Electrostatic wave noise in the neutral sheet in the earth's geomagnetic tail

Numerical solutions are obtained from analytic dispersion relations for electrostatic waves in a self-consistent, one-dimensional magnetic neutral sheet. The dispersion relations are solved in the real wave number and complex frequency domain. The properties of wave modes will be described, with special emphasis on instability. Several regimes of instability are identified which may generally be divided into two classes. Wave growth is associated firstly with counterstreaming between ions and electrons, giving rise to low frequency waves similar to the usual electrostatic two-stream mode. In addition, high frequency growing waves occur, associated with harmonics of the electron oscillation frequency across the neutral plane.     

Some properties of the current sheet in the geomagnetic tail

The topic of this report is that of the influence of noise, and of the finite length and width of the tail on the behaviour of the current sheet.The presence of a weak magnetic field linking through the current sheet leads to plasma containment and counterstreaming, with the consequence that both the plasma temperature and density are increased in the vicinity of the current sheet. The effect of these changes on the relationship between steady bulk parameters is discussed.The finite length of the tail significantly modifies the equilibrium situation in the near Earth tail, for streams mirroring at the Earthwards end of field lines lead to a reduction of merging. The finite width of the tail restricts the region of reduced merging rate to a triangular shaped area extending from the dusk magnetopause into the tail. The finite tail width is also important in the more distant tail, where magnetosheath particles which penetrate the magnetopause ends of the current sheet may become major current carriers, especially if B_z, is small and northwards.Finally, it is shown that the above factors, together with a non-adiabatic current sheet, are important to our understanding of the temporal behaviour of the tail.     

Consequences of an isotropic static plasma sheet in models of the geomagnetic tail

The equation of momentum balance and magnetic flux conservation are given for a static tail model with an isotropic plasma sheet. The possibility of magnetic field leakage into the solar wind and across the neutral sheet is allowed. Numerical integrations for a wide variety of adjustable model parameters are presented that give the dependence on distance from Earth of all tail parameters (field strength inside and outside of the plasma sheet, plasma pressure, plasma sheet area, tail radius, and normal field component to the neutral sheet). The model gives good agreement with the observed distance dependence of the tail field strength, and accounts for the scatter in the data in terms of a mixture of the fields inside and outside the plasma sheet in the data averages. However, compared with the present interpretations of the observations the model gives a too large plasma pressure at large distances and a too small normal component to the neutral sheet. The discrepancies imply that plasma flow and/or pressure anisotropy are required for an adequate model.     

Particle motion and currents in the neutral sheet of the magnetospheric tail

The trajectories of plasma-sheet protons are computed numerically in magnetic-field models which simulate the neutral-sheet-type configuration observed in experiments. No electric field is included, in contrast with the reconnection theory. Entering the neutral sheet and then exiting from it, the particle performs an ordered displacement across the tail. A continuous interchange between the neutral and plasma sheets will give rise to an electric current which may be responsible for the observed magnetic-field configuration. An estimate of this current is made from the tension balance requirement, showing that a substantial anisotropy of the plasma-sheet pressure is necessary to maintain the steady state. It is shown that the neutral sheet itself can be a source of such an anisotropy, due to the non-adiabatic behaviour of protons. Other anisotropy origins are discussed briefly.     

Electric and magnetic drift of non-adiabatic ions in the Earth's geomagnetic tail current sheet

It has been shown recently that non-adiabatic particles in the Earth's magnetotail drift across the tail roughly as predicted for adiabatic particles with 90° pitch angles. In this paper we show that this result implies the existence of an approximate invariant of the motion. Adding the effect of convection associated electric fields, we can then obtain the approximate bounce averaged motion of non-adiabatic particles in the magnetotail. Thus the particle motion and energization due to combined magnetic and electric drifts in the magnetotail are easily predicted.     

Electron counts in the neutral sheet and magnetic variations at a geomagnetic longitude associated ground station

A comparison of the variations in the count of electrons E > 36 keV on the satellite Vela 4A, and in the Macquarie Island magnetometer H trace, shows for a time lag of 22-8 min a correlation, r = 0.95, over a 90 min period of the recovery phase of a magnetospheric substorm on 17 August 1968. All-sky camera data suggest that during the correlation period the auroral electrojet showed very little latitudinal movement. Each peak in electron count relates to a current surge in the electrojet as shown by a deepening of the negative bay at Macquarie Island.Using the Fairfield (1968) model of the location of auroral shells in the solar magnetic equatorial plane, and the known location of the satellite, an estimate of the velocity of tail to Earth plasma convection in the plasma sheet of about 0·33 R_e/min is obtained for the recovery phase.The relationship is discussed between plasma sheet thinning and subsequent broadening, and the extension of the magnetic field lines into the tail region and their subsequent return. This discussion makes use of the estimated time lags between electron count at the satellite and the time of arrival of auroral particles at the antisolar meridian.From a somewhat speculative explanation, but one largely supported from the literature, of the magnetospheric processes involved in this auroral substorm, a plasma velocity estimate of 0·42 R_e/min for the initial phase of the substorm is obtained. These velocities are of the same order as the 0·5 R_e/min obtained by Lezniak and Winkler (1970) at 6·6 R_e.     

The warm current sheet model, and its implications on the temporal behaviour of the geomagnetic tail

A simple model current sheet is studied numerically. Consistent fields and particle trajectories, and their dependence on electron and proton temperature, convection velocity and normal field, B_z, linking through the current sheet, are presented and discussed. It is shown that the protons, which are the major current carriers, largely retain the decoupling of the motion in the x-y plane from the normal oscillations as in the ‘cold’ current sheet. The positive potential of the current sheet is shown to be sufficient to trap some energetic electrons, the motion of which enables the predominance of energetic electrons towards the dawn side of the tail to be understood. Semi-empirical relationships for the thickness and the potential of the current sheet are obtained.

The consequences of such a current sheet on the behaviour of the geomagnetic tail are investigated. Using Faraday's law and the consistent cross tail electric field it is shown that the effect of a southward turning of the interplanetary field is to lead to a decrease in B_z,an increase of the current sheet conductivity, and a growth of stored field energy, i.e. the current sheet blocks merging. The decrease of the resistance of the current sheet is limited by the finite width of the tail. Finally, it is pointed out that if the conditions which bring about the growth of field energy persist, then the collapse of the field lines characteristic of substorms may occur.     

Anomalous resistivity in the geomagnetic tail region

The beam cyclotron instability and electron acoustic instability, driven by cross-tail current and inhomogeneity in density and magnetic field, are found to be unstable in the earth's magnetic tail region. The anomalous resistivities due to these instabilities are found to be of the order of $\text{(10}{}^{\mathrm{?1}}\text{?10}{}^{\mathrm{?3}}\text{)Ω}{}_{\mathrm{e}}{}^{\mathrm{?1}}$ (Ω_e being the electron gyro frequency). It is also suggested that the non-linear saturation of the beam cyclotron instability may lead to conditions favourable for exciting ion acoustic instability.     

Current sheet acceleration of ions in the geomagnetic tail and the properties of ion bursts observed at the lunar distance

Recent analyses of measurements obtained from the Rice University Apollo 14 SIDE on the lunar surface have revealed the frequent appearance of fast tailward-streaming ion “bursts” near the centre plane of the geomagnetic tail. In this paper the properties of these “bursts” are tested for compatibility with tail current sheet tangential stress balance conditions assuming that they are produced by current sheet acceleration of tail lobe plasma downstream and tailward of a magnetic neutral line. Calculations are performed taking the ions to be either protons or singly charged oxygen, the latter possibility being directly suggested by several recent observations. When “burst” bulk parameters are calculated by assuming that the ion distribution functions are convecting isotropic Maxwellians, the results are found to be difficult to reconcile with current sheet stress balance conditions for either protons or oxygen. Use of a different ion distribution based on theoretical expectations and observations in the near-Earth tail, however, results in number density estimates being increased by factors of around an order of magnitude. When the revised densities and ion distribution functions are taken into account, reasonable agreement between observed and expected ion bulk speeds is obtained. In some cases the agreement is better assuming oxygen ions rather than protons, but not by a large factor.     

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.     

A note on the magnetic field topology in the vicinity of neutral points in the resistive MHD and collisionless plasma approximations; Geometry of field-lines in the geomagnetic tail

Two-dimensional models of the reconnection process are, under the appropriate boundary and initial conditions, feasible for a resistive MHD continuum, but not for a collisionless plasma. Here, the field-lines entering the neutral line neighbourhood (of the size of ion-gyroradius) are swept by the electron motion in the direction perpendicular to the plane in which the distant field-lines lie.The sweeping effect and the convection of field-lines in the geomagnetic tail explain the magnetic field observations in tailward flowing plasmas at substorm onsets.     

Substorm related changes in the geomagnetic tail: the growth phase

Changes in the configuration of the geomagnetic tail are known to play a fundamental role in magnetospheric substorms. Observations with the UCLA magnetometer on the eccentric orbiter OGO-5 indicate that the most pronounced changes in the midnight meridian occur in the cusp between 8 and 11 R_e. In order to organize the observations it is necessary to separate effects on the tail due to the solar wind magnetic field and effects due to substorms. Provided there are no changes in the solar wind there are two distinct phases of a substorm in the near tail: a growth phase and an expansion phase. During each phase the observations depend on the location of the satellite relative to the plasma sheet boundaries. Far behind the Earth is the pure tail region which consists of the lobe and the plasma sheet. In the lobe the field magnitude is characteristically enhanced relative to the dipole. Closer to the Earth is a region of transition. The field magnitude is close to that of the dipole but its orientation is distorted forming a cusp-like field line. Near the Earth is a region of depressed field. Here the field magnitude is much less than that of the dipole, but its orientation is similar. The growth phase of a substorm appears to be the direct consequence of the onset of a southward solar wind magnetic field. In the pure tail region the lobe field begins to increase in magnitude and the plasma sheet thins. The transition region moves earthward and the field lines become more tail-like as the field magnitude increases. In the inner region of depressed field, the field magnitude decreases rapidly. The onset of the expansion phase appears to be a process internal to the magnetosphere and independent of the solar wind. In the depressed field region there is a rapid, turbulent increase in field magnitude. In the transition region there is a sudden decrease in the field magnitude and a return to dipolar orientation. In the tail region the plasma sheet expands rapidly with the field becoming quite dipolar, decreasing slowly in the lobe of the tail.     

Nonlinear properties of electron acoustic wave turbulence in the geomagnetic tail

The nonlinear properties of electron acoustic waves in a magnetized plasma consisting of hot electrons, hot ions, and cold electrons are investigated. Using a fluid-guiding center model for the cold electrons and Boltzmann distributions for the hot species, a set of nonlinear mode-coupling equations is derived. Monopole and dipole-vortex solutions are shown to exist for the system of nonlinear equations. Spectrum cascade by mode-coupling in the electron acoustic wave turbulence is investigated. Relevance of our investigation to broadband electrostatic noise (BEN) in the geomagnetic tail is discussed.     

Magnetohydrodynamic waves in a neutral sheet

The magnetohydrodynamic continua and normal modes for waves propagating in a finite magnetic neutral sheet are identified. The normal modes have characteristics similar to hydromagnetic waves observed near the Earth in association with geomagnetic substorms.     

Observation of a possible neutral sheet in the corona

A linear coronal ray, centered on a large helmet, is prominent in white-light photographs taken at the 1922 eclipse. It extends from near the limb to 4 R , has minimum width 9 arc, and persisted for at least 35 min. Examination reveals that the ray marks the cleavage between the domes of a twin-arch streamer which in turn is associated with two large, distinct chromospheric active regions. The ray is interpreted as the edge-on aspect of a coronal neutral sheet which separates areas of presumed opposite magnetic polarity in the two surface regions.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.