Generalized analytical models of Syrovatskii’s current sheet

Two-dimensional stationary magnetic reconnection models that include a thin Syrovatskii-type current sheet and four discontinuous magnetohydrodynamic flows of finite length attached to its endpoints are considered. The flow pattern is not specified but is determined from a self-consistent solution of the problem in the approximation of a strong magnetic field. Generalized analytical solutions that take into account the possibility of a current sheet discontinuity in the region of anomalous plasma resistivity have been found. The global structure of the magnetic field in the reconnection region and its local properties near the current sheet and attached discontinuities are studied. In the reconnection regime in which reverse currents are present in the current sheet, the attached discontinuities are trans-Alfvénic shock waves near the current sheet endpoints. Two types of transitions from nonevolutionary shocks to evolutionary ones along discontinuous flows are shown to be possible, depending on the geometrical model parameters. The relationship between the results obtained and numerical magnetic reconnection experiments is discussed.     

Transverse oscillations in solar spicules induced by propagating Alfvénic pulses

The excitation of Alfvénic waves in solar spicules by localized Alfvénic pulses is investigated. A set of incompressible MHD equations in the two-dimensional x–z plane with steady flows and sheared magnetic fields is solved. Stratification due to gravity and transition region between chromosphere and corona is taken into account. An initially localized Alfvénic pulse launched below the transition region can penetrate from transition region into the corona. We show that the period of the transversal oscillations is in agreement with those observed in spicules. Moreover, it is found that the excited Alfvénic waves spread during propagation along the spicule length, and suffer efficient damping of the oscillations amplitude. The damping time of the transverse oscillations increased with decreasing k _b values.     

A Global Model of MHD Wave Support of a Stratified Molecular Cloud

We perform numerical simulations of nonlinear MHD waves in a gravitationally stratified molecular cloud that is bounded by a hot and tenuous external medium, within a 1.5-dimensional approximation. Under the influence of a driving source of Alfvénic disturbances, the cloud is lifted up by the pressure of MHD waves and reaches a steady state characterized by oscillations about a new time-averaged equilibrium state. The nonlinear effect results in the generation of longitudinal motions and many shock waves. Models of an ensemble of clouds show that, for various strengths of the input energy, the velocity dispersion in the cloud σ ∝ Z ^0.5, where Z is a characteristic size of the cloud. Furthermore, σ is always comparable to the mean Alfvén velocity of the cloud, consistent with observational results.     

Large-scale zonal flow and magnetic field generation due to drift-Alfven turbulence in ionosphere plasma

In the present work, the generation of large-scale zonal flows and magnetic field by short-scale collision-less electron skin depth order drift-Alfven turbulence in the ionosphere is investigated. The self-consistent system of two model nonlinear equations, describing the dynamics of wave structures with characteristic scales till to the skin value, is obtained. Evolution equations for the shear flows and the magnetic field is obtained by means of the averaging of model equations for the fast-high-frequency and small-scale fluctuations. It is shown that the large-scale disturbances of plasma motion and magnetic field are spontaneously generated by small-scale drift-Alfven wave turbulence through the nonlinear action of the stresses of Reynolds and Maxwell. Positive feedback in the system is achieved via modulation of the skin size drift-Alfven waves by the large-scale zonal flow and/or by the excited large-scale magnetic field. As a result, the propagation of small-scale wave packets in the ionospheric medium is accompanied by low-frequency, long-wave disturbances generated by parametric instability. Two regimes of this instability, resonance kinetic and hydrodynamic ones, are studied. The increments of the corresponding instabilities are also found. The conditions for the instability development and possibility of the generation of large-scale structures are determined. The nonlinear increment of this interaction substantially depends on the wave vector of Alfven pumping and on the characteristic scale of the generated zonal structures. This means that the instability pumps the energy of primarily small-scale Alfven waves into that of the large-scale zonal structures which is typical for an inverse turbulent cascade. The increment of energy pumping into the large-scale region noticeably depends also on the width of the pumping wave spectrum and with an increase of the width of the initial wave spectrum the instability can be suppressed. It is assumed that the investigated mechanism can refer directly to the generation of mean flow in the atmosphere of the rotating planets and the magnetized plasma.     

Collapse of weakly ionized rotating turbulent Cloud Cores

In view of the Turbulent Cooling Flows scenario we carry out several 3D axisymmetric calculations to follow the evolution of magnetically subcritical weakly ionized and rotating turbulent cloud cores. Turbulent Cooling Flows appear to pronounce the effects of ambipolar diffusion considerably, inducing thereby a runaway collapse of the core already on a diluted free-fall time scale. Ambipolar diffusion significantly weakens the efficiency of magnetic braking. This implies that most of the rotational energy is trapped into the dynamically collapsing core and that initiation of outflows is prevented at least in the early isothermal phases. The trapped rotational energy is found to enhance the formation of rings that may afterwards fragment. It is shown that the central region of a strongly ionized magnetically subcritical core is principally overdense, with central density up to one order of magnitude larger than the surroundings. These results confirm that large scale magnetic fields threading a cloud core relax the supersonic random motions on an Alfvén wave crossing time. Moreover, ambipolar diffusion enhances dissipation of supersonic turbulence even more.     

The solar dynamo

The basic features of the solar activity mechanism are explained in terms of the dynamo theory of mean magnetic fields. The field generation sources are the differential rotation and the mean helicity of turbulent motions in the convective zone. A nonlinear effect of the magnetic field upon the mean helicity results in stabilizing the amplitude of the 22-year oscillations and forming a basic limiting cycle. When two magnetic modes (with dipole and quadrupole symmetry) are excited nonlinear beats appear, which may be related to the secular cycle modulation.The torsional waves observed may be explained as a result of the magnetic field effect upon rotation. The magnetic field evokes also meriodional flows.Adctual variations of the solar activity are nonperiodic since there are recurrent random periods of low activity of the Maunder minimum type. A regime of such a magnetic hydrodynamic chaos may be revealed even in rather simple nonlinear solar dynamo models.The solar dynamo gives rise also to three-dimensional, non-axisymmetric magnetic fields which may be related to a sector structure of the solar field.     

Amplification of primordial magnetic fields by anisotropic gravitational collapse

If a magnetic field is frozen into a plasma that undergoes spherical compression, then the magnetic field B varies with the plasma density ρ according to   B ∝ρ^2/3  . In the gravitational collapse of cosmological density perturbations, however, quasi-spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using a relation of the form   B ∝ρ^α  , we show that the median value of α can be much larger than the value  α= 2/3  resulting from spherical collapse, even if there is no initial correlation between magnetic field and principal collapse directions. These analytic arguments go some way towards understanding the results of numerical simulations.     

Magnetorotational supernovae. Magnetorotational instability. Jet formation

2D numerical simulations of magnetorotational (MR) supernova mechanism are described. It is shown that magnetic field is amplified due to the differential rotation after core collapse. When magnetic pressure reaches some level, a compression wave starts to move outwards. Moving along steeply decreasing density profile the compression wave transforms quickly into fast MHD shock. The magnetorotational instability (MRI) was found in our simulations. MRI leads to the exponential growth of the components of the magnetic field. The MRI significantly reduces MR supernova explosion time. Configuration of the initial magnetic field qualitatively defines the shape of MR supernova explosion. For the quadrupole-like initial poloidal field the MR supernova explosion develops mainly along equatorial plane, the dipole-like initial field results in MR supernova developing as mildly collimated jet along axis of rotation. The explosion energy of MR supernova found in our simulations is ∼0.5–0.6×10⁵¹ erg.     

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.     

Helioseismology of Time-Varying Flows Through The Solar Cycle

Flows in the upper convection zone are measured by helioseismology on a wide variety of scales. These include differential rotation and meridional circulation, local flows around complexes of magnetic activity and sunspots, and convective flows. The temporal evolution of flows through cycle 23 reveals connections between mass motions in the solar interior and the large-scale characteristics of the magnetic cycle. Here I summarize the latest observations and their implications. Observations from local helioseismology suggest that subsurface flows around active regions introduce a solar-cycle variation in the meridional circulation.     

Gravitational collapse in an expanding background and the role of substructure – I. Planar collapse

We study the interplay of clumping at small scales with the collapse and relaxation of perturbations at much larger scales. We present results of our analysis when the large-scale perturbation is modelled as a plane wave. We find that in the absence of substructure, collapse leads to formation of a pancake with multistream regions. Dynamical relaxation of the plane wave is faster in the presence of substructure. Scattering of substructures and the resulting enhancement of transverse motions of haloes in the multistream region lead to a thinner pancake. In turn, collapse of the plane wave leads to formation of more massive collapsed haloes as compared to the collapse of substructure in the absence of the plane wave. The formation of more massive haloes happens without any increase in the total mass in collapsed haloes. A comparison with the Burgers equation approach in the absence of any substructure suggests that the preferred value of effective viscosity depends primarily on the number of streams in a region.     

Slip-Running Reconnection in Quasi-Separatrix Layers

Using time dependent MHD simulations, we study the nature of three-dimensional magnetic reconnection in thin quasi-separatrix layers (QSLs), in the absence of null points. This process is believed to take place in the solar atmosphere, in many solar flares and possibly in coronal heating. We consider magnetic field configurations which have previously been weakly stressed by asymmetric line-tied twisting motions and whose potential fields already possessed thin QSLs. When the line-tied driving is suppressed, magnetic reconnection is solely due to the self-pinching and dissipation of narrow current layers previously formed along the QSLs. A generic property of this reconnection process is the continuous slippage of magnetic field lines along each other, while they pass through the current layers. This is contrary to standard null point reconnection, in which field lines clearly reconnect by pair and abruptly exchange their connectivities. For sufficiently thin QSLs and high resistivities, the field line footpoints slip-run at super-Alfvénic speeds along the intersection of the QSLs with the line-tied boundary, even though the plasma velocity and resistivity are there fixed to zero. The slip-running velocities of a given footpoint have a well-defined maximum when the field line crosses the thinnest regions of the QSLs. QSLs can then physically behave as true separatrices on MHD time scales, since magnetic field lines can change their connections on time scales far shorter than the travel-time of Alfvén waves along them. Since particles accelerated in the diffusive regions travel along the field much faster than the Alfvén speed, slip-running reconnection may also naturally account for the fast motion of hard X-ray sources along chromospheric ribbons, as observed during solar flares. Electronic Supplementary Material Supplementary material is available for this article at     

Gravitational collapse in an expanding background and the role of substructure – II. Excess power at small scales and its effect on collapse of structures at larger scales

We study the interplay of clumping at small scales with the collapse and relaxation of perturbations at larger scales using N -body simulations. We quantify the effect of collapsed haloes on perturbations at larger scales using the two-point correlation function, moments of counts in cells and the mass function. The purpose of the study is twofold and the primary aim is to quantify the role played by collapsed low-mass haloes in the evolution of perturbations at large scales; this is in view of the strong effect seen when the large scale perturbation is highly symmetric. Another reason for this study is to ask whether features or a cut-off in the initial power spectrum can be detected using measures of clustering at scales that are already non-linear. The final aim is to understand the effect of ignoring perturbations at scales smaller than the resolution of N -body simulations. We find that these effects are ignorable if the scale of non-linearity is larger than the average interparticle separation in simulations. Features in the initial power spectrum can be detected easily if the scale of these features is in the linear regime; detecting such features becomes difficult as the relevant scales become non-linear. We find no effect of features in initial power spectra at small scales on the evolved power spectra at large scales. We may conclude that, in general, the effect on the evolution of perturbations at large scales of clumping on small scales is very small and may be ignored in most situations.     

Three-Dimensional Simulations of Jets from Keplerian Disks: Stability Issues

Three-dimensional simulations of the time-dependent evolution of non-relativistic outflows from the surface of Keplerian accretion disks are presented. We investigate the outflow that arises from a magnetized accretion disk that is initially in hydrostatic balance with its surrounding cold corona. Our simulations show that jets maintain their long-term stability through a self-limiting process wherein the average Alfvénic Mach number within the jet is maintained to order unity. This is accomplished in at least two ways. First, poloidal magnetic field is concentrated along the central axis of the jet forming a `backbone' in which the Alfvén speed is sufficiently high to reduce the average jet Alfvénic Mach number to unity. Second, the onset of higher order Kelvin-Helmholtz `flute' modes (m ≥ 2) reduce the efficiency with which the jet material is accelerated, and transfer kinetic energy of the out flow into the stretched, poloidal field lines of the distorted jet. This too has the effect of increasing the Alfvén speed and thereby reducing the Alfvénic Mach number. The jet is able to survive the onset of the more destructive m=1 mode in this way.     

Flapping motions of the tail plasma sheet induced by the interplanetary magnetic field variations

Flapping motions of the magnetotail with an amplitude of several earth radii are studied by analysing the observations made in the near (x = ?25 ~ ?30 R_E and the distant (x? ?60 R_E) tail regions. It is found that the flapping motions result from fluctuations in the interplanetary magnetic field, especially Alfvénic fluctuations, when the magnitude of the interplanetary magnetic field is larger than ~10 γ and they propagate behind the Earth with the solar wind flow. Flappings tend to be observed in early phases of the magnetospheric substorm, and they have two fundamental modes with periods of ~200 and ~500 sec. In some limited cases a good correspondence with the long period micropulsations (Pc5) in the polar cap region is observed. These observational results are explained by the model in which the Alfvénic fluctuations in the solar wind penetrate into the magnetosphere along the connected interplanetary-magnetospheric field lines. The characteristics of the flapping reveal that the geomagnetic tail is a good resonator for the hydromagnetic disturbances in the solar wind.     

Large-scale flows excited by magnetic fields in the solar convective zone

Observations demonstrate a nearly 22-year periodic zonal flow superimposed on general solar differential rotation (LaBonte and Howard, 1982) and some meridional motions (e.g., Tuominen, Tuominen, and Kyrolänen, 1983). Such flows can be excited by the magnetic wave generated by the dynamo in the solar convective zone.An approximate analytical solution for the zonal and meridional flows for a given magnetic wave is constructed. This approach is justified by the fact that the magnetic field is generated by differential rotation and mean helicity, and the magnetic field in the time interval under consideration does not affect much this main flow; it can, however, strongly influence the perturbations of this flow.The density gradient in the convective zone is taken into account as an essential point in the solution construction. The solution agreed well with observational features and, in particular, it gives a phase shift between the rotational (zonal) wave and solar activity. A polar branch of the rotational wave can be described as an effect created by a poleward moving dynamo wave.Secular variations in the symmetrical part of the differential rotation and in the asymmetry between the north and south hemispheres are predicted.The alternative approaches to the explanation of the origin of the observed large-scale flows are discussed.     

NONLINEAR MHD SIMULATIONS OF WAVE DISSIPATION IN FLUX TUBES

The phase mixing and resonant dissipation of Alfvén waves is studied in both the 'closed' magnetic loops and the 'open' coronal holes observed in the hot solar corona. The resulting energy transfer from large to small length scales contributes to the heating of these magnetic structures. The nonlinear simulations show that the periodically varying shear flows that occur in the resonant layers are unstable. In coronal holes, the phase mixing of running Alfvén waves is speeded up by the 'flaring out' of the magnetic field lines in the lower chromosphere.     

Stationary incompressible MHD perturbationsgenerated by a current source in a moving plasma

We consider the inductive interaction between a conducting body and a magnetizedincompressible plasma in relative uniform motion, which has application to the Io–Jupitersystem, for example. An incompressible plasma only supports one mode of propagation, namelythe Alfvén mode. In the case of free oscillations, this mode propagates the perturbations in themagnetic field and in the plasma velocity unattenuated along the direction of the backgroundfield, while the plasma pressure balances the magnetic pressure. The situation changes in thepresence of source currents and in a flowing plasma. In particular, the parallel plasma vorticityand parallel plasma current are propagated unattenuated along the familiar Alfvéncharacteristics, while the field and velocity perturbations suffer Laplacian decay in the near field.We study these perturbations in the frame of the body and compare them to the case of no sourceterms.     

The effect of magnetic fields on star cluster formation

We examine the effect of magnetic fields on star cluster formation by performing simulations following the self-gravitating collapse of a turbulent molecular cloud to form stars in ideal magnetohydrodynamics. The collapse of the cloud is computed for global mass-to-flux ratios of  ∞, 20, 10, 5  and 3, i.e. using both weak and strong magnetic fields. Whilst even at very low strengths the magnetic field is able to significantly influence the star formation process, for magnetic fields with plasma  β < 1  the results are substantially different to the hydrodynamic case. In these cases we find large-scale magnetically supported voids imprinted in the cloud structure; anisotropic turbulent motions and column density striations aligned with the magnetic field lines, both of which have recently been observed in the Taurus molecular cloud. We also find strongly suppressed accretion in the magnetized runs, leading to up to a 75 per cent reduction in the amount of mass converted into stars over the course of the calculations and a more quiescent mode of star formation. There is also some indication that the relative formation efficiency of brown dwarfs is lower in the strongly magnetized runs due to a reduction in the importance of protostellar ejections.     

Does the large-scale solar magnetic field distribution really reflect the convective velocity fields?

We have tried to decide whether the typical circular cellular-like features, which are striking during some intervals in the large-scale distribution of weak magnetic fields measured with low resolution, are related to large-scale convective motions. Two scales of such patterns were found and their morphological, kinematical and evolutionary behaviour was estimated. Their slower and overall rotation is also demonstrated in comparison with the rotation of highly averaged sunspot and magnetic fields. It is difficult to explain all the observed characteristics as random, or due to the method of field measurement and map construction used. We also discuss the change of their magnetic field polarities with the solar polar field reversal.