Ya. I. Feldstein
Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Troitsk, Russia
Geoforschungszentrum, Potsdam, Germany
Akasofu , Baker et al. , Stern , and Weiss et al.  discussed the main processes of energy storage and dissipation in the Earth's magnetosphere during geomagnetic disturbances. Feldstein et al.  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:
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. . Other terms in (1) were calculated in Watts through the relations given by Akasofu , Baumjohann and Kamide , and Spiro et al. :
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 . 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.  and Sumaruk et al.  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 . 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. , 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
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  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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