On generation of magnetic field in astrophysical bodies

Fluids, 2021

In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range.

Physical Review E, 2001

A weak fluctuating magnetic field embedded into a turbulent conducting medium grows exponentially while its characteristic scale decays. In the interstellar medium and protogalactic plasmas, the magnetic Prandtl number is very large, so a broad spectrum of growing magnetic fluctuations is excited at small (subviscous) scales. The condition for the onset of nonlinear back reaction depends on the structure of the field lines. We study the statistical correlations that are set up in the field pattern and show that the magnetic-field lines possess a folding structure, where most of the scale decrease is due to the field variation across itself (rapid transverse direction reversals), while the scale of the field variation along itself stays approximately constant. Specifically, we find that, though both the magnetic energy and the mean-square curvature of the field lines grow exponentially, the field strength and the field-line curvature are anticorrelated, i.e., the curved field is relatively weak, while the growing field is relatively flat. The detailed analysis of the statistics of the curvature shows that it possesses a stationary limiting distribution with the bulk located at the values of curvature comparable to the characteristic wave number of the velocity field and a power tail extending to large values of curvature where it is eventually cut off by the resistive regularization. The regions of large curvature, therefore, occupy only a small fraction of the total volume of the system. Our theoretical results are corroborated by direct numerical simulations. The implication of the folding effect is that the advent of the Lorentz back reaction occurs when the magnetic energy approaches that of the smallest turbulent eddies. Our results also directly apply to the problem of statistical geometry of the material lines in a random flow.

International Journal of Modern Physics A, 2008

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what's most important, is that, at late times, the magnetic-induction contrast (δB/B) grows, resulting in the enhancement of the ambient magnetic field. This process can be particularly favored by condensations, formed within the plasma fluid due to gravitational instabilities.

Lecture Notes in Physics, 2003

2001

We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers. The field grows exponentially with the Kulsrud-Anderson k 3/2 spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity. Further growth proceeds more slowly until a saturated state is reached where the magnetic and kinetic energies are equal, and where the magnetic energy exists primarily at the resistive scale. We discuss the structure of this turbulence and the extrapolation of the results to astrophysicallylarge Prandtl numbers.

Journal of Turbulence, 2019

We use direct numerical simulations to study the dynamics of incompressible homogeneous turbulence subjected to a uniform magnetic field B (the Alfvén velocity) in a rotating frame with rotation vector Ω. We consider two cases: Ω B and Ω ⊥ B. The initial flow state is homogeneous isotropic hydrodynamic turbulence with kinetic Reynolds number Re = u l l/ν 170. The magnetic Prandtl number is Pm = ν/η = 1 and the Elsasser number Λ = B 2 /(2Ωη) = 0.5, 0.9 or 2. Both for Ω B and Ω ⊥ B, the total (kinetic + magnetic) energy E decays as ∼ t −5/7 for Λ = 0.5 and 0.9, and as ∼ t −6/7 for Λ = 2. In the spectral range 2 < k < 20, the radial (spherically averaged) spectrum of kinetic energy scales as ∼ k −p where the index p increases with time (2 ≤ p ≤ 4.2), or equivalently, with the interaction parameter N = B 2 l/(ηu l). This time-dependent scaling is similar to that observed in quasi-static MHD. The two rotating MHD flow cases differ mainly in how kinetic and magnetic fluctuations exchange energy, with a mechanism mostly driven by the dynamics of the spectral buffer layer around k Ω = |Ω•k|/Ω ≈ 0. At k Ω = 0, both the frequencies of inertial and Alfvén waves vanish when Ω B, but only the frequency of inertial waves vanishes for the case when Ω ⊥ B. When Ω B, rotation results in an increased reduction of magnetic fluctuations generation. In terms of anisotropy, we show that the elongated structures occurring in rapidly non-magnetized rotating flows are distorted or inhibited for Ω ⊥ B, and their intensity is weakened for Ω B.

Journal of Plasma Physics, 2019

In hydrodynamic and MHD (magnetohydrodynamic) turbulence, formal expressions for the transfer rates rely on integrals over wavenumber triads (k, p, q) satisfying k+p+q = 0. As an example S uu E (k|p, q) denotes the kinetic energy transfer rate to the mode k, from the two other modes in the triad, p and q. However as noted by , in S uu E (k|p, q), what fraction of the energy transferred to the mode k originated from p and which from q is unknown . Such an expression is thus incongruent with the customary description of turbulence in terms of two-scale energy exchange. Notwithstanding this issue, further decomposed these transfers into separate contributions from p-to-k and q-to-k, thus introducing the concept of mode-to-mode transfers that they applied to MHD turbulence. Doing so, they had to set aside additional transfers circulating within each triad, but failed to calculate them. In the present paper we explain how to derive the complete expressions of the mode-tomode transfers, including the circulating transfers. We do it for kinetic energy and kinetic helicity in hydrodynamic turbulence, for kinetic energy, magnetic energy and magnetic helicity in MHD turbulence. We find that the degree of non-uniqueness of the energy transfers derived from the induction equation is a priori higher than the one derived from the Navier-Stokes equations. However separating the contribution of magnetic advection from magnetic stretching, the energy mode-to-mode transfer rates involving the magnetic field become uniquely defined, in striking contrast to the hydrodynamic case. The magnetic helicity mode-to-mode transfer rate is also found to be uniquely defined, contrary to kinetic helicity in hydrodynamics. We find that shell-to-shell transfer rates have the same properties as mode-to-mode transfer rates. Finally calculating the fluxes, we show how the circulating transfers cancel in accordance with conservation laws.

The Astrophysical Journal, 2009

We present numerical simulations of driven magnetohydrodynamic (MHD) turbulence with weak/moderate imposed magnetic fields. The main goal is to clarify dynamics of magnetic field growth. We also investigate the effects of the imposed magnetic fields on the MHD turbulence, including, as a limit, the case of zero external field. Our findings are as follows. First, when we start off simulations with weak mean magnetic field only (or with small scale random field with zero imposed field), we observe that there is a stage at which magnetic energy density grows linearly with time. Runs with different numerical resolutions and/or different simulation parameters show consistent results for the growth rate at the linear stage. Second, we find that, when the strength of the external field increases, the equilibrium kinetic energy density drops by roughly the product of the rms velocity and the strength of the external field. The equilibrium magnetic energy density rises by roughly the same amount. Third, when the external magnetic field is not very strong (say, less than ∼ 0.2 times the rms velocity when measured in the units of Alfven speed), the turbulence at large scales remains statistically isotropic, i.e. there is no apparent global anisotropy of order B 0 /v. We discuss implications of our results on astrophysical fluids.

The Astrophysical Journal, 2019

We demonstrate the conversion process of helical (nonhelical) kinetic energy into magnetic energy using a fieldstructure model based on the magnetic induction equation. This approach aims to explain the generation, transport, and conservation of magnetic helicity dependent on a forcing method such as kinetic or magnetic forcing. When a system is driven by helical kinetic or magnetic energy, two kinds of magnetic helicities with opposite signs are induced. Then, asymmetric competing processes between them determine the dominant magnetic helicity. Also, the model shows that the conservation of magnetic helicity is related to a common current density and antiparallel magnetic fields in the large-and small-scale regimes. In addition to the intuitive method, we suggest an analytical method to find the α and β coefficients using temporally evolving large-scale magnetic energy and magnetic helicity. The method implies that the α effect and its quenching are generally consistent with the conventional theory. However, the β coefficient implies that the role of kinetic energy in a dynamo may be somewhat different from our conventional understanding. We also show how the kinetic energy near the viscous scale can suppress the dynamo process when the magnetic Prandtl number (Pr M ) is small. We verify this using simulation results. Finally, using the α 2 effect and differential rotation effect, we suggest a solar dynamo model that explains the periodic magnetic evolution in the Sun.

New Journal of Physics, 2002

The growth and saturation of magnetic field in conducting turbulent media with large magnetic Prandtl numbers are investigated. This regime is very common in low-density hot astrophysical plasmas. During the early (kinematic) stage, weak magnetic fluctuations grow exponentially and concentrate at the resistive scale, which lies far below the hydrodynamic viscous scale. The evolution becomes nonlinear when the magnetic energy is comparable to the kinetic energy of the viscous-scale eddies. A physical picture of the ensuing nonlinear evolution of the MHD dynamo is proposed. Phenomenological considerations are supplemented with a simple Fokker-Planck model of the nonlinear evolution of the magnetic-energy spectrum. It is found that, while the shift of the bulk of the magnetic energy from the subviscous scales to the velocity scales may be possible, it occurs very slowly-at the resistive, rather than dynamical, time scale (for galaxies, this means that generation of large-scale magnetic fields cannot be explained by this mechanism). The role of Alfvénic motions and the implications for the fully developed isotropic MHD turbulence are discussed.

2002

The Astrophysical Journal, 2011

Recent observations indicate that kinetic and magnetic energies are not in equipartition in the solar wind turbulence. Rather, magnetic fluctuations are more energetic and have somewhat steeper energy spectrum compared to the velocity fluctuations. This leads to the presence of the so-called residual energy E r = E v − E b in the inertial interval of turbulence. This puzzling effect is addressed in the present paper in the framework of weak turbulence theory. Using a simple model of weakly colliding Alfvén waves, we demonstrate that the kinetic-magnetic equipartition indeed gets broken as a result of nonlinear interaction of Alfvén waves. We establish that magnetic energy is indeed generated more efficiently as a result of these interactions, which proposes an explanation for the solar wind observations.

Astronomy &amp; Astrophysics, 2015

The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes.

The Astrophysical Journal, 2017

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

The Astrophysical Journal, 2002

We study the intermittency and field-line structure of the MHD turbulence in plasmas with very large magnetic Prandtl numbers. In this regime, which is realized in the interstellar medium, some accretion disks, protogalaxies, galaxy-cluster gas, early Universe, etc., magnetic fluctuations can be excited at scales below the viscous cutoff. The salient feature of the resulting small-scale magnetic turbulence is the folded structure of the fields. It is characterized by very rapid transverse spatial oscillation of the field direction, while the field lines remain largely unbent up to the scale of the flow. Quantitatively, the fluctuation level and the field-line geometry can be studied in terms of the statistics of the field strength and of the field-line curvature. In the kinematic limit, the distribution of the field strength is an expanding lognormal, while that of the field-line curvature K is stationary and has a power tail ∼ K −13/7. The field strength and curvature are anticorrelated, i.e. the growing fields are mostly flat, while the sharply curved fields remain relatively weak. The field, therefore, settles into a reduced-tension state. Numerical simulations demonstrate three essential features of the nonlinear regime. First, the total magnetic energy is equal to the total kinetic energy. Second, the intermittency is partially suppressed compared to the kinematic case, as the fields become more volume-filling and their distribution develops an exponential tail. Third, the folding structure of the field is unchanged from the kinematic case: the anticorrelation between the field strength and the curvature persists and the distribution of the latter retains the same power tail. We propose a model of back reaction based on the folding picture that reproduces all of the above numerical results.