Ya. I. Feldstein
Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Troitsk, Russia
A. Grafe
Geoforschungszentrum, Potsdam, Germany
Akasofu [1981], Baker et al. [1984], Stern [1984], and Weiss et al. [1992] discussed the main processes of energy storage and dissipation in the Earth's magnetosphere during geomagnetic disturbances. Feldstein et al. [1986] considered the energy balance of the magnetosphere both in magnetospheric quiet time intervals and during magnetospheric substorms. The total power UT dissipating in the magnetosphere is the sum of three terms:
![]() | (1) |
where UDR is the power injection into the ring current, Uj is the power of Joule dissipation in the high-latitude ionosphere, and UA is the power connected with particle precepitations. The factor 2 in (1) accounts for energy dissipation in both hemispheres. The Uj term consists of two components: Uconj is connected with the quasi-stationary convection, and Usubj is connected with substorm current systems. The Uconj is controlled by the viscous interaction between the solar wind and magnetosphere. This term can be calculated [see Feldstein et al., 1986] from
![]() |
where integration is performed throughout the surface of the high-latitude ionosphere, SGp is the Pedersen conductivity integrated with respect to the height, and E is the quasi-stationary electric field whose intensity is given by Levitin et al. [1984]. Other terms in (1) were calculated in Watts through the relations given by Akasofu [1981], Baumjohann and Kamide [1984], and Spiro et al. [1982]:
![]() | (2) |
![]() | (3) |
![]() | (4) |
Here AE is the intensity index of auroral electrojets in nanoteslas, DR is the magnetic field of the ring current at the ground, and t is the ring current decay parameter. During magnetic storms the auroral electrojets are displaced to subauroral latitudes. When calculating the AE intensity in (2) and (3), we must take into account this displacement. For this purpose, we have to supplement the data from auroral observatories with magnetic field observations at subauroral stations [Feldstein et al., 1994; Sumaruk et al., 1989].
Supposing that the Dst variation is a combination of the fields of magnetopause current ( DCF ) and the magnetospheric ring current ( DR ), we can write
where d and q indices designate disturbed and quiet conditions, respectively, and DCFd and DCFq are determined using empirical relations between DCF and the solar wind pressure upon the magnetosphere.
Being defined in such a way, DR also includes the magnetic effects of the magnetotail currents. The values of t in (4) are given by Feldstein [1992]. Calculation of AE indices using the data from subauroral observatories is a rather tedious process. Therefore we consider below the energy balance in the magnetosphere during two magnetic storms whose AE indices have been obtained by Feldstein et al. [1994] and Sumaruk et al. [1989] taking into account the equatorward displacement of electrojets.
Figure 1
shows the
AE and
DR variations for the storms of
March 31-April 3, 1973 (Figure 1a) and of March 23-24, 1969 (Figure 1b).
Using these hourly data for the indices we determined
Uj,
UA,
UDR, and
UT
through (1)-(4). Figure 2 presents simultaneously
the variations in
Uj,
UA,
UDR, and
UT from 1200 UT on March 31
until 0400 UT on April 3, 1973, and the solar wind power injected
into the magnetosphere which is just the
e function
[Perreault and Akasofu, 1978;
Pudovkin and Semenov, 1986]. This time
interval involves the magnetospheric substorm (1700-2000 UT on
March 31) and the intense magnetic storm (after 1200 UT on April 1,
1973). During the substorm and prior to the intense plasma injection
into the ring current (~1400 UT on April 1), the energy
dissipation in the auroral ionosphere exceeds the injection into the
ring current. The sharp
DR increase during the main phase of the
storm (1500-2200 UT on April 1) is accompanied by the
UDR growth
up to
6
1011 W which is comparable
with
Uj. During the
recovery phase (after 2200 UT),
Uj distinctly exceeds
UDR. The
total injection into the ring current during the main phase of the
storm from 0700 until 2100 UT is
1.8
1016 J,
and
during the recovery phase until 0400 UT on April 3 it is
1016 J. For the Joule dissipation
these values are
2.2
1016 and
2.6
1016 J,
respectively. Therefore, at the
main phase of the magnetic storm the energy injection into the ring
current is approximately the same as the Joule dissipation. At the
recovery phase,
Uj is higher than
UDR. During the storm the
energy dissipation in both hemispheres of the auroral ionosphere
exceeds considerably the energy injected into the ring current. The
values of
UA are typically less than those of
Uj but are
comparable with
UDR at the recovery phase.
Figure 3
shows variations in the energy emission from various
sources during the magnetic storm of March 23-24, 1969. They behave
quite similar to those during the storm of April 1, 1973. Prior to
the intense injection into the ring current (1800 UT on March 23),
Uj > UDR. The sharp increase in
DR after 1800 UT results in the
UDR growth up to
1012 W which is somewhat higher
than
Uj
7
1011 W. At the recovery phase (after 1000 UT on
March 24)
Uj
UDR.
The total injection into the ring current
throughout the main phase of the storm is about
2.7
1016 J,
and during the recovery phase from 1000 until 1700 UT on March 24 the
injection is
1.5
1015 J.
The associated values of the
Joule dissipation are
3.0
1016
and
7
1015 J.
Figure 3 (bottom panel) shows the results of comparison between the total energy dissipated in the inner magnetosphere and ionosphere UT calculated through (1) and the energy injected into the magnetosphere from the solar wind whose measure is e. During both storms, UT > e before and after the storm main phase, but e > UT at the storm main phase. The integral value of e (Se) is approximately 2 times higher than the integral value of UT (SUT) at the main phase of the magnetic storm. However, SUT is 1.4 times higher than Se at the recovery phase.
During the magnetic storm main phase, Uj is approximately the same as the energy injected into the magnetosphere in the form of a ring current UDR. This results both from use of the AE indices corrected (taking into account the equatorward electrojet displacement) and from a more accurate selection of the parameters of the ring current decay used in calculations. Therefore even at the main phase of an intense magnetic storm the energy injected into the auroral ionosphere and dissipated in the ionosphere in the form of Joule heating is comparable with the energy injected into the ring current. The values of AE used to calculate Uj may be slightly underestimated (up to 20%) owing to spatial diversity of observatory locations and electrojet intensity maxima. If one takes into account this effect, the Uj values presented above would be respectively higher.
The
UDR values are determined by both the rate of
DR intensity
change and the
t values. In the calculations,
t was taken to be equal
to 5 to 10 hours depending on magnetic storm phase. Under
t 0.1 h
the
UDR increases by an order of magnitude. Such low
values of
t were used in the literature. Detailed discussion
of the problem
was given by
Feldstein [1992].
It was shown there that such low values of
t cannot exist. The conclusion on
Uj predominance over
UDR would be
even more reasonable
when taking into account the magnetotail current contribution to the
magnetic field variations ( HT ) observed at the ground during the
magnetic storm. For the storm of March 23-24, 1969, the intensities
of
HT and
HDR were calculated by
Alekseev et al. [1992],
and the
HT intensity appeared to be approximately equal to
HDR intensity. It means that the estimates presented earlier
are
overestimated by at least 2 times, and thus a considerable portion of the
energy injected into the magnetosphere is expended in an increase of
the magnetic energy in the form of the magnetic flux which forms the
magnetotail.
Since the e function is the measure of the energy injected into the magnetosphere, there should be an additional mechanism for the energy dissipation in the magnetosphere at the magnetic storm main phase. It seems that not all the energy coming into the magnetosphere dissipates inside it. A portion of this energy returns directly into the solar wind together with plasma. Another possible mechanism for dissipation of the energy stored in the magnetotail is its subsequent ejection into the solar wind together with the plasmoid [Baker et al., 1990]. In this case the UM term which accounts for the rate of energy storage in the magnetotail must be introduced into the energy balance relation. As a result, the balance relation is
![]() | (5) |
The energy storage in the magnetotail is a result of the predominance of the reconnection process in the dayside magnetopause over that in the magnetotail. At the recovery phase of the magnetic storm the magnetic energy stored in the magnetotail is partly transformed into the energy of auroral particles and field-aligned currents which finally dissipate in the upper atmosphere.
We can estimate
UM quantitatively
in (5) by using the measurements of
the magnetic flux which forms the magnetotail. This flux is
projected on the high-latitude upper atmosphere regions located to
the pole of the auroral oval equatorial boundary. The estimates
obtained by
Frank and Craven [1988]
showed that to balance out the
energy of processes in the Earth's magnetosphere during the
disturbed periods, one has to take into account the
UM term.
Assuming that
Uj UDR
and
e
6UDR
and that the energy injected into the magnetosphere dissipates fully
within it, we obtain
UM
3UDR
for the
magnetic storm
main
phases under consideration. As was discussed above, a portion of the
energy can pass through the magnetosphere without dissipation. In
this case,
UM < 3UDR, the difference being equal
to the energy
coming into the magnetosphere from the solar wind without
dissipation within the magnetosphere. The estimates show that the
situation inside the Earth's magnetosphere can be such that only a
small portion of the energy injected into the magnetosphere
dissipates in the form of Joule heating and ring current generation.
Its major portion is stored in the magnetotail. This conclusion is
based on the assumption that the total energy injected into the
magnetosphere from the solar wind dissipates in various
magnetosphere regions, from the ionosphere to the magnetotail.
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