma β are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L/ η, where η is the turbulent diffusivity and L is the scale of the domain. DNSs are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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19. Ejections of Magnetic Structures Above a Spherical Wedge Driven by a Convective Dynamo with Differential Rotation.
- Author
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Warnecke, Jörn, Käpylä, Petri, Mantere, Maarit, and Brandenburg, Axel
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MAGNETIC structure ,WEDGES ,HEAT convection ,ROTATIONAL motion ,ISOTHERMAL processes ,TURBULENCE ,SIMULATION methods & models ,MAGNETIC fields - Abstract
We combine a convectively driven dynamo in a spherical shell with a nearly isothermal density-stratified cooling layer that mimics some aspects of a stellar corona to study the emergence and ejections of magnetic field structures. This approach is an extension of earlier models, where forced turbulence simulations were employed to generate magnetic fields. A spherical wedge is used which consists of a convection zone and an extended coronal region to ≈ 1.5 times the radius of the sphere. The wedge contains a quarter of the azimuthal extent of the sphere and 150 in latitude. The magnetic field is self-consistently generated by the turbulent motions due to convection beneath the surface. Magnetic fields are found to emerge at the surface and are ejected to the coronal part of the domain. These ejections occur at irregular intervals and are weaker than in earlier work. We tentatively associate these events with coronal mass ejections on the Sun, even though our model of the solar atmosphere is rather simplistic. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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20. THE NEGATIVE EFFECTIVE MAGNETIC PRESSURE IN STRATIFIED FORCED TURBULENCE.
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BRANDENBURG, AXEL, KEMEL, KOEN, KLEEORIN, NATHAN, and ROGACHEVSKII, IGOR
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MAGNETIC flux measurement , *TURBULENCE , *KINETIC energy , *ENERGY density , *REYNOLDS number , *PRANDTL number - Abstract
To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to converge for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models, the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
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21. Scaling and intermittency in incoherent α-shear dynamo.
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Mitra, Dhrubaditya and Brandenburg, Axel
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SHEAR (Mechanics) , *INTERMITTENCY (Nuclear physics) , *MEAN field theory , *RANDOM noise theory , *ANALYSIS of covariance , *MAGNETIC fields , *DENSITY functionals - Abstract
ABSTRACT We consider mean-field dynamo models with fluctuating α effect, both with and without large-scale shear. The α effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent α2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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22. Model of driven and decaying magnetic turbulence in a cylinder.
- Author
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Kemel, Koen, Brandenburg, Axel, and Hantao Ji
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FIELD theory (Physics) , *MAGNETIC fields , *ELECTRIC fields , *HELICITY of nuclear particles , *PLASMA astrophysics - Abstract
Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries and imposed axial magnetic and electric fields. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the α effect in astrophysical applications. A stronger field reversal can be obtained if there is also a significant kinetic α effect. Application to the reversed field pinch in plasma confinement devices is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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23. NONLINEAR SMALL-SCALE DYNAMOS AT LOW MAGNETIC PRANDTL NUMBERS.
- Author
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BRANDENBURG, AXEL
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ELECTRIC generators , *TURBULENCE , *ENERGY dissipation , *MAGNETIC fields , *SPECTRUM analysis - Abstract
Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers PrM down to 0.01. For PrM < 0.1, most of the energy is dissipated via Joule heat and, in agreement with earlier results for helical large-scale dynamos, kinetic energy dissipation is shown to diminish proportional to Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. down to values of 0.1. In agreement with earlier work, there is, in addition to a short Golitsyn k-11/3 spectrum near the resistive scale, also some evidence for a short k-1 spectrum on larger scales. The rms magnetic field strength of the small-scale dynamo is found to depend only weakly on the value of PrM and decreases by about a factor of two as PrM is decreased from 1 to 0.01. The possibility of dynamo action at PrM = 0.1 in the nonlinear regime is argued to be a consequence of a suppression of the bottleneck seen in the kinetic energy spectrum in the absence of a dynamo and, more generally, a suppression of kinetic energy near the dissipation wavenumber. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
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24. SHEAR-DRIVEN INSTABILITIES IN HALL-MAGNETOHYDRODYNAMIC PLASMAS.
- Author
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BEJARANO, CECILIA, GÓMEZ, DANIEL O., and BRANDENBURG, AXEL
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MAGNETOHYDRODYNAMIC instabilities ,SPACE plasmas ,ASTROPHYSICS ,MAGNETIC fields ,MAGNETIC resonance imaging - Abstract
The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence, or MHD instabilities. In particular, the development of smallscale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability (MRI), which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper, we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that an instability develops when the Hall effect is present, which we therefore term as the Hall magneto-shear instability. As a particular case, we recover the so-called MRI and quantitatively assess the role of the Hall effect on its development and evolution. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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25. Decay of helical and nonhelical magnetic knots.
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Candelaresi, Simon and Brandenburg, Axel
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MAGNETIC fields , *FERROMAGNETIC materials , *MAGNETIC domain , *HELICITY of nuclear particles , *KNOT theory , *TOPOLOGY - Abstract
We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call n-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the n-foil knots the decay is described by power laws that range form t-2/3 to t-1/3, which can be as slow as the t-1/3 behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like t-1, which is somewhat slower than the previously obtained t-3/2 behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
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26. Chandrasekhar-Kendall functions in astrophysical dynamos.
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BRANDENBURG, AXEL
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MAGNETOHYDRODYNAMICS , *ASTROPHYSICS , *MATHEMATICAL decomposition , *VECTOR fields , *MAGNETIC fields , *SIMULATION methods & models , *SPECTRUM analysis , *REYNOLDS number - Abstract
Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar-Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
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27. Magnetic helicity transport in the advective gauge family.
- Author
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Candelaresi, Simon, Hubbard, Alexander, Brandenburg, Axel, and Mitra, Dhrubaditya
- Subjects
TRANSPORT theory ,MAGNETIC fields ,MAGNETOHYDRODYNAMICS ,NUMERICAL analysis ,SIMULATION methods & models ,TURBULENCE ,GAUGE invariance ,REYNOLDS number - Abstract
Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
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28. Magnetic helicity fluxes in an α2 dynamo embedded in a halo.
- Author
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Hubbard, Alexander and Brandenburg, Axel
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- *
TURBULENCE , *DYNAMICS , *MAGNETIC fields , *STRAINS & stresses (Mechanics) , *BUFFER states (International relations) , *COMPUTER simulation - Abstract
We present the results of simulations of forced turbulence in a slab where the mean kinetic helicity has a maximum near the mid-plane, generating gradients of magnetic helicity of both large and small-scale fields. We also study systems that have poorly conducting buffer zones away from the midplane in order to assess the effects of boundaries. The dynamical α quenching phenomenology requires that the magnetic helicity in the small-scale fields approaches a nearly static, gauge independent state. To stress-test this steady state condition we choose a system with a uniform sign of kinetic helicity, so that the total magnetic helicity can reach a steady state value only through fluxes through the boundary, which are themselves suppressed by the velocity boundary conditions. Even with such a set up, the small-scale magnetic helicity is found to reach a steady state. In agreement with the earlier work, the magnetic helicity fluxes of small-scale fields are found to be turbulently diffusive. By comparing results with and without halos, we show that artificial constraints on magnetic helicity at the boundary do not have a significant impact on the evolution of the magnetic helicity, except that 'softer' (halo) boundary conditions give a lower energy of the saturated mean magnetic field. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
29. Magnetic field evolution in simulations with Euler potentials.
- Author
-
Brandenburg, Axel
- Subjects
- *
MAGNETOHYDRODYNAMIC waves , *EULER characteristic , *LORENTZ force , *PARTICLES (Nuclear physics) , *ELECTROMAGNETIC fields - Abstract
Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
30. The role of the Yoshizawa effect in the Archontis dynamo.
- Author
-
Sur, Sharanya and Brandenburg, Axel
- Subjects
- *
MAGNETIC fields , *SOLAR activity , *SOLAR wind , *ELECTRIC generators , *STELLAR winds - Abstract
The generation of mean magnetic fields is studied for a simple non-helical flow where a net cross-helicity of either sign can emerge. This flow, which is also known as the Archontis flow, is a generalization of the Arnold–Beltrami–Childress flow, but with the cosine terms omitted. The presence of cross-helicity leads to a mean-field dynamo effect that is known as the Yoshizawa effect. Direct numerical simulations of such flows demonstrate the presence of magnetic fields on scales larger than the scale of the flow. Contrary to earlier expectations, the Yoshizawa effect is found to be proportional to the mean magnetic field and can therefore lead to its exponential instead of just linear amplification for magnetic Reynolds numbers that exceed a certain critical value. Unlike α effect dynamos, it is found that the Yoshizawa effect is not notably constrained by the presence of a conservation law. It is argued that this is due to the presence of a forcing term in the momentum equation, which leads to a non-zero correlation with the magnetic field. Finally, the application to energy convergence in solar wind turbulence is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
31. Small-scale magnetic helicity losses from a mean-field dynamo.
- Author
-
Brandenburg, Axel, Candelaresi, Simon, and Chatterjee, Piyali
- Subjects
- *
SOLAR activity , *MAGNETIC fields , *CORONAL mass ejections , *SOLAR radiation , *FIELD theory (Physics) - Abstract
Using mean-field models with a dynamical quenching formalism, we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong for both large- and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
32. Turbulent diffusion with rotation or magnetic fields.
- Author
-
Brandenburg, Axel, Svedin, Andreas, and Vasil, Geoffrey M.
- Subjects
- *
MAGNETIC fields , *MAGNETOHYDRODYNAMICS , *SCALAR field theory , *TURBULENT diffusion (Meteorology) , *EDDIES , *ENERGY transfer , *SUN , *ANISOTROPY - Abstract
The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
33. Mean-field effects in the Galloway–Proctor flow.
- Author
-
Rädler, Karl-Heinz and Brandenburg, Axel
- Subjects
- *
ELECTRODYNAMICS , *ELECTRIC potential , *CENTRIPETAL force , *REYNOLDS number , *HYDRODYNAMICS , *MAGNETIC fields - Abstract
In the framework of mean-field electrodynamics the coefficients defining the mean electromotive force in Galloway–Proctor flows are determined. These flows show a two-dimensional pattern and are helical. The pattern wobbles in its plane. Apart from one exception a circularly polarized Galloway–Proctor flow, i.e. a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes & Tobias. An analytic theory of the α effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an α effect but no γ effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for α and show that γ is in general non-zero. Both α and γ show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the circular motion. Some results for the magnetic diffusivity and a related quantity are given, too. Finally, a result for α in the case of a randomly varying linearly polarized Galloway–Proctor flow, without the aforementioned circular motion, is presented. The flows investigated show quite interesting effects. There is, however, no straightforward way to relate these flows to turbulence and to use them for studying properties of the α effect and associated effects under realistic conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
34. A growing dynamo from a saturated Roberts flow dynamo.
- Author
-
Tilgner, Andreas and Brandenburg, Axel
- Subjects
- *
HYDRODYNAMICS , *DYNAMO theory (Physics) , *MAGNETIC fields , *CONTINUUM mechanics , *TURBULENCE , *ASTROPHYSICS - Abstract
Using direct simulations, weakly non-linear theory and non-linear mean-field theory, it is shown that the quenched velocity field of a saturated non-linear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by Cattaneo & Tobias for the more complicated case of turbulent convection, suggesting that this may be a common property of non-linear dynamos; see also the talk given online at the Kavli Institute for Theoretical Physics ( ). It is argued that this property can be used to test non-linear mean-field dynamo theories. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
35. Advances in Theory and Simulations of Large-Scale Dynamos.
- Author
-
Brandenburg, Axel
- Subjects
- *
ELECTRIC generators , *HELICITY of nuclear particles , *MEAN field theory , *HELIOSEISMOLOGY , *FUTURES studies - Abstract
Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
36. Kinematic α-effect in isotropic turbulence simulations.
- Author
-
Sur, Sharanya, Brandenburg, Axel, and Subramanian, Kandaswamy
- Subjects
- *
REYNOLDS number , *VISCOUS flow , *ELECTRIC potential , *DYNAMO theory (Physics) , *ASTROPHYSICS - Abstract
Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an α-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of Rm, α and turbulent diffusivity are proportional to Rm. Over finite time-intervals, meaningful values of α and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
37. Kinetic and magnetic α-effects in non-linear dynamo theory.
- Author
-
Sur, Sharanya, Subramanian, Kandaswamy, and Brandenburg, Axel
- Subjects
DYNAMO theory (Physics) ,REYNOLDS number ,MAGNETIC fields ,DYNAMICS ,MAGNETICS ,NUMERICAL analysis - Abstract
The backreaction of the Lorentz force on the α-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first-order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time-dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The non-linear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On one hand, one can express α completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small-scale magnetic field. These results hold for both steady and time-dependent forcing at arbitrary strength of the mean field. In addition, the τ-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time-dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force–field correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in the τ-approximation closure hypothesis. In the limit of strong imposed fields, B
0 , we find for delta-correlated forcing, in contrast to the well-known behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows. [ABSTRACT FROM AUTHOR]- Published
- 2007
- Full Text
- View/download PDF
38. Simulating field-aligned diffusion of a cosmic ray gas.
- Author
-
Snodin, Andrew P., Brandenburg, Axel, Mee, Antony J., and Shukurov, Anvar
- Subjects
- *
COSMIC rays , *ASTROPHYSICAL radiation , *NUCLEAR physics , *IONIZING radiation , *MAGNETIC fields , *RADIOACTIVITY - Abstract
The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference magnetohydrodynamic code is discussed. It is shown that the standard implementation fails near singular -points of the magnetic field, which are common if the field is random. A modification to the diffusion model for cosmic rays is described and the resulting telegraph equation (implemented by solving a dynamic equation for the diffusive flux of cosmic rays) is used; it is argued that this modification may better describe the physics of cosmic ray diffusion. The present model reproduces several processes important for the propagation and local confinement of cosmic rays, including spreading perpendicular to the local large-scale magnetic field, controlled by the random-to-total magnetic field ratio, and the balance between cosmic ray pressure and magnetic tension. Cosmic ray diffusion is discussed in the context of a random magnetic field produced by turbulent dynamo action. It is argued that energy equipartition between cosmic rays and other constituents of the interstellar medium does not necessarily imply that cosmic rays play a significant role in the balance of forces. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
39. Near-surface shear layer dynamics.
- Author
-
Brandenburg, Axel
- Abstract
The outer surface layers of the sun show a clear deceleration at low latitudes. This is generally thought to be the result of a strong dominance of vertical turbulent motions associated with strong downdrafts. This strong negative radial shear should not only contribute to amplifying the toroidal field locally and to expelling magnetic helicity, but it may also be responsible for producing a strong prograde pattern speed in the supergranulation layer. Using simulations of rotating stratified convection in cartesian boxes located at low latitudes around the equator it is shown that in the surface layers patterns move in the prograde direction on top of a retrograde mean background flow. These patterns may also be associated with magnetic tracers and even sunspot proper motions that are known to be prograde relative to the much slower surface plasma. [ABSTRACT FROM PUBLISHER]
- Published
- 2006
- Full Text
- View/download PDF
40. Turbulence from localized random expansion waves.
- Author
-
Mee, Antony J. and Brandenburg, Axel
- Subjects
- *
STELLAR dynamics , *INTERSTELLAR medium , *SUPERNOVAE , *GAUSSIAN processes , *COSMIC magnetic fields , *DYNAMO theory (Physics) - Abstract
In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of Gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function, we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the Gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power-law behaviour at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of −2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the non-linear term is found to be insignificant. No evidence for small-scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
41. Hydrodynamic and hydromagnetic energy spectra from large eddy simulations.
- Author
-
Haugen, Nils Erland L. and Brandenburg, Axel
- Subjects
- *
HYDRODYNAMICS , *TURBULENCE , *MAGNETIC fields , *SPECTRUM analysis , *MAGNETOHYDRODYNAMICS , *MATHEMATICAL analysis - Abstract
Direct and large eddy simulations of hydrodynamic and hydromagnetic turbulence have been performed in an attempt to isolate artifacts from real and possibly asymptotic features in the energy spectra. It is shown that in a hydrodynamic turbulence simulation with a Smagorinsky subgrid scale model using 5123 mesh points, two important features of the 40963 simulation on the Earth simulator [Y. Kaneda et al., Phys. Fluids 15, L21 (2003)] are reproduced: a k-0.1 correction to the inertial range with a k-5/3 Kolmogorov slope and the form of the bottleneck just before the dissipative subrange. Furthermore, it is shown that, while a Smagorinsky-type model for the induction equation causes an artificial and unacceptable reduction in the dynamo efficiency, hyper-resistivity yields good agreement with direct simulations. In the large-scale part of the inertial range, an excess of the spectral magnetic energy over the spectral kinetic energy is confirmed. However, a trend toward spectral equipartition at smaller scales in the inertial range can be identified. With magnetic fields, no explicit bottleneck effect is seen. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
42. Astrophysical magnetic fields and nonlinear dynamo theory
- Author
-
Brandenburg, Axel and Subramanian, Kandaswamy
- Subjects
- *
MAGNETIC fields , *ASTROPHYSICS , *DYNAMO theory (Physics) , *TURBULENCE - Abstract
Abstract: The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak ‘seed’ magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
43. Mach number dependence of the onset of dynamo action.
- Author
-
Haugen, Nils Erland L., Brandenburg, Axel, and Mee, Antony J.
- Subjects
- *
MAGNETIC fields , *SHOCK waves , *TURBULENCE , *REYNOLDS number , *AERODYNAMICS , *VISCOUS flow - Abstract
The effect of compressibility on the onset of non-helical turbulent dynamo action is investigated using both direct simulations as well as simulations with shock-capturing viscosities, keeping, however, the regular magnetic diffusivity. It is found that the critical magnetic Reynolds number increases from about 35 in the subsonic regime to about 70 in the supersonic regime. Although the shock structures are sharper in the high-resolution direct simulations compared with the low-resolution shock-capturing simulations, the magnetic field looks roughly similar in both cases and does not show any shock structures. Similarly, the onset of dynamo action is not significantly affected by the shock-capturing viscosity. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
44. Local and Nonlocal Magnetic Diffusion and Alpha-Effect Tensors in Shear Flow Turbulence.
- Author
-
Brandenburg, Axel and Sokoloff, Dmitry
- Subjects
- *
TURBULENCE , *HYDRODYNAMICS , *MAGNETIC fields - Abstract
Various approaches to estimate turbulent transport coefficients from numerical simulations of hydromagnetic turbulence are discussed. A quantitative comparison between the averaged magnetic field obtained from a specific three-dimensional simulation of a rotating turbulent shear flow in a slab and a simple one-dimensional alpha-omega dynamo model is given. A direct determination of transport coefficients is attempted by calculating the correlation matrix of different components of the field and its derivatives. This matrix relates the electromotive force to physically relevant parameters like the tensor components of the α-effect and the turbulent diffusivity. The α-effect operating on the toroidal field is found to be negative and of similar magnitude as the value obtained in previous work by correlating the electromotive force with the mean magnetic field. The turbulent diffusion of the toroidal field is comparable to the kinematic viscosity that was determined earlier by comparing the stress with the shear. However, the turbulent diffusion of the radial field component is smaller and can even be formally negative. The method is then modified to obtain the spectral dependence of the turbulent transport coefficients on the wavenumber. There is evidence for nonlocal behaviour in that most of the response comes from the smallest wavenumbers corresponding to the largest scale possible in the simulation. Again, the turbulent diffusion coefficient for the radial field component is small, or even negative, which is considered unphysical. However, when the diffusion tensor is assumed to be diagonal the radial component of the diffusion tensor is positive, supporting thus the relevance of a nonlocal approach. Finally, model calculations are presented using nonlocal prescriptions of the α-effect and the turbulent diffusion. We emphasize that in all cases the electromotive force exhibits a strong stochastic component which make the α-effect and the turbulent diffusion intrinsically noisy. [ABSTRACT FROM AUTHOR]
- Published
- 2002
- Full Text
- View/download PDF
45. The size and dynamics of magnetic flux structures in magnetohydrodynamic turbulence.
- Author
-
Brandenburg, Axel, Procaccia, Itamar, and Segel, Daniel
- Subjects
- *
MAGNETOHYDRODYNAMICS , *MAGNETIC flux , *MAGNETIC fields - Abstract
Investigates the structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, with respect to coherence in the direction of the magnetic field. Length scale derviced from the MHD equations; Tendency towards alignment of flux lines in tubes; Dynamics of the tubes.
- Published
- 1995
- Full Text
- View/download PDF
46. Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation.
- Author
-
Brandenburg, Axel, Durrer, Ruth, Yiwen Huang, Kahniashvili, Tina, Mandal, Sayan, and Shinji Mukohyama
- Subjects
- *
MAGNETIC fields , *WAVENUMBER , *INFLATIONARY universe , *HELICITY of nuclear particles , *WAVE forces - Abstract
Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions--(i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic helicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
47. Evolution of hydromagnetic turbulence from the electroweak phase transition.
- Author
-
Brandenburg, Axel, Kahniashvili, Tina, Mandal, Sayan, Pol, Alberto Roper, Tevzadze, Alexander G., and Vachaspati, Tanmay
- Subjects
- *
INFLATIONARY universe , *PHASE transitions , *MAGNETIC fields - Abstract
We present new simulations of decaying hydromagnetic turbulence for a relativistic equation of state relevant to the early Universe. We compare helical and nonhelical cases either with kinetically or magnetically dominated initial fields. Both kinetic and magnetic initial helicities lead to maximally helical magnetic fields after some time, but with different temporal decay laws. Both are relevant to the early Universe, although no mechanisms have yet been identified that produce magnetic helicity with strengths comparable to the big bang nucleosynthesis limit at scales comparable to the Hubble horizon at the electroweak phase transition. Nonhelical magnetically dominated fields could still produce picoGauss magnetic fields under most optimistic conditions. Only helical magnetic fields can potentially have nanoGauss strengths at scales up to 30 kpc today. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
48. Introduction.
- Author
-
Brandenburg, Axel and Rogachevskii, Igor
- Subjects
- *
TURBULENCE , *ELECTRIC generators , *MAGNETIC fields - Abstract
An introduction is presented in which the editor discusses various reports within the issue on topics including mean-field dynamo theory, the description of turbulence in terms of a restricted number of modes, and convectively driven dynamos.
- Published
- 2013
- Full Text
- View/download PDF
49. QUENCHING AND ANISOTROPY OF HYDROMAGNETIC TURBULENT TRANSPORT.
- Author
-
Karak, Bidya Binay, Rheinhardt, Matthias, Brandenburg, Axel, Käpylä, Petri J., and Käpylä, Maarit J.
- Subjects
MAGNETOHYDRODYNAMIC waves ,TURBULENCE ,MAGNETIC fields ,EQUIPARTITION theorem ,CONVECTION (Astrophysics) - Abstract
Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
50. MAGNETIC FIELDS FROM QCD PHASE TRANSITIONS.
- Author
-
Tevzadze, Alexander G., Kisslinger, Leonard, Brandenburg, Axel, and Kahniashvili, Tina
- Subjects
QUANTUM chromodynamics ,MAGNETIC fields ,STOCHASTIC processes ,METAPHYSICAL cosmology ,GALACTIC magnetic fields - Abstract
We study the evolution of QCD phase transition-generated magnetic fields (MFs) in freely decaying MHD turbulence of the expanding universe. We consider an MF generation model that starts from basic non-perturbative QCD theory and predicts stochastic MFs with an amplitude of the order of 0.02 μG and small magnetic helicity. We employ direct numerical simulations to model the MHD turbulence decay and identify two different regimes: a “weakly helical” turbulence regime, when magnetic helicity increases during decay, and “fully helical” turbulence, when maximal magnetic helicity is reached and an inverse cascade develops. The results of our analysis show that in the most optimistic scenario the magnetic correlation length in the comoving frame can reach 10 kpc with the amplitude of the effective MF being 0.007 nG. We demonstrate that the considered model of magnetogenesis can provide the seed MF for galaxies and clusters. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
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