ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus GmbHGöttingen, Germany10.5194/angeo-33-1485-2015Magnetospheric conditions near the equatorial footpoints of proton isotropy boundariesSergeevV. A.victor@geo.phys.spbu.ruhttps://orcid.org/0000-0002-4569-9631ChernyaevI. A.AngelopoulosVGanushkinaN. Y.St. Petersburg State University, Ulyanovskaya 1, 198504
St. Petersburg, RussiaDepartment of Earth, Planetary and Space Sciences and Institute of
Geophysics and Planetary Physics, University of California, Los
Angeles, USADepartment of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor MI,
USAFinnish Meteorological Institute, Helsinki, FinlandV. A. Sergeev (victor@geo.phys.spbu.ru)9December20153312148514931September201513November201526November2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/33/1485/2015/angeo-33-1485-2015.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/33/1485/2015/angeo-33-1485-2015.pdf
Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft during
February–March 2009 frequently provide an opportunity to
construct local data-adaptive magnetospheric models, which are
suitable for the accurate mapping along the magnetic field lines
at distances of 6–9 Re in the nightside magnetosphere. This
allows us to map the isotropy boundaries (IBs) of 30 and 80 keV
protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites) to the
equatorial magnetosphere (to find the projected isotropy boundary,
PIB) and study the magnetospheric conditions, particularly to
evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to
the particle gyroradius) in the neutral sheet at that point.
Special care is taken to control the factors which influence the
accuracy of the adaptive models and mapping. Data indicate that
better accuracy of an adaptive model is achieved when the PIB
distance from the closest spacecraft is as small as 1–2 Re. For
this group of most accurate predictions, the spread of KIB
values is still large (from 4 to 32), with the median value
KIB∼13 being larger than the critical value Kcr∼8
expected at the inner boundary of nonadiabatic angular scattering
in the current sheet. It appears that two different mechanisms
may contribute to form the isotropy boundary. The group with
K∼[4,12] is most likely formed by current sheet scattering,
whereas the group having KIB∼[12,32] could be formed by
the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC) waves.
The energy dependence of the upper K limit and close proximity of
the latter event to the plasmapause locations support this
conclusion. We also discuss other reasons why the K∼8
criterion for isotropization may fail to work, as well as a
possible relationship between the two scattering mechanisms.
Magnetospheric physics (energetic particlesprecipitating; magnetospheric configuration and dynamics)Introduction
Adiabatic motion of charged particles in the trap geometry of the
geomagnetic field conserves the empty atmospheric loss cone in the
particle distributions. However, in the regions where the particle
gyroradius ρ becomes comparable to the magnetic curvature
radius (Rc) and adiabatic approximation is violated, the
pitch-angle scattering fills the loss cone and leads to particle
precipitation into the ionosphere. For the protons with energies
ranging between a few tens and 100 keV, the boundary between
adiabatic and nonadiabatic particle motion occurs near the
center of the tail current sheet on the nightside at r∼6-9 Re (e.g., Sergeev and Tsyganenko, 1982; Shevchenko et al., 2010; Wang et al., 2012; Yue et al., 2014). Tailward of that
boundary a strong current sheet scattering (CSS) provides the
nearly isotropic proton angular distributions in the tail plasma
sheet (e.g., Ganushkina et al., 2005; Yue et al., 2014) whose
precipitation forms an extended isotropic proton precipitation
region, the proton auroral oval (Sergeev et al., 1983; Donovan et
al., 2003; Meurant et al., 2007). The equatorward boundary at
which the ratio of precipitated to trapped fluxes quickly drops
down below 1 (called the isotropy boundary, IB) is usually sharply
defined and well-observed at any particular energy. It provides an
important low-altitude marker of the boundary between adiabatic
and nonadiabatic motion in the equatorial current sheet for the particle population.
The normal (Bz) and radial (Br) magnetic field components
and their gradients usually control the angular scattering
amplitude in the tail current sheet. In the tail-like geometry the
rough criterion separating full loss cone coverage (strong
scattering) from partial (incomplete) cone filling conditions for
this mechanism is approximately
Kcr=Rc/ρ≈Bz2/(dBr/dz⋅G)≅8,
where G=mV/e is the particle rigidity. This value
Kcr=8 was previously obtained using particle tracing in the
simple 1-d current sheet models (e.g., Sergeev and Tsyganenko,
1982; Delcourt et al., 1996) or using a superposed 1-d current sheet
and dipole field (Sergeev and Malkov, 1988); up to now the
criterion (1) has been used in the majority of papers addressing the
CSS-based isotropy boundaries (e.g., Shevchenko et al., 2010; Yue
et al., 2014; Liang et al., 2014). The uncertainty regarding this numerical
criterion and its dependence on the B-field parameters (e.g., distance etc) have not been systematically investigated.
The observational test of this relationship is an important task, which
is difficult to perform because the isotropy boundary is formed
in the equatorial magnetotail where the filling of the loss cone
is hard to observe due to the small size of the loss cone (about 1∘). At the same time, the IB is robustly and easily observed
at low altitudes, far from its formation place. Therefore, to
test the conditions at the IB footpoints in the current sheet, we
need nearly conjugate observations in both regions, reliable
magnetic field line tracing between them as well as a way to control the
accuracy of this mapping. The two latter requirements are very
difficult to implement. Previous works comparing magnetospheric
and ionospheric observations were mostly based on statistical
empirical Tsyganenko models (Tsyganenko, 1995) or
average-pressure-based models (e.g., Yue et al., 2014) used to
find the isotropy boundary location in the neutral sheet according
to Eq. (1). Then this location was mapped to the ionosphere, to
compare predictions with the IB observations at low altitudes.
Such comparisons typically confirm similarities in their
local time, solar wind and activity dependencies, the predicted
and observed IB latitudes agreed on average to within
1–2∘ CGLat. The standard deviations were also comparable to
that value (see, e.g., Sergeev and Gvozdevsky, 1995; Shevchenko et al., 2010; Yue et al., 2014), which characterizes the typical
mapping uncertainty of statistical models (Nishimura et al., 2011). Therefore, observational confirmation of the CSS mechanism
and validation of its numerical criterion (of Eq. 1) still
awaits a better model and a better control of the
mapping uncertainty.
Recently some evidence has been published that another mechanism – pitch-angle scattering by the electromagnetic ion-cyclotron (EMIC) plasma waves – can act
in the flux tubes adjacent to the isotropy boundary. An association
between EMIC waves and proton precipitation (often isotropic) is
easier to establish for the detached precipitation structures
(Yahnin and Yahnina, 2007) than for the isotropy boundary case.
Liang et al. (2014) analyzed numerous cases of the inverse proton
energy dispersion of low-energy (1–20 keV) protons, provided their
theoretical explanation, and showed a couple of cases in which EMIC
waves were directly observed in the equatorial magnetosphere in
the sector where the inverse IB dispersion was identified. Sergeev
et al. (2015) presented a statistical survey of the IB morphology
on the nightside. They identified a few morphological features
(such as frequent occurrence of coincident IBs in 30 and 80 keV
proton energy channels, frequent multiple dropouts of
precipitated to trapped flux ratio near the IB location, and
observations of newly emerging isotropic precipitation equatorward
of the previous IB) which are inconsistent with a simple CSS-based
model but can be explained in terms of a wave–particle interaction
mechanism. These results put a question mark over the roles of
the CSS and wave mechanisms in forming the proton isotropy
boundary.
An obvious way to address these problems and to test the K value
in the magnetospheric projection of the isotropy boundary is to
use the data-adapted magnetospheric modeling in which several
free model parameters are tuned to achieve the best possible
agreement between the modeled magnetic field and the spacecraft
magnetic field observations (e.g., Kubyshkina et al., 2011). The
advantage of such models is that the model predictions are based
on real observations, and they also allow us to perform some model
quality estimates. Their difficulty is that the amount of data for
the modeling (the number of the spacecraft which measure the
magnetic field) is usually small and the results are very
sensitive to the spacecraft coverage. In this paper we test the
adaptive modeling approach by using the unique possibility of
THEMIS (Time History of Events and Macroscale Interactions during Substorms) orbits during the 2009 tail season, in which a cluster of
three spacecraft frequently occurred in the equatorial region in
the vicinity of the field line connected to the low-altitude
NOAA POES (Polar Orbiting Environmental Satellites), which at that time observed the isotropy
boundary. We construct adaptive models for these events, analyze
the K values in about 50 such conjunctions and discuss the
implications concerning the mechanism which is responsible for
the formation of the proton isotropy boundaries.
Count rates of trapped (J90, black dotted line) and
precipitating (J0, red line) energetic ion fluxes provided by
NOAA-19 in premidnight sector. Isotropy boundaries are marked by
vertical lines. Event (a) corresponds to the standard energy
dispersion and event (b) to the “no IB dispersion” case.
Observations
Observations of trapped (J90) and precipitating (J0)
energetic proton fluxes by the Space Environment Monitor-2 (SEM-2)
onboard the low-altitude (∼850 km) NOAA POES
were available from http://ngdc.noaa.gov/stp/satellite/poes/.
Here we use the low-energy Medium Energy Proton and Electron
Detector (MEPED) proton channels (nominally 30–80 keV (P1) and
80–240 keV (P2) at 2 s time resolution; Evans and Greer, 2004).
Figure 1 provides two examples of isotropic fluxes (J0∼J90) seen on the poleward (right) side of each panel but with a (grey shaded) highly anisotropic (J0≫J90) flux region on
the equatorial side (left side of each panel). The boundary
between these two regions, namely the last isotropic flux
measurement before the sharp drop of precipitated flux on the
low-latitude side of the isotropic zone, is usually well defined,
and it is the isotropy boundary (IB) which is the focus of our
study. The current sheet scattering (CSS) mechanism predicts that
higher-energy protons should have their adiabatic-to-nonadiabatic
scattering boundary closer to the Earth than lower-energy protons.
In other words, the 80 keV proton IB should be observed at a lower
latitude, compared to the 30 keV proton IB. Such energy-dependent
IB displacement is seen in event (a), but virtually no dispersion
is observed in event (b). According to a recent NOAA-POES-based
survey of the IB energy dispersion patterns presented by Sergeev
et al. (2015), these two categories are most frequently observed
in the nightside auroral oval. Due to the radiation-related
detector degradation with time, the lower energies of 30/80 keV
proton channels evolve with time; below we use their corrected values for March 2009 according to the Asikainen et
al. (2012) results. Specifically, for a different NOAA-type satellite
the corresponding corrected energies were taken to be 30/80 keV
(NOAA-19), 30/94 keV (NOAA-18), 36/92 keV (METOP-2) and 46/122 keV
(NOAA-17). (Here we note that the corrected energy thresholds
are slightly different for precipitated and trapped particles at
every spacecraft and that improved correction factors have been
recently published by Sadanger et al. (2015). However, these
differences do not seriously affect any of the results in our paper.)
Previous modeling studies by Lvova et al. (2005) and Shevchenko et al. (2010) identified that, for the wide range of
disturbed-to-quiet activity conditions, the proton IBs in the
equatorial nightside magnetosphere (due to the CSS mechanism)
should be located at geocentric distances of 5–9 Re. Ideally, to
ensure accurate mapping, magnetospheric observations should be
available at a few locations covering this distance range in the
conjugate equatorial magnetosphere. This requirement was
frequently satisfied for the group of three THEMIS spacecraft in
February–March 2009. During that time ThA, ThD and ThE moved
closely to each other along similar near-equatorial orbits, all
having a ∼24 h orbital period and the apogee of ∼12 Re. As
illustrated in Fig. 2, during one orbit three spacecraft crossed
this distance range of interest twice (on the outbound and inbound
portions of each orbit) at distances of 1 to 4 Re. The next step was
to identify those NOAA spacecraft auroral zone crossings which
are magnetically conjugate to THEMIS in the region of interest. If
the time difference between THEMIS and NOAA exceeded 3 h,
the crossing was removed from further analysis.
In the next step, adaptive modeling was performed (see below)
to refine the conjunction and to perform the accurate mapping of the observed isotropy boundary from the NOAA altitude (∼850 km)
to the neutral sheet region of the equatorial magnetosphere, namely to
the field line point where the radial magnetic field component
changes its sign. The location of this projected IB (PIB in Fig. 2)
was then compared to the location of the closest THEMIS spacecraft,
and the points whose distance exceeded 6 Re were discarded. After
this procedure the list of 50 conjunctions which occurred between
24 February and 27 March in the year 2009 was obtained for
detailed study; the conjunctions are shown in Fig. 2b. Selected crossings are
located in the nightside MLT sector clustering at 21–23 and
01–03 h MLT. A gap near midnight is due to the
combination of a low occurrence of NOAA crossings in that MLT sector
and the necessity to discard the conjunction when any of three
THEMIS spacecraft was in the Earth shadow.
Panel (a): XZ projections of the magnetic field line starting
from the observed isotropy boundary (red; labeled PIB) and of
the field line crossing the critical equatorial point (where K=8;
blue; labeled MIB), together with locations of three THEMIS
spacecraft. Panel (b): equatorial mapping of sample ThA trajectory on
4 March 2009 (dashed line) and the locations of projected
isotropy boundaries (PIBs) in the final selected conjunction
events.
A typical configuration of three THEMIS spacecraft on the outbound
portion of their orbit is illustrated in Fig. 2a. Here the ThD leads the group, being separated by 3–4 Re from the ThE–ThA
pair; this provides the information about the radial gradient of
the magnetic field. In the pair, the ThE spacecraft is ∼1 Re above ThA, providing information about the vertical
B gradients, that is about the current density in the equatorial
current sheet. This information is invaluable for the accurate
evaluation of the CSS-related isotropy boundary (see below). As
for the dawnside crossings, they follow in the same order, but ThD
is now at the smallest geocentric distance
in the group. A peculiarity of the
inbound orbits is that, besides the three near-Earth THEMIS
spacecraft, the other two THEMIS spacecraft (ThB and ThC, which have
the apogees in the middle tail) occasionally crossed the
inner magnetosphere inwards simultaneously with other spacecraft, so in
a few events the data of four to five spacecraft were also available for
the modeling.
The generation of the EMIC waves
and the wave scattering efficiency are known to be sensitive to
the cold plasma distribution, and the associated detached proton
precipitation regions are known to be observed near the plasmapause location (Yahnin and Yahnina, 2007). To characterize
the plasmapause position we looked through the variation in the
spacecraft potential along the THEMIS trajectories. Strong (and
often sharp) potential variation (roughly between 5 and 10 V,
characteristic of large plasma density changes) was regarded as
the plasmapause signature. The plasmapause observation closest in
time to (usually within 2 h of) the isotropy boundary
observations was taken as the plasmapause location in our data set.
Adaptive models and control of the model accuracy
The adaptive modeling approach uses the magnetospheric model, which
describes different current systems. In each particular event (at
any specific time during the event), several free model parameters
are varied to fit the magnetic fields, which are observed
simultaneously by a few (several) magnetospheric spacecraft. In
the case of good spacecraft coverage in a localized magnetospheric
region of interest (like in our case), this method provides the
model configuration for any specific time which is expected to
represent the real configuration in this localized domain as
closely as possible (in our case – in the near-equatorial region
in the vicinity of the mapped isotropy boundary). In our study we
use the AM03 version of the adaptive model previously described by
Kubyshkina et al. (2009, 2011). The formulation for the model
current systems is borrowed from the T96 model (Tsyganenko, 1995) with
a couple of additions. That is to say, the AM03 model includes the additional
embedded thin current sheet and a possibility to vary the current
sheet tilt in the tail. The initial fit is obtained by varying the
input model parameters (solar wind flow pressure, IMF Bz,
Dst, treated as free parameters) and intensities of all model
current systems. The following step is to include the additional
thin current sheet and vary its parameters (sheet thickness and
intensity) to improve the fit (see more details in Kubyshkina et
al., 2011). In the trial-and-search procedure, the least
square minimization solution is looked for for the fit function
δBAM03=(Σij(Bijmod-Bijobs)2/N)1/2,
where Bij is the jth B component at the ith (of
N) spacecraft. This parameter can also characterize the accuracy
of the fit solution.
After specifying the magnetic field model for the time of the IB
measurement and after performing the field line mapping of the IB
magnetic field line to the equatorial magnetosphere until its
crossing with the neutral sheet surface (point PIB in Fig. 2a), the
value of the K parameter was computed at this neutral sheet point as
K=eBRc/(2mpE)1/2,
where E is the proton energy and the curvature radius
Rc is numerically evaluated at this point using the coordinates
of the traced field line. We emphasize that in the simple model
with a central current sheet the Rc value is controlled by both
the Bz component value in the neutral sheet and the current sheet
density (Rc=Bz/(dBr/dz) in the case of zero dipole tilt),
so a control of the Z gradient using a pair of vertically separated
ThA and ThE spacecraft is a necessary condition for the accurate
evaluation of the K value. How closely the model represents this
gradient can be evaluated by computing the difference.
δBXCS=|(BX(ThE,obs)-BX(ThA,obs))-(BX(ThE,mod)-BX(ThA,mod))|,
where the indices obs (or mod) denote the Bx
component values observed (or modeled) at the corresponding
spacecraft locations.
For the equatorial current sheet the T96 and AM03 models exploit
the smooth functions which describe a simple equatorial
Harris-like current sheet with a peak current being in the current
sheet central plane. During the growth phase this picture should
be modified by the growth of the embedded thin current sheet (see, e.g., Petrukovich et al., 2011). This feature can be represented by
the AM03 model, which includes the possibility of an embedded
current sheet with variable thickness (e.g., Kubyshkina et
al., 2011). However, during the local dipolarizations and other
substorm-related (or flow-burst-related) perturbations which disturb a
smooth configuration, the quality of the adaptive model
degrades. To control these effects quantitatively, we computed the
detrended B-field standard deviation δBobs averaged over
the 10 min time interval centered on the time of the IB observation.
Furthermore, we visually examined the THEMIS B-field time series and
removed a few cases showing the dipolarization fronts and
injection features during this 10 min time interval. We also
removed a couple of events in which the AE (auroral electrojet)
index exceeded 250 nT and
demonstrated substorm signatures. Finally, based on the
B-field variability index, we excluded a few events in which
δBAM03 exceeded 10 nT.
Parameter distributions characterizing our data set. (a) corrected magnetic latitudes (absolute values) of isotropy boundaries
(30 and 80 keV IBs are plotted together); (b) radial distances of
projected IBs; (c) plasmapause positions (along THEMIS
trajectories); (d) AE index; (e–f) distances between PIB and THEMIS
spacecraft closest to this point; (g–i) parameters used to
characterize the model accuracy (see text for explanations). The
red vertical lines show the maximal parameter value allowed for
the subgroup of the most accurate models (D1).
For our purpose, a useful measure to characterize the coverage can
be the distance between the projected IB point and the THEMIS
spacecraft closest to it. We tried two such measures, one
characterizing the difference between the geocentric distances of
these two points (scalar difference ΔR1, which ignores
azimuthal separation between two points) and another one
characterizing the true distance between two points (ΔR2). The events with δR2 exceeding 6 Re were discarded
from the analysis.
Finally, after applying all the abovementioned selection procedures,
we selected a list of 50 conjugate isotropy boundary crossings,
each including two isotropy boundaries (at 30 and 80 keV
nominal energies; 100 data points available altogether). For these
IB conjunctions a system of diagnostic parameters (δBAM03, δBobs, δBxCS, ΔR1,
ΔR2) is available to characterize the quality of the
adaptive modeling. The distribution of parameters for this data
set is shown in Fig. 3. The data set is predominantly obtained
during very quiet conditions (AE<80 nT for 3/4 of data points,
Fig. 3d), with the bulk of the isotropy boundaries staying at
relatively high latitudes 65–68∘ CGLat (Fig. 3a). The
mapped IB distances nevertheless cover the expected range between
5 and 9 Re (Fig. 3b). In addition to their normal values of 5 to 7 Re, The concurrent plasmapause positions (Fig. 3c) show a group of 12 events with unusually distant (8–9 Re) plasmapause locations. This is a specific feature of very quiet year 2009. (The distant
plasmapause cases are real, as is confirmed by the observations
made by three THEMIS spacecraft which crossed this boundary at
different times.)
A vast majority of the data points have low variability (δBobs<0.8 nT, Fig. 3i), a reasonably good fit to the spacecraft
data (δBAM03<4 nT, Fig. 3h) and a reasonably good
approximation of the vertical Bx component gradients (δBxCS<3 nT, Fig. 3g). For the vast majority of selected
events the coverage indicators are very good: the distance between
isotropy boundary projection (PIB) and closest spacecraft is
within 3 Re, with a big group of the IB crossings having ΔR1<1 Re and ΔR2<2 Re.
Based on these quality indicators, after some investigation we
divided the data set into two groups, predominantly based on the
coverage indicators. In the most reliable mapping (group D1), we have
23 events, characterized by ΔR1<1.4 Re, ΔR2<3 Re, δBAM03<3.5 nT, δBobs<1.2 nT, and δBxCS<4 nT. In group D2 we have the remaining 27 events.
Evaluation of K parameters and local conditions in the
vicinity of the isotropy boundary projection
Using the relationship (3) the K parameter values were
evaluated in the intersection point of the neutral sheet and the
magnetic field line, passing through the observed isotropy
boundary (at the point PIB in Fig. 2a). A few important results
are evident from Fig. 4, which shows the K distribution.
The first is that K values show a large spread. In many cases the
K values are shifted considerably to high values compared to the
K=8 value, predicted by the current sheet scattering (CSS)
mechanism. Although the distribution has a peak at around K=8
(48 points within a factor of 2 from this value), the majority of
data (about two thirds) have values exceeding the CSS threshold
by a factor of 2 or more. This may have either physical
reasons or be due to errors in the magnetic field model and,
consequently, in the field line mapping. Another feature is that
high K values are more often seen in the lowest-energy channel P1 compared to P2.
Distribution of the K-parameter values in the
equatorial projection of the proton isotropy boundaries in the P1
(blue) and P2 (green) channels. The arrows show the median
K values in both channels as well as the K=8 critical
threshold previously defined for the current sheet scattering
mechanism.
To test how the quality of the models influences these results, we compare the K distributions for two groups of
events in Fig. 5. A more reliable group of models D1 (shown by red symbols)
displays a compact K distribution (ranging between 4 and 35),
whereas the K values between 35 and 67 are only observed in the
group of less reliable models (D2; shown by black symbols). In our
interpretation this means that the distance between modeled IB
field line and closest observation point should not exceed 1.5–2 Re to guarantee good accuracy of the mapping in the near
magnetosphere. The linear regression lines shown in Fig. 5a
confirm quantitatively that deviation from K=8 toward high K values increases for decreasing energy, being stronger than 17.1
and 12.7 for P1 and P2 channels, respectively (as indicated by
blue crosses).
K distribution depending on (a) degradation-corrected
lower energy of the proton channel and (b) latitudinal distance
between PIB and equatorial point MOB where K=8 (see Fig. 2a for
the
illustration).
In the group of the most accurate models the spread is still large
enough, and on average the K values still significantly
exceed the critical number 8. Suggesting that the K values
between 4 and 12 may be generated by the CSS mechanism, whereas
the remaining large K events can be due to some other reason, we
investigated the differences between these two data sets and found
one remarkable difference illustrated in Fig. 6. The more
distant location of the low K value boundaries is not
surprising. Remarkably, there seems to be a systematic
relationship between these points and plasmapause locations. The
blue points (small K values, possibly CSS mechanism) are
systematically observed outside of the plasmapause, whereas a
majority of the red triangles (large K values) are observed
within 1 Re from the plasmapause, and about one third of these
points are seated inside the plasmasphere. Some scatter is expected
because the IB and plasmapause observations are made at different
UT and MLT times. In addition, we found that a few cases showing anomalous energy dispersion (3 of 50 conjunctions, in which the
30 keV IB occurred at lower latitude compared to the 80 keV proton
IB) lie within the plasmasphere. Anomalous energy dispersion is
inconsistent with the CSS scenario and indicates that the IBs are
formed by another scattering mechanism. As discussed in the next
section, these observations may provide an indication of the
wave-related scattering mechanism.
Comparison of mapped IB radial distances (RPIB) with the
concurrent plasmapause distances (RPP) for the groups with small
K (blue) and large K (red) values. Only the group D1, with the most
accurate models, has been analyzed in this plot.
Discussion
Using excellent coverage provided by the cluster of three THEMIS
spacecraft, we investigated the values of the K parameter in the equatorial roots of the proton isotropy
boundaries statistically and compared them with the critical value Kcr=8
predicted by the current sheet scattering mechanism. Most events occurred during quiet conditions; special care was taken
to avoid the potential cases of inaccurate mapping. Nevertheless,
the KPIB values, obtained by the IB mapping onto the neutral
sheet along the model magnetic field line, show a wide spread
(Fig. 4). The KPIB values far exceed the critical value 8 in
the majority of events, implying that the PIB is located closer to
the Earth compared to predictions of the CSS mechanism. The
origin of this large spread and earthward PIB shift may have physical reasons and/or be partly due to errors in the
magnetic field model and, consequently, in the field line mapping.
Comparison of K distributions for the groups with more accurate
(or less accurate) adaptive models show significant differences
between them (Fig. 5), indicating that the accuracy of the
modeling and mapping is a strong factor affecting the K values. From
this, we got indications that the mapping accuracy mainly depends
on the coverage (closest distance of observing spacecraft to the
projected field line) and that it degrades notably if this
distance exceeds ∼2 Re in the inner magnetosphere modeling
study. This is a critical and very restrictive requirement for
this kind of studies. For the best accuracy group, the
KPIB values do not exceed 35; all these points stay within 2 Re distance from the K=8 boundary in the equatorial magnetosphere.
In this best-coverage group, a significant number of cases still
have KPIB values exceeding 2Kcr=16, suggesting that
other mechanisms (different from the current sheet scattering) may
be responsible for the strong pitch-angle diffusion in the flux
tube adjacent to the isotropy boundary. A plausible mechanism is
the resonant interaction with the EMIC waves. Recently, Liang et al. (2014) invoked this mechanism for the explanation of inverse
IB energy dispersion for low-energy proton components
(Ep<20 keV); they also directly observed EMIC waves and
demonstrated the consistency between the observations and the
theory predictions. In the statistical survey of proton IB
dispersion using NOAA observations, Sergeev et al. (2015) also
identified a few morphological features (such as frequent occurrence
of coincident IBs in P1 and P2 energy channels, frequent multiple
structure of the precipitated to trapped flux ratio near the IB
location, or observations of newly emerging isotropic
precipitation equatorward of the previous IB) which are
inconsistent with a simple CSS-based model but can be explained in
terms of a wave–particle interaction mechanism.
Three of our results are consistent with the wave mechanism. The first
is that large KPIB, far exceeding the Kcr=8 value, is observed in the majority of our events, pointing to some
wave-interaction-based, strong diffusion mechanism operating in the
inner magnetosphere, in the region being 1–2 Re closer to the
Earth compared to the CSS-scattering (Kcr=8) boundary.
Second, the EMIC wave generation is known to be sensitive to the
cold plasma density whose increase leads to the decrease in the
minimum resonant energy. The observed tendency of the projected
isotropy boundary to occur near the plasmapause or even inside the
plasmasphere for large K events (Fig. 6) is, therefore, quite
natural for the resonant wave mechanism of strong pitch-angle
diffusion. The third fact, that average K values are larger for
30 keV than for 80 keV protons is also consistent with theoretical
predictions; see, e.g., Fig. 3 and the discussion in Liang et al. (2014). Direct observations of the intense EMIC waves near the
foot of the large K isotropy boundary event are an important future
task for observational studies.
For the sake of completeness, one has to consider another possibility
of explaining large K values, which does not rule out the main
role of the current sheet scattering mechanism. In fact, the
Kcr≈8 criterion was obtained by the tracing of charged-particle trajectories in the simple model field, including the
parabolic 1-d current sheet (e.g., Sergeev and Tsyganenko, 1982;
Delcourt et al., 1996) or the superposition of this 1-d sheet on the
dipole field (Sergeev and Malkov, 1988). Changing the current
distribution in the model may alter the pitch-angle scattering
results and modify the critical K value (or make it entirely unusable). For example, the addition of a significant By component will make
the scattering amplitude different for particles moving toward the
Northern or Southern Hemisphere (Delcourt et al., 2000). Another
example is the bifurcated thin current sheet, in which the K value
estimated in the neutral sheet is actually meaningless (Delcourt
et al., 2004). One more possibility is a case of radially thin
current structures, in which the term dBz/dr may play the main
role (instead of dBx/dz) in determining the scattering
amplitude. Such localized current filaments and associated large
radial B gradients may be formed in the region of interest
(6–8 Re) by the enhanced convection during the substorm growth
phase or during the flow burst interaction with the plasma sheet
as has been shown numerically in self-consistent Rice Convection Model simulations
(Yang et al., 2013, 2014). Previously, thin plasma boundaries (of
30 keV proton gyroradius scale) have been inferred based on
Cluster observations and interpreted as a result of flow burst
interaction with the inner magnetosphere (Sergeev et al., 2003).
These questions provide an interesting topic for a future study.
Unfortunately, we have very few opportunities to diagnose such
unusual current distributions based on spacecraft observations.
Acknowledgements
This study was supported by the Russian Foundation of Basic
Research grant 13-05-00132. The NOAA-POES particle data were
provided from NOAA National Geophysical Data Center,
http://ngdc.noaa.gov. We thank K. H. Glassmeier, U. Auster and
W. Baumjohann for the use of FGM data provided under the lead of
the Technical University of Braunschweig and with financial
support through the German Ministry for Economy and Technology and
the German Center for Aviation and Space (DLR) under contract 50
OC 0302. The work by V. Angelopoulos was partly supported by THEMIS contract
NAS5-02099. The work by N. Y. Ganushkina was partly supported by the Academy of
Finland and by NASA Award NNX14AF34G. We thank M. Holeva for help in manuscript preparation. The topical editor C. Owen thanks F. Soraas and one anonymous referee for help in evaluating this paper.
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