Examples of Pc2-3 in the F layer, on the ground, and in the
magnetosphere
Below we give three examples of coherent Pc2-3 (f>70 mHz) pulsations
recorded in the topside ionosphere by CHAMP together with signals
simultaneously recorded on the ground or in the magnetosphere by THEMIS-C.
The events were initially selected by an automated program developed for the
detection of coherent Pc2-3s; then the signal waveforms were analyzed
visually. All the events are presented in the same format: a figure with the
signal time series, and another figure with the corresponding PSD spectra,
spectral coherence, and phase difference. The data shown in time Figs. 2, 4,
and 6 are high-pass filtered with a cutoff frequency fL=20 mHz. All the
intervals in this section have the same 128 s duration, interval starts
are given in UT, and dates are given in the YYYYDDD format, where YYYY is a
year and DDD is a day number from the beginning of the year.
The events considered show that at least in some cases the Pc2-3s
(f>70 mHz) observed in the topside ionosphere were seen simultaneously
with the same central frequency by an independent quasi-stationary sensor.
High-pass filtered (fL=20 mHz) magnetograms for the CHAMP
horizontal (bH and bD) components and the ground bH registered at
the NUR station for the 128 s interval starting at 05:21:36 UT on day
2007254. CHAMP latitude and longitude values in CGM coordinates at the
start and end of the interval shown and NUR CGM coordinates are given in the
figure title.
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A Pc2-3 event recorded simultaneously in the F layer and on the ground
starting at 05:21:36 UT on day 2007254
An example of pulsations with a central
frequency f0≈110 mHz recorded by CHAMP and at the NUR station
during a 128 s interval starting at 05:21:36 UT on day 2007254 UT is
shown in Figs. 2 and 3. During this interval, CHAMP passed from CGM latitude
Φ≈43 to 52∘ CGM along the MM218 (magnetic meridian along
218∘ CGM longitude) in the afternoon sector (MLT ≈ 14:00).
NUR is located at MM100 at the CGM latitude Φ≈57 (L=3.42).
During this interval, MLT = 08:00 at NUR, i.e., the station and the
satellite were separated by 6 h in MLT.
Magnetograms for two horizontal components at CHAMP and the H component at
NUR are shown in Fig. 2. Peak-to-peak amplitude reaches 0.5/0.3 nT for the
D / H component in the F layer and 0.2 nT on the ground surface.
The amplitude of the D component on the ground is below 0.1 nT (not
shown). The visible period is about 9 s. It is more clearly seen in the
CHAMP D component and in the ground H component.
The PSD spectra, spectral coherence, and phase difference for this interval
are given in Fig. 3. A spectral maximum at f0=112 mHz is clearly seen in
the PSD spectrum of the CHAMP D component. The H component spectrum has
no maximum at f0 but there is a plateau near f0 and a wide maximum in
the spectral coherence between the two CHAMP horizontal components at
95<f<107 mHz, i.e., it is shifted to lower frequencies from f0. The
maximal spectral coherence between the two CHAMP horizontal components
exceeds 0.75, and the phase difference between the components at the
frequency of maximal coherence Δφ=140∘, i.e., the
polarization, is elliptical. The most interesting observation is the existence
of a spectral maximum at NUR at the same frequency as at CHAMP (green curve
in the upper panel of Fig. 3).
The spectral coherence also has a maximum near f0, where
γ(f0)=0.77 (green curve in the middle panel of Fig. 3). The other
maximum in spectral coherence with nearly the same value of γ is seen
at f1≈80 mHz. The phase differences in these two bands of high
coherence are -130∘ and 25∘, respectively (green curve in
the bottom panel of Fig. 3).
PSD spectra, spectral coherence, γ, and phase difference,
Δφ, for the interval shown in Fig. 2.
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So we see coherent pulsations with the central frequency f0=110 mHz in
the F layer in the afternoon (MLT) sector and on the ground surface in the
morning sector. The PSD is higher in the azimuthal component in the F layer
and in the meridional component on the ground surface. These components also
demonstrate the maximal coherence among all the satellite-ground component
combinations. The wave polarization in the ionosphere and on the ground
surface corresponds to the shear Alfven mode.
An example of a Pc2-3 event recorded simultaneously in the F layer
and in the outer magnetosphere starting at 08:03:44 UT on day 2007257
Only a small fraction of CHAMP Pc2-3 pulsations can be recorded on
the ground surface. That is why some other quasi-stationary
reference observations are needed so that spatial and temporal
variations can be distinguished. The other possibility to
discriminate temporal and spatial variations is to compare the
variations of the magnetic field measured simultaneously in the
ionosphere and in the magnetosphere. For the pulsations in the
frequency range studied (contrary to spatial variations or Pc4-5
pulsations recorded in the ionosphere as Pc2-3 due to the Doppler
effect) the spectral coherence between the magnetosphere and the
ionosphere should be high. Below we give some examples of such
oscillations.
Pc2-3 pulsations are recorded simultaneously by the CHAMP and THEMIS-C
satellites during a 128 s interval starting at 08:03:44 UT on day 2007257.
CHAMP and THEMIS-C orbits are shifted from each other by about 2.5 h in MLT;
CHAMP passes from Φ=59 to 67∘. THEMIS-C is located at L=10, at
-7∘ from the equatorial plane; the CGM latitude of THEMIS-C
ionospheric projection is 71∘. Both satellites are in the near-noon
sector (MLT ≈ 15:00 for CHAMP and 11:00 for THEMIS-C).
Magnetograms of the CHAMP D component and the THEMIS-C azimuthal
(φ) component are shown in Fig. 4. The peak-to-peak amplitude is
about 0.4 nT at CHAMP and 2 nT at THEMIS-C. Two apparent periods at
about 12 and 7 s are clearly seen both in the CHAMP and THEMIS-C
magnetograms.
Filtered magnetograms for THEMIS-C (bφ) and CHAMP (bD)
components for the 128 s interval starting at 08:03:44 UT on day 2007257.
Average latitude and longitude values in CGM coordinates of the northern
magnetic field line footprint of THEMIS-C's location during the interval
shown are given in the figure title.
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The PSD spectra of all the THEMIS-C components and the CHAMP horizontal
components are shown in Fig. 5. Two spectral maxima at f=85 and 130 mHz
are seen in the PSD spectra of both the CHAMP and the THEMIS-C azimuthal
components (solid lines in the upper panel of Fig. 5). The maximum at
130 mHz is seen also in the PSD spectra of the THEMIS-C radial component
and the CHAMP H component (dashed lines in the upper panel of Fig. 5) and
in the THEMIS-C longitudinal component (red dash–dot line in the upper panel
of Fig. 5). At f=85 mHz the azimuthal component PSDs (the THEMIS-C
Pf,φ and the CHAMP Pf,D) are higher than the
radial/meridional PSDs for both satellites. The THEMIS-C longitudinal PSD is
comparable with the azimuthal one. At f=130 mHz, the spectral ratio
Pf,τ / Pf,φ reaches 2.5 and the THEMIS-C radial and
azimuthal PSDs are approximately equal. The CHAMP meridional-to-azimuthal
spectral ratio Pf,H / Pf,D≈3. Thus, both the CHAMP and the
THEMIS-C wave polarizations correspond to the sum of the compressional and
the shear Alfven modes with a higher contribution of the compressional mode
at the higher frequency maximum.
The spectral coherence is shown in the middle panel of Fig. 5 for the all
three CHAMP D–THEMIS-C component combinations. Both spectral maxima are
clearly seen in the spectral coherence with γ>0.5 for both THEMIS-C
transverse components (blue and green lines in the middle panel of Fig. 5).
For the longitudinal THEMIS-C component, only the maximum at the higher
frequency f=130 mHz is seen in the spectral coherence. The spectral
coherence for the THEMIS-C–CHAMP H component pairs has maxima at nearly
the same frequencies as for the THEMIS-C–CHAMP D component pairs but
γ is somewhat lower: the inter-component spectral coherence for each
satellite both at 85 and 130mHz exceeds 0.5 (not shown).
Phase differences are shown in the bottom panel of Fig. 5. The signal
polarization also differs at the frequencies of two spectral maxima. The
THEMIS-C azimuthal and radial components are shifted by about π/2 both at
85 and 130 mHz (green line in the bottom panel of Fig. 5). The phase
difference between the THEMIS-C azimuthal and longitudinal components changes
from 0 at 85 mHz to -π/2 at 130 mHz (red line in the bottom panel
of Fig. 5), and the phase difference between the longitudinal and the radial
components is -π/2 at 85 mHz and π at 130 mHz (not shown). The
CHAMP D component is shifted by π/2 at 85 mHz from the azimuthal
THEMIS-C component (magenta line in the bottom panel of Fig. 5) and they are
in phase at f=130 mHz. The phase difference between the CHAMP H and D
components is approximately the same as between the THEMIS-C azimuthal and
longitudinal components. It changes from 0 at 85 mHz to -π/2 at
130 mHz (cyan line in the bottom panel of Fig. 5).
Taking into account that the compressional mode contributes mostly to the
CHAMP H component and the shear Alfven wave dominates in the D component
in the F layer and in the azimuthal component in the magnetosphere, we can
speculate that the observed correspondence in the polarizations between the
magnetospheric and the ionospheric signals, along with the similar PSD
spectra and the high spectral coherence indicate that the signals in these
two locations are of the same origin. The phase shift between the pulsations
in the magnetosphere and in the F layer may be caused by wave propagation.
An example of a Pc2-3 event recorded simultaneously in the F layer
and in the plasmasphere starting at 01:38:40 UT on day 2007286
The next example presents a Pc2-3 pulsation recorded simultaneously by CHAMP
in the F layer and by THEMIS-C inside the plasmasphere during a 128 s
interval starting at 01:38:40 UT on day 2007286. During this interval,
THEMIS-C was near the plasmapause position (L=4.3) and CHAMP was passing
from Φ=-35 to -27∘ along MM230. Both satellites were in the
near-noon sector (MLT ≈ 12:00 for CHAMP and ≈10:00 for
THEMIS).
Magnetograms of the THEMIS-C azimuthal component and the CHAMP D component
are shown in Fig. 6. Pulsations with 90 mHz central frequency and
peak-to-peak amplitude 0.3–0.5 nT were seen by both satellites on the
background of ≈25 mHz Pc4 pulsations with the peak-to-peak amplitude
of ≈1 nT.
PSD spectra, spectral coherence, γ, and phase difference,
Δφ, for the three THEMIS-C and the two horizontal CHAMP
components for the interval shown in Fig. 4.
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The PSD spectra for this event are given in the upper panel of Fig. 7 for
three THEMIS-C components (green, blue, and red lines) and the CHAMP
horizontal components (cyan and magenta lines). Two maxima are seen at about
90 and 130 mHz. At f=90 mHz, the THEMIS-C radial PSD is at about
2–3 times higher than the azimuthal and the longitudinal PSD. At
f=130 mHz PSDs of all three THEMIS-C components are similar. The CHAMP-to-THEMIS-C spectral ratio
Pf,CHAMP,D / Pf,THC,φ≈7 for the
azimuthal components and
Pf,CHAMP,H / Pf,THC,R≈2 at
f=90 mHz. At 130 mHz
Pf,CHAMP,D / Pf,THC,φ≈3 and
Pf,CHAMP,H / Pf,THC,φ≈1.
Thus, for this event the wave amplitude in the F layer is
significantly higher than in the magnetosphere. The
CHAMP-to-THEMIS PSD ratio at f=90 mHz is higher in the azimuthal component
corresponding to the shear Alfven mode at f=90 mHz. During this interval, a
Pc2-3 pulsation occurs simultaneously with a Pc4 pulsation with a period of
about 40 s (25 mHz). Pc4 amplitudes are the same in the ionosphere and
in the magnetosphere (Fig. 6).
Spectral coherence for all the CHAMP D–THEMIS-C component pairs is shown
in the middle panel of Fig. 7. Both 90 and 130 mHz spectral maxima are
also seen in the spectral coherence. The higher frequency maximum is seen in
all three THEMIS-C components, and for all three components, the maximal
values of coherence reach or exceed 0.5. The coherence maximum at
f=90 mHz can be seen only in the transverse components (green and blue
curves in the middle panel of Fig. 7). The spectral coherence between the
CHAMP D component and the THEMIS-C longitudinal component has a maximum at
f=70 mHz. The maxima of the CHAMP H component spectral coherence are at
nearly the same frequencies but maximal coherence is lower than for the
CHAMP D component (not shown).
Filtered magnetograms for THEMIS-C (bφ) and CHAMP (bD)
components for the 128 s interval starting at 01:38:40 UT on day
2007286. Average latitude and longitude values in CGM coordinates of the
northern magnetic field line footprint of THEMIS-C's location during the
interval shown are given in the figure title.
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The phase differences for this event are shown in the bottom panel of Fig. 7.
The phase difference between the azimuthal and the radial (green) and the
azimuthal and the longitudinal (red) THEMIS-C components is about π/4 at
f=90 mHz, and thus the radial and the longitudinal pulsations are in phase
at this frequency. At f=130 mHz ΔφTHC,φ-THC,R is about zero and ΔφTHC,φ-THC,τ is almost π, i.e., the
pulsation polarization in the magnetosphere is elliptical at f=90 mHz and
almost linear at f=130 mHz. The phase difference between the CHAMP
horizontal components (cyan) changes from 3/4π at f=90 mHz to -π/2
at f=130 mHz, and thus the difference in polarization is almost π like
for the THEMIS-C azimuthal–longitudinal component pair. The phase
difference between the THEMIS-C azimuthal component and the CHAMP D
component ΔφTHC,φ-CHAMP,D is about
π at f=90 mHz and it is almost zero at f=130 mHz. The phase
difference between the THEMIS-C longitudinal and the CHAMP H component
ΔφTHC,τ-CHAMP,H (not shown) changes
from -π/2 at f=90 mHz to π/2 at f=130 mHz, i.e., the
corresponding components in the two locations demonstrate similar phase
dependence on frequency.
Pc2-3 in the F layer, in the magnetosphere, and on
the ground surface: spatial distribution
In this subsection some statistical results for the pulsations shown as
examples in the previous subsection are presented. The latitude distribution
of the Pc2-3 (70–140 mHz) occurrence rate (PPc2-3) and
that of the PSD are given in Fig. 8 for pulsations recorded by CHAMP in two
MLT sectors over 2 months in 2007 (days 241–300). The Pc2-3 occurrence
rate is higher for the CHAMP D component in both the afternoon (left
panels) and the post-midnight (right panels) sectors. The occurrence rate
during the night has a clear maximum at Φ±57∘ CGM and a
second one at low latitudes at |Φ|<30∘ CGM. During the day
the picture differs for the two hemispheres.
In the Southern Hemisphere PPc2-3 for the D component
grows from low to high latitudes and in the Northern Hemisphere the maximum
is expressed weakly. PPc2-3 in the meridional component
during the day has a low-latitude maximum at Φ±30∘, but during
the night, pulsations in the H component almost disappear. The PSD grows
towards high latitudes, and during the day it is higher in the azimuthal than
in the meridional component. During the night, the difference in PSD between
components is not significant. The highest occurrence rates and amplitudes
are seen at night at about Φ=±57∘ and in the afternoon at
Φ>60∘.
PSD spectra, spectral coherence, γ, and phase difference,
Δφ, for the three THEMIS-C and the two horizontal CHAMP
components for the interval shown in Fig. 6.
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Pc2-3 at f>70 mHz are regularly seen on the ground surface at night in the
H component. The latitude distribution of the Pc2-3 occurrence rate and the
PSD for the H component pulsations recorded along the MM100 magnetometer
array in the post-midnight (MLT) sector (00:00 < MLT < 06:00) are
presented in Fig. 9. Under the same set of selection parameters as for CHAMP
(1), the occurrence rate is an order of magnitude lower, and the PSD is
3–5 times lower on the ground in comparison with the F layer. The main
maximum corresponds to L=5 (Φ=64∘, SOD) and a secondary maximum
is seen at L=3.4 (Φ=57∘, NUR). At THY (Φ=47∘, L=1.8),
Pc2-3 disappears almost completely.
We analyze the spatial distribution of the magnetospheric Pc2-3s with the set
of parameters (1) in the same MLT sectors as for CHAMP, using the THEMIS-C
data in the MLT intervals (00:00–06:00) and (12:00–20:00) (the last
interval is extended to provide a sufficient data array) and during the same
days (241–300). During the days selected for the analysis THEMIS-C crossed
L shells from 1.5 to 7.5 in the afternoon (MLT) sector, while in the
post-midnight sector it crossed all the L shells outside L=2. The results
for the THEMIS-C Pc2-3 occurrence rate and PSD are given in Fig. 10 in the
same format as for CHAMP in Fig. 8. The maximum of the occurrence rate falls
within L values from 4 to 6 in both the afternoon and post-midnight
sectors. In both sectors at high L, the occurrence rate and the PSD for the
field-aligned (bτ, green stars) component pulsations are nearly the
same as for transverse components (bR, bφ), while at low L
they are small in comparison with bR, bφ. The occurrence rate
is higher in the afternoon sector. In the post-midnight sector, the Pc2-3
occurrence rate and PSD slowly decrease with L for L>6 and Pc2-3 are
recorded at least up to L=10.
Latitude distribution of the occurrence rate (upper panel)and PSD
(bottom panel) for CHAMP Pc2-3 in two MLT sectors over 2 months in 2007.
Two components are given by different markers and colors.
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Comparison of Pc2-3 parameters near the equatorial plane of the magnetosphere
and in the F layer shows that in the post-midnight (MLT) sector, the maximum of
the F layer occurrence rate is found at L≈3.5
(|Φ|≈57∘) in the F layer and at 4<L<6 in the
magnetosphere. The Pc2-3 occurrence rate in the ionosphere is several times
higher than in the magnetosphere. During the night, pulsation amplitudes are
comparable in the ionosphere and the magnetosphere, and the maximal PSD of
afternoon pulsations is 3–5 times higher in the F layer. The polarization is
also different. In the F layer, pulsation spectral power and occurrence rate
are higher in the azimuthal component, and in the magnetosphere all three
components have comparable amplitudes at L>4. Inside the plasmasphere,
amplitude and occurrence rate of bτ Pc2-3 are low in comparison with
those for transverse components.
The high-latitude boundary of the F layer Pc2-3 occurrences lies at about
L=4 and may be related to the plasmapause. To check this assumption we
compare the day-to-day variations of the L value of the Pc2-3 occurrence
rate maximum (LPc2-3) with the plasmapause position
determined from the Carpenter formula Lpp=5.7-0.47 Kp
. For low and moderate Kp, the empirical formula
obtained from CHAMP observations by gives similar results.
Two-day mean values of LPc2-3, determined from CHAMP
measurements in the 00:00–06:00 MLT sector in the Southern Hemisphere
during the best data coverage for 2 months, are shown in Fig. 11 together
with Lpp estimated from 3-day mean Kp values.
LPc2-3(t) and Lpp(t) in Fig. 11 are
determined as 〈LPc2-3〉|τPc2-3 and 〈Lpp〉|τpp, respectively, where angle brackets indicate time
averaging over an interval τ, and where τPc2-3=[-2,0] days, and τpp=[-3,0] days.
LPc2-3 varies within the range 2<L<4.1, i.e., at about
Lpp-2 and the day-to-day variations of L for the Pc2-3
occurrence rate maximum and plasmapause demonstrate positive correlation.
L distribution of the occurrence rate (upper panel)and PSD (bottom
panel) along MM100 in the 00:00–06:00 MLT sector over 2 months in 2007
for the meridional (bH) component.
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Model calculations
MHD wave transmission through and reflection from a thin ionosphere has been
studied theoretically in numerous papers beginning with
. After this initial period, the problem has
also been studied for more general geometries of the background magnetic
field (see, e.g.,
).
Below we present a model and numerical results for the problem of
magnetohydrodynamic wave transmission through and reflection from the
ionosphere within a more realistic “thick ionosphere” model
. Our analysis follows the scheme developed by
and . It is shown in Sect.
that the Pc2-3 polarization corresponding to the shear Alfven mode dominates
in the plasmasphere and in the mid-latitude ionosphere. In this section, we
consider theoretically an incident shear Alfven wave transmission through and
reflection from the ionosphere.
L distribution of the occurrence rate (upper panel) and PSD
(bottom panel) for THEMIS-C Pc2-3 in two MLT sectors over 2 months in
2007. Three components are given by different markers and colors.
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We assume a plane stratified model of the ionosphere: the dip-angle I of
the geomagnetic field B0 is constant, and the dielectric permeability
tensor ε^=ε^(z) depends only on height. We
introduce an oblique coordinate system x1,x2,x3
with a southward x1 axis, and an eastward x2 axis. The angle
between x3 and x1 is equal to the dip-angle I. The x3 axis
is parallel to the field-lines, and the coordinate surface
x3=const is a horizontal plane;
x3=0 is at the Earth's surface, and x3=z is a horizontal plane
at a height z above the Earth's surface.
We consider the case of waves propagating in the
meridional plane. For the harmonics ∝exp(-iωt+ik1x1),
the horizontal components of the electric E and magnetic
B fields can be written as
B(x3)E(x3)exp(ik1x1-iωt),
where ω is the angular frequency of the wave, k1 is a wave vector
component, and t is time. Taking into account that the longitudinal
component of the electric field E3 is zero, from Maxwell's equations we
get
∂3B1=-μ0σ2E1/sinI+μ0σ1E2+ik1B1cotI,∂3B2=-μ0σ1E1/sin2I-μ0σ2E2/sinI,∂3E1=iωB2,∂3E2=ik1E2cotI-iωB1.
Here k0=ω/c and σ1,2(x3)=-iωε1,2(x3) are the complex conductivities. In the E layer of the ionosphere
σ1,2=σP,H(x3), i.e., the Pedersen and Hall
conductivities, and in the F2 layer and further up
σ1=-iω/μ0VA2.
Day-to-day variations of the position of maximal Pc2-3 occurrence
rate at CHAMP, in the 00:00-06:00 MLT sector for two months in 2007, and the
plasmapause position, determined from the two-day mean Kp with Carpenter's
formula.
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Let a shear Alfven wave with an amplitude B(i),E(i) at
x3=z1 be incident on the ionosphere. The total field at x3=z1 can be
represented as B(i)+B(r), where B(i) is the
magnetic component of the incident wave and B(r) is the reflected
field. The matrix for the reflected and incident waves is
B(r)=RB(i), where R is the reflection
coefficient matrix. To find the wave amplitudes on the ground surface, first
the fields reflected from the ionosphere are found and then, from the known
values of the initial incident field and the reflected field, the full field
at some reference level z1 is calculated. Then the ground electric and
magnetic field are found from the electric and magnetic field at z1.
Reflection coefficients at z1 are calculated via the admittance Y
or impedance Z=Y-1 matrices, which relate horizontal
components of the electric Eτ and magnetic Bτ fields,
Bτ=YEτ, and
Eτ=ZBτ. By substituting
Bτ=YEτ and
Eτ=ZBτ into Maxwell equations, the Ricatti-type
matrix equations are obtained for the admittance and impedance matrices (see,
e.g., ).
If the Wait–Price condition (the strong skin effect approximation,
kδg≪1, where δg=(2/ωμ0σg)1/2 is the skin
depth) is valid, the impedance conditions at the ground surface are E1=-ZgB2, E2=ZgB1. A surface impedance Zg=Zg(ω) is determined by
the Earth conductivity distribution
σg(x3) and within the strong skin effect approximation
Zg does not depend on the wave's spatial structure. For a homogeneous
half-space under strong skin effect Zg=exp(-iπ/4)ωμ0/σg. Then the admittance Y(x3) and Z(x3)
matrices are recalculated step-by-step through the atmosphere and the
ionosphere with Ricatti-type matrix equations from the ground surface to the
altitude z1 (we set z1=2000 km). The matrix Y(z1) is used to
calculate the reflection matrix R and the total field at the altitude
z1.
Ground-to-ionosphere amplitude ratio for Alfven waves obtained from
the full wave equation with International Reference Ionosphere (IRI) model ionosphere at two different k
values (solid lines) and the NUR to CHAMP amplitude ratio, averaged over two
months, in three frequency bands (magenta circles)
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The transmission coefficient depends on wave frequency and wave number.
Pulsations with a spatial scale less than the Earth–ionosphere distance are
attenuated as exp(-kh) by the ionosphere . We have
calculated the spectrum of the ground-to-ionosphere amplitude ratio for
2×10-3<k<10-2 km-1. The results are shown in Fig. 12 for
350km altitude. The IRI ionosphere model is used with
the following parameters: day 2007253 (12 September), MLT = 02:00, CGM
latitude Φ=57∘, and CGM longitude Λ=102∘. The
ground-to-ionosphere amplitude ratio decreases with frequency and wave
number. For comparison, we used the ground-to-ionosphere amplitude ratio of
Pc2-3s recorded at NUR in the H component and by CHAMP in the D
component. Pc2-3 events are automatically selected for all CHAMP orbit
segments at CGM latitudes -60<Φ<-35∘ in three frequency bands
(50–80, 105–130, and 130–160 mHz) in the post-midnight (MLT) sector
(00:00–06:00) for two months of observations: 2007, days 241–300. The best
agreement between calculated and measured data is found for
k=5×10-3 km-1. The maximal Doppler shift corresponds to the
case k=k∥. For the k=5×10-3 km-1 waves
recorded by a spacecraft moving at a 8 km s-1 speed,
Δω=kv=4×10-2 s-1, i.e., Δf=6.4 mHz. Thus,
the observed ground-to-ionosphere amplitude ratio corresponds to a wave
spatial scale which could provide a Doppler shift within a few percent of the
apparent frequency of the Pc2-3 pulsations as recorded by a low-orbiting
spacecraft.