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  • 51.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Gressel, O.
    Jabbari, Sarah
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, N.
    Rogachevskii, I.
    Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field2014Inngår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 562, artikkel-id A53Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots. Aims. We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. Methods. We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. Results. Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about eight density scale heights. Despite being <= 1% equipartition strength, it is important that their lower part is included within the computational domain to achieve the full strength of the instability. Conclusions. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated. Application to sunspots remains a viable possibility.

  • 52.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Gressel, Oliver
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Käpylä, Petri J.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Helsinki, Finland.
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Mantere, M. J.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    NEW SCALING FOR THE ALPHA EFFECT IN SLOWLY ROTATING TURBULENCE2013Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 762, nr 2, artikkel-id 127Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers and slow rotation. Thus, the contribution of density stratification is less important than that of turbulent velocity. The a effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence), we find that the contribution of density stratification might be even less important than suggested by the analytic theory.

  • 53.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Haugen, N. E. L.
    Li, Xiang-Yu
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). University of Colorado, USA.
    Subramanian, K.
    Varying the forcing scale in low Prandtl number dynamos2018Inngår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 479, nr 2, s. 2827-2833Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion discs, where theymay also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here, we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale separation between the size of the simulation domain and the integral scale of the turbulence, i.e. the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.

  • 54.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Haugen, Nils Erland L.
    Babkovskaia, Natalia
    Turbulent front speed in the Fisher equation: Dependence on Damkohler number2011Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 83, nr 1, s. 016304-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Direct numerical simulations and mean-field theory are used to model reactive front propagation in a turbulent medium. In the mean-field approach, memory effects of turbulent diffusion are taken into account to estimate the front speed in cases in which the Damkohler number is large. This effect is found to saturate the front speed to values comparable with the speed of the turbulent motions. By comparing with direct numerical simulations, it is found that the effective correlation time is much shorter than for nonreacting flows. The nonlinearity of the reaction term is found to make the front speed slightly faster.

  • 55.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Carnegie Mellon University, USA; Ilia State University, Georgia.
    He, Yutong
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Kahniashvili, Tina
    Rheinhardt, Matthias
    Schober, Jennifer
    Relic Gravitational Waves from the Chiral Magnetic Effect2021Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 911, nr 2, artikkel-id 110Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 56.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Carnegie Mellon University, USA; Ilia State University, Georgia.
    He, Yutong
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Sharma, Ramkishor
    Simulations of Helical Inflationary Magnetogenesis and Gravitational Waves2021Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 922, nr 2, artikkel-id 192Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Using numerical simulations of helical inflationary magnetogenesis in a low reheating temperature scenario, we show that the magnetic energy spectrum is strongly peaked at a particular wavenumber that depends on the reheating temperature. Gravitational waves (GWs) are produced at frequencies between 3 nHz and 50 mHz for reheating temperatures between 150 MeV and 3 x 10(5) GeV, respectively. At and below the peak frequency, the stress spectrum is always found to be that of white noise. This implies a linear increase of GW energy per logarithmic wavenumber interval, instead of a cubic one. Both in the helical and nonhelical cases, the GW spectrum is followed by a sharp drop for frequencies above the respective peak frequency. In this magnetogenesis scenario, the presence of a helical term extends the peak of the GW spectrum and therefore also the position of the aforementioned drop toward larger frequencies compared to the case without helicity. This might make a difference in it being detectable with space interferometers. The efficiency of GW production is found to be almost the same as in the nonhelical case, and independent of the reheating temperature, provided the electromagnetic energy at the end of reheating is fixed to be a certain fraction of the radiation energy density. Also, contrary to the case without helicity, the electric energy is now less than the magnetic energy during reheating. The fractional circular polarization is found to be nearly 100% in a certain range below the peak frequency range.

  • 57.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Hochberg, David
    Introduction to Origins of Biological Homochirality2022Inngår i: Origins of life and evolution of the biosphere, ISSN 0169-6149, E-ISSN 1573-0875, Vol. 52, nr 1-3, s. 1-2Artikkel i tidsskrift (Annet vitenskapelig)
  • 58.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Hubbard, A.
    Käpylä, P. J.
    Dynamical quenching with non-local alpha and downward pumping2015Inngår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 336, nr 1, s. 91-96Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In light of new results, the one-dimensional mean-field dynamo model of Brandenburg & Kapyla (2007) with dynamical quenching and a nonlocal Babcock-Leighton a effect is re-examined for the solar dynamo. We extend the one-dimensional model to include the effects of turbulent downward pumping (Kitchatinov & Olemskoy 2011), and to combine dynamical quenching with shear. We use both the conventional dynamical quenching model of Kleeorin & Ruzmaikin (1982) and the alternate one of Hubbard & Brandenburg (2011), and confirm that with varying levels of non-locality in the a effect, and possibly shear as well, the saturation field strength can be independent of the magnetic Reynolds number.

  • 59.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Kahniashvili, Tina
    Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay2017Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 118, nr 5, artikkel-id 055102Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wave number k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k(4)).

  • 60.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Carnegie Mellon University, USA.
    Kahniashvili, Tina
    Mandal, Sayan
    Pol, Alberto Roper
    Tevzadze, Alexander G.
    Vachaspati, Tanmay
    Dynamo effect in decaying helical turbulence2019Inngår i: Physical Review Fluids, E-ISSN 2469-990X, Vol. 4, nr 2, artikkel-id 024608Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity-regardless of whether the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t(-1/2). This is even slower than in the fully helical case, where it decays like t(-2/3). In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity is approximately constant. This scaling of magnetic energy persists over long timescales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a crossover to the t(-2/3) decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe.

  • 61.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Kahniashvili, Tina
    Mandal, Sayan
    Pol, Alberto Roper
    Tevzadze, Alexander G.
    Vachaspati, Tanmay
    Evolution of hydromagnetic turbulence from the electroweak phase transition2017Inngår i: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 96, nr 12, artikkel-id 123528Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 62.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kahniashvili, Tina
    Tevzadze, Alexander G.
    Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field2015Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 114, nr 7Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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 k(2) subinertial range spectrum of kinetic energy forcing the magnetic field with a k(4) 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.

  • 63.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Ilia State University, Georgia; Carnegie Mellon University, USA.
    Kamada, Kohei
    Mukaida, Kyohei
    Schmitz, Kai
    Schober, Jennifer
    Chiral magnetohydrodynamics with zero total chirality2023Inngår i: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 108, nr 6, artikkel-id 063529Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the evolution of magnetic fields coupled with chiral fermion asymmetry in the framework of chiral magnetohydrodynamics with zero initial total chirality. The initial magnetic field has a turbulent spectrum peaking at a certain characteristic scale and is fully helical with positive helicity. The initial chiral chemical potential is spatially uniform and negative. We consider two opposite cases where the ratio of the length scale of the chiral plasma instability (CPI) to the characteristic scale of the turbulence is smaller and larger than unity. These initial conditions might be realized in cosmological models, including certain types of axion inflation. The magnetic field and chiral chemical potential evolve with inverse cascading in such a way that the magnetic helicity and chirality cancel each other at all times, provided there is no spin flipping. The CPI timescale is found to determine mainly the time when the magnetic helicity spectrum attains negative values at high wave numbers. The turnover time of the energy-carrying eddies, on the other hand, determines the time when the peak of the spectrum starts to shift to smaller wave numbers via an inverse cascade. The onset of helicity decay is determined by the time when the chiral magnetic effect becomes efficient at the peak of the initial magnetic energy spectrum, provided the CPI does not grow much. When spin flipping is important, the chiral chemical potential vanishes at late times and the magnetic helicity becomes constant, which leads to a faster increase of the correlation length. This is in agreement with what is expected from magnetic helicity conservation and also happens when the initial total chirality is imbalanced. Our findings have important implications for baryogenesis after axion inflation.

  • 64.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Ilia State University, Georgia; Carnegie Mellon University, USA.
    Kamada, Kohei
    Schober, Jennifer
    Decay law of magnetic turbulence with helicity balanced by chiral fermions2023Inngår i: Physical Review Research, E-ISSN 2643-1564, Vol. 5, nr 2, artikkel-id L022028Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In plasmas composed of massless electrically charged fermions, chirality can be interchanged with magnetic helicity while preserving the total chirality through the quantum chiral anomaly. The decay of turbulent energy in plasmas such as those in the early Universe and compact stars is usually controlled by certain conservation laws. In the case of zero total chirality, when the magnetic helicity density balances with the appropriately scaled chiral chemical potential to zero, the total chirality no longer determines the decay. We propose that in such a case, an adaptation to the Hosking integral, which is conserved in nonhelical magnetically dominated turbulence, controls the decay in turbulence with helicity balanced by chiral fermions. We show, using a high resolution numerical simulation, that this is indeed the case. The magnetic energy density decays and the correlation length increases with time just like in nonhelical turbulence with vanishing chiral chemical potential. But here, the magnetic helicity density is nearly maximum and shows a scaling with time t proportional to t-2/3. This is unrelated to the t-2/3 decay of magnetic energy in fully helical magnetic turbulence. The modulus of the chiral chemical potential decays in the same fashion. This is much slower than the exponential decay previously expected in theories of asymmetric baryon production from the hypermagnetic helicity decay after axion inflation.

  • 65.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kemel, Koen
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, Nathan
    Mitra, Dhrubaditya
    Rogachevskii, Igor
    Detection of Negative Effective Magnetic Pressure Instability in Turbulence Simulations2011Inngår i: Astrophysical Journal, ISSN 0004-637X, EISSN 1538-4357, Vol. 740, nr 2, s. L50-Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 66.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kemel, Koen
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    NEGATIVE EFFECTIVE MAGNETIC PRESSURE IN STRATIFIED FORCED TURBULENCE2012Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 749, nr 2, artikkel-id 179Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 67.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    SELF-ASSEMBLY OF SHALLOW MAGNETIC SPOTS THROUGH STRONGLY STRATIFIED TURBULENCE2013Inngår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 776, nr 2, artikkel-id L23Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Recent studies have demonstrated that in fully developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. In the presence of strongly stratified turbulence, this was shown to lead to a large-scale instability that produces spontaneous magnetic flux concentrations. Furthermore, using a horizontal magnetic field, elongated flux concentrations with a strength of a few percent of the equipartition value were found. Here we show that a uniform vertical magnetic field leads to circular magnetic spots of equipartition field strengths. This could represent a minimalistic model of sunspot formation and highlights the importance of two critical ingredients: turbulence and strong stratification. Radiation, ionization, and supergranulation may be important for realistic simulations, but are not critical at the level of a minimalistic model of magnetic spot formation.

  • 68.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Ilia State University, Georgia; Carnegie Mellon University, USA.
    Larsson, Gustav
    Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Turbulence with Magnetic Helicity That Is Absent on Average2023Inngår i: Atmosphere, E-ISSN 2073-4433, Vol. 14, nr 6, artikkel-id 932Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Magnetic helicity plays a tremendously important role when it is different from zero on average. Most notably, it leads to the phenomenon of an inverse cascade. Here, we consider decaying magnetohydrodynamic (MHD) turbulence as well as some less common examples of magnetic evolution under the Hall effect and ambipolar diffusion, as well as cases in which the magnetic field evolution is constrained by the presence of an asymmetry in the number density of chiral fermions, whose spin is systematically either aligned or anti-aligned with its momentum. In all those cases, there is a new conserved quantity: the Hosking integral. We present quantitative scaling results for the magnetic integral scale as well as the magnetic energy density and its spectrum. We also compare with cases were a magnetic version of the Saffman integral is initially finite. Rotation in MHD turbulence tends to suppress nonlinearity and thereby also inverse cascading. Finally, the role of the Hosking and magnetic Saffman integrals in shell models of turbulence is examined.

  • 69.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Lazarian, A.
    Astrophysical Hydromagnetic Turbulence2014Inngår i: Microphysics of Cosmic Plasmas / [ed] Balogh, A.; Bykov, A.; Cargill, P.; Dendy, R.; DeWit, T. D.; Raymond, J., Dordrecht: Springer, 2014, s. 87-124Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich-Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered.

  • 70.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Lazarian, A.
    Astrophysical Hydromagnetic Turbulence2013Inngår i: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 178, nr 2-4, s. 163-200Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich-Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered.

  • 71.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Mathur, Savita
    Metcalfe, Travis S.
    Evolution of Co-existing Long and Short Period Stellar Activity Cycles2017Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 845, nr 1, artikkel-id 79Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The magnetic activity of the Sun becomes stronger and weaker over roughly an 11 year cycle, modulating the radiation and charged particle environment experienced by the Earth as space weather. Decades of observations from the Mount Wilson Observatory have revealed that other stars also show regular activity cycles in their Ca II H+K line emission, and identified two different relationships between the length of the cycle and the rotation rate of the star. Recent observations at higher cadence have allowed the discovery of shorter cycles with periods between 1-3 years. Some of these shorter cycles coexist with longer cycle periods, suggesting that two underlying dynamos can operate simultaneously. We combine these new observations with previous data, and show that the longer and shorter cycle periods agree remarkably well with those expected from an earlier analysis based on the mean activity level and the rotation period. The relative turbulent length scales associated with the two branches of cyclic behavior suggest that a near-surface dynamo may be the dominant mechanism that drives cycles in more active stars, whereas a dynamo operating in deeper layers may dominate in less active stars. However, several examples of equally prominent long and short cycles have been found at all levels of activity of stars younger than 2.3 Gyr. Deviations from the expected cycle periods show no dependence on the depth of the convection zone or on the metallicity. For some stars that exhibit longer cycles, we compute the periods of shorter cycles that might be detected with future high-cadence observations.

  • 72.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Nordlund, Åke
    Astrophysical turbulence modeling2011Inngår i: Reports on progress in physics (Print), ISSN 0034-4885, E-ISSN 1361-6633, Vol. 74, nr 4, s. 046901-Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non-coarse-grained) fields.

  • 73.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Ntormousi, Evangelia
    Dynamo effect in unstirred self-gravitating turbulence2022Inngår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 513, nr 2, s. 2136-2151Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In many astrophysical environments, self-gravity can generate kinetic energy, which, in principle, is available for driving dynamo action. Using direct numerical simulations, we show that in unstirred self-gravitating subsonic turbulence with helicity and a magnetic Prandtl number of unity, there is a critical magnetic Reynolds number of about 25 above which the work done against the Lorentz force exceeds the Ohmic dissipation. The collapse itself drives predominantly irrotational motions that cannot be responsible for dynamo action. We find that, with a weak magnetic field, one-third of the work done by the gravitational force goes into compressional heating and the remaining two-thirds go first into kinetic energy of the turbulence before a fraction of it is converted further into magnetic and finally thermal energies. Close to the collapse, however, these fractions change toward 1/4 and 3/4 for compressional heating and kinetic energy, respectively. When the magnetic field is strong, the compressional heating fraction is unchanged. Out of the remaining kinetic energy, one quarter goes directly into magnetic energy via work against the Lorentz force. The fraction of vortical motions diminishes in favour of compressive motions that are almost exclusively driven by the Jeans instability. For an initially uniform magnetic field, field amplification at scales larger than those of the initial turbulence are driven by tangling.

  • 74.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Carnegie Mellon University, USA; Ilia State University, Georgia.
    Ntormousi, Evangelia
    Galactic Dynamos2023Inngår i: Annual Review of Astronomy and Astrophysics, ISSN 0066-4146, E-ISSN 1545-4282, Vol. 61, s. 561-606Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    Spiral galaxies, including the Milky Way, have large-scale magnetic fields with significant energy densities. The dominant theory attributes these magnetic fields to a large-scale dynamo.We review the current status of dynamo theory and discuss various numerical simulations designed either to explain particular aspects of the problem or to reproduce galactic magnetic fields globally. Our main conclusions can be summarized as follows: Idealized direct numerical simulations produce mean magnetic fields, whose saturation energy density tends to decline with increasing magnetic Reynolds number. This is still an unsolved problem. Large-scale galactic magnetic fields of microgauss strengths can probably be explained only if helical magnetic fields of small or moderate length scales can be rapidly ejected or destroyed. Small-scale dynamos are important throughout a galaxy's life and probably provide strong seed fields at early stages. The circumgalactic medium (CGM) may play an important role in driving dynamo action at small and large length scales. These interactions between the galactic disk and the CGM may provide important insights into our understanding of galactic dynamos. We expect future research in galactic dynamos to focus on the cosmological history of galaxies and the interaction with the CGM as means of replacing the idealized boundary conditions used in earlier work.

  • 75.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Carnegie Mellon University, USA; University of Waikato, New Zealand.
    Oughton, S.
    Cross-helically forced and decaying hydromagnetic turbulence2018Inngår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, nr 9-10, s. 641-646Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find a weak inverse transfer of kinetic energy toward the smallest wavenumber. This is plausibly explained by the finiteness of scale separation between the injection wavenumber and the smallest wavenumber of the domain, which here is a factor of 15. In the decaying case, there is a slight increase at the smallest wavenumber, which is probably explained by the dominance of kinetic energy over magnetic energy at the smallest wavenumbers. Within a range of wavenumbers covering almost an order of magnitude, the decay is purely exponential, which is argued to be a consequence of a suppression of nonlinearity due to the presence of strong cross helicity.

  • 76.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Petrie, Gordon J. D.
    Singh, Nishant K.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Two-scale Analysis of Solar Magnetic Helicity2017Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 836, nr 1, artikkel-id 21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancellation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three dimensional a effect-type dynamo-generated magnetic field, with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161-2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at approximate to 0.06 Mm(-1) (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven a effect-type dynamos.

  • 77.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Petrosyan, A.
    Kinetic helicity decay in linearly forced turbulence2012Inngår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, nr 3, s. 195-201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is found to decay on a turbulent time scale regardless of the nature of the forcing and the value of the Reynolds number

  • 78.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). School of Natural Sciences and Medicine, Ilia State University, Georgia; McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, USA.
    Protiti, Nousaba Nasrin
    Electromagnetic Conversion into Kinetic and Thermal Energies2023Inngår i: Entropy, E-ISSN 1099-4300, Vol. 25, nr 9, artikkel-id 1270Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The conversion of electromagnetic energy into magnetohydrodynamic energy occurs when the electric conductivity changes from negligible to finite values. This process is relevant during the epoch of reheating in the early universe at the end of inflation and before the emergence of the radiation-dominated era. We find that the conversion into kinetic and thermal energies is primarily the result of electric energy dissipation, while magnetic energy only plays a secondary role in this process. This means that since electric energy dominates over magnetic energy during inflation and reheating, significant amounts of electric energy can be converted into magnetohydrodynamic energy when conductivity emerges before the relevant length scales become stable.

  • 79.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Raedler, K-H
    Yoshizawa's cross-helicity effect and its quenching2013Inngår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 107, nr 1-2, s. 207-217Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A central quantity in mean-field magnetohydrodynamics is the mean electromotive force , which in general depends on the mean magnetic field. It may however also have a part independent of the mean magnetic field. Here we study an example of a rotating conducting body of turbulent fluid with non-zero cross-helicity, in which a contribution to proportional to the angular velocity occurs (Yoshizawa, A., Self-consistent turbulent dynamo modeling of reversed field pinches and planetary magnetic fields. Phys. Fluids B 1990, 2, 15891600). If the forcing is helical, it also leads to an effect, and large-scale magnetic fields can be generated. For not too rapid rotation, the field configuration is such that Yoshizawa's contribution to is considerably reduced compared to the case without effect. In that case, large-scale flows are also found to be generated.

  • 80.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Raedler, K-H
    Kemel, Koen
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Mean field transport in stratified and/or rotating turbulence2012Inngår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 539, s. A35-Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 81.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Carnegie Mellon University, USA.
    Rempel, Matthias
    Reversed Dynamo at Small Scales and Large Magnetic Prandtl Number2019Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 879, nr 1, artikkel-id 57Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is the opposite of that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action occurs, i.e., magnetic energy is converted back into kinetic energy at small scales. We demonstrate this in both direct numerical simulations forced by volume stirring and in large eddy simulations (LESs) of solar convectively driven small-scale dynamos. Low-density plasmas such as stellar coronae tend to have large magnetic Prandtl numbers, i.e., the viscosity is large compared with the magnetic diffusivity. The regime in which viscous dissipation dominates over resistive dissipation for large magnetic Prandtl numbers was also previously found in LESs of the solar corona, i.e., our findings are a more fundamental property of MHD that is not just restricted to dynamos. Viscous energy dissipation is a consequence of positive Lorentz force work, which may partly correspond to particle acceleration in close-to-collisionless plasmas. This is, however, not modeled in the MHD approximation employed. By contrast, resistive energy dissipation on current sheets is expected to be unimportant in stellar coronae.

  • 82.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Magnetic concentrations in stratified turbulence: the negative effective magnetic pressure instability2016Inngår i: New Journal of Physics, E-ISSN 1367-2630, Vol. 18, artikkel-id 125011Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the presence of strong density stratification, hydromagnetic turbulence attains qualitatively new properties: the formation of magnetic flux concentrations. We review here the theoretical foundations of this mechanism in terms of what is now called the negative effective magnetic pressure instability. We also present direct numerical simulations of forced turbulence in strongly stratified layers and discuss the qualitative and quantitative similarities with corresponding mean-field simulations. Finally, the relevance to sunspot formation is discussed.

  • 83.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Schober, Jennifer
    Dissipative magnetic structures and scales in small-scale dynamos2023Inngår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 518, nr 4, s. 6367-6375Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Small-scale dynamos play important roles in modern astrophysics, especially on galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time-scale of galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that, during the kinematic phase of the small-scale dynamo, the cutoff wavenumber of the magnetic energy spectra scales as expected for large magnetic Prandtl numbers, but continues in the same way also for moderately small values – contrary to what is expected. For a critical magnetic Prandtl number of about 0.3, the dissipative and resistive cutoffs are found to occur at the same wavenumber. In the non-linearly saturated regime, the critical magnetic Prandtl number becomes unity. The cutoff scale now has a shallower scaling with magnetic Prandtl number below a value of about three, and a steeper one otherwise compared to the kinematic regime.

  • 84.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Carnegie Mellon University, USA.
    Scannapieco, Evan
    Magnetic Helicity Dissipation and Production in an Ideal MHD Code2020Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 889, nr 1, artikkel-id 55Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales. As a consequence, the small-scale current helicity is too small compared with that of the DNS. The resulting net current helicity has then always the wrong sign, and its statistical average also does not approach zero at late times, as expected from the DNS. Our results have implications for astrophysical dynamo simulations of stellar and galactic magnetism using ideal MHD codes.

  • 85.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA; University of the Negev, Israel.
    The contribution of kinetic helicity to turbulent magnetic diffusivity2017Inngår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 338, nr 7, s. 790-793Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 86.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA; Ben-Gurion University of the Negev, Israel.
    Kahniashvili, Tina
    Boyarsky, Alexey
    Fröhlich, Jürg
    Ruchayskiy, Oleg
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    The Turbulent Chiral Magnetic Cascade in the Early Universe2017Inngår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, nr 2, artikkel-id L21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The presence of asymmetry between fermions of opposite handedness in plasmas of relativistic particles can lead to exponential growth of a helical magnetic field via a small-scale chiral dynamo instability known as the chiral magnetic effect. Here, we show, using dimensional arguments and numerical simulations, that this process produces through the Lorentz force chiral magnetically driven turbulence. A k(-2) magnetic energy spectrum emerges via inverse transfer over a certain range of wavenumbers k. The total chirality (magnetic helicity plus normalized chiral chemical potential) is conserved in this system. Therefore, as the helical magnetic field grows, most of the total chirality gets transferred into magnetic helicity until the chiral magnetic effect terminates. Quantitative results for height, slope, and extent of the spectrum are obtained. Consequences of this effect for cosmic magnetic fields are discussed.

  • 87.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Carnegie Mellon University, USA; Ilia State University, Georgia.
    Sharma, Ramkishor
    Simulating Relic Gravitational Waves from Inflationary Magnetogenesis2021Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 920, nr 1, artikkel-id 26Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present three-dimensional direct numerical simulations of the production of magnetic fields and gravitational waves (GWs) in the early universe during a low energy scale matter-dominated post-inflationary reheating era, and during the early subsequent radiative era, which is strongly turbulent. The parameters of the model are determined such that it avoids a number of known physical problems and produces magnetic energy densities between 0.03% and 0.5% of the critical energy density at the end of reheating. During the subsequent development of a turbulent magnetohydrodynamic cascade, magnetic fields and GWs develop a spectrum that extends to higher frequencies in the millihertz (nanohertz) range for models with reheating temperatures of around 100 GeV (150 MeV) at the beginning of the radiation-dominated era. However, even though the turbulent cascade is fully developed, the GW spectrum shows a sharp drop for frequencies above the peak value. This suggests that the turbulence is less efficient in driving GWs than previously thought. The peaks of the resulting GW spectra may well be in the range accessible to space interferometers, pulsar timing arrays, and other facilities.

  • 88.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Sharma, Ramkishor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Vachaspati, Tanmay
    Inverse cascading for initial magnetohydrodynamic turbulence spectra between Saffman and Batchelor2023Inngår i: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 89, nr 6, artikkel-id 905890606Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic field, the spectral magnetic energy density is known to increase with time at small wavenumbers k, provided the spectrum at low k is sufficiently steep. This process is called inverse cascading and occurs for an initial Batchelor spectrum, where the magnetic energy per linear wavenumber interval increases like k(4). For an initial Saffman spectrum that is proportional to k(2), however, inverse cascading has not been found in the past. We study here the case of an intermediate k(3) spectrum, which may be relevant for magnetogenesis in the early Universe during the electroweak epoch. This case is not well understood in view of the standard Taylor expansion of the magnetic energy spectrum for small k. Using high resolution MHD simulations, we show that, also in this case, there is inverse cascading with a strength just as expected from the conservation of the Hosking integral, which governs the decay of an initial Batchelor spectrum. Even for shallower k(alpha) spectra with spectral index alpha > 3/2, our simulations suggest a spectral increase at small k with time t proportional to t(4 alpha/9-2/3). The critical spectral index of alpha = 3/2 is related to the slope of the spectral envelope in the Hosking phenomenology. Our simulations with 2048(3) mesh points now suggest inverse cascading even for an initial Saffman spectrum.

  • 89.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Sokoloff, Dmitry
    Subramanian, Kandaswamy
    Current Status of Turbulent Dynamo Theory From Large Scale to Small-Scale Dynamos2012Inngår i: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 169, nr 1-4, s. 123-157Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

  • 90.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Stepanov, Rodion
    FARADAY SIGNATURE OF MAGNETIC HELICITY FROM REDUCED DEPOLARIZATION2014Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 786, nr 2, s. 91-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Using one-dimensional models, we show that a helical magnetic field with an appropriate sign of helicity can compensate the Faraday depolarization resulting from the superposition of Faraday-rotated polarization planes from a spatially extended source. For radio emission from a helical magnetic field, the polarization as a function of the square of the wavelength becomes asymmetric with respect to zero. Mathematically speaking, the resulting emission occurs then either at observable or at unobservable (imaginary) wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the reconstruction of the underlying Faraday dispersion function in the former case, but not in the latter. The presence of positive magnetic helicity can thus be detected by observing positive RM in highly polarized regions in the sky and negative RM in weakly polarized regions. Conversely, negative magnetic helicity can be detected by observing negative RM in highly polarized regions and positive RM in weakly polarized regions. The simultaneous presence of two magnetic constituents with opposite signs of helicity is shown to possess signatures that can be quantified through polarization peaks at specific wavelengths and the gradient of the phase of the Faraday dispersion function. Similar polarization peaks can tentatively also be identified for the bi-helical magnetic fields that are generated self-consistently by a dynamo from helically forced turbulence, even though the magnetic energy spectrum is then continuous. Finally, we discuss the possibility of detecting magnetic fields with helical and non-helical properties in external galaxies using the Square Kilometre Array.

  • 91.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Subramanian, Kandaswamy
    Balogh, Andre
    Goldstein, Melvyn L.
    SCALE DEPENDENCE OF MAGNETIC HELICITY IN THE SOLAR WIND2011Inngår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 734, nr 1, s. 9-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k approximate to 2 AU(-1) (or frequency nu approximate to 2 mu Hz) at distances below 2.8 AU and at k approximate to 30 AU(-1) (or nu approximate to 25 mu Hz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 10(45) Mx(2) cycle(-1) at large scales and to a three times lower value at smaller scales.

  • 92.
    Brandenburg, Axel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Zhou, Hongzhe
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Shanghai Jiao Tong University, People’s Republic of China.
    Sharma, Ramkishor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos2023Inngår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 518, nr 3, s. 3312-3325Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The magnetic fields in galaxy clusters and probably also in the interstellar medium are believed to be generated by a small-scale dynamo. Theoretically, during its kinematic stage, it is characterized by a Kazantsev spectrum, which peaks at the resistive scale. It is only slightly shallower than the Saffman spectrum that is expected for random and causally connected magnetic fields. Causally disconnected fields have the even steeper Batchelor spectrum. Here, we show that all three spectra are present in the small-scale dynamo. During the kinematic stage, the Batchelor spectrum occurs on scales larger than the energy-carrying scale of the turbulence, and the Kazantsev spectrum on smaller scales within the inertial range of the turbulence – even for a magnetic Prandtl number of unity. In the saturated state, the dynamo develops a Saffman spectrum on large scales, suggestive of the build-up of long-range correlations. At large magnetic Prandtl numbers, elongated structures are seen in synthetic synchrotron emission maps showing the parity-even E polarization. We also observe a significant excess in the E polarization over the parity-odd B polarization at subresistive scales, and a deficiency at larger scales. This finding is at odds with the observed excess in the Galactic microwave foreground emission, which is believed to be associated with larger scales. The E and B polarizations may be highly non-Gaussian and skewed in the kinematic regime of the dynamo. For dust emission, however, the polarized emission is always nearly Gaussian, and the excess in the E polarization is much weaker. 

  • 93. Bushby, P. J.
    et al.
    Käpylä, P. J.
    Masada, Y.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Favier, B.
    Guervilly, C.
    Käpylä, M. J.
    Large-scale dynamos in rapidly rotating plane layer convection2018Inngår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 612, artikkel-id A97Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 94. Bykov, A. M.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Malkov, M. A.
    Osipov, S. M.
    Microphysics of Cosmic Ray Driven Plasma Instabilities2014Inngår i: Microphysics of Cosmic Plasmas / [ed] Balogh, A.; Bykov, A.; Cargill, P.; Dendy, R.; DeWit, T. D.; Raymond, J., Dordrcht: Springer, 2014, s. 125-156Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.

  • 95. Bykov, A. M.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Malkov, M. A.
    Osipov, S. M.