Richard L. Kaufmann

Plasma sheet thickness and electric currents

Two years of Geotail data in the (−30 < x < −8, |y| < 15) RE region first were sorted into (x, y, β) boxes. Direct measurements of the average electron and ion current densities, symmetry assumptions, and the momentum equation were used to get three different estimates of the electric current in each box. The momentum equation method gave the most consistent results, while the other two methods provided complementary information about particle drifts. The average common drift of electrons and ions was found to be comparable to the average differential drift of ions with respect to electrons. These two components of the ion drift velocity tended to cancel on the dawnside, resulting in currents that were primarily carried by electrons moving at the common drift speed. The two ion drifts added on the duskside where ions carried most of the cross-tail current. The particle and magnetic field measurements were used to estimate the z thickness of each β box. A concentration of the long-term-averaged cross-tail current was seen near the neutral sheet. The region of nonadiabatic orbital motion had an average characteristic length scale of ∼0.4 RE. The principal plasma sheet extended to ∼2.5 RE from the neutral sheet at midnight and to ∼5 RE in the flanks. The final result is a method to create models in (x, y, z) coordinates of the long-term-averaged values of any of the measured fluid parameters or fields. The isotropic portion of the pressure tensor was used as an example of one parameter that can be modeled. These pressure plots showed that the z component of the long-term-averaged magnetic field line tension force is important everywhere, that the y component is small everywhere, and that the y component is significant in the flanks.

Pressure, volume, density relationships in the plasma sheet

The entropy parameter Pn � 5/3 was found to be relatively uniform throughout the region studied. The energy parameter TV 2/3 decreased by 40% for ions and 10% for electrons near midnight between � 29.5 and � 11.5 RE. These energy parameter changes suggest that the most energetic ions and electrons are either being deenergized or preferentially lost, processes that may be associated with gradient and curvature drifts through the sides of the convecting flux tubes or by wave instabilities and a parallel heat flux. INDEX TERMS: 2764 Magnetospheric Physics: Plasma sheet; 2744 Magnetospheric Physics: Magnetotail; 2760 Magnetospheric Physics: Plasma convection; 2740 Magnetospheric Physics: Magnetospheric configuration and dynamics; KEYWORDS: plasma sheet, magnetotail, pressure balance inconsistency, 3-D models

Mapping and energization in the magnetotail: 1. Magnetospheric boundaries

A set of boundaries was chosen to model the principal observed magnetospheric regions. Those regions which extended out to the distant magnetotail were defined at xsm = −20 RE. The Tsyganenko (1989) magnetic field model (T89) was used to project the boundaries down to the ionosphere. It was found that all field lines which passed within 3 RE of the magnetopause projected to the dayside ionosphere. Dayside arcs therefore generally map to the low-latitude boundary layer, the cusp/cleft, or the entry layer. The nightside auroral zone, and therefore field lines associated with the substorm current diversion process, primarily traced to portions of the plasma sheet that do not come in direct contact with flowing solar wind plasma. Several mapping problems were encountered. The first involved identifying certain boundaries in the magnetosphere model. The flanks of the magnetotail are not modeled realistically. As a result, we had difficulty in defining a T89 magnetopause in the equatorial plane. Other problems were that some magnetotail boundaries may have no ionospheric signature, and that some boundaries are influenced by cross-field plasma drift. Plasma boundaries are not tangent to field lines when drift is present, but all mapping was done by following field lines. Uncertainties of about 1° of latitude in the resulting ionospheric projections were found for each 1 RE of drift near midnight at xsm = −20 RE. The steady state magnetotail then was subdivided out to xsm = −22 RE according to the expected characteristics of charged particle orbits. Orbits were traced in the modified Harris magnetic field model, with parameters adjusted to approximate the shapes of T89 magnetic field lines. The one-dimensional Harris model was used to eliminate some drift effects. This permitted a detailed study of each separate subregion. Curves defining various orbit types were projected to the ionosphere. It is suggested that low- or middle-altitude satellites may be able to detect regions of quasi-adiabatic and nonadiabatic equatorial orbits by monitoring the loss cones. For these highly field aligned loss cone particles, we found that the net effect of the complex interaction with the current sheet can be explained by an extremely simple model. The model involves shifting all generally field-aligned ions as a block through an energy-dependent “scatter” angle. When viewed microscopically, the resulting pitch angle changes are highly structured. Macroscopically it may be possible to describe the process in terms of pitch angle diffusion.

Three-dimensional analyses of electric currents and pressure anisotropies in the plasma sheet

[1] Long-term averaged three-dimensional (3-D) databased magnetotail models have been created for many plasma and field parameters. A simple modeling technique that was used in earlier work is compared with a new more comprehensive procedure. Good agreement between the two methods was found when both produced stable results. The simpler method generated reliable models from any of the available data sets, while the more complex method did not. It is shown how analyses of the models can determine plasma and field parameters that are too small to be measured directly. The magnetic field data was used to calculate average electric currents flowing in the x and y directions. Full 3-D distributions of j x and j y were determined from the models even though these currents were too small to measure directly with adequate accuracy. Changes of the electron and ion pressure anisotropies as a function of distance along an average magnetic field line then were analyzed. It was concluded that the electron anisotropy was created by an electric field with a parallel component near the neutral sheet. The parallel electric field is small but is required to maintain charge neutrality in the region containing guiding center electron and nonguiding center ion orbits. In addition to creating anisotropic electron distributions the presence ofthis parallel electric field violates the ideal MHD assumptions near the neutral sheet. The ion anisotropy suggests that the net effect of chaotic ion motion near the neutral sheet is to create a weak source cone distribution superimposed on a denser isotropic component.

Cross‐tail current, field‐aligned current, and By

Orbits of individual charged particles were traced in a one-dimensional magnetic field model that included a uniform cross-tail component Byo. The effects of Byo on the cross-tail current distribution jy (z), the average cross-tail drift velocity 〈νy(z)〉, and the average pitch angle change 〈Δα〉 experienced during current sheet encounters were calculated. The addition of a Byo that exceeded several tenths of one nanotesla completely eliminated all resonance effects for odd-N orbits. An odd-N resonance involves ions that enter and exit the current sheet on the same side. Pitch angles of nearly all such ions changed substantially during a typical current sheet interaction, and there was no region of large cross-tail drift velocity in the presence of a modest Byo. The addition of a very large Byo guide field in the direction that enhances the natural drift produces a large jy and small 〈Δα〉 for ions with all energies. The addition of a modest Byo had less effect near even-N resonances. In this case, ions in a small energy range were found to undergo so little change in pitch angle that particles which originated in the ionosphere would pass through the current sheet and return to the conjugate ionosphere. Finally, the cross-tail drift of ions from regions dominated by stochastic orbits to regions dominated by either resonant or guiding center orbits was considered. The ion drift speed changed substantially during such transitions. The accompanying electrons obey the guiding center equations, so electron drift is more uniform. Any difference between gradients in the fluxes associated with electron and ion drifts requires the presence of a Birkeland current in order to maintain charge neutrality. This plasma sheet region therefore serves as a current generator. The analysis predicts that the resulting Birkeland current connects to the lowest altitude equatorial regions in which ions drift to or from a point at which stochastic orbits predominate. The proposed mechanism appears only in analyses that include non-guiding-center effects.

Nonguiding Center Motion and Substorm Effects in the Magnetotail

Thick and thin models of the middle magnetotail were developed using a consistent orbit tracing technique. It was found that currents carried near the equator by groups of ions with anisotropic distribution functions are not well approximated by the guiding center expressions. The guiding center equations fail primarily because the calculated pressure tensor is not magnetic field aligned. The pressure tensor becomes field aligned as one moves away from the equator, but here there is a small region in which the guiding center equations remain inadequate because the two perpendicular components of the pressure tensor are unequal. The significance of nonguiding center motion to substorm processes then was examined. One mechanism that may disrupt a thin cross-tail current sheet involves field changes that cause ions to begin following chaotic orbits. The lowest-altitude chaotic region, characterized by an adiabaticity parameter kappa approx. equal to 0.8, is especially important. The average cross-tail particle drift is slow, and we were unable to generate a thin current sheet using such ions. Therefore, any process that tends to create a thin current sheet in a region with kappa approaching 0.8 may cause the cross-tail current to get so low that it becomes insufficient to support the lobes. A different limit may be important in resonant orbit regions of a thin current sheet because particles reach a maximum cross-tail drift velocity. If the number of ions per unit length decreases as the tail is stretched, this part of the plasma sheet also may become unable to carry the cross-tail current needed to support the lobes. Thin sheets are needed for both resonant and chaotic orbit mechanisms because the distribution function must be highly structured. A description of current continuity is included to show how field aligned currents can evolve during the transition from a two-dimensional (2-D) to a 3-D configuration.

Structure of the magnetotail current sheet

An orbit tracing technique was used to generate current sheets for three magnetotail models. Groups of ions were followed to calculate the resulting cross-tail current. Several groups then were combined to produce a current sheet. The goal is a model in which the ions and associated electrons carry the electric current distribution needed to generate the magnetic field B in which ion orbits were traced. The region −20 RE < x < −14 RE in geocentric solar magnetospheric coordinates was studied. Emphasis was placed on identifying the categories of ion orbits which contribute most to the cross-tail current and on gaining physical insight into the manner by which the ions carry the observed current distribution. Ions that were trapped near z = 0, ions that magnetically mirrored throughout the current sheet, and ions that mirrored near the Earth all were needed. The current sheet structure was determined primarily by ion magnetization currents. Electrons of the observed energies carried relatively little cross-tail current in these quiet time current sheets. Distribution functions were generated and integrated to evaluate fluid parameters. An earlier model in which B depended only on z produced a consistent current sheet, but it did not provide a realistic representation of the Earths middle magnetotail. In the present study, B changed substantially in the x and z directions but only weakly in the y direction within our region of interest. Plasmas with three characteristic particle energies were used with each of the magnetic field models. A plasma was found for each model in which the density, average energy, cross-tail current, and bulk flow velocity agreed well with satellite observations.

What auroral electron and ion beams tell us about magnetosphere-ionosphere coupling

The electron and ion beams which have been detected on many rockets and satellites are of particular interest because beam particles carry information about both the ionosphere and the magnetosphere out to the distant tail. Stability analyses have shown that even the most dramatic beams have evolved until the particle distribution functions are only weakly unstable. The shortest plasma wave growth lengths in the auroral region are usually comparable to the size of an arc. The resulting clearest electron beams generally are relatively minor features of distribution functions which are dominated by plateaus, loss cones, broad or stretched out field aligned features, and hot or cold isotropic components. The true electron beams therefore represent a small fraction of the total electron number density. Ion beams carry a much larger fraction of all ions, but also are only weakly unstable. The electron beams seen at low altitudes can drive whistlers (both electromagnetic and electrostatic, including lower hybrid waves) and upper hybrid waves, which may be particularly intense near electron gyroharmonics. Ion beams can drive low frequency electromagnetic waves that are related to gyrofrequencies of several ion species as well as ion acoustic and electrostatic ion cyclotron waves. These latter waves can be driven both by the drift of ion beams relative to cold stationary ions and by the drift of electrons relative to either stationary or drifting ions. Abrupt changes or boundaries in the electron and ion velocity space distribution functions (e.g. beams and loss cones) have been analyzed to provide information about the plasma source, acceleration process, and regions of strong wave-particle interactions. Fluid analyses have shown that upgoing ion beams carry a great deal of momentum flux from the ionosphere. This aspect of ion beams is analyzed by treating the entire acceleration region as a black box, and determining the forces that must be applied to support the upgoing beams. This force could be provided by moderate energy (10s of eV) electrons which are heated near the lower border of the acceleration region. It is difficult to use standard particle detectors to measure the particles which carry electric current in much of the magnetosphere. Such measurements may be relatively easy within upgoing ion beams because there is some evidence that few of the hard-to-measure cold plasma particles are present. Therefore, ion beam regions may be good places to study fluid or MHD properties of magnetospheric plasmas, including the identification of current carriers, a study of current continuity, and some aspects of the substorm and particle energization processes. Finally, some of the experimental results which would be helpful in an analysis of several magnetospheric problems are summarized.

Force balance and substorm effects in the magnetotail

A model of the quiet time middle magnetotail is developed using a consistent orbit tracing technique. The momentum equation is used to calculate geocentric solar magnetospheric components of the particle and electromagnetic forces throughout the current sheet. Ions generate the dominant x and z force components. Electron and ion forces almost cancel in the y direction because the two species drift earthward at comparable speeds. The force viewpoint is applied to a study of some substorm processes. Generation of the rapid flows seen during substorm injection and bursty bulk flow events implies substantial force imbalances. The formation of a substorm diversion loop is one cause of changes in the magnetic field and therefore in the electromagnetic force. It is found that larger forces are produced when the cross-tail current is diverted to the ionosphere than would be produced if the entire tail current system simply decreased. Plasma is accelerated while the forces are unbalanced resulting in field lines within a diversion loop becoming more dipolar. Field lines become more stretched and the plasma sheet becomes thinner outside a diversion loop. Mechanisms that require thin current sheets to produce current disruption then can create additional diversion loops in the newly thinned regions. This process may be important during multiple expansion substorms and in differentiating pseudoexpansions from full substorms. It is found that the tail field model used here can be generated by a variety of particle distribution functions. However, for a given energy distribution the mixture of particle mirror or reflection points is constrained by the consistency requirement. The study of uniqueness also leads to the development of a technique to select guiding center electrons that will produce charge neutrality all along a flux tube containing nonguiding center ions without the imposition of a parallel electric field.

Birkeland currents in the plasma sheet

Received 30 August 2002; revised 1 April 2003; accepted 22 April 2003; published 23 July 2003. [1] Geotail particle and magnetic field measurements were combined to generate long-term-averaged 3-D models of the plasma sheet. Ampere’s law was used to calculate the Birkeland current jk in the � 30 1 RE region. Current diversion, or the growth of current in a unit flux tube jk/B, took place throughout the region studied. This suggests that electron scattering is broadly distributed. No substantial change in jk/B could be detected between the plasma sheet boundary layer and the ionosphere. Birkeland currents were strongest and exhibited a dawn-dusk asymmetry when the interplanetary magnetic field (IMF) was southward. This asymmetry may be associated with the formation of thin current sheets on the dusk side during disturbed periods. Symmetries were apparent above and below the neutral sheet when the IMF was northward or southward, but these symmetries were not present when the IMF pointed dawnward or duskward. For these latter cases, separate surfaces were found on which Bx =0 ,By = 0, and jk = 0. This apparently complex structure could be understood as a consequence of the tendency for By in the neutral sheet to have the same sign as the IMF By. The observed Birkeland currents were in the region 1 sense when leaving the plasma sheet for all IMF orientations. Current diversion was analyzed in an MHD framework. The analysis suggested that the reduction of gradient and curvature guiding center drifts, and the presence of polarization currents in the diversion region can provide sources of electrons to sustain a steady jk. It also was noted that the formation of an Ek region in the topside ionosphere can make it appear to the conducting ionosphere as if it is being driven by a current source rather than by the plasma sheet electric field. INDEX TERMS: 2764 Magnetospheric Physics: Plasma sheet; 2708 Magnetospheric Physics: Current systems (2409); 2744 Magnetospheric Physics: Magnetotail; 2736 Magnetospheric Physics: Magnetosphere/ionosphere interactions;