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 [1970] and Cowley and Ashour-Abdalla [1976], 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 [1974]) have been explained as a consequence of drift trajectory morphology. On the other hand DeForest and McIlwain [1971] 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 [1974] 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 [1979] 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. [1981] 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 [1983] 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 [1983], 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. [1981].
A very simple model for the drift path calculation has been
employed. The basic formulae used
have been given by Chen [1970]
and Cowley and Ashour-Abdalla
[1976]. 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 [1983]). 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 [1983] 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. [1982] 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
[1974] 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 [1983], 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
[1976]. 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 [1976] 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 [1983] 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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