The formation of prominences by thermal instability: A numerical study

A two-dimensional model of prominence formation in a region containing a magnetic neutral sheet is constructed for a variety of initial conditions, assuming the coronal plasma to be described by the usual hydromagnetic approximation, with infinite electric conductivity. In each case the magnetic field is initially vertical, varying antisymmetrically with respect to the neutral sheet, to a maximum value at a distance of 70 000 km from the neutral sheet. In the first case, the plasma is initially in hydrostatic equilibrium, whereas in successive cases, the pressure is assumed to be of such a value that the plasma is in lateral equilibrium of total pressure (gas plus magnetic). In a variation of this case, the value of the solar gravitational field was artificially reduced, and the effects considered. Large lateral motions are produced in each case, thus apparently inhibiting the condensation of prominences, with the exception of the unrealistic case of artificially reduced gravity. The results suggest that consideration either of a third component of the magnetic field (horizontal and parallel to the neutral sheet), or a finite conductivity, allowing magnetic recombination across the neutral sheet, or both, would more realistically represent the problem and might thus show the development of prominences.     

Magnetospheric surface flow with strong discontinuities

The theory of strong discontinuities in plasma with anisotropic pressure is applied for interpretation of the recent plasma and magnetic experiments on the boundary and in the tail of the magnetosphere. The properties of the discontinuities are described. It is supposed that on the boundary and in the tail of the magnetosphere anisotropic discontinuities occur with a nonzero normal component of the magnetic field. The general consequence of this assumption is the existence of the magnetospheric surface flow expanding from the subsolar point. The consequence does not contradict the data obtained on IMP 5. For the investigation of the low latitude part of the flow, the use of electrostatic analysers is desirable with the entrance oriented along the magnetospheric surface. The well-known qualitative scheme of the hydrodynamical flow with strong discontinuities in the tail is generalized by means of the three anisotropic discontinuities: the contact one coinciding with the magnetic neutral sheet, and the two discontinuities with the nonzero normal flow of the mass simulating the boundary of the plasma sheet. The result of the scheme of the components of the bulk velocity in the plasma sheet agrees with the recent observations on the Vela 4B. The scheme connects the well-known phenomena of the blocking and the thinning of the plasma sheet in the initial phase of the substorm. According to the general principles of the reconnection the dynamical dissipation is decreased by the blocking of the flow in the plasma sheet. The decrease leads to a drift of the plasma sheet boundary in the neutral sheet direction. The reverse picture is probably a result of a relaxation of the blocking.     

The magnetic field in the Earth's tail

Detailed magnetic fields in the Earth's tail are calculated from a proposed model containing Beard's tail surface and a current sheet inferred from satellite observations. The component inside and perpendicular to the neutral sheet permits us to construct the drift pattern in the magnetic equatorial plane for charged particles. The computed results are in reasonable agreement with the experimental results, although some deviations are noted.     

A mechanism for the growth phase of magnetospheric substorms

A mechanism is presented whereby the rate of energy dissipation in the magnetosphere is controlled by the particle density in the plasma sheet in the near geomagnetic tail. The mechanism is based on a model in which the plasma sheet is sustained by injection of solar-wind particles into the dayside magnetosphere. The efficiency of the injection is controlled by solarwind parameters, in particular, the north-south component of the interplanetary magnetic field; the maximum injection rate occurs when the interplanetary field is northward. During geomagnetically quiet times, this source balances the loss of particles from the edges of the tail current sheet. If the dayside source rate is reduced (e.g. by a southward-turning interplanetary magnetic field), then the plasma sheet is depleted and the rate of magnetic merging is enhanced in the earthward portion of the tail current sheet. This period of steadily-enhanced merging is associated with the growth phase, i.e. the period of enhanced magnetospheric convection for about one hour preceding the breakup of a polar magnetic or auroral substorm. The breakup can be understood as the result of the collapse of a portion of the tail current sheet following the local depletion of the plasma sheet.     

On the convective mechanism for formation of the plasma sheet in the magnetospheric tail

Calculation of stationary distributions of the most important plasma parameters (particle energy, density, field-aligned and transversal pressure) is performed for a model magnetotail plasma sheet which is formed by convecting plasma mantle particles injected into the closed geomagnetic field line tubes. Computations have been done for two convection models: (i) a model of completely adiabatic particle motion with conservation of the first two invariants and (ii) a model with a strong pitch-angle diffusion which maintains isotropy. It is found that in both cases the heating and compression of the plasma are somewhat more effective than is necessary to account for the observed gradients of magnetic field in the magnetospheric tail. A leakage of accelerated particles through the dawn and dusk edges of the plasma sheet is proposed as a possible mechanism for maintenance of stationary convection in the magnetotail. The question of the dependence of the stationary magnetotail parameters on the solar wind state is discussed briefly.     

Plasma-sheet dynamics and magnetospheric substorms

We present a conceptual model of the formation of the plasma sheet and of its dynamical behavior in association with magnetospheric substorms. We assume that plasma mantle particles $\text{E}\text{～}\text{×}\text{B}\text{～}$ drift toward the current sheet in the center of the tail where they are accelerated by magnetic-field annihilation to form the plasma sheet. Because of the velocity-dependent access of mantle particles to the current sheet, we argue that the convection electric field and the corresponding rate of field annihilation decrease with increasing radial distance. As a consequence, there exists no steady-state configuration for the plasma sheet, which must instead shrink continuously in thickness until the near-earth portion of the current sheet is disrupted by the formation of a magnetic neutral line. The current-sheet disruption launches a large-amplitude hydromagnetic wave which is largely reflected from the ionosphere. The reflected wave sets the neutral line in motion away from the earth; the neutral line comes to rest at a distance (which we estimate to be a few hundred earth radii) where the incoming mantle particles enter the current sheet at the local Alfvén velocity. At this “Alfvén point” reconnection ceases and the thinning of the plasma sheet begins again. Within this model, the magnetospheric substorm (which is associated with the current-sheet disruption) is a cyclical phenomenon whose frequency is proportional to the rate of convection in the magnetospheric tail.     

A short wavelength instability in the neutral sheet of the earth's geomagnetic tail

In an earlier paper, Bowers (1973), ion plasma oscillations were found to be unstable in the steady state developed by Cowley (1972) for the neutral sheet in the Earth's geomagnetic tail. In this paper a similar stability analysis is carried out but for a different steady state, suggested by Dungey, with the result that unstable waves with frequencies near the electron plasma frequency are found. In the Dungey steady state the current necessary for magnetic field reversal is carried by plasma originating from both the magnetosheath and the lobes of the tail. This modifies the steady state proposed by Alfvén and subsequently developed by Cowley in which all the current is carried by plasma from the lobes of the tail thereby fixing the cross-tail potential Φ. With magnetosheath plasma present the value of Φ is no longer fixed solely by parameters in the lobes of the tail but the cross-tail electric field is still assumed localised in the dusk region of the sheet as in the Cowley model due to the balance of charge required in the neutral sheet. The value of Φ can be expected to increase as magnetic flux is transported to the tail which inflates and causes flux annihilation because the magneto-sheath plasma in the neutral sheet has insufficient pressure to keep the two lobes of the tail apart. The Vlasov-Maxwell set of equations is perturbed and linearised enabling a critical condition for instability to be found for modes propagating across the tail. Typically, this condition requireseΦ≳KT _m whereT _m is the temperature of magnetosheath electrons. The instability occurs in the presence of cold plasma which hasE×B drifted into the neutral sheet from the lobes of the tail. This contrasts with the usual two stream instability which is stabilised by the cold plasma. Once precipitated the instability may be explosive provided current disruption occurs, for then a further increase in Φ will result which drives a greater range of wave numbers unstable thereby causing even more turbulence and an even larger cross-tail electric field. Because of this behaviour the instability may be a trigger for a substorm.     

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.     

Adiabatic plasma convection in the tail plasma sheet

We investigate the transport process of electrons in the tail plasma sheet by convection electric fields, under the assumption of conservation of the first two adiabatic invariants. The variation of the electron distribution function, and hence the bulk parameters with distance from the Earth are calculated. The results show that the electron distribution has a pressure anisotropy with p/p< 1 in the plasma sheet. Finally, the effects of the pressure anisotropy are qualitatively considered in terms of the modification of the geomagnetic field structure in the tail plasma sheet and instabilities due to wave-particle interactions.     

Magnetospheric substorm models: Comparison with neutral sheet magnetic field observations

Four models for geomagnetic substorms, a quiet tail model, and models incorporating structural effects of the tail are examined for consistency with magnetic-field data during satellite crossings of the tail neutral sheet/plasma sheet. For this data the tearing mode instability model is always consistent, and inward moving distant neutral line is sometimes consistent, quasi-steady reconnection with slow shock and intermediate wave structure and locally quiet tail rarely consistent, and an outward propagating rarefaction wave is never consistent with the magnetic observations. In several cases structural effects of the tail are consistent with key features of the magnetic signatures.     

Neutral line motion due to reconnection in two-ribbon solar flares and magnetospheric substorms

Two kinematic models of line-tied reconnection are considered which describe the motion of a magnetic neutral line (NL) during the main phase of a two-ribbon solar flare and during the recovery phase of a magnetospheric substorm in the geomagnetic tail. The models are kinematic in that they use only the magnetic induction equation, which suffices to determine the position and velocity of the NL as functions of time if the rate of reconnection is prescribed. The solar flare model shows that the observed large decrease in the rate at which “post”-flare loops rise upward from the photosphere during the main phase does not require a corresponding decrease in the rate of reconnection. Instead it is found that a constant rate of reconnection can account for the motion of the loops for almost the entire period during which they are observed. By contrast, application of the same procedures to the recovery phase of the magnetospheric substorm in the tail predicts a slightly increasing speed of NL motion if the rate of reconnection is constant. Furthermore, it is found that the motion of the NL relative to the ambient medium may account for much of the observed asymmetry in the magnetic field in the plasma sheet during recovery. Due to this motion, the plasma sheet thickness may be up to 4 times smaller and the normal magnetic field component up to 2 times weaker in the region tailward of the NL than in the corresponding region earthward of the NL.     

Formation of the plasma mantle in the Venusian magnetosphere

A model of the interaction of the solar wind with Venus is proposed including magnetic barrier formation, ionopause structure, plasma dynamics in the magnetic barrier, and the formation of the Venusian tail (wake). It is shown that under stationary conditions the ionopause is practically an equipotential boundary and its current is determined by a diamagnetic drift. The source of the plasma mantle can be provided by photoions appearing in the magnetic barrier and convecting toward the wake as a result of both magnetic pressure gradient and magnetic tension. The formation of the magnetic tail is determined by convection of magnetic barrier flux tubes in which the solar-wind plasma is replaced by ions of planetary origin. Compared to observational data the proposed model gives somewhat overestimated values of ion convective velocity and magnetic barrier thickness near the terminator and underestimated values of number density and magnetic field strength in the tail. Accordingly this suggests the possible influence of the anomalous ionization effects in the solar wind—Venus interaction.     

Mercury’s magnetospheric magnetic field after the first two MESSENGER flybys

The “paraboloid” model of Mercury’s magnetospheric magnetic field is used to determine the best-fit magnetospheric current system and internal dipole parameters from magnetic field measurements taken during the first and second MESSENGER flybys of Mercury on 14 January and 6 October 2008. Together with magnetic field measurements taken during the Mariner 10 flybys on 29 March 1974 and 16 March 1975, there exist three low-latitude traversals separated in longitude and one high-latitude encounter. From our model formulation and fitting procedure a Mercury dipole moment of 196 nT ·  (where R_M is Mercury’s radius) was determined. The dipole is offset from Mercury’s center by 405 km in the northward direction. The dipole inclination to Mercury’s rotation axis is relatively small, ∼4°, with an eastern longitude of 193° for the dipole northern pole. Our model is based on the a priori assumption that the dipole position and the moment orientation and strength do not change in time. The root mean square (rms) deviation between the Mariner 10 and MESSENGER magnetic field measurements and the predictions of our model for all four flybys is 10.7 nT. For each magnetic field component the rms residual is ∼6 nT or about 1.5% of the maximum measured magnetic field, ∼400 nT. This level of agreement is possible only because the magnetospheric current system parameters have been determined separately for each flyby. The magnetospheric stand-off distance, the distance from the planet’s center to the inner edge of the tail current sheet, the tail lobe magnetic flux, and the displacement of the tail current sheet relative to the Mercury solar-magnetospheric equatorial plane have been determined independently for each flyby. The magnetic flux in the tail lobes varied from 3.8 to 5.9 MWb; the subsolar magnetopause stand-off distance from 1.28 to 1.43 R_M; and the distance to the inner edge of the current sheet from 1.23 to 1.32 R_M. The differences in the current systems between the first and second MESSENGER flybys are attributed to the effects of strong magnetic reconnection driven by southward interplanetary magnetic field during the latter flyby.     

Instability of the cometary plasma tail—the instability in a plasma sheet

We consider the instability of the cometary plasma tail which is composed of a neutral sheet,two lobes of the ion tail and solar wind.The plasma is assumed to be highly conductive and incompressible.The unstable state yields a magnetic field which is perpendicular to the tail axis.Our result is consistent with findings about plasma from the International Cometary Explorer(ICE).     

A self-consistent model of the jovian plasma sheet

An axially-symmetric, rapidly-rotating magnetosphere containing low-energy plasma is considered. The resulting plasma sheet is presumed isothermal and thin compared with the radius of the sheet. Solutions of the model equations are found which include the effects of centrifugal, pressure and electro-magnetic forces. These solutions show that the sheet has a constant thickness and that the pressure decays exponentially with distance from the equatorial plane. The calculated curves for the magnetic induction field are compared with the observed field of Jupiter.     

Time-dependent configuration changes of the magnetotail and plasma sheet thinning

The configuration of the magnetotail magnetic field has been calculated for a situation where a disruption of a portion of the tail current system develops. The decrease of the current in a localized region of the magnetotail leads to a collapse of the magnetic field in that vicinity. The calculated configuration of the field resembles what is predicted by reconnection models with the field lines moving toward the neutral sheet and then connecting and either moving toward or away from the earth. Associated with this changing magnetic field there is an induced electric field which will then influence the motion of the plasma in the magnetotail via E × B drifts.When the current from X_sm = ?20 to ?40 R_E in the tail is decreasing with a tune-constant of 0.5 h the electric field produced, which is primarily westward, has a maximum value of 0.83 mV m^?1 and produces plasma sheet thinning velocities of 0.3 km s^?1. Higher velocities result for more rapid rates of current decrease, and they agree well with experimental observations. The plasma flows in the sunward direction are, however, much smaller than what has been observed. This is due in part to the inability of the magnetic field model to adequately represent the magnetic field in the immediate vicinity of the neutral sheet. Use of an improved model would give better agreement with the observations.The calculations show that the induced electric field of a time-dependent magnetic field is able to explain certain observed features of the plasma sheet motions. Also, this agreement suggests that the assumption that there is no charge separation contribution to the electric field may be reasonable during situations of large scale and rapid current disruptions in the magnetotail.     

A theoretical prediction of ion plasma oscillations in a neutral sheet

Starting from the Vlasov equation the steady state and stability properties of the electron sheet in the Cowley neutral sheet model of the geomagnetic tail are considered. Electrostatic ion plasma oscillations propagating from dusk to dawn are found to be unstable provided the thermal spread normal to the current is sufficiently large. Assuming the population of the neutral sheet to be supplied by the polar wind it is shown how a localisation of the cross tail electric field could lead to the instability first appearing around midnight. It is conjectured that the localisation of the cross tail electric field could continually feed the instability, so leading to enough turbulence to give enhanced reconnection of the magnetic field.List of symbols f distribution function - B magnetic field strength far from the neutral sheet - a sheet half thickness - total potential drop across the tail which is localised to the dusk end of the tail in Cowley's model - potential for the steady state electric field normal to the electron current sheet. This potential exists in that region of the tail that excludes the localised region of cross tail electric field - average velocity across the tail of electrons in the current sheet - v average velocity of the electrons normal to the current sheet - p canonical momentum of a particle - energy of a particle - KT electron energy normal to the sheet (1/2m ^e v ² ) - KT ⁱ ion energy (1/2m ⁱ V ² ) - electron gyrofrequency far from the neutral sheet - ⁱ ion gyrofrequency far from the neutral sheet - Ay steady state vector potential for the magnetic field - A –Ay/aB ₀ (normalised vector potential) When perturbing the steady state, dashes have been used to denote the time dependent first order quantities. Where no confusion could arise the dashes are dropped, e.g.Ey=Ey since there is no zero orderEy in the region considered in the stability analysis.     

Explorer 34 magnetic field measurements near the tail current sheet and auroral activity

Explorer 34 (Imp 4) 2.56 s magnetic data during 131 traversals of the tail current sheet are presented along with simultaneous 2.5 min auroral electrojet indices AE and AL. The normal magnetic field,B , satellite crossing times and positions are tabulated for these 131 crossings.B is defined in the center of the sheet: it is the vector magnetic field at the time of field minimum during the crossing (B _x component changes sign). It is remarkable that the only normal components too large in magnitude to be classified as fine structure occur near the time of onset of an AE event. Cases are discussed where the normal component, defined near the plasma sheet edges, has the opposite sign compared to the normal component defined at the sheet center. For quiet times, the current sheet may be only about 1000 km thick within a 3R _e (Earth-radii) plasma sheet, and may carry some 10–15% of the total tail current.     

Structure of the Jovian magnetodisk current sheet:: initial Galileo observations

The ten-degree tilt of the Jovian magnetic dipole causes the magnetic equator to move back and forth across Jupiters rotational equator and the Galileo orbit that lies therein. Beyond about 24 Jovian radii, the equatorial current sheet thins and the magnetic structure changes from quasi-dipolar into magnetodisk-like with two regions of nearly radial but antiparallel magnetic field separated by a strong current layer. The magnetic field at the center of the current sheet is very weak in this region. Herein we examine the current sheet at radial distances from 24–55 Jovian radii. We find that the magnetic structure very much resembles the structure seen at planetary magnetopause and tail current sheet crossings. The magnetic field variation is mainly linear with little rotation of the field direction. At times there is almost no small-scale structure present and the normal component of the magnetic field is almost constant through the current sheet. At other times there are strong small-scale structures present in both the southward and northward directions. This small-scale structure appears to grow with radial distance and may provide the seeds for the explosive reconnection observed at even greater radial distances on the nightside. Beyond about 40 Jovian radii, the thin current sheet also appears to be almost constantly in oscillatory motion with periods of about 10 min. The amplitude of these oscillations also appears to grow with radial distance. The source of these fluctuations may be dynamical events in the more distant magnetodisk.