Geophysical Research Letters, 10, 549-552, 1983
(Received February 9, 1983; accepted March 3, 1983.)
Copyright 1983 by the American Geophysical Union.
Paper number 3L0706.
A simple particle drift model is used to investigate the applicability of the injection boundary concept to the ion dispersion event observed on March 22 (day 81), 1979. The model consists of a dipole magnetic field with a uniform cross-tail electric field plus a corotation field. A full spectrum of particles from 100 eV to 32 keV is injected at the K = 6- Mauk and McIlwain injection boundary at the time of substorm onset on this day (1100 UT). A new approach is presented for displaying the model-produced ion drift trajectories to make the large scale spatial characteristics of the evolving energy distributions easier to envision and to facilitate the comparison of the model results with experimental observations. The resultant prediction for the dispersion signature is compared with Scatha mass spectrometer measurements, and a 2.0 kV/R cross-tail convection electric field is found to give a good fit to the observed dispersion signature. It is determined that for this particular event, injection only at that portion of the injection boundary close to 1800 local time is required to produce the dispersion curve.
Much work has been carried out on magnetospheric plasma convection and the associated particle signatures. Chen  and Cowley and Ashour-Abdalla , amongst others, have calculated drift trajectories for ions in the earth's magnetosphere. From steady-state drift analyses such as these, proton nose events (Smith and Hoffman ) have been explained as a consequence of drift trajectory morphology. On the other hand DeForest and McIlwain  have reported observations of dispersing particle signatures at geosynchronous altitude associated with substorms. These signatures are usually considered to be associated with impulsive changes in the magnetosphere. As a consequence the substorm-related injection boundary model as first formulated by Mauk and McIlwain  has frequently been used as a starting point when discussing dispersion signatures.
There is still some controversy concerning the nature and possible existence of the injection boundary. For example, Kaye and Kivelson  have modeled substorm-related particle signatures using steady state convection boundaries in their initial conditions. These boundaries have a radial dependence as a function of energy, whereas the injection boundary implies a co-located source for all energies. Taking elements from both these models, Moore et al.  argued that the injection boundary marks the innermost excursion of a substorm related shock front which is propagating from the plasma sheet to lower L-shells. Strangeway and Johnson  have suggested, from mass composition data, that there may be enhanced ionospheric plasma injected into the magnetosphere near the injection boundary. Their conclusion is not definitive, in that mass dependent radial gradients in the plasma sheet may alone be responsible for the composition differences observed in the dispersing ion signatures. Nevertheless one may speculate that an inward propagating shock front will perturb the ionosphere, possibly through field-aligned currents, and so result in enhanced deposition of ionospheric plasma into the magnetosphere.
In this letter we present some initial results of an investigation into the usefulness of an injection boundary model for producing the ion energy-time dispersion signatures observed near geosynchronous altitudes. In addition, we present a new approach for displaying the model-produced ion drift trajectories which makes the large scale spatial characteristics of the evolving ion energy distributions easier to envision and facilitates the comparison of the model results with energy-time spectrograms of the experimental data. The results from a simplified injection boundary model are compared with the ion dispersion event observed on 22 March (day 81) 1979. This event has been analyzed and discussed by Strangeway and Johnson , but no detailed model comparisons were made. We have chosen to further analyze this event since 22 March 1979 is a day which has been the subject of a major research effort arising from the Sixth Coordinated Data Analysis Workshop (CDAW-6). The data presented in this letter were acquired from the Lockheed mass spectrometer flown on board the near geosynchronous Scatha spacecraft. The ion measurements cover the energy range from 0.1 to 32 keV in 24 energy steps, and only proton and oxygen data are discussed here. For a more detailed description of the mass spectrometer characteristics and of the Scatha spacecraft orbit (L, 5-8), see Kaye et al. .
A very simple model for the drift path calculation has been employed. The basic formulae used have been given by Chen  and Cowley and Ashour-Abdalla . To summarize, we use a dipole magnetic field model, with a uniform cross-tail electric field plus a corotation electric field. No corrections due to shielding or magnetic field distortion have been included. In the model calculations we trace drift paths forward in time for an ensemble of ions starting at 128 locations on the Mauk and McIlwain injection boundary for K = 6-. The boundary was truncated at 1800 and 2400 LT. This boundary was chosen since K was equal to 6- at 1055 UT on March 22, 1979 when a substorm occurred (Strangeway and Johnson ). At each particular location the drift paths for 96 different energy particles are traced. The energies are equally spaced on a logarithmic scale from 100 eV to 32 keV, which is the energy range of the Scatha mass spectrometer. For the particular event under consideration we have calculated drift paths for 90° equatorial pitch angle particles. It should be noted that we have assumed an impulsive injection of particles at the boundary coincident with the substorm onset, and no additional particles are included in the model subsequent to this time.
Figure 1 shows the results of the drift path calculation with 2.0 kV/R cross-tail convection field. There is a large amount of information shown in this figure. Firstly the figure consists of 16 panels, each of which contains a snap-shot of the particle positions at a particular time, the times are given in the upper right hand corner of each panel, starting at 1100 UT (near the time of substorm onset on March 22, 1979), until 1445 UT at 15 minute intervals. The convection field strength is given in the upper left hand corner of each panel. A nominal magnetopause location is given by the yellow curve to the left of each panel, with the half illuminated circle giving the location of the earth. The small cross-hair indicates the Scatha spacecraft location as determined from the ephemeris information for March 22 (day 81), 1979, projected into L and local time (LT). As the cross-hair encounters the drifting ions, the color changes, so that the spacecraft location is always given in complementary color as shown, for example, in the first panel, second row. In the same panel some small white dots are present on the lower energy edge (blue) of the drifting plasma cloud. These dots mark the location on the original injection boundary of the ions which are at the Scatha spacecraft location at this time. In addition, we also build up a pseudo-spectrogram in the box in the lower right-hand side of each panel. The color coding of the dispersion signature thus produced is not a flux level, but is only given for reference to the color table given at the right of each panel. Notice that the energy is plotted downwards in this pseudo-spectrogram.
Fig. 1. Summary plot of ion drift paths from the injection boundary. Drift paths are color-coded as a function of particle energy. the format of the figure is discussed in more detail in the text.
As mentioned above, the color coding employed in the diagram corresponds to energy, not flux as is usually the case. The scale to the right of the panel gives the energies corresponding to each color, starting at 100 eV (blue) to 32 keV (red), spaced logarithmically in energy. In the first panel the injection boundary is green, since this is the middle color in the color table and we have added up the contribution at each location due to all the particles present in a particular pixel. As time progresses, the ions disperse, with the higher energy ions gradient drifting through dusk. The lower energy ions (~ 100 eV) do not drift very far for the particular choice of convection field. Most of the middle energy ions eventually drift to the dayside magnetopause, where their drift paths are truncated.
At first sight the striations apparent in the display might be thought to be individual particle drift paths, especially since this is the usual manner in which drift paths are shown (see Chen [19701, for example). In fact each striation corresponds to a mapping due to the drift motion of the injection boundary for a single initial ion energy. The change in energy resulting from conservation of magnetic moment produces a change in color along each line. The actual energy of a particle at any particular location is used to color code that point, not the initial particle energy. It should be noted that if two or more particles are coincident, within the spatial resolution of the display, the energy used to compute the color is the geometric mean energy of all particles at that location with no weighting as a function of energy (i.e. a flat source spectrum).
We have carried out similar calculations for a lower convection field (1.0 kV/R) and a higher convection field (4.0 kV/R). As might be expected, most of the lower energy ions tend to drift through midnight when the convection field is lower. For the higher convection field, most of the ions convect sunwards, and even some of the 100 eV ions convect as far as the dayside magnetopause during the 3.75 hour time period.
Figure 2 shows energy-time spectrograms of Scatha mass composition data for March 22 (day 81), 1979. Differential energy flux in keV/(cm-sec-ster-keV) is plotted as a function of energy from 0.1 to 32 keV, and time from 0700 to 1900 UT, for protons in the upper panel and oxygen in the lower panel. For consistency with other synchronous altitude particle data presentations, the energy scale is plotted vertically downwards. The flux values for each species are given by the color table to the right of each spectrogram. It should be noted that the flux scale is a factor of five smaller for the oxygen than for the protons. The bottom two traces give ephemeris information, the yellow curve giving magnetic local time (MLT) minus universal time (UT) and the light blue curve giving L-shell. For ease of reference, the symbols on the yellow curve mark from left to right 1200, 1800 and 2400 MLT respectively. In addition to the data points, some white traces have been plotted on the spectrograms. We shall explain these below.
Fig. 2. Energy-time spectrograms of mass composition data acquired with the Scatha mass spectrometer. Differential energy is plotted as a function of energy and time for protons and oxygen ions. Model dispersion curves are plotted on the spectrograms. The figure is described more fully in the text.
The dispersing ion signature which we wish to model can be seen beginning near 1145 UT for the protons and near 1200 UT for the oxygen ions. The high flux values then move to lower energy for both species, until the lower energy (~ 100 eV) part of the dispersion signature is observed near 1445 UT. Strangeway and Johnson  have pointed out that the ridge-like structure apparent in the oxygen dispersion signature is indicative of a restricted source in both space and time. This supports the model assumption of an impulsive injection at the Mauk and McIlwain injection boundary.
The white points plotted on the spectrograms give the energies of the particles observed at the Scatha spacecraft location assuming that these particles have been injected at the Mauk and McIlwain injection boundary for K = 6- at 1100 UT. Three traces have been included, all for 90° equatorial pitch angle particles drifting in a dipole field with a uniform cross-tail electric field plus corotation. From left to right, the traces are for 4.0, 2.0, and 1.0 kV/R cross-tail electric field strengths respectively.
It is apparent that the 1.0 kV/R convection field model does not reproduce the dispersion signature well. In fact the lower energy part of the dispersion signature is not modeled at all. This is because the lower energy particles in the injection boundary drift inwards and towards midnight, and so are never encountered by the spacecraft. Obviously then, a 1.0 kV/R convection field requires additional sources of low energy plasma tailwards of the injection boundary to produce the dispersion signature all the way down to 100 eV. Even then, the lower energy part of the dispersion signature as measured by the mass spectrometer is observed too soon to be consistent with this particular choice of convection field strength.
The 4.0 kV/R convection field model does produce a dispersion signature throughout the whole energy range of the mass spectrometer. As noted in the previous section, however, this large convection field value results in sunward convection of even the low energy part of the plasma injected at the injection boundary. Consequently the model predicts that the dispersing ion signature should occur much earlier than observed.
On the other hand, the 2.0 kV/R convection field produces a dispersion signature which follows the observed signature remarkably well. There are some differences in the dispersing ion signature and the model dispersion curve shape, and also some differences in mass species. Nevertheless, the qualitative agreement is very good. Obviously the model can be tuned so as to give much better agreement for this particular event. However, unless additional independent data are used as a guide for the field model, such as has been done by Harel et al.  this is probably not worthwhile with the present simplified model.
One last point to be made concerning the predicted dispersion signature is that the arrival time of the high energy ( ~ 32 keV) ions is nearly independent of the convection electric field strength. This is to be expected since the drifts for these particles are gradient drift dominated. Also the differences in the measured dispersion signatures for the protons and oxygen ions at the higher energies indicates a different spatial/temporal history for the more energetic particles.
The Mauk and McIlwain injection boundary model provides a qualitatively good source location for ions observed in the substorm related dispersion event as observed at the Scatha orbit on March 22, 1979. The best prediction for the dispersion signature is found for a 2.0 kV/R uniform cross-tail convection field assuming a dipole magnetic field plus a corotation electric field. Other magnetic and electric field models may produce an even better fit, and clearly more generally applicable time dependent models are required. However, some general conclusions can be drawn from the present analysis with the simplified model.
Firstly, as to be expected, the high energy part of the dispersion signature is largely independent of the electric field model. In fact once these particles have been injected near geosynchronous altitudes by whatever mechanism is responsible for the injection, they tend to drift on constant L-shells, and so the source location of these particles can be tailored to any magnetic field model used. For the event under consideration, the 32 keV ions are first observed about one hour after substorm onset. From Figure 1, it can be seen that K = 6 - injection boundary is near geosynchronous altitude around dusk, and the drift times for high energy particles is of the right order to give a reasonable estimate for the arrival time at the Scatha spacecraft location.
Secondly, the low energy part of the predicted dispersion signature is closest to the observed signature when a 2.0 kV/R convection field is used. Refering to Figure 1, we note that the lower energy particles do not drift very much with respect to the original injection boundary as evidenced by the white dots marking the source location of the particles which are predicted to be at the Scatha spacecraft location. A good low energy fit may be expected as a consequence of this. Specifically, the injection boundary location as deduced by Mauk and McIlwain  was found using the spacecraft location when the low (< 100 eV) energy part of the dispersing ion signature was observed. It was assumed that these energy particles had not drifted very far from the original site of the injection boundary. For the drift model employed in this letter, a 2.0 kV/R convection field results in nearly stagnant How for the low energy ions, and so a good prediction is to be expected.
Having fixed the end points of the dispersion curve, a fairly close fit to the observed signature is not unreasonable. However as can be seen from Figure 2, the mismatch between prediction and observation shows some species dependence. As noted by Strangeway and Johnson , there is also some pitch angle dependence to the dispersion signature. Obviously, the analysis should be extended to investigate these differences and hence to investigate the source locations for the different species. We note that for the particular event under consideration, the difference in location for a plasma sheet source and a direct ionospheric source may be quite small. Specifically, the zero energy Alfven layer for a 2.0 kV/R uniform convection electric field is within one earth radius of the K = 6 - Mauk and McIlwain injection boundary in the dusk to midnight local time sector. The two boundaries cross, with the Alfven layer showing the greater decrease in radial distance as a function of increasing local time. Such effects as shielding could be invoked to bring these boundaries into closer alignment.
To further confirm the close correspondence of the two boundaries, we consider the work of Kivelson . Kivelson used empirical relationships such as the Mauk and McIlwain injection boundary together with the theoretical formula for the zero energy Alfven layer to produce scaling laws for the convection electric field as a function of K. Using the scaling law for the Mauk and McIlwain injection boundary (equation (11) in Kivelson  with K = 6 -), we find the convection field strength to be 2.16 kV/R. This is remarkable close to the value for which the best prediction for the dispersion curve was found.
One last remark concerning the use of the Mauk and McIlwain injection boundary is that it should be noted that the dispersing ions which produce the model dispersion curve do not come from all locations on the injection boundary. Only that part of the injection boundary near dusk, which for the particular Kp value is also near geosynchronous altitudes, appears to be necessary to produce the observed dispersion signature. Additional comparisons of model results with experimental data are required to determine if the lower L-shell part of the injection boundary is necessary for the production of a dispersing ion signature near geosynchronous altitudes. Mauk and Meng  have discussed some of the signatures one might expect if there is a low altitude 'nose' in the injection boundary near midnight.
Acknowledgements. One of us (R. J. S.) would like to thank Stan Cowley of Imperial College for supplying the drift trajectory programs which formed the basis of the software developed for this study. This work was funded by the Office of Naval Research under contract N00014-76-C-0444, The National Science Foundation under grant ATM 8119340 and NASA under contract NASW-3395.
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