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ISSN 1990-7931, Russian Journal of Physical Chemistry B, 2018, Vol. 12, No. 3, pp. 522–526. © Pleiades Publishing, Ltd., 2018.
Original Russian Text © D.V. Chugunin, M.V. Klimenko, V.V. Klimenko, 2018, published in Khimicheskaya Fizika, 2018, Vol. 37, No. 5, pp. 34–36.
Characteristics of Polar Wind Flows at Altitudes of about 20000 km
D. V. Chugunina, *, M. V. Klimenkob, c, an d V. V. K li me nk ob
aSpace Research Institute, the Russian Academy of Sciences, Moscow, 117997 Russia
bPushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation,
West Branch, Russian Academy of Sciences, Kaliningrad, 236010 Russia
cImmanuel Kant Baltic Federal University, Russian Academy of Sciences, Kaliningrad, 236041 Russia
*e-mail: dimokch@iki.rssi.ru
Received November 3, 2017
Abstract⎯The problem of the outflow of ionospheric plasma into the magnetosphere is considered. In par-
ticular, the phenomenon of the polar wind observed in the polar cap is studied. The study of this phenomenon
is complicated by the fact that the field-alined velocities of individual ions are small, and therefore, the elec-
tric field of the positively charged satellite prevents their measurement. This paper examines the measure-
ments carried out on the Interball-2 satellite at altitudes of ~20000 km and compares them with the results of
simulations within the framework of the GSM TIP model. It has been demonstrated the GSM TIP model
well describes the outflow of H+ ions from the ionosphere to the magnetosphere in the polar cap.
Keywords: ionosphere, magnetosphere, polar wind, numerical model, satellite observations
DOI: 10.1134/S1990793118030077
INTRODUCTION
The ionosphere is an important source of plasma
for the Earth’s magnetosphere. Plasma of ionospheric
origin can constitute a significant and even a larger
part of the magnetospheric plasma [1]. This fact shows
how important it is to know the mechanisms of the
transfer of ionospheric plasma into the magnetosphere
and to have models capable of describing this process.
One of the first mechanisms of the outflow of iono-
spheric plasma suggested the transport of low-energy
H+ and He+ ions and electrons in the static electric
field created by ambipolar diffusion due to the separa-
tion of ions and electrons, which was called the polar
wind, by analogy with the solar wind [2, 3]. The source
of the polar wind is exclusively the pressure of the ion-
ospheric plasma, which pushes electrons and ions into
“empty” magnetic force tubes in the polar cap region.
As for heavier ions, such as O+ and others, the species
that make up the core of their distribution function,
remain in the ionosphere, so only ions from the tail of
the distribution function or ions heated or accelerated
by existing additional energy sources can overcome the
gravity barrier.
The detection of energetic ions of ionospheric ori-
gin by satellites prompted researchers to study the ion-
osphere as a source of magnetospheric plasma. The
ISEE satellite was used to measure the characteristics
of ions, but the presence of a low geometric factor and
the positive potential of the satellite prevented mea-
surements of polar wind flows. Note that one of the
main obstacles to studying the polar wind is the posi-
tive potential that an illuminated spacecraft acquires
in a rarefied plasma. This potential, several volts, is
comparable or even greater than the energy of the ions
in the polar wind, so that they cannot reach the detec-
tor. The DE-1 and DE-2 satellites, intended for study-
ing the ionosphere−magnetosphere coupling, were
able to measure the characteristics of the upward flow
of ions with energies from several electronvolts [4] to
several kilo-electronvolts [5–8]. However, it has been
shown that the flows of charged particles of the polar
wind mix with the flows of ions from the cusp, which
are convected into the polar cap (cleft ion fountain);
therefore, to study the polar wind, it is necessary to
learn how to separate these flows. Based on the mea-
surements of DE satellites, the authors of [9] showed
that the flows of ionospheric plasma are sufficient to
fill the main regions of the magnetosphere. Subse-
quently, various models of the polar wind and the
acceleration of charged particles in it have been pro-
posed, in particular, as a result of the action of centrif-
ugal force on strongly curved segments of magnetic
lines of force [10, 11]. The Polar satellite was equipped
with a TIDE instrument, capable of measuring the
composition and energy of low-energy ions [12]. The
satellite was also equipped with a device for neutraliz-
ing its positive potential. By lowering the satellite
potential, it became possible to detect ion flows with
energies below 10 eV [13, 14]. However, due to the
influence on the other instruments, this mode was
used very rarely. A large number of measurements of
CHEMICAL PHYSICS
OF ATMOSPHERIC PHENOMENA
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 12 No. 3 2018
CHARACTERISTICS OF POLAR WIND FLOWS 523
ion flows in the polar cap were performed with an
SMS device installed on the Akebono satellite. These
measurements showed the presence of a large concen-
tration of O+ ions, a finding poorly consistent with the
existing models of the polar wind. As in the previous
studies, mixed flows of polar wind particles and ion
flows from the cusp/cleft, carried to the polar cap by
the magnetospheric convection field, were most likely
measured [15–19]. The satellites of the CLUSTER
mission were equipped with a CODIF mass spec-
trometer, which measured ions in the energy range of
40 eV–40 keV. An analysis of the data obtained using
this instrument revealed low-energy ion flows above
the polar cap [20–25]. However, it should be noted
again that a lower energy threshold of this instrument
makes it difficult to measure the polar wind if it is not
accelerated by additional mechanisms. The authors
[26] even used the concept of a “generalized” polar
wind, a combination of ion flows in the polar cap
regardless of the physical mechanisms of their forma-
tion. To explain the presence of these flows in the
polar cap, the authors introduced mechanisms of
additional heating.
Most of the published characteristics of the f lows
of polar-wind ions are the result of averaging the mea-
surements in the polar capillary at various altitudes
and geomagnetic activity levels. Moreover, the polar
cap typically means the entire region between the pole
and a chosen invariant latitude. In [27], the polar cap
boundary was set at 77°, whereas in [28], it was posi-
tioned at 70°. However, as mentioned above, in the
polar cap at high altitudes, there can be several types of
ionospheric ion outflows, with only one of them being
associated with the mechanism of the formation of the
polar wind. All existing flows at high altitudes in the
polar cap can be caused by the following reasons:
(1) The outflow of ions in the region of auroral
fields and currents (mainly in the auroral oval), where
the main fraction of the energy of superthermal ions is
transformed from field-alined currents of magneto-
spheric origin.
(2) “The cleft ion fountain,” where the direct pen-
etration of energetic particles from the magnetosheath
is observed, which leads to the formation of intense
conic beams (conics) heated in the transverse velocity
component due to the wave–particle interaction.
Energetic ions from the “ion fountain” are transferred
to the polar cap as a result of large-scale magneto-
spheric convection.
(3) As in [1, 2], the polar wind is meant to be the
outflow of thermal ions from the ionosphere along
open force tubes in the polar cap at the expense of the
thermal energy of ionospheric ions and electrons (i.e.,
without taking into account the effects of field-alined
currents and particle precipitation). Exceptions may
be photoelectrons, electrons, and ions of the polar rain
if it occurs at a given time in the area under consider-
ation.
In order to somehow reduce possible uncertainties
in the interpretation of measurement data in an analy-
sis of low-energy ions on the Interball-2 [29] and
IMAGE satellites [30], an attempt was made to more
accurately define the polar cap region. In [29], based
on measurements of energetic particles, periods were
identified that satisfied the condition of the least heat-
ing of the ionosphere by energetic particles at the base
of the plasma tube. In [30], the model of the polar cap
boundary was chosen based on the Kp index, and all
the measurements that fell inside this boundary were
selected. This was done because of the fact that the
IMAGE satellite was not equipped with instruments
for measuring energetic charged particles. The use of
such an averaged boundary of the polar cap, however,
does not eliminate the possibility that the result
includes contributions from the aforementioned dif-
ferent ion flows.
From the above, it can be concluded that the
authors of [29] carried out the most thorough selec-
tion of measurements, which met the criteria for the
region in which flows of polar-wind particles can be
observed. Unfortunately, the INTERBALL-2 satel-
lite, the measurements from which are used in this
work, did not reach the invariant latitudes greater than
81°. According to [29], it turned out that the selected
measurement sites on which the presence of the polar
wind is possible are on the night side of the polar cap
and nearly coincide with the ion depletion zone [31].
In this region, the sensitivity of the SMS instrument
on the Akebono satellite turned out to be too low to
determine the characteristics of the flows of thermal
ionospheric ions, that is, the contributions from the
flows in this region were almost not included in the
statistics of these measurements.
The ion flows measured by the Interball-2 satellite
within selected sections of the orbits were divided into
types that differ significantly from each other. Four of
them can be qualified as f lows of particles of the polar
wind:
(1) sufficiently intense flows of cold (thermal) H+
ions, with O+ ions not reaching the detector (desig-
nated as “H”);
(2) the same f lows of thermal H+ ions, with O+ ion
flows also detected (denoted as “Ho”);
(3) weak flows of H+ ions in the absence of O+ ions
(denoted as “h”);
(4) the indicated ions do not reach the detector,
that is, the positive potential of the satellite and a weak
intensity of the flows does not allow them to be mea-
sured (denoted as “na”).
The authors of [29] demonstrated that, in the sum-
mertime, only flows of types “H” and “Ho” are pres-
ent, whereas in the wintertime, “h” and “na” are
observed. This is indicative of an obvious dependence
of the intensity of the polar wind on the illumination
524
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 12 No. 3 2018
CHUGUNIN et al.
of the ionosphere. It was also suggested that the O+
flows depend on the presence of polar rain.
In the present paper, we compare the data of mea-
surements performed using the Hyperboloid energy-
angular mass spectrometer [32] installed onboard the
Interball-2 satellite (Auroral probe) with the results of
calculations of the characteristics of the the polar wind
within the framework of the GSM TIP model [33, 34].
CHARACTERISTICS OF IONS
IN THE POLAR CAP
The Hyperboloid mass-spectrometer made it pos-
sible to measure the three-dimensional distribution of
H+, He+, O++, and O+ ions in the energy range ~1−80 eV
(it is obvious that the lower energy threshold below
which measurement data should not be considered is
determined by the satellite potential, typically less
than +8 V). The total three-dimensional distribution
function was measured during the period of rotation of
the satellite, which was 2 min. Most of the measure-
ments in the polar cap were carried out at the altitude
of the apogee of the satellite, ~20000 km. In addition,
it should be noted that the measurement data consid-
ered in our work were obtained in 1996−1997, that is,
in the period of minimum solar activity.
For each 2-min measurement, the moments of the
distribution function were calculated (n is the concen-
tration, V|| is the parallel velocity, T⊥ and T|| are the
transverse and parallel temperatures, respectively)
with consideration given to the possible potential of
the satellite. Unfortunately, the inverse problem of
reconstructing from measurements the real distribu-
tion function of ions passing through the electric field
that surrounds the satellite in plasma for the real con-
figuration of the satellite has not yet been solved. Nev-
ertheless, an algorithm was developed for calculating
the moments of the ion distribution function from the
Hyperboloid mass spectrometer data, which yielded
satisfactory results for sufficiently intense flows. The
balance of the currents on the surface of a metallized
satellite at high altitudes depends on the density of the
surrounding plasma and the potential of the satellite
with respect to this plasma. In the first stage, it was
assumed that the satellite has a certain potential, and
based on its value, the plasma density was calculated
from the moments of the ion distribution function
measured by the Hyperboloid mass spectrometer. The
computed density and the satellite potential were sub-
stituted into the balance equation for the currents. If
the equation could not be solved in the first attempt,
which usually was the case, then the iteration method
was applied to determine the potential at which the
calculated density would correspond to the balance
equation for the currents. The obtained potential was
subsequently used to calculate the parallel velocity and
temperatures of the ions. To verify how accurately this
method determines the moments of the distribution
function, the results obtained by this method were
compared to those determined from concurrent wave
measurements. The values of the density of the sur-
rounding plasma obtained from the mass spectrometer
measurements and those calculated from the low-
hybrid resonance frequency were close to each other.
It is worth noting that low-energy measurements
sometimes showed a background, most likely associ-
ated with the passage of a part of the ion distribution
function through a complex configuration of the elec-
tric field around the satellite, and therefore, not
describing the actual situation for a given energy and
angle. At very weak flows, this background became
comparable with the useful signal and, therefore,
introduced a large error in the obtained moments of
the distribution function, so that, under these condi-
tions, it was not always possible to obtain reliable
results. Such measurements were, if possible, dis-
carded and were not included into the analysis. As a
result, more than 300 values of the parallel velocity of
O+ and He+ ions and more than 700 values of all the
moments of the distribution function for H+ ions were
obtained.
Statistical distributions of the characteristics of the
polar wind obtained by processing the Hyperboloid
measurements were presented in detail in [35]. Table 1
lists the mean values of n, V||, T⊥, and T|| for the H+,
He+, and O+ ions.
The authors of [35] noted a peak in the distribution
of the velocities of O+ ions near 3 km/s. This suggests
that, because of the positive potential of the satellite,
particles with lower velocities did not reach the detec-
tor. Thus, even in the summertime, when the flows of
O+ ions are much larger than the wintertime flux, it is
still impossible to reliably determine the characteris-
tics of the O+ ion f lows in the polar wind without
decreasing the satellite potential relative to the sur-
rounding plasma. This once again emphasizes that, in
the previous experiments and studies, averaged flows
of oxygen ions in the polar cap were considered and
that it is practically impossible to identify them exactly
as polar wind flows rather than flows from the cleft ion
fountain. As a result, in many studies, the parallel
velocities and temperatures of O+ ions turned out to be
much larger than the simulation results.
The temperatures of the H+ ions are measured
most accurately. For flows of type H, the maximum of
the parallel temperature is located at 3500 K, whereas
the maximum of the transverse temperature is posi-
tioned at 2000 K. As expected, at high altitudes, where
no heating across the magnetic field occurs, T⊥< T||
because of the conservation of the first adiabatic
invariant. The T||/T⊥ ratio is generally greater than 1,
but there are cases where this ratio is smaller than 1.
There were also measurements in which T⊥ was 1000 K
or even lower. The temperature of beams of Ho type is
greater than the temperature of H type beams. The
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 12 No. 3 2018
CHARACTERISTICS OF POLAR WIND FLOWS 525
maxima of the distribution function of Ho type beams
were located at T|| ∼ 6500 K, T⊥ ∼ 5500 K, with the
ratio of these temperatures being close to 1. This
increase in the temperatures and the ratio thereof sug-
gests that there is a weak heating of the H+ ions below
the satellite, in contrast to the situation where the
flows belong to type H. The rate of outflow of H+ ions
is only slightly affected by this heating, since the ener-
gies of ions in the ionosphere are sufficient to over-
come the gravity barrier. All this serves as additional
evidence that the flows of types H and Ho are of dif-
ferent physical nature and that, at low altitudes in the
polar cap, ionospheric ions are often additionally
heated. Thus, it is obvious that the measured f lows of
O+ ions do not belong to the polar wind proper, but to
ionospheric ion flows experiencing additional heating
and/or acceleration at altitudes below the satellite’s
altitude (~20000 km). This suggests that the nature of
O+ ions in the polar wind remains poorly understood.
Similar to the Interball-2 satellite, measurements of
polar wind currents on other satellites (Akebono,
CLUSTER, POLAR, DE) faced significant difficul-
ties, so that the characteristics of the O+ ion flows do
not refer to the polar wind proper.
In the present study, to compare measurement
results with theoretical predictions, we used the GSM
TIP, which yields the distribution of the parameters of
the thermosphere–ionosphere–protonosphere sys-
tem for quiet geomagnetic conditions in the summer-
time during the lowest solar activity at different
moments of the local time. The GSM TIP model
enables to calculate the global nonstationary three-
dimensional distributions of temperature, composi-
tion (O2, N2, O), and the components of the velocity
vector of the neutral gas, as well as the concentrations,
temperatures, and components of the velocity vectors
of atomic (O+, H+) and molecular ( , , NO+)
ions and electrons, along with a two-dimensional dis-
tribution of the electrical potential of ionospheric
(dynamo field) and magnetospheric origin. In the
GSM TIP model, the system of quasi-hydrodynamic
+
2
N
+
2
O
equations of continuity, motion, and heat balance of
the neutral and charged components of a multicom-
ponent gas mixture is numerically integrated, as well
as a three-dimensional equation describing the law of
conservation of the total current in the ionosphere.
The thermosphere parameters in the GSM TIP model
are calculated in a spherical geomagnetic coordinate
system for an altitude range of 80–526 km, whereas
the ionospheric parameters are described in a dipolar
coordinate system associated with the geomagnetic
field, which is approximated by a central dipole, with
consideration given to the mismatch between the geo-
graphic and geomagnetic axes over the altitude range
from 80 km to the geocentric distance, ~15 Earth
radii, at time steps of 1−2 min and spatial resolutions
in latitude and longitude of 5° and 15°, respectively.
All equations of the model are solved by the finite dif-
ference method.
Table 1 lists the results of calculations of the polar
wind flows within the framework of the GSM TIP
model for summertime conditions in the northern
hemisphere at a minimum of solar activity. The calcu-
lations were carried out until a steady periodic varia-
tion of the calculated parameters was established in
quiet geomagnetic conditions throughout the globe.
The obtained values of the calculated parameters for
an altitude of 20000 km are listed in Table 1. As can be
seen, the measured concentration and parallel velocity
of H+ ions are in good agreement with the model pre-
dictions. The temperature of the H+ ions measured by
the satellite coincides with the model predictions only
for the H type f low, while for the Ho type flow,
whereas the measured temperature turned out to be
twice the model-predicted temperature. This con-
firms once again the fact that the selection of mea-
surements that refer to the polar wind was carried out
correctly and that the model adequately describes not
only the thermosphere–ionosphere coupling, but also
well predicts the outflow of light ions from the iono-
sphere. Arising due to an additional heating at alti-
tudes below the satellite, Ho type f lows cannot be con-
sidered “classical” polar winds. This comparison is an
Table 1. Mean values of the parameters of ion flows in the polar wind measured by the Interball-2 satellite and the results
of simulations within the framework of the GSM TIP model
,
cm–3
,
km/s , K ,
cm–3
,
km/s , K ,
cm–3
,
km/s , K
Interball-2,
Summer 1997 0.5–2 21
Type Н
Т|| = 3500
Т⊥ = 2000 – 14 7500 0.1 5 10000
Type Но
Т|| = 6500
Т⊥ = 5500
GSM TIP model 0.5 15–25 3200 – – – 0.05 – –
+
H
n
+
H
V
+
H
T
+
He
n
+
He
V
+
He
T
+
O
n
+
O
V
+
O
T
526
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 12 No. 3 2018
CHUGUNIN et al.
excellent test of the model for the adequacy of its
description of ionosphere–magnetosphere interac-
tions.
The concentration and velocities of O+ ions pre-
dicted by the GSM TIP model turned out to be very
low, substantially smaller than the measured values. At
the same time, as discussed above, in cases where a
classical polar wind (flows of H type) was detected,
the velocities of O+ ion were too small to overcome the
positive potential of the satellite, preventing them
from getting into the detector. Therefore, it is incorrect
to compare flows of O+ ions of Ho type with the results
of model calculations. To describe Ho type flows, it is
necessary to take into account additional heating at
ionospheric altitudes.
CONCLUSIONS
The present work compares results of measure-
ments of the polar wind ion flows by the Hyperboloid
energy-angle mass spectrometer mounted on the
Interball-2 satellite with predictions of the GSM TIP
model. Periods were selected within which the
detected ion flows could be most probably referred to
the classical polar wind. It corresponds to the flow of
ionospheric ions from the polar caps into a magneto-
sphere tail highly rarefied with respect to the thermal
plasma along “open” lines of force of the geomagnetic
field. It was established that the model adequately
describes the f lows of light ions from the ionosphere.
It was impossible to compare the characteristics of O+
ions in the polar wind, since it is extremely difficult to
perform these measurements because of the barrier
created by the positive potential of the satellite. This
study has shown that the GSM TIP model closely
describes the ionosphere−magnetosphere interaction
from the point of view of the outflow of light ions from
the ionosphere into the magnetosphere.
ACKNOWLEDGMENTS
This work was supported by the Russian Science
Foundation, project no. 17-77-20009.
REFERENCES
1. C. R. Chappell, Space Sci. Rev. 192, 5 (2015).
2. A. J. Dessler and F. C. Michel, J. Geophys. Res. 71,
1421 (1966).
3. P. M. Banks and E. N. Holzer, J. Geophys. Res. 73,
6846 (1968).
4. T. Nagai, J. H. Waite, Jr., J. L. Green, et al., Geophys.
Rev. Lett. 11, 669 (1984).
5. C. Gurgiolo and J. L. Burch, Geophys. Rev. Lett. 9,
945 (1982).
6. A. W. Yau, L. Lenchyshyn, E. Shelley, et al., J. Geo-
phys. Res. 90, 8417 (1985).
7. M. Lockwood, J. H. Waite, Jr., T. E. Moore, et al.,
J. Geophys. Res. 90, 4099 (1985).
8. M. O. Chandler, T. E. Moore, and J. H. Waite, J. Geo-
phys. Res. 96, 1412 (1991).
9. C. R. Chappell, T. E. Moore, and J. H. Waite, Jr.,
J. Geophys. Res. 92, 5896 (1987).
10. J. B. Cladis, Geophys. Rev. Lett. 13, 893 (1986).
11. R. W. Schunk and J. J. Sojka, J. Geophys. Res. 11, 625
(1997).
12. T. E. Moore, C. R. Chappell, M. O. Chandler, et al.,
Space Sci. Rev. 71, 409 (1995).
13. T. E. Moore, C. R. Chappell, M. O. Chandler, et al.,
Science (Washington, DC, U. S.) 277, 349 (1997).
14. Y.-J. Su, J. L. Horwitz, T. E. Moore, et al., J. Geophys.
Res. 103, 29305 (1998).
15. T. Abe, B. A. Whalen, A. W. Yau, et al., J. Geophys.
Res. 98, 11191 (1993).
16. T. Abe, S. Watanabe, B. A. Whalen, et al., J. Geomagn.
Geoelectr. 48, 319 (1996).
17. A. W. Yau and M. Andre, Space Sci. Rev. 80, 1 (1997).
18. M. Andre and A. W. Yau, Space Sci. Rev. 80, 27 (1997).
19. C. M. Cully, E. F. Donovan, A. W. Yau, et al., J. Geo-
phys. Res. 108, A1093 (2003).
20. E. Engwall, A. I. Eriksson, M. Andre, et al., Geophys.
Rev. Lett. 33, L06110 (2006).
21. E. Engwall, A. I. Eriksson, C. M. Cully, et al., Ann.
Geophys. 27, 3185 (2009).
22. E. Engwall, A. I. Eriksson, C. M. Cully, et al., Nat.
Geosci. 2, 24 (2009).
23. H. Nilsson, E. Engwall, A. Eriksson, et al., Ann. Geo-
phys. 28, 569 (2010).
24. S. Haaland, A. Eriksson, E. Engwall, et al., J. Geophys.
Res. 117, A07311 (2012).
25. M. Andre and C. M. Cully, Geophys. Rev. Lett. 39,
L03101 (2012).
26. I. A. Barghouthi, H. A. Abudayyeh, R. Slapak, et al.,
J. Geophys. Res. 121, 459 (2016).
27. T. Abe, A. W. Yau, S. Watanabe, et al., J. Geophys. Res.
109, A09305 (2004).
28. P. A. Nsumei, X. Huang, B. W. Reinisch, et al., J. Geo-
phys. Res. 108, 1078 (2003).
29. D. V. Chugunin, L. V. Zinin, Yu. I. Galperin,
N. Dubouloz, and M. Bouhram, Cosmic Res. 40, 387
(2002).
30. P. A. Nsumei, B. W. Reinisch, P. Song, et al., J. Geo-
phys. Res. 113, A01217 (2008).
31. R. E. Horita, A. W. Yau, B. A. Whalen, et al., J. Geo-
phys. Res. 98, 11439 (1993).
32. N. Dubouloz, J.-J. Berthelier, M. Malingre, et al.,
Ann. Geophys. 16, 1070 (1998).
33. A. A. Namgaladze, Yu. N. Korenkov, V. V. Klimenko,
et al., Pure Appl. Geophys. 127, 219 (1988).
34. M. V. Klim en ko , V. V. Klim en ko , a nd V. V. B ryukh a-
nov, Geomagn. Aeron. 46, 457 (2006).
35. D. V. Chugunin, Cosmic Res. 47, 449 (2009).
Translated by V. Smirnov
