D. J. Larson

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.

Testing electric and magnetic field models of the storm‐time inner magnetosphere

We calculate the equipotential contours, drift trajectories, and predicted proton energy spectra in the inner magnetosphere using combinations of dipole or Tsyganenko magnetic field models and Volland-Stern or Weimer electric fields models. We compare the results with observations of proton energy spectra at L=4–5 over a range of local times from the Active Magnetospheric Particle Tracer Explorers/charge-energy-mass instrument. We find that the trajectories, and in particular the source location in the tail and the exit location on the dayside, depend significantly on both the electric and magnetic field models. However, the predicted energy spectra in the inner magnetosphere depended almost entirely on the choice of electric field. Using the Weimer electric field gives less loss along the trajectories, which is usually in better agreement with the observed energy spectra.

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.

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.

Mapping and energization in the magnetotail: 2. Particle acceleration

The selection of magnetic and electric field models specifies the rate at which charged particles must be accelerated throughout the magnetosphere during steady state conditions. This rate is estimated in the mid-tail region (−60 RE < xsm < −10 RE) using the Tsyganenko (1989) magnetic field model and the assumption that E is approximately uniform in the plasma sheet. The uniform E assumption is found to be consistent with a projection of the Heppner and Maynard (1987) electric field model, and with observations in the magnetotail. The resulting energization rate decreases from 4 and 50 GW/RE at xsm = −10 RE to 0.8 and 5 GW/RE at xsm = −60 RE during quiet and disturbed times, respectively. The total energization rate throughout this entire tail region varies from 100 GW when Kp = 0 to 700 GW when Kp = 5. Ions carry most of the cross-tail current, and therefore gain most of the kinetic energy within the plasma sheet. Electrons, which are responsible for most auroral phenomena, are primarily accelerated at lower altitudes. For quasi-static conditions, the electromagnetic energy flow to low altitudes is controlled by the magnitude and location of Birkeland currents, even when the current-carrying particles have negligible kinetic energy. The typical power deposited in the entire nightside auroral zone during steady conditions is approximately 15% to 20% of the Poynting flux entering the plasma sheet. Induced electric fields are known to produce most of the energetic ring current and radiation belt particles during substorm injection events. The energization rate goes well above 1000 GW during brief intervals. A simple injection model is used to compare the structure of induced and potential fields. This model shows plasma drifting earthward, equatorward, and toward midnight during a localized injection event.

The decay of suprathermal ion fluxes during the substorm recovery phase

During a magnetospheric substorm, the energetic particle flux in the plasma sheet increases by as much as 2 orders of magnitude. During the recovery phase the ion flux decreases. The decay rate is energy dependent, with the decay time constant decreasing for increasing energies. By comparing the decay rates of different species, we are able to test whether the decay rate is organized by total energy, energy per charge, velocity, or rigidity. Using the suprathermal energetic ion charge analyzer (SULEICA) instrument on Active Magnetospheric Particle Tracer Explorers Ion Release Module (AMPTE IRM), we have determined the decay rates for the species H+, He+, O+, and He++ for individual cases and by using a superposed epoch analysis. We find that the decay rate is organized by energy per charge. We have calculated the decay rates predicted by two different models: adiabatic cooling in a radially expanding plasma sheet, and particle drift loss, or “leakage,” from the plasma sheet. Both models predict that the decay rates will be organized by energy per charge, and in both cases the predicted decay rate is faster than that actually observed. This indicates that the production of energetic particles continues at a reduced rate in the the tail during the recovery phase, as the neutral line retreats down the tail.