An amended magnetohydrodynamic equation which predicts field-aligned current sheets

A derivation of the physical conditions for magnetohydrodynamic equilibrium from first principles establishes a set of equations which differ slightly from the usual ones. The difference is only relevant in the special case when the current is parallel to the magnetic field. What is noteworthy is that these modified equations predict that the simplest magnetohydrodynamic equilibria can only exist in regions of field-aligned current sheets. This prediction is entirely consistent with the observed large-scale structures in the Earth's magnetosphere.     

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.     

The Auroral electrojet and field-aligned current

The location of field-aligned currents in the evening sector with respect to the auroral electrojets is examined. The tri-axial TRIAD satellite data and the simultaneous ground magnetometer data from along the Alaska meridian are analysed. It is shown that an intense upward fieldaligned current flows out from the region of the westward electrojet where discrete auroras are located. The downward flowing current exists in the region further equatorward, namely in the region of the eastward electrojet. However, the downward current is present even when there is no eastward electrojet. The boundary between the upward and the downward currents coincides, in most cases, with the boundary between the westward and the eastward auroral electrojets. Thus, the Harang discontinuity, a narrow area separating the positive and negative H bays, is the region where there is no field-aligned current.     

Magnetic field energy dissipation in neutral current sheets

An extended current sheet characterized by two peculiarities was formed in a configuration with opposite magnetic fields in a laboratory plasma on a -pinch device. First, development of the small scale turbulence leads to abnormal low sheet conductivity, through-sheet plasma diffusion and establishes the sheet thickness an order greater than the skin thicknessc/ _pe ( _pe is electron plasma frequency). Second, there develops and quickly stabilizes in a sheet the magnetic force line reconnection. As a result, a stable neutral sheet has the complicated structure of a magnetic field, including closed magnetic loops elongated along the axis of the system. The neutral sheet plasma becomes intensively heated, probably due to ion-sound turbulence, while a group of accelerated electrons, which on the energy spectrum lead to a plateau formation, are observed. The absence of any predominant direction is a typical feature for the motion of accelerated particles. The experimental data, obtained over a broad range of plasma densities and magnetic field values typical for the solar atmosphere, show that the antiparallel magnetic field turbulent dissipation could play an important role in the mechanism of solar energy release. The parameters of accelerated particles (energy 4–12 keV, the energy content being 10^–1–10² of all the energy dissipated in a sheet) agree nicely with the data of astrophysical observations.     

Acoustic wave ducting along magnetic flux tubes in the sunspot regions

The acoustic waves generated in the solar atmosphere propagate globally as well as upwards. These waves interact with the solar magnetic field structures and are ducted upwards. The velocity of these modified acoustic waves is shown to vary in a modelled solar atmosphere. The solar plasma propagating upwards with these waves are likely to alter the observed features of spicules, granules, and supergranules during changing phases of sunspot regions.     

An Alfvén wave approach to auroral field-aligned currents

The theoretical work presented here was stimulated by the interpretation of auroral field-aligned currents in terms of an Alfvén wave generated in the neutral sheet. Allowing for convection such a wave can be stationary relative to the Earth, and with an Alfvén Mach number of about 10^?2, hydromagnetics predict that the wave normal should be nearly perpendicular to the magnetic field. All the theory presented here is limited to the cold plasma approximation, which is the next step after hydromagnetics, but should have validity here as the wave is propagating into the cold polar wind plasma.The approach is similar to that of Kellogg (1964) except here we consider only the Alfvén mode, and only for Alfvén Mach numbers of about 10^?2. Initially a linear approach was adopted but further computation showed that non-linear effects were responsible for making the current density approximately uniform.The final section presents a plasma sheet boundary crossing selected to illustrate the theory, and is taken from ISEE 1 and 2. The data is such that it permits a first-order estimation of scale sizes to be made in the tail, which in this case was found to be about 1000 km. Subsequent mapping to ionospheric altitudes produced a scale of about a few tens of kilometers.     

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.     

Magnetic field and field-aligned current variations in the polar cusp controlled by interplanetary medium parameters

The distribution of large-scale field-aligned currents in the dayside sector of the auroral oval has been presented for different situations in the interplanetary space. The j_∥ distribution has been calculated on the basis of a model, each part of which is controlled by a corresponding parameter of the interplanetary space. It has been shown that the field-aligned current models, proposed by Iijima and Potemra and by McDiarmid et al. describe the planetary j_∥ distribution for only particular situations in the interplanetary space and represent some particular cases of a more general model.     

The radiation of energy by a current in a plasma

The derivation of the differential power emitted in any given direction by a current J in a linear, homogeneous and non-absorbing plasma is reviewed in detail. The conventional derivation is shown to give the poweremitted; a formalism for the powerreceived is established by evaluating the Poynting vector in terms of the far field. It is pointed out that the two power expressions differ because the same energy dE is emitted in a time dt _e but received over a different time dt _r . Moreover, a careful scrutiny of both the formalism for the power emission and for the power reception exposes implicit assumptions which do not hold if the plasma is anisotropic. The necessary steps for establishing a valid formalism for anisotropic media are briefly sketched.     

Particle acceleration in reconnecting current sheets

We study motions of charged particles in reconnecting current sheets (CS) which have both transverse (perpendicular to the current sheet plane) and longitudinal (parallel to the electric current inside the sheet) components of the magnetic field. Such CS, called non-neutral, are formed in regions of magnetic field line reconnection in the solar atmosphere. We develop an analytical technique which allows us to reproduce previous results concerning the influence of transverse fields on particle motion and acceleration. This technique also allows us to evaluate the effect of the longitudinal field. The latter increases considerably the efficiency of particle acceleration in CS. The energizing of electrons during the main phase of solar flares can be interpreted as their acceleration in non-neutral CS.     

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.     

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.     

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.     

The effect of pressure anisotropy on the equilibrium structure of magnetic current sheets

The equilibrium structure of two-dimensional magnetic current sheets is investigated for systems in which the plasma pressure dominates the bulk flow energy, as appears appropriate for the quiet time plasmasheet in the geomagnetic tail. A simple model is studied in which the field is contained between plane parallel boundaries and varies exponentially along the system, while the plasma pressure is anisotropic, the anisotropy being arbitrary but constant along the centre plane. When the field is highly inflated by the plasma current it is found that adiabatic solutions exist only when the plasma pressure is close to isotropic. For the case P_∥ > P_⊥ it is argued that a thin, non-adiabatic current layer will in general form at the sheet centre, usually embedded within a much broader adiabatic current distribution. When P_⊥ > P_∥, a broad region of very depressed fields develops about the centre of the current sheet, terminated at its outer boundary by a spike in the current density. This central region becomes unstable to the mirror mode well before the limiting adiabatic solution is reached.     

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 dependence of the value of the field-aligned current in the ionosphere on the local time for low velocity of convection

For low velocities of convection, the normal component of the current near the magnetopause is calculated in a case when the magnetopause is a tangential discontinuity. It is shown that for the great pressure of the magnetospheric plasma this component of the current, closing through the ionosphere, create the global system of field-aligned currents which is consistent with the Triad data on the value, the direction and the distribution with the local time.     

An investigation of the field-aligned currents associated with a large-scale ULF wave in the morning sector

Previous work by Scoffield, H.C., Yeoman, T.K., Wright, D.M., Milan, S.E., Wright, A.N., Strangeway, R.J. [2005. An investigation of the field aligned currents associated with a large scale ULF wave using data from CUTLASS and FAST. Ann. Geophys. 23, 487–498) investigated a large-scale ULF wave, occurring in the dusk sector (∼1900 MLT). The wave had a period of ∼800 s (corresponding to 1.2 mHz frequency), an azimuthal wave number of ∼7 and a full-width at half-maximum (FWHM) across the resonance of 350 km. IMAGE ground magnetometer and SuperDARN radar observations of the wave's spatial and temporal characteristics were used to parameterise a simple, two-dimensional field line resonance (FLR) model. The model-calculated field-aligned current (FAC) was compared with FACs derived from the FAST energetic particle spectra and magnetic field measurement. Here the authors use the same method to investigate the FAC structure of a second large-scale ULF wave, with a period of ∼450 s, occurring the dawn sector (∼0500 MLT) with an opposite sense background region 1–region 2 current system. This wave has a much larger longitudinal scale (m∼4.5) and a smaller latitude scale (FWHM=150 km). Unlike the dusk sector wave, which was dominated by upward FAC, FAST observations of the dawn sector wave show an interval of large-scale downward FAC of ∼1.5 μA m⁻². Downgoing magnetospheric electrons with energies of a few keV were observed, which are associated with upward FACs of ∼1 μA m⁻². For both wave studies, downward currents appear to be carried partially by upgoing electrons below the FAST energy detection threshold (5 eV), but also consist of a mixture of hotter downgoing magnetospheric electrons and upgoing ionospheric electrons of energies 30 eV–1 keV. Strong intervals of upward current show that small-scale structuring of scale ∼50 km has been imposed on the current carriers. In general, this study confirms the findings of Scoffield, H.C., Yeoman, T.K., Wright, D.M., Milan, S.E., Wright, A.N., Strangeway, R.J. [2005. An investigation of the FACs associated with a large-scale ULF wave using data from CUTLASS and FAST. Ann. Geophys. 23, 487–498).     

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.     

Thermal evolution of current sheets and flash phase of solar flares

The physical conditions in a stationary flow of the Petchek type, allowing reconnection between flux emerging from below the solar photosphere and a preexisting magnetic field, are discussed. It is shown that, when rising in the solar atmosphere, the reconnection region has at first a rather low temperature as compared with its environment. Above a certain critical height, however, this low temperature thermal equilibrium often ceases to be possible, and the sheet rapidly heats, seeking a new thermal equilibrium. During this dynamical process, current-driven microinstabilities may be triggered in the current sheet, giving rise to an enhanced resistivity. High energy particles might be produced by the induced electric field developed during the rapid readjustment of MHD flows that results from this change in the transport properties of the plasma.