Dynamo mechanism for turbulent wave in celestial bodies

It is well known that under cosmic conditions the various modes of plasma turbulence waves (including MHD waves) are easily excited. In this paper we are trying to show that the turbulent wave also generates a source-term for the magnetic induced equations as does the turbulent fluid with nonzero helicity. By expanding the turbulent field in Fourier series, we have obtained dynamo equation for turbulent wave and a reasonable solution which indicates that the poloidal field may be built-up in the turbulent source region. Perhaps, we may think that the poloidal field of Equation (9) is the analytical form of the magnetic field in a turbulent source region of celestial bodies.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

Radiative modes of a weakly ionized,collision-dominated,turbulent plasma

We obtain, and discuss, the roots of the dispersion relation describing normal mode propagation in a weakly ionized, collision dominated turbulent plasma with an isotropically distributed turbulent magnetic field. We demonstrate that, depending on the level of the turbulent field relative to the collision frequency, there may, or may not, be propagating, but decaying, modes present in the system. The structure and properties of the modes depend on both the precise level of the turbulent magnetic field and its spatial and temporal correlation.For simple correlation functions we estimate the decay rate of the radiative modes. Using galactic parameters as an illustration we show that only the long-wavelength (low-frequency) modes last for a significant length of time ( a collision time).We have done this calculation to demonstrate that the response of turbulent plasma systems is more complicated than simple order of magnitude calculations indicate; and to illustrate a method which may, perhaps, be gainfully employed in more complex turbulent astrophysical plasma situations than considered here.     

On accretion flow penetration of magnetospheres

We address the problem of plasma penetration of astrophysical magnetospheres, an important issue in a wide variety of contexts, ranging from accretion in cataclysmic variables to flows in protostellar systems. We point out that under well-defined conditions, penetration can occur without any turbulent mixing (driven, for example, by Rayleigh–Taylor or Kelvin–Helmholtz instabilities) caused by charge polarization effects, if the inflowing plasma is bounded in the direction transverse to both the flow velocity and the magnetic field. Depolarization effects limit the penetration depth, which nevertheless can, under specific circumstances, be comparable to the size of the magnetosphere. We discuss the effect of ambient medium on plasma propagation across the stellar magnetic field and determine the criteria for deep magnetosphere penetration. We show that, under conditions appropriate to magnetized white dwarfs in AM Her type cataclysmic variables, charge polarization effects can lead to deep penetration of the magnetosphere.     

Magnetic Reconnection and Turbulent Mixing: From ISM to Clusters of Galaxies

Magnetic reconnection, or the ability of the magnetic field lines that are frozen in plasma to change their topology, is a fundamental problem of magnetohydrodynamics (MHD). Webriefly examine the problem starting with the well-known Sweet-Parker scheme, discuss effectsof tearing modes, anomalous resistivity and the concept of hyperresistivity. We show that the field stochasticity by itself provides a way toenable fast reconnection even if, at the scale of individual turbulent wiggles,the reconnection happens at the slow Sweet-Parker rate. We show that fast reconnectionallows efficient mixing of magnetic field in the direction perpendicular tothe local direction of magnetic field. While the idea of stochastic reconnection still requiresnumerical confirmation,our numerical simulations testify that mixing motions perpendicular to the local magnetic field are upto high degree hydrodynamical. This suggests that the turbulent heattransport should be similar to that in non-magnetized turbulent fluid, namely,should have a diffusion coefficient ～V _L L, whereV _L is the amplitude of the turbulent velocity and L is the scale of the turbulent motions. We present numericalsimulations which support this conclusion. The applicationof this idea to thermal conductivity in clusters of galaxies shows that thismechanism may dominate the diffusion of heat and may be efficient enoughto prevent cooling flow formation.     

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.     

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.     

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.     

The dynamo theory of plasma turbulence wave in rotating celestial bodies

The various modes of plasma turbulence waves (including MHD waves) are easily excited under cosmic circumstances. In this paper, if we consider that the celestial bodies rotate, there is a source term generated for the magnetic induced equation by the excited plasma turbulence waves. If we expand the turbulent field in the Fourier series and include rotation velocity, the dynamo equation for turbulent waves is obtained. We have also obtained the solutions of various wave forms corresponding to different rotation velocities and then we significantly discuss the magnetic fields in the Sun, planets, and other celestial bodies.     

Turbulent spectrum of Alfvén waves excited by a kinetic instability for explaining the modulations with multi-timescales in solar flares

A low-frequency wave is treated as a local oscillation to modulate the guiding center of electrons beam, which is considered as free energy to excite Alfvén waves by a kinetic plasma instability under low-frequency approximation. The nonlinearity of the model is shown by a critical value of the amplitude of the low-frequency wave, and Alfvén waves are growing in a broad turbulent spectrum with fractional harmonics, which strongly depend on the criterion. The instability is limited in the direction nearly perpendicular to the ambient magnetic field. The growth rates are very sensitive to the beam speed that perpendicular to the magnetic field, the propagational angle, and the magnetic field strength, but not sensitive to the beam speed parallel to the magnetic field. This model is used to explain the modulations with multiple timescales in the flare light curves at radio, hard X-ray and H-alpha bands.     

List of forthcoming papers

This paper is largely a reply to Cowling's review of the present status of cosmic dynamo theory and its alternatives of primordial or fossil field models. Central is the question of turbulent diffusion, without which plasma dynamos will not work but primordial magnetic fields are retained. Turbulence does not shred or divide fields into small-scale elements as claimed; instead it creates these elements in addition to the large-scale field which remains after Ohmic diffusion has destroyed the small fields. The significance of the existence of a terrestrial dynamo is stressed and various objections to the existence of a solar-type dynamo are discussed, including the steady divergence of theory and observational evidence over a quarter century. Cowling's criticisms of the primordial field theory are discussed; these include turbulent diffusion, the timing of the solar magnetic cycle, and the importance attached to observations in active and quiet magnetic regions.Since this paper was communicated, a personal communication from Professor Cowling has partially resolved the difference of opinion about turbulent diffusion and its effects. This is discussed in a letter to the Editor, at the end of this volume, p. 477.     

Significance of the turbulent sheath following the interplanetary shocks in producing forbush decreases

The physical processes responsible for transient cosmic-ray decreases have been investigated for two types of interplanetary shock events associated with helium enhancement (He-shocks) and those not associated with helium enhancement (non-He-shocks). The Calgary cosmic-ray neutron monitor data and the interplanetary field data have been subjected to a superposed-epoch Chree analysis. The difference in the profiles of the cosmic-ray intensity have been compared with the interplanetary field data and its variance. It is suggested that the turbulence sheath following the shock front is very effective and of major importance for producing cosmic-ray decreases. A simple model has been proposed to explain the observations which show that a Forbush decrease modulating region consists of a shock front associated with a plasma sheath in which the magnetic field is turbulent and the sheath, in turn, is followed by an ejected plasma cloud having ordered structure and high magnetic field strength.     

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.     

Transient Modulation of Cosmic Ray Intensity: Role of Magnetic Clouds and Turbulent Interaction Regions

Two distinct regions of shock-associated magnetic clouds, (i) magnetically turbulent regions formed due to interaction between magnetic cloud and ambient magnetic field i.e. turbulent interaction region (TIR), and magnetically quiet region called magnetic cloud have been considered separately and correlation of interplanetary plasma and field parameters, magnetic field strength (B) and solar wind speed (V), with cosmic ray intensity (I) have been studied during the passage of these two regions. A good correlation between B and I and between V and I has been obtained during the passage of sheath when the magnetic field is high and turbulent, while these correlation have been found to be poor during the passage of magnetic clouds when the field is strong and smooth. Further, there is a positive correlation between enhancement in field strength and its variance in the sheath region. These results strongly support the hypothesis that most Forbush decreases are due to scattering of particles by region of enhanced magnetic turbulence. These results also suggest that it will provide a better insight if not the magnetic field enhancement alone but in addition, the nature of magnetic field enhancement is also considered while correlating the field enhancements with depressions in cosmic rays. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Die Wechselwirkung zwischen homogener Turbulenz und inhomogenem magnetischen Feld in der Umgebung neutraler Flächen

Continuing an investigation concerning the influence of a uniform mean magnetic field on turbulence (RÜDIGER, 1974) we now consider a weak magnetic field changing spatially weakly and containing a neutral sheet. An originally homogeneous and isotropic turbulent field becomes inhomogeneous and anisotropic if such a magnetic field is present. Because of the finite correlation length the turbulent field is also affected in a neutral sheet. For a special class of spectral functions of two- und three-dimensional turbulence the anisotropic damping of the motions is given in the vicinity of the neutral sheet. Furthermore, we point out the consequence for the mean magnetic field which is affected by such an inhomogeneous turbulent field. Using BOCHNER'S theorem concerning the spectral tensor of the originally homogeneous turbulence we obtain an additional decay of thr mean magnetic field.     

Distributions of tangential discontinuity in the corotating solar wind structure

Distributions of the tangential discontinuity (TD) in the solar wind sector structure are investigated on the basis of the magnetic field data and the ion plasma parameters from the Explorer 33 satellite from 23 January to 23 March 1968. The TD is separated from the observed field fluctuations by calculating the direction of the plasma flow and also the direction of the minimum field fluctuation with respect to the ambient magnetic field direction.It is found that the TD is formed by the thin layered field-aligned currents (the current sheets), and that the TD is predominantly built up in the leading edge of the solar wind where the compression of the plasma and the magnetic field takes place.It is suggested that the current sheets might be locally generated in the leading edge in the turbulent conditions arising from collisions between the fast- and the slow-stream of the solar sector structure.     

A two-fluid modeling of kinetic Alfvén wave turbulence

We present an analytical model to explore the magnetic field turbulent spectrum by coupled high-frequency kinetic Alfvén wave (KAW) and slow mode of Alfvén wave (AW). The spectrum is computed as a realization of energy cascades from larger to smaller scales for a specific case of solar wind plasma at 1 AU. A two-fluid technique is implemented for the derivation of model equations leading two wave modes. These coupled, nonlinear equations are solved numerically. The nonlinearity in the system arises due to nonlinear ponderomotive force, which is believed to be responsible for the wave localization and magnetic islands formation. The numerical results show that the magnetic islands grow with time and attain a quasi-steady state after the modulation instability is saturated. The magnetic field spectrum and associated spectral indices are computed near the time of saturation of instability. The simulated spectrum in dispersion region follows a power-law with an index of ?2.5. The steeper spectrum could be attributed as energy transfer from larger to smaller scales and helps to study turbulence in solar wind. The magnetic field spectrum and spectral index show a good agreement with the observation of solar wind turbulent spectra.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.