Magnetosphere energetics at various phases of a magnetic storm

Ya. I. Feldstein

Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Troitsk, Russia

A. Grafe

Geoforschungszentrum, Potsdam, Germany

Contents

Abstract

Introduction

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 U_T dissipating in the magnetosphere is the sum of three terms:

(1)

where U_DR is the power injection into the ring current, U_j is the power of Joule dissipation in the high-latitude ionosphere, and U_A is the power connected with particle precepitations. The factor 2 in (1) accounts for energy dissipation in both hemispheres. The U_j term consists of two components: U^con_j is connected with the quasi-stationary convection, and U^sub_j is connected with substorm current systems. The U^con_j 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, SG_p 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.

Energy Dissipation During Magnetic Storms

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 U_j, U_A, U_DR, and U_T through (1)-(4). Figure 2 presents simultaneously the variations in U_j, U_A, U_DR, and U_T 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 U_DR growth up to 6 10¹¹ W which is comparable with U_j. During the recovery phase (after 2200 UT), U_j distinctly exceeds U_DR. 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, U_j is higher than U_DR. 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 U_A are typically less than those of U_j but are comparable with U_DR 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), U_j > U_DR. The sharp increase in DR after 1800 UT results in the U_DR growth up to 10¹² W which is somewhat higher than U_j 7 10¹¹ W. At the recovery phase (after 1000 UT on March 24) U_j U_DR. 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 U_T calculated through (1) and the energy injected into the magnetosphere from the solar wind whose measure is e. During both storms, U_T > e before and after the storm main phase, but e > U_T at the storm main phase. The integral value of e (Se) is approximately 2 times higher than the integral value of U_T (SU_T) at the main phase of the magnetic storm. However, SU_T is 1.4 times higher than Se at the recovery phase.

Discussion and Summary

During the magnetic storm main phase, U_j is approximately the same as the energy injected into the magnetosphere in the form of a ring current U_DR. 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 U_j 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 U_j values presented above would be respectively higher.

The U_DR 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 U_DR 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 U_j predominance over U_DR would be even more reasonable when taking into account the magnetotail current contribution to the magnetic field variations ( H_T ) observed at the ground during the magnetic storm. For the storm of March 23-24, 1969, the intensities of H_T and H_DR were calculated by Alekseev et al. [1992], and the H_T intensity appeared to be approximately equal to H_DR 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 U_M 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 U_M 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 U_M term. Assuming that U_j U_DR and e 6U_DR and that the energy injected into the magnetosphere dissipates fully within it, we obtain U_M 3U_DR 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, U_M < 3U_DR, 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.

Acknowledgments

References

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