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ISSN 0016?7932, Geomagnetism and Aeronomy, 2010, Vol. 50, No. 5, pp. 576–587. © Pleiades Publishing, Ltd., 2010.
Original Russian Text © I.V. Golovchanskaya, B.V. Kozelov, 2010, published in Geomagnetizm i Aeronomiya, 2010, Vol. 50, No. 5, pp. 603–615.
576
1. INTRODUCTION
Until recently, small?scale electric and magnetic
fields in the polar cap have not attracted careful atten?
tion of researchers apparently because the amplitude
of these fields is as a rule small (sometimes, smaller
than the resolution of instruments). In contrast to the
auroral zone, small?scale fields in the polar cap only
sometimes result in structured particle precipitation
and an optical aurora. For a long time, these fields
have been interpreted as a random noise component.
At the same time, beginning in the mid?1970s, sev?
eral works indicated (mostly based on the character of
the Fourier spectra of the satellite data) that small?
scale electric and magnetic fields in the auroral zone
are of turbulent origin [Kintner, 1976; Weimer et al.,
1985; Basu et al., 1988; Antonova, 2002, and refer?
ences therein]. Later, the wavelet analysis and special
statistical methods made it possible to confidently
indicate that small?scale electric fields in the auroral
zone reflect intermittent turbulence, which develops
in the regions of large?scale field?aligned currents
(see, e.g., [Tam et al., 2005; Golovchanskaya et al.,
2006; Kozelov and Golovchanskaya, 2006; Kozelov
et al., 2008]). Such a conclusion was based on (1) the
power character of the logarithmic diagrams con?
structed using the wavelet transform of registered fields
in the range of scales from ~1 km to several hundreds
of kilometers, (2) the power character of the structure
functions of the order of 1—6, (3) the non?Gaussian
form of the probability density function P(δE, s) of the
field fluctuations (δE) considered on different scales
(s) with wings intensified by several orders of magni?
tude as compared to the normal distribution, (4) col?
lapse of the probability density normalized functions
Ps(δE/sγ) on one curve, and (5) positive excess values
(the fourth moment of field distributions) increasing
with decreasing scale (s).
It became unclear whether small?scale electric
fields in the polar cap show similar properties.
Stepanova et al. [2003] showed the non?Gaussian
probability density function P(δPC, τ) of the PC index
time fluctuations with intensified wings. It was indi?
cated that parameter λ2, appearing in the Castaing dis?
tribution, which was used to approximate P(δPC, τ),
Properties of Electric Turbulence in the Polar Cap Ionosphere
I. V. Golovchanskaya and B. V. Kozelov
Polar Geophysical Institute, Apatity Division, Kola Science Center, Russian Academy of Sciences,
ul. Fersmana 14, Apatity, Murmansk oblast, 184209 Russia
e?mail: golovchanskaya@pgia.ru
Received January 18, 2010; in final form, April 5, 2010
Abstract—Small?scale (scales of ~0.5–256 km) electric fields in the polar cap ionosphere are studied on the
basis of measurements of the Dynamics Explorer 2 (DE?2) low?altitude satellite with a polar orbit. Nineteen
DE?2 passes through the high?latitude ionosphere from the morning side to the evening side are considered
when the IMF z component was southward. A rather extensive polar cap, which could be identified using the
ε–t spectrograms of precipitating particles with auroral energies, was formed during the analyzed events. It is
shown that the logarithmic diagrams (LDs), constructed using the discrete wavelet transform of electric fields
in the polar cap, are power law (μ ~ sα). Here, μ is the variance of the detail coefficients of the signal discrete
wavelet transform, s is the wavelet scale, and index α characterizes the LD slope. The probability density
functions P(δE, s) of the electric field fluctuations δE observed on different scales s are non?Gaussian and
have intensified wings. When the probability density functions are renormalized, that is constructed of δE/sγ,
where γ is the scaling exponent, they lie near a single curve, which indicates that the studied fields are statis?
tically self?similar. In spite of the fact that the amplitude of electric fluctuations in the polar cap is much
smaller than in the auroral zone, the quantitative characteristics of field scaling in the two regions are similar.
Two possible causes of the observed turbulent structure of the electric field in the polar cap are considered:
(1) the structure is transferred from the solar wind, which is known to have turbulent properties, and (2) the
structure is generated by convection velocity shears in the region of open magnetic field lines. The detected
dependence of the characteristic distribution of turbulent electric fields over the polar cap region on IMF By
and the correlation of the rms amplitudes of δE fluctuations with IMF Bz and the solar wind transfer function
(By2+ Bz2)1/2sin(θ/2), where θ is the angle between the geomagnetic field and IMF reconnecting on the day?
side magnetopause when IMF Bz < 0, together with the absence of dependence on the IMF variability are
arguments for the second mechanism.
DOI: 10.1134/S001679321005004X
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GEOMAGNETISM AND AERONOMY Vol. 50 No. 5 2010
PROPERTIES OF ELECTRIC TURBULENCE 577
and characterizing the degree of P(δPC, τ) deviation
from the normal distribution (in other words, inter?
mittency), shows a power law dependence on time
scales (τ) varying from 10 min to 2 h.
Abel et al. [2006, 2007] studied the spatial structure
of electric fields in the polar cap using the SuperDARN
radar observations and a special technique that made
it possible to localize the boundary between the
regions of open and closed magnetic field lines based
on the radar data [Chisham and Freeman, 2004]. Abel
et al. [2006, 2007] indicated that the structure function
of the first order constructed for the convection veloc?
ity spatial fluctuations in the polar cap and the depen?
dence of the peak values of the probability density
function P(0, s) of the convection velocity fluctuations
on the scale have a power law shape at scales varying
from 45 to ~1000 km. Abel et al. [2006] assumed that
the detected structure of convection velocities and,
consequently, electric fields is transferred to the polar
cap from the solar wind, which is known to have tur?
bulent properties (see, e.g., [Goldstein and Roberts,
1999]).
However, Abel et al. [2006, 2007] noted that the
radar measurements of electric fields in the polar cap
were performed in several isolated regions. Although
this circumstance does not hinder the construction of
the structure and probability density functions of spa?
tial field fluctuations on different scales, especially
during repeated radar measurements, the absence of
regularly sampled data series does not make it possible
to thoroughly trace variations in the δE fluctuation
amplitude in going from the polar cap periphery to its
center, to compare the δE amplitudes on the morning
and evening polar cap flanks at different IMF By direc?
tions, etc. In addition, in this case, it is impossible to
apply the wavelet analysis methods, which can be most
adequately used to determine scaling properties (in
other terms, self?similarity, scaling, fractal structure,
and scale?free structure) of data and characteristics of
scaling (see [Kozelov and Golovchanskaya, 2010].
The DE?2 electric field measurements, which are
used in the present work and are briefly described in
Section 2, are free of the above disadvantage. The res?
olution of the data 16 s–1 (~500 m) is almost two orders
of magnitude higher than that of the radar measure?
ments used in [Abel et al., 2006, 2007] (45 km). Sec?
tion 2 also illustrates the localization of the boundary
between the auroral zone and the polar cap, using the
DE?2 data on charged particles precipitating into the
ionosphere. The scaling properties of electric fields in
the polar cap on scales of 0.5–256 km are illustrated in
Section 3; the scaling parameters are compared here
with their values for electric fields in the auroral zone.
The relation of turbulent fields in the polar cap to IMF
and its variability is studied in Section 4. The achieved
results are discussed in Section 5.
2. DATA
The present work analyzed the DE?2 VEFI (Vector
Electric Field Instrument) measurements of the iono?
spheric electric field using the symmetric double?
floating probe technique. A detailed description of
VEFI is presented in [Maynard et al., 1981]. The
device time resolution was 16 s–1, which corresponds
to a spatial resolution of ~500 m at a satellite velocity
of 7.55 km/s.
It was discussed in detail whether the δE fluctua?
tions observed on the satellite should be considered
time or spatial [Temerin, 1978; Weimer et al., 1985;
Pokhotelov et al., 2003; Kozelov et al., 2008]. Differ?
ent methods indicated that fluctuations in the consid?
ered frequency region are mainly related to the satel?
lite motion through the electric field spatial structures.
The present work considered 19 DE?2 passes
through the high?latitude ionosphere of the Northern
Hemisphere (altitudes of 300–900 km). The upper
panel of Fig. 1 shows the electric component along the
satellite orbit for a representative event of 1981: day
316, 0223–0240 UT (event 1 in the Table). This com?
ponent is compared in time with the spectrograms of
electrons and ions with energies of 0.01–30 keV pre?
cipitating into the ionosphere (the middle and lower
panels of Fig. 1, respectively), constructed using the
DE?2 LAPI (Low?Altitude Plasma Instrument) data
[Winningham et al., 1981]. By comparing the electric
field variations with the precipitation character along
the satellite orbit, we identified the morning auroral
zone, polar cap, and evening auroral zone for this pass
with the regions crossed by DE?2 at 0222:48–0227:00,
0227:00–0235:45, and 0235:45–0239:36 UT, respec?
tively.
The table presents the UT intervals (in fractions of
an hour rounded off to 0.01 h) when DE?2 crossed the
morning and evening auroral zones (the region of
closed magnetic field lines, CFLs) and the polar cap
(open magnetic field lines, OFLs) of the Northern
Hemisphere for the considered 19 passes. The table
also indicates the corresponding hourly average values
of IMF By and Bz and the IMF variability (σ) taken
from the OMNI
web.gsfc.nasa.gov). One can see that the events pre?
sented in the table correspond to the periods when the
IMF y component was positive (i.e., IMF is directed
from morning to evening). We also analyzed seven
events corresponding to the periods when IMF By was
negative. Since the conclusions on the nature of small?
scale electric fields in the polar cap did not change sig?
nificantly in this case, we will subsequently present
only the results for the periods with IMF By > 0 (table).
database (http://omni?
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GEOMAGNETISM AND AERONOMY
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GOLOVCHANSKAYA, KOZELOV
300
0224
65.19
0814
69.55
73.7
834
108
200
100
0
–100
–200
–300
10
1
0.1
0.01
10
1
0.1
0.01
UT
IL
MLT
Lat
Lon
Alt
0227
74.26
0845
80.05
73.7
790
0230
82.70
1010
89.31
249.6
738
0236
75.93
1734
67.51
250.5
619
0239
65.63
1824
56.30
249.8
557
0233
*******
1443
78.57
251.2
681
106
104
102
100
108
106
104
102
100
Ion energy, keV
Electron energy, keV
Ex, mV/m
Particle flux, cm–2 sr–1 eV–1 s–1
Particle flux, cm–2 sr–1 eV–1 s–1
Fig. 1. (Top panel) The electric field component (Ex) along the DE?2 orbit, measured in Event 1 from table; (middle and lower
panels) the ε–t spectrograms of precipitating electrons and ions, respectively; gray scale shows differential particle fluxes. Vertical
dashed lines show the polar cap boundaries.
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PROPERTIES OF ELECTRIC TURBULENCE 579
3. COMPARATIVE ANALYSIS
OF THE ELECTRIC FIELD SCALING
CHARACTERISTICS IN THE AURORAL ZONE
AND POLAR CAP
3.1. Method of Logarithmic Diagrams
We first studied the scaling properties of electric
fluctuations using the wavelet analysis method pro?
posed by Abry et al. [2000]. As compared to the tradi?
tional spectral methods, the approach based on the
wavelet transform using Daubechies wavelets is most
preferential when self?similarity of data is sought and
quantitatively estimated since the wavelet transform
basis functions have not only the property of scale
invariance but also a compact carrier in contrast to the
Fourier transform basis functions. Precisely this prop?
erty of basis functions makes it possible to obtain
undistorted values of the scaling indices (α) [Abry
et al., 2000]. In addition, when wavelets of a certain
type (e.g., the Daubechies wavelets of a rather high
order) are used, this makes it possible to eliminate the
Events of turbulent electric fields in the auroral zone (CFLs) and polar cap (OFLs) according to the DE?2 data
No.
Year/day
CFLs, UT OFLs, UT
IMF
By, nT
IMF
Bz, nT
Bt sin(θ/2),
nT
IMF
σ, nT
δE
(s < 128 km)
mV m–1
δE
(s < 8 km)
mV m–1
1 81/316 02.38–02.45;
02.60–02.66
22.40–22.47;
22.64–22.68
22.56–22.67;
22.75–22.83
23.05–23.11;
23.23–23.28
10.24–10.31;
10.43–10.49
12.45–12.48;
12.68–12.80
20.60–20.67;
20.81–20.90
03.05–03.13;
03.28–03.40
17.15–17.22;
17.35–17.45
04.45–04.55;
04.65–04.75
06.05–06.14;
06.24–06.35
14.65–14.71;
14.97–15.00
13.05–13.12;
13.37–13.45
02.10–02.21;
02.40–02.50
02.70–02.73;
02.93–03.00
19.35–19.42;
19.54–19.65
06.05–06.10;
06.23–06.35
07.65–07.72;
07.85–07.95
04.65–04.73;
04.82–04.95
02.45–02.60 8.2 –8.811.18 6.97.632.00
2 81/327 22.48–22.631.8 –5.25.420.9 2.140.44
3 81/33722.68–22.75 3.2–2.23.43 2.90.810.11
4 81/340 23.14–23.213.9 –1.93.672.7 0.63 0.09
5 81/341 10.33–10.424.9–1.5 4.11 1.80.880.23
6 81/311 12.48–12.68 4.7–7.5 8.501.72.59 0.83
7 81/31120.67–20.81 4.6 –3.0 4.822.86.231.59
8 81/312 03.13–03.2811.1–6.611.22 4.9 7.352.18
9 81/325 17.22–17.356.8–3.5 6.522.93.78 0.97
10 81/32604.55–04.65 4.2–4.3 5.56 0.94.08 0.90
1181/326 06.14–06.243.9 –4.2 5.33 0.63.18 0.69
1281/28414.71–14.977.8 –9.0 11.152.0 8.932.62
1381/295 13.12–13.37 0.4 –15.115.13.4 6.842.08
1481/296 02.21–02.405.2–4.46.17 4.33.7 0.85
15 81/298 02.73–02.937.1 –4.67.432.74.230.62
16 81/30619.42–19.541.7–3.33.603.63.93 0.55
17 81/31106.10–06.235.2–5.46.95 3.94.10 1.11
18 81/32607.72–07.85 4.1–3.14.60 3.23.440.87
19 81/327 04.73–04.824.2–4.15.41 0.95.871.10
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GEOMAGNETISM AND AERONOMY
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GOLOVCHANSKAYA, KOZELOV
effect of polynomial trends on α values, if such trends
are present in data [Abry et al., 2000].
The proposed method is based on a discrete wavelet
transform, in which ever rougher signal approxima?
tions are successively studied since a progressively
larger number of “details” are eliminated from a sig?
nal. In this case, the selected wavelet scale (s) is as a
rule a multiple of two; i.e., s = Δ ⋅ 2j (here, Δ is the ini?
tial data resolution scale, and j = 0, 1, 2, … is called the
resolution level or octave). At each step, a discrete
wavelet decomposition gives two groups of coeffi?
cients: approximating coefficients a(j, k), describing a
rough signal approximation, and detail coefficients
d(j, k), describing “details” (k is the current index of a
wavelet translation along the data series at a specified
resolution level). According to the Abry et al. [2000]
method, the variance of the wavelet detail coefficients
Kj
∑
μj =
(where Kj is the number of wavelet
detail coefficients at specified j) is calculated for each
octave j. Scaling index α is determined from the slope
of the regression dependence on j yj = log2μj (the so?
called logarithmic diagram, LD), which is constructed
taking into account confidence intervals of μj esti?
mates in the region j where this dependence is linear. If
data are self?similar, the α values are in the range (1, 3)
[Abry et al., 2000]. Vörös et al. [2004] and Golovchan?
skaya et al. [2008] used the described method in order
to study magnetic turbulence in the magnetospheric
plasma sheet and the properties of auroral fluctuation
self?similarity during a substorm, respectively.
A new element of this work consists in that the
bootstrap procedure was used to calculate confidence
intervals of μj and α values [Efron, 1982; Sabatini,
1999; Wendt et al., 2007]. Actually observed distribu?
1
Kj
? ? ? ?
d2j k
, (
1
)
k
=
tions (different from Gaussian distributions in the case
of intermittent turbulence) of the wavelet transform
coefficients of studied electric fields are used accord?
ing to this procedure. In a standard Abry algorithm
[http://www.cubinlab.ee.unimelb.edu.au/~darryl/],
these intervals are calculated in a far?from?reality
assumption of Gaussian distributions.
Figure 2 presents the logarithmic diagrams con?
structed for electric fields in event 1 from the table in
the auroral zone (Fig. 2a) and in the polar cap
(Fig. 2b). One can see that the character of the loga?
rithmic diagrams is evidently similar in these two
regions. In the auroral zone and polar cap, the yj values
vary according to the power law depending on the
scale; in this case, the scaling index values obtained
from the LD slope (α = 2.08 and 2.19 for s < 32 km)
are indiscernible within the accuracy. Insignificant
statistics do not make it possible to estimate the α
index on large scales for an isolated pass; nevertheless,
the LD slope on scales of s > 32 km tends to decrease
in both regions (Figs. 2a, 2b). If we collect the data for
all events in one set and construct LD for this data set,
the LD slope in the region of large scales (s > 32 km) is
close to 5/3.
The logarithmic diagrams constructed for electric
fields on open and closed magnetic field lines were also
similar in other events presented in the table. Statisti?
cally significant differences in the scaling exponents
characterizing electric fields in the auroral zone and
polar cap were not found.
The change in the LD slope on a scale of s0 ~ 32 km
(on scales of 32 < s0 < 64 km for other events) is appar?
ently caused by the transition from a quasistatic turbu?
lent structure, which is transferred from the magneto?
sphere on large scales [Mozer and Serlin, 1969;
Mozer, 1971], to a turbulent structure related to
−10
2
yj
Octave j
8
Scale, km
5
846
−5
0
2 32 128
(а)
α
2.080.28
–
+0.19
=
−10
2
yj
Octave j
8
Scale, km
5
846
−5
0
2 32128
(b)
α
2.190.29
–
+0.10
=
Fig. 2. The logarithmic diagrams constructed according to the Abry et al. [2000] method completed with the bootstrap procedures
for the electric fields observed in event 1 from table on (a) closed and (b) open magnetic field lines. The Daubechies wavelets of
the fifth order were used. Vertical lines show the 95% confidence intervals calculated using the bootstrap procedure for octaves (j)
of 1–6 and on the assumption of Gaussian statistics for j > 6.
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GEOMAGNETISM AND AERONOMY Vol. 50 No. 5 2010
PROPERTIES OF ELECTRIC TURBULENCE 581
Alfvén waves [Dubinin et al., 1988; Volokitin and
Dubinin, 1989; Pokhotelov et al., 2003]. Knudsen
et al. [1990] discussed the transition from the electro?
static mode to wave mode on scales (s0) close to those
obtained in the present work.
3.2. The Method of Normalized Probability Density
Function of Electric Fluctuations
Electric field scaling properties can also be studied
by analyzing the probability density functions P(δE, s)
and field fluctuation amplitudes δE = E(x + s) – E(x)
on different scales s. When fluctuations are statistically
self?similar in a certain scale range (or in the cases
close to self?similarity), it is possible to renormalize
the probability density functions P(δE, s) to a single
curve independent of scale. This property is known as
collapse of normalized probability density functions
on one curve [Hnat et al., 2005]. In the case of self?
similarity, the rms deviation of electric field values σ
(as well as other distribution moments) depends on
scale according to the power law (σ ~ sγ), where γ is the
scaling exponent; therefore, normalized probability
density functions are obtained from the Ps(δE/σ) =
σP(δE, s) relationship. (Here, we do not discuss finer
and subtler (when actual data are analyzed) effects
related to a deviation from an exact self?similarity
owing to multifractality.)
Figure 3 shows the normalized distribution func?
tions of field fluctuations on four scales from the 0.5–
32 km range. According to the Figs. 3a, 3b, collapse on
one curve of the normalized distribution functions of
electric fluctuations takes place in the auroral zone
and polar cap. In this case, the scaling exponents γ,
which were obtained from the slope of the logσ–logs
regression curves, are close for fluctuations in the
auroral zone (γ = 0.53) and polar cap (γ = 0.56). As it
was for scaling indices α, we did not find statistically
significant differences in scaling exponents γ for elec?
tric fluctuations in the auroral zone and polar cap.
This makes it possible to assume that the physical
mechanisms by which turbulent fields are generated in
these two high?latitude regions are of common nature.
4. RELATIONSHIP BETWEEN ELECTRIC
FIELDS IN THE POLAR CAP AND IMF
An analysis of the small?scale electric field distri?
bution in the region of closed magnetic field lines at
different IMF values and variability indicated that
these fields as a rule predominate on the polar cap
flanks and have smaller amplitudes at the polar cap
center. Moreover, the position of the region with most
intense fields systematically depends on IMF By: tur?
bulent fields are mostly generated on the polar cap
morning (Fig. 1) and evening (Fig. 4) flanks when
IMF By > 0 and <0, respectively. These specific fea?
tures contradict the Abel et al. [2006] concept that tur?
bulent electric fields in the polar cap are controlled by
the solar wind variability.
We assumed that plasma turbulization in the polar
cap (as well as in the auroral zone) is caused by con?
vection velocity shears related to large?scale field?
aligned currents (Region 0 currents) on open mag?
netic field lines. The relation between a convection
velocity shear (at the DE?2 altitudes, the frozen?in
condition is satisfied for electrons and ions) and the
field?aligned current follows from the equation
(1)
Since B = (0, 0, B0z), magnetic field lines are equipo?
tential (∂/∂z = 0) and ∇ ⋅ B ≡ 0 for the polar cap region,
the first three terms on the right?hand side of (1) are
zero, and the last term is proportional to the field?
aligned current if the ionospheric conductivity is uni?
form.
The fact that the LD slope is about 5/3 on large
scales, which can be explained by direct or inverse
rotv
E ∇⋅(
rot E
)B
B
×[]∼
= B ∇(⋅)EE ∇ B
(⋅)
B ∇ E
(⋅).
–++
–10
σP(dX)
dX/σ
100
10 –505
10−1
10−2
10−3
(а)
Scale, km
0.5
1.9
5.6
15
–10
σP(dX)
dX/σ
100
10 –505
10−1
10−2
10−3
(b)
Scale, km
0.5
1.9
5.6
15
Fig. 3. Collapse of the normalized probability density functions of electric field fluctuations on scales of 0.5, 1.9, 5.6, and 15 km
observed on DE?2 on (a) closed and (b) open magnetic field lines in event 1 from table.
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GOLOVCHANSKAYA, KOZELOV
energy cascade in the wavenumber space [Kolmog?
orov, 1941; Kraichnan, 1967; Frisch, 1995], also indi?
cates that a velocity convection shear can cause plasma
turbulization in the considered region. In this context,
we should also mention the work by Earle and Kelley
[1993], who discuss the difficulties in explaining the
observed electric field spectra in the auroral zone by
locally developing ionospheric instabilities and pro?
pose to consider convection velocity shears of mag?
netospheric origin as a cause of plasma turbulization.
The theory of Region 0 field?aligned currents, by
which we generally mean all field?aligned currents
flowing poleward of the Region 1 field?aligned cur?
rents, is far from complete (the physical mechanisms
by which these currents are generated were discussed
in [Potemra, 1994; Watanabe et al., 1996; Watanabe,
2000; Belenkaya, 2002]). However, it is generally
accepted that the intensity and spatial distribution of
the Region 0 currents on the dayside are controlled by
the reconnection process on the dayside magneto?
pause (note that most DE?2 passes considered in the
present work are shifted onto the dayside relative to the
0600–1800 MLT meridian as, e.g., in the cases illus?
trated in Figs. 1 and 4). If small?scale electric fields on
open magnetic field lines are actually related to the
Region 0 currents, we can anticipate that the rms
amplitudes of these fields will depend on the IMF Bz
value and on the solar wind transfer function (
+
)1/2sin(θ/2), where θ is the angle between the geo?
magnetic field and IMF, θ = π –
[Gonzalez and Mozer, 1974].
Figure 5 presents the correlation dependences of
the rms amplitudes of electric fields on the polar cap
By
2
Bz
2
By/ Bz
()
arctan
morning flank at scales of <128 km (δE128, Fig. 5a) and
<8 km (δE8, Fig. 5b) on IMF Bz for 19 events from the
table. The correlation coefficients (r = –0.64 and
⎯0.73) are rather high. The correlation between δE128
(δE8) and the solar wind transfer function is even more
pronounced (r = 0.73 and 0.82; Figs 6a, 6b, respec?
tively). At the same time, Fig. 7 indicates that the cor?
relation between these parameters and the IMF vari?
ability (σ) is almost absent.
5. DISCUSSION
Many works indicated that small?scale spatial and
temporal disturbances in the magnetosphere–iono?
sphere system are turbulent [Kintner, 1976; Kintner
and Seyler, 1985; Antonova and Ovchinnikov, 1999;
Borovsky and Funsten, 2003; Chang et al., 2004;
Vörös et al., 2004]. However, most previous works
studied the development of turbulence in the region of
closed magnetic field lines.
The problem of turbulent properties of electric
field spatial fluctuations and, consequently, convec?
tion velocities on open magnetic field lines was for the
first time posed in [Abel et al., 2006, 2007]. Heppner
et al. [1993] demonstrated that the electric field spec?
tra at the polar cap latitudes are power law; however,
these researchers did not accurately identify the polar
cap itself.
As was mentioned above, Abel et al. [2006, 2007]
indicated that the spatial structure function of the first
order in the range of scales from 45 to ~1000 km for
velocity fluctuations in the auroral zone and polar cap
has a power law shape, using the convection velocity
fluctuations measured with the SuperDARN Halley
radar over several years. On the basis of a minor (in our
opinion) difference in the scaling exponents estimated
for fluctuations on open and closed magnetic field
lines (in this case, the error range was not indicated for
the obtained values), these researchers assumed that
the nature of turbulent fluctuations in these two
regions is substantially different: structured fields
reflect the structure of a turbulent solar wind in the
polar cap and result from internal magnetospheric
processes, leading to turbulization, in the auroral
zone. The role of turbulence in the magnetosheath
(see, e.g., [Rossolenko et al., 2008]) in the transfer of
the electric field turbulent structure from the solar
wind into the polar cap was not considered by Abel et
al. [2006, 2007].
Note that several works that previously studied the
turbulent properties of convection velocities in the
polar cap considered substantially larger (than in our
study) scales of temporal and spatial fluctuations. An
analysis performed in [Stepanova et al., 2003] is based
on using 1?min values of the PC index, and the results
of that study correspond to time scales of several tens
of minutes. The spatial resolution of the radar data
used in [Abel et al., 2006, 2007] was 45 km. Therefore,
−150
UT 0130
64.28
0634 MLT
Ex, mV m–1
150
0145
58.37
1700
0142
70.03
1557
0136
83.37
0933
0133
74.77
0719
0139
80.48
1403
IL
100
50
0
−50
−100
Fig. 4. An example of the characteristic distribution of tur?
bulent electric fields over the polar cap region in the case of
IMF By < 0. Event 1982, day 340, IMF By = –4.6 nT, IMF
Bz = –3.2 nT, and IMF σ = 1.4 nT.
Page 8
GEOMAGNETISM AND AERONOMY Vol. 50 No. 5 2010
PROPERTIES OF ELECTRIC TURBULENCE 583
the scaling characteristics of convection velocity fluc?
tuations in the polar cap determined by these
researchers correspond to scales varying from several
hundred kilometers to 1000 km. Our results, achieved
using the DE?2 data with a resolution of 1/16 s
(~500 m), correspond to scales from 1 km to several
tens of km. The difference in the scale ranges consid?
ered by different researchers makes it difficult to
directly compare results.
A study performed in the present work indicates
that statistically significant differences in the proper?
ties of turbulent electric fields in the auroral zone and
polar cap are absent, which may suggest that the tur?
bulization mechanism is common and is related to
convection velocity shears in the regions of large?scale
field?aligned currents on closed and open magnetic
field lines (see also [Golovchanskaya et al., 2006]).
The assumption that electric turbulence in the
polar cap develops in the region of field?aligned cur?
rents on open magnetic field lines agrees with the DE?
2 measurements of magnetic fields in the events con?
sidered here. Figure 8 presents the electric component
(Ex) along the satellite orbit and the transverse mag?
netic field component with respect to the DE?2 orbit
(By) measured in event 1 from the table. A dotted line
shows the variation in the large?scale magnetic com?
ponent obtained by smoothing magnetic measure?
ments on a scale of 512 km. The observed correlation
between Ex and By (the correlation coefficient is r =
0.8) makes it possible to roughly consider that the sat?
ellite crosses zonally stretched field?aligned current
sheets (see, e.g., [Sugiura et al., 1982]) and to estimate
the field?aligned current density (j||) as , where
μ0 = 4π × 10–7 H m–1. Figure 8 indicates that < 0
on the polar cap morning flank, which corresponds to
the field?aligned current flowing out of the iono?
sphere. Although the current is maximal near the
boundary between the polar cap and the morning
auroral zone, j|| does not immediately vanish toward
the polar cap center and is observed as a weak current
(with a density of ~7 × 10–8 A m–2) distributed over a
distance of >1000 km on OFLs. When DE?2
approaches the boundary between the polar cap and
1
??? ?∂By
?????? ?
μ0
∂x
∂By
∂x
?????? ?
0−15
δE128, mV m–1
12
IMF Bz, nT
0
−5
−10
10
8
6
4
2
(а)
r = –0.64
0−15
δE8, mV m–1
3.0
IMF Bz, nT
0
−5
−10
2.5
2.0
1.5
1.0
0.5
(b)
r = –0.73
Fig. 5. Correlation between the electric field rms amplitudes on the polar cap morning flank on scales of (a) <128 and (b) < 8 km
with IMF Bz for 19 events from table.
0
δE128, mV m–1
12
Btsin(θ/2), nT
15105
10
8
6
4
2
(а)
r = 0.73
0
δE8, mV m–1
3
Btsin(θ/2), nT
15 105
(b)
r = 0.82
2
1
Fig. 6. The correlation between the electric field rms amplitudes and the solar wind transfer function.
Page 9
584
GEOMAGNETISM AND AERONOMY
Vol. 50 No. 5 2010
GOLOVCHANSKAYA, KOZELOV
the evening auroral zone, it registers > 0, which
corresponds to the inflowing field?aligned current in
this region. The observed values and features of the j||
distribution (specifically, the predominance of this
current on the polar cap morning flank under IMF
By> 0) are consistent with those for the Region 0 cur?
rents [Belenkaya, 2002]. It is easy to indicate that the
outflowing field?aligned current, which has a density
of ~7 × 10–8 A m–2 and is distributed over the polar cap,
can be maintained by the fluxes of precipitating elec?
trons (~105–106 cm–2 sr–1 eV–1 s–1) supposedly of
∂By
∂x
?????? ?
mantle origin, which can be visually distinguished on
the electron spectrogram shown in Fig. 1 (the middle
panel, energies of <100 eV, 0227–0231 UT).
When simultaneous measurements of the electric
(Ex) and magnetic (By) components were available (as
in the case illustrated in Fig. 8), it was possible to esti?
mate the Poynting flux related to turbulent fields in the
polar cap. The inset in Fig. 8 shows the flux values cal?
culated using the formula δP = δEx × δBy, where turbu?
lent fields δEx and δBy were obtained by filtering the
initial data and correspond to scales of <128 km. The
δP values are positive if the Poynting vector is directed
0
δE128, mV m–1
12
IMF σ, nT
842
10
8
6
4
2
(а)
r = 0.37
0
δE8, mV m–1
3
σ sin(θ/2), nT
862
(b)
r = 0.39
2
1
64
Fig. 7. The correlation between the electric field rms amplitudes and the IMF variability.
−1000
UT
IL
MLT
0224
65.19
0814
Ex, mV m–1, By, nT
500
0239
65.63
1824
0
−500
0236
75.93
1734
0233
*****
1443
0230
82.70
1010
0227
74.26
0845
Ex
By
0.4
0.2
0
δP, mW m–2
Fig. 8. The magnetic field transverse component (By) with respect to the DE?2 orbit measured in event 1 from table. The corre?
lation coefficient (r) with the electric component (Ex) is 0.8. The model (IGRF) geomagnetic field was subtracted from the mag?
netic data. Dots show the large?scale magnetic component By obtained by smoothing magnetic measurements on a scale of
512 km. The inset shows the Poynting flux values (δP = δEx × δBy), related to turbulent electric and magnetic fields in the polar
cap on scales of <128 km. Positive δP values correspond to the Poynting vector direction from the magnetosphere into the iono?
sphere.
Page 10
GEOMAGNETISM AND AERONOMY Vol. 50 No. 5 2010
PROPERTIES OF ELECTRIC TURBULENCE 585
from the magnetosphere into the ionosphere. The δP
values presented in Fig. 8 indicate that the electromag?
netic power of turbulent fluctuations in the region of
open magnetic field lines is approximately a factor of
4–5 lower than the threshold power necessary for gen?
eration of optical aurora (~1 mW m–2).
The character of the electric field distributions
shown in Fig. 1 (the upper panel) and Fig. 4 makes it
possible to assume that the turbulence level depends
not only on the electric field non?uniformity, which is
proportional to the convection velocity shear accord?
ing to (1), but also on the value of the large?scale elec?
tric field (E) in the polar cap. However, this assump?
tion is not confirmed by the consideration of other
numerous DE?2 passes through the polar cap, when
rather large (~30–40 mV m–1) but uniform electric
fields were not accompanied by the development of
turbulence. An example of such a case is presented in
Fig. 9, which indicates that fluctuations are absent in
the polar cap central region (crossed by the satellite at
0405–0409 UT), where the electric field is compara?
tively large (~40 mV m–1) but uniform. Fluctuations
are observed only on the polar cap flanks, where E
becomes substantially inhomogeneous.
We now consider in more detail the restrictions of
the performed analysis.
Table indicates that the studied events were charac?
terized by rather large IMF By and Bz magnitudes. In
this case, the Region 0 currents on the dayside lie on
open magnetic field lines [Watanabe et al., 1996]. In
the cases of small IMF values (|By| < 1.5 nT, |Bz| <
0.5 nT), which were not analyzed, the zone 0 currents
close in the low?latitude boundary layer [Watanabe,
2000]. Using the hourly average OMNI database, we
checked that the |By| < 1.5 nT and |Bz| < 0.5 nT condi?
tions are realized only in approximately 5% of cases;
i.e., the events considered by us are more typical.
The uncertainty can be caused by the fact that we
analyzed the hourly average IMF values and variabil?
ity (σ), which can differ from these quantities during
the periods when DE?2 passed over the polar cap
region (5–10 min). Only the IMP?8 satellite per?
formed both magnetic and plasma measurements in
the solar wind and delivered data to the OMNI data?
base during the DE?2 mission (August 1981–Febru?
ary 1983). Unfortunately, a rather complex proce?
dure of shifting 1?min IMP?8 data in time toward the
bow shock, according to which three solar wind
velocity components should be continuously mea?
sured in rather long time intervals, resulted in
numerous gaps in data shifted toward the bow shock
[http://omniweb.gsfc.nasa.gov/form/sc_merge_min1.
html]. As a result, conjugate 1?min data of measure?
ments in the solar wind, shifted toward the bow shock,
were absent for most DE?2 passes.
As was shown in Section 2, we determined the
boundary between open and closed magnetic field
lines on the basis of visual examination of the spectro?
grams of precipitating particles with auroral energies,
which could result in the boundary localization error.
Assuming that the error of such a method for deter?
mining the boundary is not more than ±200 km rela?
tive to its true position, we repeated an analysis
described in Sections 3 and 4, having shifted the polar
cap boundary by 200 km northward and the high?lati?
tude boundary of the auroral zone by 200 km equator?
ward relative to the positions of these boundaries pre?
sented in the table, and ascertained that the electric
field scaling characteristics on open and closed mag?
netic field lines changed no more than within the
errors presented above.
6. CONCLUSIONS
(1) Using the methods of wavelet and statistical
analyses, we indicated that electric fields exhibit scal?
ing properties on scales of 0.5–256 km in the polar cap
ionosphere.
(2) The scaling characteristics are close for electric
fields in the polar cap and auroral zone.
(3) The rms amplitudes of electric fields in the
polar cap distinctly correlate with IMF Bz and with the
solar wind transfer function and weakly correlate with
the IMF variability.
(4) The possible mechanism by which turbulent
electric fields are generated in the polar cap can be
related to convection velocity shears on open magnetic
field lines in the areas of Region 0 field?aligned cur?
rents.
ACKNOWLEDGMENTS
We are grateful to A.S. Volokitin for a fruitful dis?
cussion.
−200
UT 0403
73.83 IL
MLT
Ex, mV m–1
200
0417
51.07
1843
0415
62.10
1818
0409
81.35
1514
0406
81.76
1130
1412
72.62
1725 0936
100
0
−100
Fig. 9. An example of the absence of turbulent electric
fields in the polar cap central region in the case of homo?
geneous large?scale convection. Event 1981, day 316, IMF
By = –9.3 nT, IMF Bz = –8.2 nT, and IMF σ = 5.2 nT.
Page 11
586
GEOMAGNETISM AND AERONOMY
Vol. 50 No. 5 2010
GOLOVCHANSKAYA, KOZELOV
This work was supported by the Presidium of the
Russian Academy of Sciences (Program 16) and by the
Department of Physical Sciences of the Russian
Academy of Sciences (Program 6.15).
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