**Electron density distribution over the northern polar region deduced
from IMAGE/RPI sounding**

P. A. Nsumei1, X. Huang1, B. W. Reinisch1, P. Song1, V. M.
Vasyliunas^2^, J. L. Green^3^, S. F. Fung^3^, R. F. Benson^3^, and D. L.
Gallagher^4^

^1^Environmental, Earth and Atmospheric Sciences Department,

Center for Atmospheric Research

University of Massachusetts Lowell, USA

^2^Max-Planck-Institut für Aeronomie, Katlenburg-Lindau, Germany

^3^NASA Goddard Space Flight Center, Greenbelt, Maryland, USA

^4^NASA Marshell Space Flight Center, Huntsville, Alabama, USA

**Abstract.** Electron density *N~e~* distributions in the northern
polar region are determined from 1.4 to 5.0 R~E~ at invariant latitudes
greater than 70 using the radio plasma imager (RPI) on the IMAGE
satellite over the period from June 2000 to November 2001. An empirical
*N~e~* model in this region is derived as a function of radial distance
and geomagnetic activity. A power law with a power index of --5.09 0.03
describes the variation of *N~e~* with radial distance. The *N~e~*
appears to increase exponentially with the *Kp* index. The altitude
dependence of the empirical model at low geomagnetic activity is
qualitatively consistent with previous models derived from the ISIS 1
and the Dynamic Explorer 1 spacecraft.

**1. Introduction**

The region above the high-latitude ionosphere is crucial to the study of
solar wind-magnetosphere-ionosphere coupling. The ionosphere is the main
plasma source in this region. Photo-ionization and recombination are the
primary processes that control the plasma population. Geomagnetic
activities, such as auroral precipitation, and large-scale motion of the
high-latitude ionosphere induced by magnetospheric convection electric
fields created by coupling processes, however, modify the ionospheric
source \[see Schunk and Nagy, 2000\]. The solar wind interaction can
also change the topological characteristics of this region from closed
to open configuration with respect to the interplanetary magnetic field
(IMF). In this brief report, we focus on the electron density N~e~
distribution in the northern polar region at invariant latitudes greater
than 70.

The electron density in this region has been measured previously using
several *in-situ* and remote techniques. The *N~e~* profiles for
altitudes below 1000 km have been measured by ground-based remote
sensing methods such as incoherent scatter radar and ionosondes
\[Knight, 1972; Reinisch et al., 1996\]. At slightly higher altitudes,
*N~e~* has been measured by *in-situ* methods such as probes carried by
satellites \[Brace et al., 1967; Brace et al., 1970\], and by remote
methods using the topside sounder satellites \[Florida, 1969; Jackson
and Warren, 1969\]. These observations have been limited to below 0.5
R~E~ in altitude.

Most measurements at higher altitudes were made using *in-situ*
techniques. The S3-3 satellite, with an apogee of 2.25 R~E~, determined
*N~e~* from the upper hybrid frequency \[Mozer et al., 1979\]. The
plasma wave instrument (PWI) and the retarding ion mass spectrometer
(RIMS) on Dynamic Explorer (DE) 1, which had an apogee of 4.66 R~E~,
measured the density in the region of interest in this study. The PWI
*N~e~* \[Persoon et al., 1983\] was measured from the whistler mode
upper-frequency cutoff. This cutoff occurs at the lower of the plasma
frequency or the electron gyrofrequency. The dependence of the polar
region *N~e~* on radial distance was found to follow a power law with an
exponent of --3.85. Persoon et al. \[1983\] also noted that the large
density fluctuations in time periods of less than 8 hours seen in the
data were suggestive of a possible dependence of *N~e~* on geomagnetic
activity, but no quantitative relation between *N~e~* and geomagnetic
activity has been reported. Chandler et al. \[1991\] presented the ion
density, *N~i~*, at low altitudes (from 1000 to 4000 km) measured with
RIMS on DE 1. Their density profile cannot be readily extrapolated from
Persoon et al.'s *N~e~* power law. More recently, an empirical model of
the near earth plasma density distribution, referred to as the Global
Core Plasma Model (GCPM) was derived \[Gallagher et al., 2000\]. The
polar region *N~e~* model of the GCPM was obtained by combining several
databases, including *N~e~* data of Persoon et al. \[1983\] and the
*N~i~* data of Chandler et al. \[1991\].

The radio plasma imager (RPI) \[Reinisch et al., 2000\] on IMAGE \[Burch
et al., 2001\] uses a radio sounding technique, similar to that of
ground-based ionosondes \[Reinisch, 1996\] and ionospheric topside
sounders \[Jackson et al., 1980\], to remotely sense *N~e~* in the
magnetosphere. The IMAGE spacecraft is in an elliptical polar orbit with
perigee and apogee altitudes of 0.2 and 7.2 R~E~, respectively. The RPI
transmits coded electromagnetic signals from 3 kHz to 3 MHz in all
directions and measures the echo delay time as a function of frequency.
Passive measurements, similar to those of conventional plasma wave
instruments, alternate with active soundings \[Green et al., 2002\].
Combining both remote and in-situ techniques, RPI measures *N~e~* from
near the satellite to remote magnetospheric regions within a few
seconds. In this report, an empirical model is developed based on the
RPI measurements showing the variation of the high-latitude *N~e~* with
geocentric distance and geomagnetic activity.

**2. Method of analysis**

Electromagnetic waves (launched from RPI) propagating in the direction
of increasing *N~e~* are reflected at places where the wave frequency
equals the cutoff frequency of the wave mode. The cutoff frequency of a
given mode is a function of *N~e~*, the magnetic field strength *B*, and
propagation angle (angle between ***B*** and the wave normal) \[Budden,
1985\]. The RPI measures the echo delay time as a function of frequency.
The echoes, reflected signals returning back to the satellite, that are
of the same wave mode and propagation direction form a distinct trace on
the "plasmagram", a display of echo amplitude as a function of frequency
and virtual range (the distance calculated from the measured echo time
delay assuming the pulse travels at the free space speed of light). A
density inversion algorithm, based on cold plasma theory \[Huang and
Reinisch, 1982\] is used to invert the frequency-virtual range trace
into a *N~e~*-true distance profile along the wave path. Discrete echo
traces in plasmagrams are often formed from field-aligned propagation
signals as demonstrated by the reproduction of observed traces of
different modes \[Reinisch et al., 2001a\]. The electron density
distributions along the magnetic field lines are derived from such
discrete field-aligned echo traces.

Figure 1 shows an example of a plasmagram measured on September 02,
2001, at 0508 UT (2.72 MLT, 77.82 ILAT and geocentric distance of 4.51
R~E~). There are two types of signals on this plasmagram: multiple
vertical lines and a curved trace. The vertical lines are formed by
local plasma resonances stimulated by the transmitted waves \[Benson et
al., 2001\] and the curved trace is formed by field-aligned propagating
X-mode echoes as shown by Reinisch et al. \[2001a\]. On the plasmagram,
the local electron cyclotron frequency, *f~ce~* (where *f~ce~*=*eB/2m;
B*, *e,* and *m* are the strength of the magnetic field, the absolute
electron charge, and the electron mass, respectively), and its second
harmonics 2*f~ce~*, and the upper hybrid frequency, *f~uh~*, can be
identified. The cutoff frequency of the X-mode wave, *f~X~*, can also be
identified. It is then easy to calculate the local plasma resonance,
*f~pe~*, from the observed values of *f~ce~*, *f~uh~* and *f~X~*. The
calculated *f~pe~* must agree with an appropriate resonance line
observed on the plasmagram. The time samples of 3.2 ms spacing (matching
the 3.2 ms pulse width) in Figure 1 correspond to a virtual range
resolution of 480 km 0.075 R~E~. The thin solid line along the echo
trace indicates the manually selected ranges used for the profile
analysis. The frequency sweep rate was linear with 0.3 kHz steps in this
operation program. RPI scanned the frequency interval containing the
trace in Figure 1 within 18 s. Usually many plasmagrams are obtained
when IMAGE flies across the polar cap providing a 2-dimensional snapshot
of the *N~e~* distribution along these field lines. Not every plasmagram
shows a clear trace, however, and there are gaps in the sequence of
*N~e~* profiles during a satellite pass. We have selected only passes
with at least two plasmagrams with clear traces every 10 minutes.

In this study, 108 plasmagrams from 20 IMAGE orbits with invariant
latitudes greater than 70 are used. Figure 2 shows the magnetic
invariant latitude and local magnetic time for each plasmagram used in
this study. Each marker indicates a complete measurement, and the
different symbols denote the prevailing geomagnetic activity (*Kp*
range) during the time of the measurement.

Each trace on a plasmagram generally makes more than 30 *N~e~*
measurements depending on the sounding program. Each RPI program has a
specific range and resolution of sounding frequency and echo delay. Some
sounding frequency ranges are linear, while others logarithmic. The
density profile, *N~e~(R),* is deduced from the echo trace using a new
numerical inversion algorithm \[Reinisch et al., 2001b\] adapted from
Huang and Reinisch's \[1982\] topside ionogram inversion algorithm.

The virtual range at frequency *f~j~*, *R(f~i~)*, can be expressed as an
integral over the group index of refraction *n* along the propagation
path ~j~ from the spacecraft to the reflection point. The true range *R*
to the reflection point is obtained by inverting the following integral
equation:

![](media/image1.wmf) (1)

The group refractive index *n* is a function of the probing frequency
*f~j~*, the density *N~e~*, the electron cyclotron frequency *f~ce~*,
and the propagation angle between the wave vector and the magnetic field
direction. To solve equation (1), a cold collisionless plasma and
geometric optics (wavelength is much shorter than the scales of spatial
variations) approximation is used. The propagation is assumed to be
field-aligned ( = 0) as demonstrated by Reinisch et al. \[2001b\]. The
magnetic field is obtained by scaling an empirical global magnetic field
model \[Tsyganenko and Stern, 1996\] using the observed local
gyrofrequency, *f~ce~*. The derived *N~e~*(*R*) profile is then used to
calculate the trace expected with such profile. Overlaying the
calculated trace on the plasmagram shows how well the measured echo
trace is reproduced with the calculated profile (see Figure 2 in
Reinisch et al. \[2001a\]). The sequence of *N~e~*(*R*) profiles
obtained during one satellite pass allows the construction of the
2-dimensional *N~e~* distribution in the plane containing the field
lines and the orbit. Figure 3 shows two examples of such 2-D
distributions projected onto the X~SM~ -- Z~SM~ plane. The distribution
shown in Figure 3a is derived from 5 plasmagrams on September 18, 2000
at 1548, 1558, 1608, 1618, and 1628 UT during a geomagnetically active
period (Kp = 6). Figure 3(b) is derived from 5 plasmagrams at 1102,
1108, 1114, 1120 and 1126 UT on October 6, 2000, during an extremely
quiet period (Kp = 0+).

Two features are obvious from Figure 3. First, *N~e~* decreases rapidly
with altitude, as expected. Second, *N~e~* is clearly much higher during
high geomagnetic activity.

**3. Empirical model**

As seen in Figure 3, *N~e~* depends on altitude and geomagnetic
activity. We have checked other possible dependences, such as on
latitude and local time. They are not as clear as the first two effects
although one may argue from the two cases shown in Figure 3 that there
is a weak dependence on the latitude. The density minimum near 80
latitude, is most likely a temporary variation although it could be
physical. We first study the altitude and geomagnetic activity
dependences separately and then combine the statistics. We also include
the invariant latitude in our analysis but the dependence in our
database is weak. In order to determine the relationship between *N~e~*
and geocentric distance, the data were divided into 0.20 R~E~ bins and
the *N~e~* average value was computed for each bin. Figure 4 presents
*N~e~* versus geocentric distance *R*, including all data without regard
to magnetic activity. The error bars correspond to the *N~e~* standard
deviation ( 0.5) from each corresponding bin average. A linear
relationship is readily seen in this log-log presentation, suggesting a
power law relationship between *N~e~* and *R*. The power law exponent
obtained from the slope of the best fit is = --5.02.

In order to study other dependences, we first remove the effect of the
*R* dependence by normalizing *N~e~* by *R*, i.e. using (*N~e~/ R*).
Figure 5 shows the bin-averaged (*N~e~/R*) versus *Kp*. The correlation
is weaker with a significant variability but the trend is still
meaningful. A linear fit yields an exponential relationship between
*N~e~* and *Kp* with an exponent = 0.24. The error bars correspond to
the *N~e~/ R* standard deviation from each corresponding bin average.
Although in principle the power law fit, , on the radial distance can
also be a function of *Kp*, we consider it as secondary and can be
verified when our database is bigger.

The lower (higher) end of the error bars (standard deviation) shown in
Figure 4 can be considered to represent the lower (higher) *Kp* cases.
Namely, the error bars give the *Kp* spread and vary by a factor of 2.4
-- 6.8 for one-. Therefore a factor-of 7 (\~2 e-folds) density variation
with *Kp* in Figure 5 is well within 3.

Next, *N~e~* is normalized by *Re^Kp^* to remove the effects of radial
distance and *Kp*. Figure 6 presents the bin-averaged *N~e~/(Re^Kp^)*
versus magnetic invariant latitude, . The figure shows that the
dependence is not so clearly defined, but linear regression shows a weak
trend of decreasing density with latitude indicating a possible
exponential dependence. From the three correlation analyses, the *N~e~*
distribution can therefore be described in the form:

![](media/image2.wmf) (2a)

After determining the functional form of *N~e~*, the parameters *N~0~,
,* , and can be determined using multivariate regression analysis
\[Wesolowsky, 1976\]: *N~o~* = 68510, *γ* = 4.95 0.03, *β* = 0.220 0.004
and *α* = 0.038 0.002, with a correlation coefficient,
![](media/image3.wmf)= 0.888. The polar region empirical model, as a
function of radial distance *R*, geomagnetic activity index *Kp*, and
invariant latitude , based on RPI data can therefore be written as:

![](media/image4.wmf)(2b)

Figure 7a shows *N~e~* as a function of *R* and *Kp* for = 88, and
Figure 7b the *N~e~* distribution in the X~SM~-Z~SM~ plane demonstrating
the weak dependence of *N~e~* on magnetic invariant latitude as
indicated by equation (2b), for *Kp* = 4. When only *R* and *Kp* are
included in the regression analysis, we obtain ![](media/image5.wmf) =
0.878, and this value is almost equal to ![](media/image6.wmf)
Obviously, including in the regression equation does not increase
*cc*^2^ by any appreciable amount over the value we obtain when only *R*
and *Kp* dependence are tested. This finding suggests that

![](media/image7.wmf) (3a)

can adequately predict the *N~e~* values. The calculated values of the
regression coefficients based on (3a) are *N~o~* = 3433, = 5.090.03, =
0.2290.004

The polar region empirical model as a function of radial distance *R*
and geomagnetic activity index *Kp* can therefore be written as:

![](media/image8.wmf) (3b)

**4. Discussion**

We first compare our empirical *N~e~* model with previously published
results. Fig. 8 compares the Persoon et al. \[1983\], Chandler et al.
\[1991\], and Gallagher et al. \[2000\] models with the RPI results for
different magnetic activity. The RPI *N~e~* values appear systematically
higher than the *N~e~* values of Persoon et al. and Gallagher et al. Our
*N~e~(R)* distributions, however, are consistent with DE measurements at
the lower heights (reported by Chandler et al. \[1991\]) when
extrapolated to the heights of the DE measurements. It is not surprising
that Gallagher et al.'s and Persoon et al.'s models have different
slopes, since Gallagher et al. combined several databases including the
Chandler et al. data. The RPI model shows for the first time the
decrease of *N~e~* value with decreasing *Kp*. At the lowest *Kp*, the
differences between our results and Persoon et al.'s and Gallagher et
al.'s become small.

There are two important limitations to the Persoon et al. model. The
first limitation is due to the propagation characteristics of the
auroral hiss, and the second limits the observations to times when
*f~pe~* \< *f~ce~*. Both these limitations cause an underestimate of the
reported polar cap densities. Auroral hiss is generated in the auroral
zone in the whistler mode. Note that the waves are generated at lower
altitudes where both *f~ce~* and *f~pe~* are higher than those where the
waves are observed. The whistler mode emissions have an upper frequency
limit of either the local *f~pe~* or *f~ce~* whichever is less. Persoon
et al. used the upper frequency limit of auroral hiss in order to
determine the local *f~pe~* and hence determine *N~e~*. A reliable
determination of the *N~e~* can only be obtained at a location in which
the propagation direction of the auroral hiss is along the magnetic
field (i.e. the auroral zone) and the *f~pe~* \< *f~ce~* condition can
be satisfied. The observation of auroral hiss over the polar cap is due
to the refraction of the auroral hiss emissions out of the auroral zone.
Based on an auroral zone source region, the wave normal angles of
auroral hiss over the polar cap will never be along the magnetic field.
The refraction of auroral hiss away from the local *f~pe~* will increase
depending on its distance from its auroral zone source region \[Calvert
and Hashimoto, 1990\]. This refraction effect was not considered by
Persoon et al. or taken into account in their results. Since a large
number of observations from a variety of distances from the auroral hiss
source region were combined, it is difficult to quantify the extent of
this underestimation in *N~e~*. In other words, knowledge of the *in
situ* wave normal angle distribution and/or source region location would
be needed for the correct determination of the upper frequency limit to
an emission as either a cutoff frequency or due to a propagation effect.

In addition, as noted above, Persoon et al.'s model was derived from
measurements limited to conditions when *f~pe~* \< *f~ce~* which most
likely occur for low *Kp* conditions. Therefore, their results
systematically underestimated the densities and were most likely
obtained during quiet times. Our method does not have such a restriction
because we observed X-mode echoes with the cutoff frequency

![](media/image9.wmf) (4)

for both *f~pe~* \> *f~ce~* and *f~pe~* \< *f~ce~* conditions. During
conditions of high geomagnetic activity, *f~pe~* could be greater than
*f~ce~* as can be seen in Figure 9, which shows an RPI plasmagram on
November, 01, 2001 at 02:32 UT, when the IMAGE satellite was in the
polar region at invariant latitude of 81.6 and radial distance of 4.52
R~E~. The recorded geomagnetic activity during this period was *Kp* = 5.
Similar results have been shown analyzing active and passive RPI data
near apogee over the northern polar-regions \[Osherovich et al., 2001\].
When *f~pe~* *f~ce~*, the whistler method is not applicable, and *N~e~*
given by the whistler mode cutoff is an underestimate of the actual
electron density.

It must be pointed out firstly, that the RPI data used in this study
were obtained from measurements made in 2000 -- 2001, i.e., near solar
maximum. Secondly, RPI data used include only few passes over the night
side polar region where the effect of ion depletion is most pronounced
\[Horita et al., 1993\]. So it is not impossible that our database
overestimates the density.

To understand the observed relationship, we first examine the radial
distance dependence. It is generally believed that the main source of
the plasma in the polar region is the ionosphere. The steady state force
balance equation in the polar region is:

![](media/image10.wmf) (5)

where , ***u***, *p*, ***j***, and ***g*** are the mass density,
velocity and thermal pressure of the plasma, the electric current
density, and the gravitational acceleration. The Coriolis and
centrifugal forces have been neglected. Note that the electron density
distribution is controlled by ion dynamics and linked by charge
neutrality condition. In the polar region, the field direction is
approximately the radial direction. Therefore along the radial
direction, the ***j**×**B*** force is negligible. In this notation, the
velocity and pressure gradient are all taken as the parallel component.
In static equilibrium, or when the flow velocity is zero, the plasma is
bound by gravity, *g*, which decreases at a rate of *R*^-2^. Since the
atomic weight of the plasma is not a strong function of height at this
altitude, the observed density profile corresponds to a parallel
temperature, *T \~ gR*, dropping at a rate of *R*^-1^. This implies a
cooling process.

In the other limit, gravity can be neglected and the force balance is
flow bound. In the presence of a field-aligned flow, the continuity
condition plays a role in the density distribution. If we assume that
above 1.4 R~E~ the photochemical processes are not important, the
combination of the magnetic flux conservation and continuity equation
gives *N~e~u/B* = const. For a dipole field, *B \~ R*^-3^, the velocity,
*u \~ BN~e~*^-1^ is then proportional to *R*^-3-^. Substituting this
relationship into the momentum equation yields that the parallel
temperature *T \~ u*^2^ is proportional to *R*^2(-3-)^. The power index
for the parallel velocity based on our observed is -3-(-5) = 2,
indicating a strong acceleration. Similarly, the power index for the
parallel temperature is 4, indicating a substantial rate of heating.
Meanwhile, the parallel pressure drops at a much slower rate of
*R*^--1^. Given a decrease in the average atomic weight with increasing
height, the rates of the heating and acceleration may be reduced
slightly. Our results may shed some new light on the polar wind
processes \[see e.g. Banks and Holzer, 1969; Raitt et al., 1978; Schunk,
1988; Shunk and Sojka, 1997; Shunk and Nagy, 2000\].

It is relatively easy to understand qualitatively the positive
dependence of *N~e~* on *Kp*. For higher geomagnetic activity, energetic
magnetospheric particles precipitate into the thermosphere at a higher
rate and collide with neutrals, leading to more ionization. Furthermore,
the enhanced field-aligned currents also dissipate more electromagnetic
energy into the ionosphere. The precipitation particles and
electromagnetic energy produce ionization in addition to that directly
produced by photo-ionization. The enhancements in the plasma source will
lead to higher outflowing flux.

We think it is premature to discuss the latitude dependence because our
database may not be sufficient to derive a robust relationship with
adequate spatial resolution. Here we recall that enhanced *N~e~* may
occur in small latitudinal ranges corresponding to dayside cusp and
nightside auroral arcs and as shown in Figures 3 and 6, there is a
possibility for a density minimum near 80 latitude.

**5. Summary**

In this brief report, we presented results derived from active RPI
measurements on IMAGE to probe the polar-region plasma. Using the echo
traces measured by RPI, a global magnetic field model \[Tsyganenko,
1995; Tsyganenko and Stern, 1996\], and the density inversion algorithm
discussed in Reinisch et al. \[2001b\], *N~e~* spatial distributions are
derived. We have conducted a statistical study of the plasma density
distribution in the northern polar region based on measurements from
June 2000 -- November 2001 above 70 degrees invariant latitude. An
empirical *N~e~* model was derived as a function of radial distance,
*Kp* index, and magnetic invariant latitude. A power law dependence was
established between *N~e~* and the geocentric distance, and the
densities were shown to grow exponentially with *Kp*. The *N~e~*
dependence on the magnetic latitude was found to be weak in our
database. The rate of the radial *N~e~* falloff indicates a cooling
process from the ionospheric plasma source if the plasma is gravity
bound. If the plasma is flow bound, as in the case of polar wind,
substantial heating is required. The *Kp* dependence indicates that
magnetospheric energetic precipitated particles and electromagnetic
energy deposited during disturbed geomagnetic conditions are important
sources for ionization in addition to normal photo-ionization. The
consistently higher *N~e~* seen by RPI, even at low *Kp* values,
compared to other models, can be explained by the deficiencies in the
previous density measurement methods, and may be related to seasonal or
solar seasonal effects. More RPI data are being processed in order to
study the polar *N~e~* latitudinal dependence in more detail. It is also
planned to examine *N~e~* seasonal variations and the dependence on
magnetic local time.

**Acknowledgments**. The authors are indebted to Ivan Galkin, Grigori
Khmyrov, Alexander Kozlov and Vadym Pasznukhov for their support during
the processing of the data used in this study. The work at UML was
supported by NASA under subcontract 83822 from Southwest Research
Institute, and by NSF under Awards NSF-ATM9729775 and NSF-ATM0077655.

**References**

Banks, P. M., and T. E. Holzer, Features of plasma transport in the
upper atmosphere, J. Geophys. Res., 74, 6304, 1969a.

Banks, P. M., and T. E. Holzer, High-latitude plasma transport: The
polar wind, J. Geophys. Res., 74, 6317, 1969b.

Benson, R. F., V. A. Osherovich, J. Fainberg, and B. W. Reinisch,
Classification of IMAGE/RPI-stimulated plasma resonances and the
determination of magnetospheric electron-density and magnetic field
values, Eos Trans. AGU, 82 (47), Fall Meet. Suppl., Abstract SM31B-0757,
2001.

Brace, L. H., B. M. Reddy, and H. G. Mayr, Global Behavior of the
Ionosphere at 1000-Kilometer Altitude, J. Geophys. Res., 72, 265, 1967.

Brace, L. H., H. G. Mayr, and K. K. Mahajan, A polar maximum of electron
concentration at 1000 km altitude, J. Atmos. Terr. Phys., 32, 1945,
1970.

Budden, K. G., The propagation of Radio waves, Cambridge Univ. Press,
New York, 1985.

Burch, J. L., S. B. Mende, D. G. Mitchell, T. E. Moore, C. J. Pollock,
B. W. Reinisch, B. R. Sandel, S. A. Fuselier, D. L. Gallagher, J. L.
Green, J. D. Perez, and P. H. Reiff, Views of Earth's Magnetosphere with
the IMAGE Satellite, Sci., 291, 2001.

Calvert, W. and K. Hashimoto, The magnetoionic modes and propagation
properties of auroral radio emissions, J. Geophys. Res., 95, 3943, 1990.

Chandler, M. O., J. H. Waite, Jr, and T. E. Moore, Observations of polar
ion outflows, J. Geophys. Res., 96, 1421, 1991.

Florida, C. D., The development of a series of ionospheric satellites,
Proc. IEEE, 57, 867, 1969.

Galkin, I., G. Khmyrov, A. Kozlov, B. Reinisch, X. Huang, and G. Sales,
New tools for analysis of space-borne sounding data, in *Proc. 2001
USNC/URSI National Radio Science Meeting, July 8-13, 2001, 304, 2001.*

Gallagher, D. L., P. D. Craven, and R. H. Comfort, Global core plasma
model, J. Geophys. Res., 105, 18819, 2000.

Green, J. L., B. R. Sandel, S. F. Fung, D. L. Gallagher, and B. W.
Reinisch, On the Origin of Kilometric Continuum, J. Geophys. Res., 2002
(*accepted*).

Horita, R. E., A. W. Yau, B. A. Whalen, T. Abe, and S. Watanabe, Ion
Depletion Zones in the Polar wind: EXOS D Suprathermal Ion Mass
Spectrometer Observation of the Polar Cap, J. Geophys. Res., 98, 11,439,
1993.

Huang, X. and B. W. Reinisch, Automated calculation of electron density
profiles from digital ionograms. 2. True height inversion of topside
ionograms with the profile-fitting method, Radio Sci., 17, 4, 837, 1982.

Jackson, J. E., and E. S. Warren, Objectives, history, and principal
achievements of the topside sounder and ISIS programs, Proc. IEEE, 57,
861, 1969.

Jackson, J. E., E. R. Schmerling, and J. H. Whitteker, Mini-review on
topside sounding, IEEE Trans. Antennas Propagat., AP-28, 284, 1980.

Knight, P., A classification of night-time electron density profiles, J.
Atmos. Terr. Phys., 34, 401, 1972.

Mozer, F. S., C. A. Cattell, M. Temerin, R. B. Torbert, S. Von Glinski,
M. Woldorff, and J. Wygant, The dc and ac electric field, plasma
density, plasma temperature, and field-aligned current experiments on
the S3-3 satellite, J. Geophys. Res., 84, 5875, 1979.

Osherovich, V. A., R. F. Benson, J. Fainberg, and B. W. Reinisch,
Increased magnetospheric f~pe~/f~ce~ values in response to
magnetic-cloud enhancements of solar-wind quasi-invariant on 31 March
2001, Eos Trans. AGU, 82 (47), Fall Meet. Suppl., Abstract SM31B-0758,
2001.

Persoon, A. M., D. A. Gurnett, and S. D. Shawhan, Polar cap electron
densities from DE 1 plasma wave observations, J. Geophys. Res., 88,
10123, 1983.

Raitt, W. J., R. W. Schunk, and P. M. Banks, Helium ion outflow from the
terrestrial ionosphere, Plant. Space Sci., 26, 255, 1978.

Reinisch, B. W., Modern Ionosondes, in Modern Ionospheric Science,
edited by H. Kohl, R. Ruster, and K. Schlegel, pp. 440 -- 458, European
Geophysical Society, Katlenburg-Lindau, Germany, 1996.

Reinisch, B. W. et al., The radio plasma imager investigation on the
IMAGE spacecraft, Space Sci. Rev., 91, 319-359, 2000.

Reinisch, B. W., X. Huang, P. Song, G. S. Sales, S. F. Fung, J. L.
Green, D. L. Gallagher, and V. M. Vasyliunas, Plasma density
distribution along the magnetospheric field: RPI observations from
IMAGE, Geophys. Res. Lett., 28, 4521, 2001a.

Reinisch, B. W. et al., First results from the radio plasma imager on
IMAGE, Geophys. Res. Lett., 28, 1167, 2001b.

Schunk, R. W., Polar wind tutorial, Space Plasma Physics, 8, 81, 1988.

Schunk, R. W., and J. J. Sojka, Global ionosphere-polar wind system
during changing magnetic activity, J. Geophys. Res., 102, 11625, 1997.

Schunk, R. W. and A. F. Nagy, Ionospheres: Physics, Plasma Physics, and
Chemistry, Cambridge Univ. Press, New York, 2000.

Shelley, E. G., W. K. Peterson, A. G. Ghielmetti, and Geiss, The polar
ionosphere as a source of energetic magnetospheric plasma, Geophys. Res.
Litt., 9, 941, 1982.

Tsyganenko, N. A., Modeling the Earth's magnetospheric magnetic field
confined within a realistic magnetopause, J. Geophys. Res., 100 (A4),
5599, 1995.

Tsyganenko, N. A. and D. P. Stern, Modeling the global magnetic field
and the large-scale Birkeland current systems, J. Geophys. Res., 101,
27187, 1996.

Wesolowsky, G. O., Multiple regression and analysis of variance, A
Wiley-Interscience Publication, New York, 1976.

Yau, A. W., W. K. Peterson, and E. G. Shelley, Quantitative
parameterization of energetic ionospheric ion outflow, in Modeling
Magnetospheric Plasma, Geophys. Monogr., 44, 229, American Geophysical
Union, Washington, D.C., 1988.

> ![](media/image11.png)

**Figure 1.** RPI plasmagram showing signal amplitude dBnV/m as function
of frequency and time delay expressed in terms of virtual range. Local
plasma and gyro resonances are seen as vertical lines and the curved
trace extending from \~23 to \~46 kHz is formed from X mode echoes.
IMAGE radial distance was 4.51 R~E~. The location of the satellite (red
dot) is shown at the upper-right corner.

**Figure 1.** RPI plasmagram showing signal amplitude dBnV/m as function
of frequency and time delay expressed in terms of virtual range. Local
plasma and gyro resonances are seen as vertical lines and the curved
trace extending from \~23 to \~46 kHz is formed from X mode echoes.
IMAGE radial distance was 4.51 R~E~. The location of the satellite (red
dot) is shown at the upper-right corner.

> ![](media/image12.png)

**Figure 2.** Magnetic invariant latitude and magnetic local time of
IMAGE polar region passes used in this study. Each marker indicates a
complete N~e~ profile. The different symbols indicate different
geomagnetic activity levels.

**Figure 2.** Magnetic invariant latitude and magnetic local time of
IMAGE polar region passes used in this study. Each marker indicates a
complete N~e~ profile. The different symbols indicate different
geomagnetic activity levels.

> ![](media/image13.png)

**Figure 3.** Snapshots of two-dimensional polar-cap N~e~ distributions
at different geomagnetic activity conditions. (a) September 18, 2000
(1548 -- 1628 UT) when Kp = 6. (b) October 06, 2000 (1102 -- 1126 UT)
when Kp = 0+.

**Figure 3.** Snapshots of two-dimensional polar-cap N~e~ distributions
at different geomagnetic activity conditions. (a) September 18, 2000
(1548 -- 1628 UT) when Kp = 6. (b) October 06, 2000 (1102 -- 1126 UT)
when Kp = 0+.

> ![](media/image14.wmf)

**Figure 4.** Bin-averaged electron density *N~e~* vs. radial distance
R.

![](media/image15.wmf)

**Figure 5.** Variation of N~e~/R with geomagnetic activity index Kp.

![](media/image16.wmf)

**Figure 6.** *N~e~/(Re^Kp^)* vs. magnetic invariant latitude .

> ![](media/image17.wmf)

**Figure 7.** RPI-derived empirical model of N~e~ showing variations (a)
with radial distance and Kp for an invariant latitude of 88, and (b)
with distance in the X~SM~-Z~SM~ plane for Kp = 4.

**Figure 7.** RPI-derived empirical model of N~e~ showing variations (a)
with radial distance and Kp for an invariant latitude of 88, and (b)
with distance in the X~SM~-Z~SM~ plane for Kp = 4.

> ![](media/image18.wmf)

**Figure 8.** Comparison of polar region N~e~ models \[Persoon et al,
1983; Gallagher et al., 2000\], DE 1 in-situ particle measurements, the
RPI-derived empirical model for Kp = 0, 3, 9.

**Figure 8.** Comparison of polar region N~e~ models \[Persoon et al,
1983; Gallagher et al., 2000\], DE 1 in-situ particle measurements, the
RPI-derived empirical model for Kp = 0, 3, 9.

> ![](media/image19.png)

**Figure 9.** RPI plasmagram showing signal amplitude dBnV/m as function
of frequency and time delay expressed in terms of virtual range. Local
plasma resonances are seen as vertical lines and the curved trace
extending from \~34 to \~46 kHz is formed from X mode echoes. IMAGE
radial distance was 4.52 R~E~. The location of the satellite (red dot)
is shown at the upper-right corner. On this plasmagram, it can seen that
*f~pe~* \> *f~ce~*.

**Figure 9.** RPI plasmagram showing signal amplitude dBnV/m as function
of frequency and time delay expressed in terms of virtual range. Local
plasma resonances are seen as vertical lines and the curved trace
extending from \~34 to \~46 kHz is formed from X mode echoes. IMAGE
radial distance was 4.52 R~E~. The location of the satellite (red dot)
is shown at the upper-right corner. On this plasmagram, it can seen that
*f~pe~* \> *f~ce~*.