The screw dynamo in a thick torus

The problem of magnetic field generation under screw motion in a toroidal channel is studied numerically. The screw dynamo in the cylinder with periodical boundary conditions was found to be a suitable approximation for generation of the magnetic field by a screw flow in a thin torus. For the thick torus, a principally new solution of the screw dynamo problem was obtained. In this case the growing global magnetic field mode has the scale of a maximal geometrical size of the torus and does not vanish on the axis of the torus (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On axisymmetric hydromagnetic equilibria

The physical characteristics of possible axisymmetric equilibria are examined on the basis of the integrals of hydromagnetic equations. It is shown for nearly spherical configurations that a surface differential rotation is possible only in the absence of a meridional circulation with either purely toroidal or purely poloidal magnetic field. In the presence of a meridional circulation, it is shown that no surface rotation or constant rotation is possible if the magnetic field is purely toroidal, and that no rotation is possible if the magnetic field is purely poloidal. A brief discussion is given on the possible solutions including the case of stellar winds with force-free magnetic fields.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Modeling Magnetic Tower Jets in the Laboratory

The twisting of magnetic fields threading an accretion system can lead to the generation on axis of toroidal field loops. As the magnetic pressure increases, the toroidal field inflates, producing a flow. Collimation is due to a background corona, which radially confines this axially growing “magnetic tower”. We investigate the possibility of studying in the laboratory the dynamics, confinement and stability of magnetic tower jets. We present two-dimensional resistive magnetohydrodynamic simulations of radial arrays, which consist of two concentric electrodes connected radially by thin metallic wires. In the laboratory, a radial wire array is driven by a 1 MA current which produces a hot, low density background plasma. During the current discharge a low plasma beta (β < 1), magnetic cavity develops in the background plasma (β is the ratio of thermal to magnetic pressure). This laboratory magnetic tower is driven by the magnetic pressure of the toroidal field and it is surrounded by a shock envelope. On axis, a high density column is produced by the pinch effect. The background plasma has >rsim1, and in the radial direction the magnetic tower is confined mostly by the thermal pressure. In contrast, in the axial direction the pressure rapidly decays and an elongated, well collimated magnetic-jet develops. This is later disrupted by the development of m = 0 instabilities arising in the axial column.     

On large-scale solar convection

We examine the effects of rotation about a vertical axis on thermal convection with a simple model in which an inviscid, incompressible fluid of zero thermal conductivity and electrical resistivity is contained in a thin annulus of rectangular cross-section. The initial steady state assumed is one of no motion relative to the rotating frame with constant (unstable) vertical temperature gradient and uniform toroidal magnetic field. Small periodic disturbances are then introduced and the linearized perturbation equations solved. We also determine the second-order mean circulations and magnetic fields that are forced by non-zero Reynolds and thermal stresses and magnetic field transports.The solutions have several properties which are relevant to large-scale solar phenomena if giant long-lived convection cells exist on the sun. In particular, the convective cells are tilted in latitude in the same sense as bipolar magnetic regions, and induce vertical magnetic fields with the same tilt. They transport momentum across latitude circles through Reynolds stresses and induced meridional circulations thus setting up a differential rotation. Cells which grow slowly compared to the rotation rate and have comparable dimensions in latitude and longitude transport momentum toward the equator. The cells also form a poloidal magnetic field from initial toroidal field, in a manner similar to that put forth by Parker.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the X-ray image of the Crab nebula: comparison with Chandra observations

An axisymmetric model for the Crab nebula is constructed to examine the flow dynamics in the nebula. The model is based on that of Kennel & Coroniti, although we assume that the kinetic-energy-dominant wind is confined to an equatorial region. The evolution of the distribution function of the electron–positron plasma flowing out in the nebula is calculated. Given viewing angles, we reproduce an image of the nebula and compare it with the Chandra observation.
The reproduced image is not ring-like, but is rather 'lip-shaped'. It is found that the assumption of a toroidal field does not reproduce the Chandra image. We must assume that there is a disordered magnetic field with an amplitude as large as the mean toroidal field. In addition, the brightness contrast between the front and back sides of the ring cannot be reproduced if we assume that the magnetization parameter σ is as small as ∼10⁻³. The brightness profile along the semimajor axis of the torus is also examined. The non-dissipative, ideal-magnetohydrodynamic approximation in the nebula appears to break down.
We speculate that if the magnetic energy is released by some process that produces a turbulent field in the nebula flow and causes heating and acceleration – for example, by magnetic reconnection – then the present difficulties may be resolved (i.e. we can reproduce a ring image and a higher brightness contrast). Thus, the magnetization parameter σ can be larger than previously expected.     

Relation between the toroidal field in the solar convective layer and the BI-polar field of sunspots

In the solar convective layer, there is a strong toroidal field and a vertical gradient in the turbulent magnetic diffusivity. As a fluid blob rises through magnetic buoyancy, a steep gradient in the turbulent magnetic diffusivity across the surface of the blob is generated. This will perturb the toroidal field, resulting in the formation of a magnetic ring around the blob. An attempt is made to account for the concentration of the bipolar sunspot field in terms of this ring.     

Double maxima of 11-year solar cycles

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ?ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ?ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ?ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.     

The evolution of loop structures in flux rings within the solar convection zone

Choudhuri and Gilman (1987) considered certain implications of the hypothesis that the magnetic flux within the Sun is generated at the bottom of the convection zone and then rises through it. Taking flux rings symmetric around the rotation axis and using reasonable values of different parameters, they found that the Coriolis force deflects these flux rings into trajectories parallel to the rotation axis so that they emerge at rather high latitudes. This paper looks into the question of whether the action of the Coriolis force is subdued when the initial configuration of the flux ring has non-axisymmetries in the form of loop structures. The results depend dramatically on whether the flux ring with the loops lies completely within the convection zone or whether the lower parts of it are embedded in the stable layers underneath the convection zone. In the first case, the Coriolis force supresses the non-axisymmetric perturbations so that the flux ring tends to remain symmetric and the trajectories are very similar to those of Choudhuri and Gilman (1987). In the second case, however, the lower parts of the flux ring may remain anchored underneath the bottom of the convection zone, but the upper parts of the loops still tend to move parallel to the rotation axis and emerge at high latitudes. Thus the problem of the magnetic flux not being able to come out at the sunspot latitudes still persists after the non-axisymmetries in the flux rings are taken into account.National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Quantitative magnetospheric magnetic field modelling with toroidal and poloidal vector fields

Toroidal and poloidal vector fields allow divergence free magnetic field representations in regions where currents flow. We derive general magnetospheric magnetic fields using combinations of spherical harmonic expansions of the toroidal and poloidal fields. Adding restrictive conditions like the field line topology symmetry or the magnetic field measurements, more specific magnetospheric magnetic field models can be derived. Two examples of this technique are given : an axisymmetric model with a ring current in the equatorial region and a time-dependent model of the Earth's magnetosphere. Our results are compared with the Olson-Pfitzer model.     

Experimental Studies of Magnetically Driven Plasma Jets

We present experimental results on the formation of supersonic, radiatively cooled jets driven by pressure due to the toroidal magnetic field generated by the 1.5 MA, 250 ns current from the MAGPIE generator. The morphology of the jet produced in the experiments is relevant to astrophysical jet scenarios in which a jet on the axis of a magnetic cavity is collimated by a toroidal magnetic field as it expands into the ambient medium. The jets in the experiments have similar Mach number, plasma beta and cooling parameter to those in protostellar jets. Additionally the Reynolds, magnetic Reynolds and Peclet numbers are much larger than unity, allowing the experiments to be scaled to astrophysical flows. The experimental configuration allows for the generation of episodic magnetic cavities, suggesting that periodic fluctuations near the source may be responsible for some of the variability observed in astrophysical jets. Preliminary measurements of kinetic, magnetic and Poynting energy of the jets in our experiments are presented and discussed, together with estimates of their temperature and trapped toroidal magnetic field.     

The role of a magnetic field in the formation of jet-like features in the crab nebula

The toroidal magnetic field frozen in the relativistic plasma ejected by pulsars must play a significant role in the formation of jet-like features observed in the central parts of plerions. We performed a semiquantitative analysis and calculations of the plasma flow in a plerion using the perturbation theory. We show that for the latitudinal magnetic-field distribution expected during the interaction of the pulsar wind with the interstellar medium, the magnetic field will have an appreciable effect on the flow primarily near the rotation axis. In the equatorial region, the effect of the magnetic field is negligible up to distances of 7r_sh.     

The stability of a velocity shear in the presence of an inhomogeneous magnetic field

The stability of a velocity shear in the presence of a parallel but non-uniform magnetic field is considered in general terms. Two special cases are then investigated; (i) the well known case of a plane interface at which a discontinuity in the magnetic field coincides with the velocity shear; (ii) an axially symmetric flow in which discontinuities in the magnetic and velocity fields occur at a cylindrical surface whose axis is parallel to the flow. In the first case the flow is stabilized if the rms Alfvén velocity of the magnetic field exceeds the shear velocity; a result consistent with that obtained by other writers. In the second case it is shown that the discontinuity in the magnetic field increases the stability of the system. The significance of this result for the stability of the flux ropes associated with sunspots in the solar convection zone is considered.     

Upper limits in the toroidal component of force-free magnetic fields in stellar atmospheres in the context of solar and stellar flares

Doing numerical calculations of axially symmetric force-free fields, Milsom and Wright (1976) have noticed that there seem to be no solutions if the toroidal component of the field exceeds a certain limit. In the present paper this problem is reexamined in the approximation of a plane stellar surface using a very simple analytic approximation. The results of Milsom and Wright (1976) are confirmed but, in contrast to their interpretation, it is shown that these limitations do not indicate the possibility of sudden changes of the topology of the magnetic field. This is because in a stellar atmosphere the toroidal component of the surface magnetic field is no independent quantity but is produced by shearing motions in the star which will prevent the toroidal magnetic field from exceeding its maximum value. To study the possibility of sudden changes in the magnetic field, which could cause stellar flares, the calculations are re-done prescribing the motion of the magnetic footpoints (shear in the stellar surface) instead of the toroidal component of the surface field. Using the same mathematical formalism it is found that no sudden changes can occur for configurations where all field lines connect to the stellar surface but that sudden changes may be possible for a more complicated field topology.     

Magnetic fields of Ap stars as a result of the Tayler instability

Ap star magnetism is often attributed to fossil magnetic fields which have not changed much since the pre‐main‐sequence epoch of the stars. Stable magnetic field configurations are known which could persist probably for the entire mainsequence life of the star, but they may not show the complexity and diversity exhibited by the Ap stars observed. We suggest that the Ap star magnetism is not a result of stable configurations, but is the result of an instability based on strong toroidal magnetic fields buried in the stars. The highly nonaxisymmetric remainders of the instability are reminiscent of the diversity of fields seen on Ap stars. The strengths of these remnant magnetic fields are actually between a few per cent up to considerable fractions of the internal toroidal field; this means field strengths of the order of kGauss being compatible with what is observed. The magnetic fields emerge at the surface rather quickly; rough estimates deliver time‐scales of the order of a few years. Since rotation stabilizes the instability, normal A stars may still host considerable, invisible toroidal magnetic fields (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Converging and diverging convection around axisymmetric magnetic flux tubes

A numerical model of idealized sunspots and pores is presented, where axisymmetric cylindrical domains are used with aspect ratios (radius versus depth) up to 4. The model contains a compressible plasma with density and temperature gradients simulating the upper layer of the Sun's convection zone. Non-linear magnetohydrodynamic equations are solved numerically and time-dependent solutions are obtained where the magnetic field is pushed to the centre of the domain by convection cells. This central magnetic flux bundle is maintained by an inner convection cell, situated next to it and with a flow such that there is an inflow at the top of the numerical domain towards the flux bundle. For aspect ratio 4, a large inner cell persists in time, but for lower aspect ratios it becomes highly time dependent. For aspect ratios 2 and 3 this inner convection cell is smaller, tends to be situated towards the top of the domain next to the flux bundle, and appears and disappears with time. When it is gone, the neighbouring cell (with an opposite sense of rotation, i.e. outflow at the top) pulls the magnetic field away from the central axis. As this happens a new inner cell forms with an inflow which pushes the magnetic field towards the centre. This suggests that to maintain their form, both pores and sunspots need a neighbouring convection cell with inflow at the top towards the magnetic flux bundle. This convection cell does not have to be at the top of the convection zone and could be underneath the penumbral structure around sunspots. For an aspect ratio of 1, there is not enough space in the numerical domain for magnetic flux and convection to separate. In this case the solution oscillates between two steady states: two dominant convection cells threaded by magnetic field and one dominant cell that pushes magnetic flux towards the central axis.     

Magnetically distorted polytropes

The oscillations of a gaseous polytrope with a magnetic field having both a toroidal and a poloidal component are examined using the second-order tensor virial equations on the assumption that the magnetic energy is small compared with the gravitational energy. The frequencies of oscillation of the transverse shear, the toroidal and the coupled pulsation modes are tabulated for polytropic indicesn=1, 1.5, 2, 3 and 3.5. It is found that the magnetic field decreases the frequency of oscillation of (i) the transverse shear mode and (ii) the mode which starts as a radial pulsation in the absence of a magnetic field while it increases the frequency of oscillation of (i) the toroidal mode and (ii) the Kelvin mode. In all cases the shift in frequency decreases with increasingn.     

Evolution of filamentary molecular clouds in the presence of magnetic fields

The purpose of this paper is to explore the effect of magnetic fields on the dynamics of magnetized filamentary molecular clouds.We suppose there is a filament with cylindrical symmetry and two components of axial and toroidal magnetic fields.In comparison to previous works,the novelty in the present work involves a similarity solution that does not define a function of the magnetic fields or density.We consider the effect of the magnetic field on the collapse of the filament in both axial and toroidal directions and show that the magnetic field has a braking effect,which means that the increasing intensity of the magnetic field reduces the velocity of collapse.This is consistent with other studies.We find that the magnetic field in the central region tends to be aligned with the filament axis.Also,the magnitude and the direction of the magnetic field depend on the magnitude and direction of the initial magnetic field in the outer region.Moreover,we show that more energy dissipation from the filament causes a rise in the infall velocity.     

Exact MHD solutions for rotating,magnetic stars

Simple exact solutions of the magnetohydrodynamic equations are found for rotating, magnetic stars. The velocity and magnetic field are axisymmetric and purely toroidal, and the magnetic energy density equals the kinetic energy density. For constant mass density, the solution reduces to that of Chandrasekhar (1956), which is stable even against non-axisymmetric perturbations. For an ideal gas equation of state, the condition for radiative thermal equilibrium is solved to lowest order in the non-spherical perturbation. The velocity, magnetic field and non-spherical pressure and temperature perturbations all vanish within cones centered around the rotation axis, |cos |>x _i a zero of a Legendre polynomial. Low-order, long-period stellar oscillations may be excited by MHD instabilities near the equatorial region which become damped near the axis.     

Large-Scale Magnetic Field of the Sun and Evolution of Sunspot Activity

The evolution of the large-scale magnetic field of the Sun has been studied using an algorithm of tomographic inversion. By analyzing line-of-sight magnetograms, we mapped the radial and toroidal components of the Sun??s large-scale magnetic field. The evolution of the radial and toroidal magnetic field components in the 11-year solar cycle has been studied in a time?Clatitude aspect. It is shown that the toroidal magnetic field of the Sun is causally related to sunspot activity; i.e., the sunspot formation zones drift in latitude and follow the toroidal magnetic fields. The results of our analysis support the idea that the high-latitude toroidal magnetic fields can serve as precursors of sunspot activity. The toroidal fields in the current cycle are anomalously weak and also show a barely noticeable equatorward drift. This behavior of the toroidal magnetic field suggests low activity levels in the current cycle and in the foreseeable future.     

Formation of buoyant magnetic structures by a localized velocity shear

Motivated by considerations of the solar tachocline, we study the generation of strong buoyant magnetic structures by a sheared velocity field localized in a convectively stable background, using non-linear three-dimensional (3D) magnetohydrodynamic (MHD) simulations. The shear flow can spontaneously create strong tube-like toroidal (streamwise) magnetic structures from an imposed weak uniform poloidal (cross-stream) magnetic field. The structures are magnetically buoyant and therefore rise, and may evolve further to a rich variety of geometries, including kinked or arched shapes. The emergence process can repeat indefinitely with a characteristic period. These mechanisms may be relevant to the MHD processes in the solar tachocline and the creation and emergence of solar active regions.