The Hall effect as the producer of current sheets in astrophysical plasmas

Our solution of the MHD equations with the Hall effect shows that this effect can produce thin current sheets in stellar atmospheres at heights where the plasma is tenuous and the Hall effect can profoundly influence the magnetic field variations. The current in the sheets is directed oppositely to the local plasma density gradient. In partiuclar, such a phenomenon is possible on the Sun near the base of the corona.     

A note on the motion of charged particles in one-dimensional magnetic current sheets

By considering the integrals of the motion of charged particles moving in one-dimensional current sheets, a simple and exact proof is given that particles which are either magnetically or electrostatically trapped about such a current sheet exhibit zero net drift. The transition to the special case of a strictly neutral sheet, a limit remaining unclear from previous studies, is also elucidated. Finally, the relationship between the results and existing self-consistent current sheet solutions is discussed.     

Observations of steady anomalous magnetic heating in thin current sheets

A faint steadily emitting loop-like structure has been observed by HXIS in its low energy channels (3.5–8.0 keV) on November 5/6, 1980. These HXIS observations have permitted us to follow the thermal evolution of this loop for a period of about 15 hr and from this study we conclude that only a fraction of 0.1% of the volume of the loop is steadily heated at the rather large rate of 0.6 erg cm^-3 s^-1. We interpret this heating as the dissipation of magnetic fields in thin current sheets and we find that the dissipation with classical resistivity is very unlikely, while ion-kinetic tearing, as proposed by Galeev et al. (1981), suits the observations very well. The enhancement of the resistivity over the classical resistivity then turns out to be a factor 4 × 10⁴. Dissipation in extremely thin sheets via the ion-acoustic instability (Duijveman et al., 1981) cannot be completely excluded when the cross-field heat conductivity is anomalously enhanced by a factor 400.We identify the source of the X-ray emission in this paper with the H filament in the same region. The hot X-ray emitting plasma and the cool plasma radiating in H are thermally separated by the strong magnetic field.The main conclusion of the paper is that for the first time direct evidence is found for the steady dissipation of coronal magnetic fields via enhanced resistivity in thin current sheets.     

The formation of current sheets during the emergence of new magnetic flux from below the photosphere

Solar flares are frequently observed to occur where new magnetic flux is emerging and pressing up against strong active region magnetic fields. Since the solar plasma is highly conducting, current sheets develop at the boundary between the emergent and ambient flux, provided the two magnetic fields are inclined at a non-zero angle to one another.The present paper gives a simple two-dimensional model for the development of such sheets under the assumptions that no reconnection occurs and that the surrounding field remains a potential one. By using complex variable techniques, the position, orientation and shape of a current sheet may be determined, as well as the excess magnetic energy associated with it. Two examples are considered. The first, in which the ambient field is bipolar, may model new flux emergence near the edge of an active region, while the second example assumes a constant ambient field and may approximate the so-called fibril crossings which occur prior to some flares. In each case, the current sheets are curved, and the magnetic energy which is stored in excess of potential is sufficient to supply a solar flare when the sheets are long enough.     

On the method of calculating two-dimensional potential magnetic fields with current sheets

The method of calculating two-dimensional potential magnetic configurations with current sheets (CS) is proposed, the number of CS in corona and the degree of asymmetry being both arbitrary. As a given boundary value the component of magnetic field normal to the photosphere is considered.     

Kink unstable coronal loops: current sheets,current saturation and magnetic reconnection

The kink instability in a coronal loop is a possible explanation of a compact loop flare as it may cause a current sheet to form allowing reconnection to take place and release the free magnetic energy stored in the loop. However, current sheets do not form in all cases. Ali and Sneyd (2001) investigated three different classes of equilibrium (determined by the form of the twist) using a magneto-frictional code. They searched for the equilibria to which the loop might evolve once it had become unstable to the kink instability. They found indications of current-sheet formation for only one class of equilibrium studied. However, as they pointed out, since their code searched for equilibria they were unable to say for certain that the loop would evolve in this way. In this paper we have considered the same three classes of equilibria but have used a code which follows the non-linear 3D MHD (magnetohydrodynamic) evolution of the loop. We have investigated whether or not there are indications of current-sheet formation. In the cases where there is evidence of this we have found that reconnection does occur and releases sufficient magnetic energy to explain a compact loop flare.     

The energy of electric current sheets

Solar Physics - The free energy associated with current sheets formed by displacing magnetic dipoles in a highly conducting medium is discussed. Specific models are illustrated, based on the idea...     

The energy of electric current sheets

This paper treats two problems on the formation of electric current sheets in the highly electrically conducting solar atmosphere. The first problem concerns a vertical current sheet formed by decreasing the distance between a pair of parallel magnetic line-dipoles lying on the photosphere. The solution to this problem was given previously by Priest and Raadu. With an interest in the flare phenomenon, they derived a formula for the energy stored through the presence of the current sheet. We show that this formula is incorrect. Firstly, there is an error of sign in the derivation of Priest and Raadu, so that, when corrected, the formula gives a negative value for the stored energy. Secondly, the formula is shown to refer to an energy quite different from the free energy associated with the current sheet. To calculate for the current free energy, it is important to account for the frozen-in condition in the highly conducting photosphere.The second problem of the paper concerns the current sheet formed by increasing the distance between the pair of line-dipoles. A different field configuration results, with a curved current sheet lying transverse to the vertical. An analysis of the energy properties is given, to compare with the properties of the Priest-Raadu model.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Freezing-in condition a magnetic field and current sheets in plasma

In the ideal magnetohydrodynamic approximation it is shown that for physically permissible boundary conditions there may exist some lines on which freezing-in condition is not valid. Such singular lines are closed magnetic lines of force and lines with both ends on the boundary surface. By analogy with the singular lines of a potential magnetic field the conclusion is made that X-type singular lines are the place where current sheets (sheet pinches) appear in plasma, whereas on O-type singular lines quasi-cylindrical pinches of a usual type appear.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

The current sheets in the magnetosphere of a pulsar

This paper presents a possible emission mechanism based on the idea of the current sheet of magnetohydrodynamics. Since the excited plasma turbulences result in the anomalous resistance near the light cylinder of a pulsar, the frozen-in condition is partly dissolved. In addition the magnetic field lines in that area cannot perfectly corotate with the star due to the relativistic effect on partly frozen-in charged particles. Therefore, the currents sheets which emit energy are formed.     

The effect of a normal magnetic field component on current sheet stability

A $\text{2}\text{2}\text{5}\text{-}\text{dimensional}$ particle-mesh computer model for the simulation of the current-sheet region of the geomagnetic tail is described. Important features are (a) the use of Fast Fourier techniques for the efficient solution of Ampere's equation, (b) the incorporation of sources and sinks of particles, (c) facilities for simulating finite width effects and (d) the option of including a normal magnetic field component linking through the sheet.Simulations carried out using this model indicate that current sheets with a non-zero normal magnetic field component and an infinite width are stable. The particles trace out Speiser-like orbits in such a case. Sheets with B_normal = 0 and a finite width are unstable with respect to the ion tearing-mode instability. However the presence of a normal magnetic field stabilises the system provided ρ₀<2L_y where ρ₀ is the characteristic length associated with the normal field and where L_y is the width of the sheet.On the basis of these results it is suggested that a geomagnetic substorm occurs when the normal magnetic field drops below the critical value needed for stability.     

A numerical simulation of magnetic reconnection and radiative cooling in line-tied current sheets

We have used the radiative MHD equations for an optically thin plasma to carry out a numerical experiment related to the formation of post-flare loops. The numerical experiment starts with a current sheet that is in mechanical and thermal equilibrium, but which is unstable to both tearing-mode and thermal-condensation instabilities. The current sheet is line-tied at one end to a photospheric-like boundary and evolves asymmetrically. The effects of thermal conduction, resistivity variation, and gravity are ignored. In general, we find that reconnection in the nonlinear stage of the tearing-mode instability can strongly affect the onset of condensations unless the radiative cooling time scale is much smaller than the tearing-mode time scale. When the ambient plasma is less than 0.2, the reconnection enters a regime where the outflow from the reconnection region is supermagnetosonic with respect to the fast-mode wave speed. In the supermagnetosonic regime the most rapidly condensing regions occur downstream of a fast-mode shock that forms where the outflow impinges on closed loops attached to the photospheric-like boundary. A similar shock-induced condensation might occur during the formation of post-flare loops.     

Internal structure of reconnecting current sheets and the emerging flux model for solar flares

We present a steady-state model for reconnecting current sheets, which relates the central values of temperature, density and pressure within the sheet to the prescribed external values of these parameters as well as the magnetic field strength and inflow velocity (or reconnection rate). The simplifying feature of our model is the assumption of quasi-one-dimensionality so that only variations across the sheet at the centre of symmetry are considered in detail. The dimensions of the sheet, the spatial profiles and their variation with the prescribed dimensionless parameters are obtained from the model. We also obtain the conditions on the dimensionless parameters for the existence of a steady state. A beta-limitation is discovered, such that steady reconnection is impossible when the plasma beta is too small. Also, the sheet dimensions may be an order of magnitude larger than previously thought. Finally, these general results are applied to the emerging flux model for solar flares. A state of thermal nonequilibrium ensues when the current sheet between the emerging and ambient flux reaches a critical height. The effect of the beta-limitation is to make this critical height decrease with increasing magnetic field strength.Now at A.W.R.E., Aldermaston, Berks., England.     

The effect of magnetic field morphology on the structure of massive IRDC clumps

Infrared dark clouds (IRDCs) have dense elongated clumps and filaments with the favorable viewing condition of being on the near-side of a bright mid-infrared background. The clumps usually have multiple cores around the center. In this work, we study the effect of magnetic field morphology on the structure of massive IRDC clumps. To achieve this goal, we consider an axisymmetric isothermal oblate IRDC clump, embedded into a constant external magnetic field. We assume a polynomial function for the magnetic field morphology inside the clump. We use the numerical iterative methods to solve the equations: the successive over-relaxation method to find the magnetic and gravitational fluxes, and then the biconjugate gradient method to find the optimized values of mass and current densities. The results show that the IRDC clump will be very elongated along the perpendicular direction of the external magnetic field lines. Also, the assumption of choosing of a polynomial function for the magnetic field morphology leads to the formation of dense regions around the center. The greater the density of the central region, the larger the density of these dense regions and the closer to the center. The presence of these dense regions can lead to the formation of cores at these points.     

Magnetostatic equilibria and current sheets in a sheared magnetic field with an X-point

When a two-dimensional magnetic field containing X-points is sheared, in general current sheets appear all along the separatrices and the X-points are structurally unstable. Their splitting into pairs of cusp points near which the magnetic field is of self-similar form is suggested. Solutions both inside and outside the cusps are obtained and are matched together by the conditions of continuity of the flux function and continuity of magnetic pressure.     

The ducting of wave energy by field-aligned current sheets

A theoretical treatment of the modes of oscillation of an idealized current sheet (in which there is no perpendicular temperature) is given. For the simple case of a monoenergetic current sheet computational results are presented. These results indicate the existence of two types of ducted mode which may have relevance to observation. The first of these is a ducted “whistler” mode and the second occurs at somewhat higher frequencies and at phase velocities comparable with the streaming velocity of the current carriers in the sheet region. A simple explanation of how the ducted “whistler” mode can arise is given.     

The analytic properties of the flapping current sheets in the earth magnetotail

The current sheet in Earth’s magnetotail often flaps, and the flapping waves could be induced propagating towards the dawn and dusk flanks, which could make the current sheet dynamic. To explore the dynamic characteristics of current sheet associated with the flapping motion holistically and provide reasonable physical interpretations, detailed direct calculation and analysis have been applied to one approximate analytic model of magnetic field in the flapping current sheet. The main results from the model demonstrate: (1) the magnetic fluctuation amplitude is attenuated from the center of current sheet to the lobe regions; The larger wave amplitude would induce the larger magnetic amplitude; (2) the curvature of magnetic field lines (MFLs), with maximum at the center of current sheet, is only dependent on the displacement Z along the south-north direction from the center of current sheet, regardless of the tilt of current sheet; (3) the half-thickness of neutral sheet, h, the minimum curvature radius of MFLs, R_cmin, and the tilt angle of current sheet, δ, satisfies h=R_cmin cos δ; (4) the gradient of magnetic strength forms a double-peak profile, and the peak value would be more intense if the local current sheet is more tilted; (5) current density j and its j_y, j_z components reach the extremum at the center of CS. j and j_z would be more intense if the local current sheet is more tilted, but it is not the case for j_y; and (6) the field-aligned component of current density mainly appears in the neutral sheet, and the sign of it would change alternatively as the flapping waves passing by. To check the validity of the model, one simulation on the virtual measurements has been made, and the results are in well consistence with actual observations of Cluster.     

Preflare current sheets in the solar atmosphere

Neutral current sheets are expected to form in the solar atmosphere when photospheric motions or the emergence of new magnetic flux causes oppositely directed magnetic fields to be pressed together. Magnetic energy may thus be stored slowly in excess of the minimum energy associated with a purely potential field and released suddenly during a solar flare. For simplicity, we investigate the neutral sheet which forms between two parallel line dipoles when either the distance between them decreases or their dipole moments increase. It is found that, when the dipoles have approached by an amount equal to a tenth of their original separation distance, the stored energy is comparable with that released in a major flare. In addition, a similarity solution for one-dimensional magnetohydro-dynamic flow within such a neutral sheet is presented; it demonstrates that rapid conversion of magnetic energy into heat is possible provided conditions at the edge of the neutral sheet are changing sufficiently quickly.     

Effect of a twisted magnetic field on the equilibrium structure of polytropic and degenerate fluid cylinders

The distribution of density and mass within an infinite gravitating cylinder is studied for cylinders made up of both polytropic and degenerate material. The equilibrium structure of the cylinder is found from a study of these properties. The effects of rotation of the cylinder are also considered.     

The temperature structure and pressure balance of magnetic loops in active regions

EUV observations show many active region loops in lines formed at temperatures between 10⁴K and 2×l0⁶K. The brightest loops are associated with flux tubes leading to the umbrae of sunspots. It is shown that the high visibility of certain loops in transition region lines is due principallly to a sharp radial decrease of temperature to chromospheric values toward the loop axis. The plasma density of these cool loops is not significantly greater than in the hot gas immediately surrounding it. Consequently, the internal gas pressure of the cool material is clearly lower. The hot material immediately surrounding the cool loops is generally denser than the external corona by a factor 3–4. When the active region is examined in coronal lines, this hot high pressure plasma shows up as loops that are generally parallel to the cool loops but significantly displaced laterally. In general the loop phenomenon in an active region is the result of temperature variations by two orders of magnitude and density variations of around a factor five between adjacent flux tubes in the corona.