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  • 1.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kemel, Koen
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Mitra, Dhrubaditya
    Rogachevskii, Igor
    Detection of Negative Effective Magnetic Pressure Instability in Turbulence Simulations2011In: Astrophysical Journal, ISSN 0004-637X, EISSN 1538-4357, Vol. 740, no 2, p. L50-Article in journal (Refereed)
    Abstract [en]

    We present the first numerical demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number. Our results support earlier mean-field calculations and analytic work that identified this instability. Applications to the formation of active regions in the Sun are discussed.

  • 2.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kemel, Koen
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    NEGATIVE EFFECTIVE MAGNETIC PRESSURE IN STRATIFIED FORCED TURBULENCE2012In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 749, no 2, article id 179Article in journal (Refereed)
    Abstract [en]

    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.

  • 3.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Raedler, K-H
    Kemel, Koen
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Mean field transport in stratified and/or rotating turbulence2012In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 539, p. A35-Article in journal (Refereed)
    Abstract [en]

    Context. The large-scale magnetic fields of stars and galaxies are often described in the framework of mean-field dynamo theory. At moderate magnetic Reynolds numbers, the transport coefficients defining the mean electromotive force can be determined from simulations. This applies analogously also to passive scalar transport. Aims. We investigate the mean electromotive force in the kinematic framework, that is, ignoring the back-reaction of the magnetic field on the fluid velocity, under the assumption of axisymmetric turbulence determined by the presence of either rotation, density stratification, or both. We use an analogous approach for the mean passive scalar flux. As an alternative to convection, we consider forced turbulence in an isothermal layer. When using standard ansatzes, the mean magnetic transport is then determined by nine, and the mean passive scalar transport by four coefficients. We give results for all these transport coefficients. Methods. We use the test-field method and the test-scalar method, where transport coefficients are determined by solving sets of equations with properly chosen mean magnetic fields or mean scalars. These methods are adapted to mean fields which may depend on all three space coordinates. Results. We find the anisotropy of turbulent diffusion to be moderate in spite of rapid rotation or strong density stratification. Contributions to the mean electromotive force determined by the symmetric part of the gradient tensor of the mean magnetic field, which were ignored in several earlier investigations, turn out to be important. In stratified rotating turbulence, the a effect is strongly anisotropic, suppressed along the rotation axis on large length scales, but strongly enhanced at intermediate length scales. Also the Omega x (J) over bar effect is enhanced at intermediate length scales. The turbulent passive scalar diffusivity is typically almost twice as large as the turbulent magnetic diffusivity. Both magnetic and passive scalar diffusion are slightly enhanced along the rotation axis, but decreased if there is gravity. Conclusions. The test-field and test-scalar methods provide powerful tools for analyzing transport properties of axisymmetric turbulence. Future applications are proposed ranging from anisotropic turbulence due to the presence of a uniform magnetic field to inhomogeneous turbulence where the specific entropy is nonuniform, for example. Some of the contributions to the mean electromotive force which have been ignored in several earlier investigations, in particular those given by the symmetric part of the gradient tensor of the mean magnetic field, turn out to be of significant magnitude.

  • 4.
    Kemel, Koen
    Stockholm University, Faculty of Science, Department of Astronomy.
    From mean-field hydromagnetics to solar magnetic flux concentrations2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The main idea behind the work presented in this thesis is to investigate if it is possible to find a mechanism that leads to surface magnetic field concentrations and could operate under solar conditions without postulating the presence of magnetic flux tubes rising from the bottom of the convection zone, a commonly used yet physically problematic approach.

    In this context we study the ‘negative effective magnetic pressure effect’: it was pointed out in earlier work (Kleeorin et al., 1989) that the presence of a weak magnetic field can lead to a reduction of the mean turbulent pressure on large length scales. This reduction is now indeed clearly observed in simulations.

    As magnetic fluctuations experience an unstable feedback through this effect, it leads, in a stratified medium, to the formation of magnetic structures, first observed numerically in the fifth paper of this thesis. While our setup is relatively simple, one wonders if this instability, as a mechanism able to concentrate magnetic fields in the near surface layers, may play a role in the formation of sunspots, starting from a weak dynamo-generated field throughout the convection zone rather than from strong flux tubes stored at the bottom.

    A generalization of the studied case is ongoing.

    Download full text (pdf)
    Comprehensive summary
  • 5.
    Kemel, Koen
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Ji, Hantao
    Model of driven and decaying magnetic turbulence in a cylinder2011In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, p. 56407-Article in journal (Refereed)
    Abstract [en]

    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.

  • 6.
    Kemel, Koen
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Active Region Formation through the Negative Effective Magnetic Pressure Instability2013In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 287, no 1-2, p. 293-313Article in journal (Refereed)
    Abstract [en]

    The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.

  • 7.
    Kemel, Koen
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Spontaneous formation of magnetic flux concentrations in stratified turbulence2012In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 280, no 2, p. 321-333Article in journal (Refereed)
    Abstract [en]

    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, L2/ηt, where ηt 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

  • 8.
    Kemel, Koen
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Non-uniformity effects in the negative effective magnetic pressure instability2013In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T155, article id 014027Article in journal (Refereed)
    Abstract [en]

    In direct numerical simulations of strongly stratified turbulence we have previously studied the development of large scale magnetic structures starting from a uniform background field. This is caused by an instability resulting from a negative contribution of small-scale turbulence to the effective (mean-field) magnetic pressure, and was qualitatively reproduced in mean-field simulations (MFS) where this pressure reduction was modeled as a function of the mean magnetic field normalized by the equipartition field. We now investigate the effect of mean current density on the turbulent pressure reduction. In our MFS, such currents are associated with sharp gradients of the growing structures. We find that an enhanced mean current density increases the suppression of the turbulent pressure.

  • 9.
    Kemel, Koen
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Rogachevskii, Igor
    Nonuniformity effects in the negative effective magnetic pressure instabilityIn: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896Article in journal (Other academic)
  • 10.
    Kemel, Koen
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben‐Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben‐Gurion University of the Negev, Israel.
    Properties of the negative effective magnetic pressure instability2012In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, no 2, p. 95-100Article in journal (Refereed)
    Abstract [en]

    As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter beta(star) characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter beta(star). The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.

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