Turbulent dynamo action in a shear flow

We consider the mean electromotive force and a dynamo-generated magnetic field, taking into account the stretching of turbulent magnetic field lines by a shear flow. Calculations are performed by making use of the second-order correlation approximation. In the presence of shear, the mirror symmetry of turbulence can be broken; thus turbulent motions become suitable for the generation of a large-scale magnetic field. Regardless of the shear law, turbulence can lead to a rapid amplification of the mean magnetic field. The growth rate of the mean magnetic field depends on the length-scale: it is faster for the fields with smaller length-scale. The mechanism considered is qualitatively different from the alpha dynamo, and can generate only a magnetic field that is inhomogeneous in the direction of flow. In contrast to the alpha dynamo, this mechanism also allows the generation of two-dimensional fields. The suggested mechanism may play an important role in the generation of magnetic fields in accretion discs, galaxies and jets.     

Radial mixing in the outer Milky Way disc caused by an orbiting satellite

The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun.     

The mean energy of a decaying magnetic field in MHD-turbulence

A magnetic field which is contained in a turbulent, electrically conducting fluid is supposed to decay. The decay time of the mean energy of the fluctuating part of the magnetic field – in contrast with the energy of the mean field – is shown to be determined by the molecular magnetic diffusivity and the correlation length of the turbulence. The investigation is carried out for weak magnetic fields in homogeneous isotropic mirror-symmetric turbulence and in the framework of the second-order correlations approximation.     

The Influence of a Uniform Magnetic Field of Arbitrary Strength on Turbulence

The spectral tensor of turbulent motion in an infinite conductive incompressible medium is given in the case of a uniform magnetic field of any strenght affecting a homogeneous turbulence. With the help of BOCHNER 's theorem we make sure that the trace u_i(x, t) u_i(x, t) is non-negative. The presence of a weak magnetic field causes a damping of the turbulence, in some cases a strengthening. For strong magnetic fields the norms of the velocity vectors parallel and perpendicular to B approach one and the same value. Compared with the correlation length measured perpendicular to the magnetic field the correlation length measured along the magnetic field increases. Furthermore, our formulas have allowed to calculate the dependence of the α-effect on the magnetic field.     

The spontaneous magnetic field direction in an anisotropic MHD dynamo

The phenomenon of magnetic field generation in an astrophysical plasma in the frame of developed magnetohydrodynamic (MHD) turbulence is considered. The functional quantum field renormalization group approach is applied to helical anisotropic MHD developed turbulence which is stabilized by the self-generated homogeneous magnetic field. The purpose of the study is to calculate the value as well as direction of the magnetic field in the stochastic dynamo model. The generated magnetic field is determined by ignoring divergent rotor part of Green function of the magnetic field. It is shown that the magnetic field direction is connected with unique existing vector n describing the anisotropic turbulence forcing.     

From Small-Scale Dynamo to Isotropic MHD Turbulence

We consider the problem of incompressible, forced, nonhelical, homogeneous, isotropic MHD turbulence with no mean magnetic field. This problem is essentially different from the case with externally imposed uniform mean field. There is no scale-by-scale equipartition between magnetic and kinetic energies as would be the case for the Alfvén-wave turbulence. The isotropic MHD turbulence is the end state of the turbulent dynamo which generates folded fields with small-scale direction reversals. We propose that the statistics seen in numerical simulations of isotropic MHD turbulence could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.     

The motion and radiation of electrons in a neutral sheet

The motion and radiation of an electron in the neighbourhood of a neutral sheet are discussed. Formulae for the synchrotron and cyclotron radiation of an electron in an inhomogeneous field are obtained. The results are compared with radiation in a homogeneous field. It is predicted that the momentum of charged particles flying from a neutral sheet may take discrete eigenvalues.     

Motion and radiation of electrons in an inhomogeneous magnetic field

The motion and radiation of electrons in the neighbourhood of a neutral sheet are discussed. Formulae for the synchroton and cyclotron radiations in an inhomogeneous field are given. These results are compared with the radiations in a homogeneous field. It is predicted that the momentum of charged particles flying from the neutral sheet may take discrete eigenvalues.     

Spontaneous Formation of Magnetic Flux Concentrations in Stratified Turbulence

The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma ?? are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L ²/?? _t, where ?? _t is the turbulent diffusivity and L is the scale of the domain. DNSs are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number.     

Large‐scale magnetic flux concentrations from turbulent stresses

In this study we provide the first numerical demonstration of the effects of turbulence on the mean Lorentz force and the resulting formation of large‐scale magnetic structures. Using three‐dimensional direct numerical simulations (DNS) of forced turbulence we show that an imposed mean magnetic field leads to a decrease of the turbulent hydromagnetic pressure and tension. This phenomenon is quantified by determining the relevant functions that relate the sum of the turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean magnetic field. Using such a parameterization, we show by means of two‐dimensional and three‐dimensional mean‐field numerical modelling that an isentropic density stratified layer becomes unstable in the presence of a uniform imposed magnetic field. This large‐scale instability results in the formation of loop‐like magnetic structures which are concentrated at the top of the stratified layer. In three dimensions these structures resemble the appearance of bipolar magnetic regions in the Sun. The results of DNS and mean‐field numerical modelling are in good agreement with theoretical predictions. We discuss our model in the context of a distributed solar dynamo where active regions and sunspots might be rather shallow phenomena (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear magnetic diffusivity in mean-field electrodynamics

We consider non-linear transport and drift processes caused by an inhomogeneous magnetic field in a turbulent fluid. The coefficients of magnetic diffusivity and drift velocity are calculated by making use of the second-order correlation approximation. Transport processes in the presence of a sufficiently strong magnetic field become anisotropic with larger diffusion rate and turbulent electrical resistivity across the field than along the field. Non-linear effects also lead to a drift of the magnetic field away from the regions with a higher magnetic energy.     

On the Influence of a Large-scale Magnetic Field on Turbulent Motions in an Electrically Conducting Medium

This paper deals with turbulent motions in a homogeneous incompressible electrically conducting medium in the presence of a magnetic field which is on average homogeneous and stationary. Using a model in which the turbulence is produced by a stochastic body force, and supposing a weak interaction between motion and magnetic field, a method is developed for calculating the pair correlation tensor of the velocity field from that occuring in a zero magnetic field. As an example, the pair-correlation tensor for a homogeneous stationary turbulence, which is isotropic and mirror-symmetric for zero magnetic field, is determined. With obvious assumptions on the correlation for zero field, two results are obtained. Firstly, the turbulent velocity is reduced by the magnetic field, the component parallel to the field, however, less than those perpendicular to it. Secondly, the correlation length parallel to the field turns out to be greater than the one perpendicular to it, indicating a tendency towards two-dimensional motion. Finally, the possibility of special situations is briefly discussed in which the turbulent velocity is enhanced by the magnetic field, and the anisotropies of the velocity components and the correlation lengths are opposite to those above.     

Mean-field dynamo in partially ionized plasmas – I

There are several astrophysical situations where one needs to study the dynamics of magnetic flux in partially ionized turbulent plasmas. In a partially ionized plasma, the magnetic induction is subjected to the ambipolar diffusion and the Hall effect in addition to the usual resistive dissipation. In this paper, we initiate the study of the kinematic dynamo in a partially ionized turbulent plasma. The Hall effect arises from the treatment of the electrons and the ions as two separate fluids and the ambipolar diffusion due to the inclusion of neutrals as the third fluid. It is shown that these non-ideal effects modify the so-called α effect and the turbulent diffusion coefficient β in a rather substantial way. The Hall effect may enhance or quench the dynamo action altogether. The ambipolar diffusion brings in an α which depends on the mean magnetic field. The new correlations embodying the coupling of the charged fluids and the neutral fluid appear in a decisive manner. The turbulence is necessarily magnetohydrodynamic with new spatial and time-scales. The nature of the new correlations is demonstrated by taking the Alfvénic turbulence as an example.     

Properties of the negative effective magnetic pressure instability

As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large‐scale instability. In this study, hydromagnetic mean‐field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two‐dimensional. The growth rate is found to depend on a parameter β_* characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter β_*. The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle acceleration during the explosive phase of a solar flare

Starting with the quasi-linear equation of the distribution function of particles in a regular electric field, a combined diffusion coefficient in the momentum space conbining the effects of the regular field and a turbulent field is obtained and a combined mechanism of acceleration by the regular and turbulent fields in the neutral sheet of solar proton flares is proposed. It is shown by calculation that conditions in solar proton flares are such that the charged particles can be effectively accelerated to tens of MeV, even ~1 GeV. It is shown that the combined acceleration by a regular electric field and ion-acoustic turbulence pumps the protons and other heavy ions into ranges of energy where they can be accelerated by Langmuir turbulence. By considering the combined acceleration by Langmuir turbulence and the regular electric field, the observed spectrum of energetic protons and the power-law spectrum of energetic electrons can be reproduced.     

Mean electromotive force proportional to mean flow in MILD turbulence

In mean‐field magnetohydrodynamics the mean electromotive force due to velocity and magnetic‐field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small‐scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the α effect, is important for large‐scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross‐helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The reason for magnetospheric substorms and solar flares

It has been proposed that magnetospheric substorms and solar flares are a result of the same mechanism. In our view this mechanism is connected with the escape, or attempted escape, of energized plasma from a region of closed magnetic field lines bounded by a magnetic bottle. In the case of the Earth, it must be plasma that is able to maintain a discrete auroral arc, and we propose that the cross-tail current connected to the arc is filamentary in nature to provide the field-aligned current sheet above the arc. A localized meander of such an intense current filament could be caused by a tearing instability in the neutral sheet. Such a meander will cause an inductive electric field opposing the current change everywhere. In trying to reduce the component of the induction electric field parallel to the magnetic field lines, the plasma must enhance the transverse or cross-tail component; this action leads to eruptive behavior, in agreement with tearing theories. This enhanced induction electric field will cause a discharge along the magnetic neutral line at the apex of the magnetic arches, constituting an impulsive acceleration of all charged particles originally near the neutral line. The products of this phase then undergo betatron acceleration for a second phase. This discharge eventually reduces the electric field along the neutral line, and thereafter the enclosed magnetic flux through the neutral line remains nearly constant. The result is a plasmoid that has definite identity; its buoyancy leads to its escape. The auroral breakup (and solar flare) is the complex plasma response to the changing electromagnetic field.     

Can turbulent plane‐shear flows support large‐scale dynamos?

Turbulent plane‐shear flow is found to show same basic effects of mean‐fieldMHD as rotating turbulence. In particular, the mean electromotive force (EMF) includes highly anisotropic turbulent diffusion and alpha‐effect. Only magnetic diffusion remains for spatially‐uniform turbulence. The question is addressed whether in this case a self‐excitation of a magnetic field by so‐called sher‐current dynamo is possible and the quasilinear theory provides a negative answer. The streamaligned component of the EMF has the sign opposite to that required for dynamo. If, however, the turbulence is not uniform across the flow direction then a dynamo‐active α ‐effect emerges. The critical magnetic Reynolds number for the alpha‐shear dynamo is estimated to be slightly above ten. Possibilities for cross‐checking theoretical predictions with MHD experiments are discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The generation and dissipation of solar and galactic magnetic fields

Turbulent diffusion of magnetic field plays an essential role in the generation of magnetic field in most astrophysical bodies. This paper reviews what can be proved, and what can be believed, about the turbulent diffusion of magnetic field. Observations indicate the dissipation of magnetic field at rates that can be understood only in terms of turbulent diffusion. Theory shows that a largescale weak magnetic field diffuses in a turbulent flow in the same way that smoke is mixed throughout the fluid by the turbulence. The small-scale fields (produced from the large-scale field by the turbulence) are limited in their growth by reconnection of field lines at neutral points, so that the turbulent mixing of field and fluid is not halted by them.Altogether, it appears that the mixing of field and fluid in the observed turbulent motions in the Sun and in the Galaxy is unavoidable. Turbulent diffusion causes decay of the general solar fields in a decade or so, and of the galactic field in 10⁸–10⁹ yr. We conclude that continual dynamo action is implied by the observed existence of the fields.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.     

Magnetic field in a fluctuating <Emphasis Type="Italic">ABC</Emphasis> flow

The standard dynamo models that explain the origin of the large-scale magnetic fields of celestial bodies are related to the view of turbulent or convective flows as a locally statistically homogeneous and isotropic, but not mirror-symmetric, random field. Using an ABC flow, which is a classical example of a flow with deterministic chaos, we ascertain the extent to which the behavior of the magnetic field in such a flow is similar to the behavior of the magnetic field in mirror-asymmetric turbulence. Such a similarity has been found to be achieved if its coefficients A, B, and C are assumed to be random processes.