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"Physics of Auroral Phenomena", Proc. XXVIII Annual Seminar, Apatity, pp. 37-43, 2005 © Kola Science Center, Russian Academy of Science, 2005

Polar Geophysical Institute

SOLAR WINDS CONTROL OF MAGNETOSPHERIC ENERGETICS DURING MAGNETIC STORMS
A. Levitin, Y. Feldstein, L. Dremukhina, L. Gromova, E. Avdeeva, D. Korzhan (Institute Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, 142 090 Troitsk, Moscow region, Russia)
DR + UT where Uj is Joule heating in the high-latitude ionosphere, Uc is the power of auroral precipitation, Udr is the ring current energization, UT is the plasma sheet energization. We have calculated the magnetosphere energy budget for four magnetic storms in 1998: on March 10-12 (Dst = -116 nT), May 02-07 (Dst = -205 nT), August 26-28 (Dst = - 205 nT), September 24-26 (Dst = -207 nT). Correlation between Us, Uj , Uc , UDR , UT and the solar wind parameters are analyzed. To our knowledge, there is no adequate procedure of magnetospheric energy budget calculation yet. All known procedures are based on rough approximations, so that calculated Uj, Uc, UDR, UT, Us may differ several times from the real values, and it is impossible to estimate calculation accuracy. It is nontrivial to establish the energy input for the magnetospheric budget. As no direct means to measure the energy input are known, various solar wind-derived proxies have been developed. Uj, Uc, UDR, UT, Us equations contain quantities which are functions of solar wind parameters. Depending on the data sets used, the underlying assumptions, and also the time-scales under consideration, different functions turned out to have better or worse correlation in different events or under different statistical approaches. We have analyzed the most widely used energy input function, the so-called parameter of Akasofu , characterizing the power input to the Earth's magnetosphere from interplanetary medium. Based on the correlation of Uj, Uc, UDR, UT, Us with solar wind parameters, we propose a new function ' similar to . It is shown that ' and have identical correlation properties with Uj, Uc, UDR, UT, Us but ' has more transparent physical meaning. As known now, geomagnetic activity is described by special geomagnetic indices, which quantify temporal scale of geomagnetic variation amplitudes only. But, in our idea, the real geomagnetic activity is described by the total energy of geomagnetic variations generated by magnetospheric and ionospheric current systems in the near-Earth space. To estimate magnetospheric current system activity, two following methods may be suggested: a) to estimate the energy of the magnetic field generated in near-Earth space with using the up-to-date models of the magnetospheric current systems, such as the paraboloid model, Tsyganenko model, Maltsev model etc.; b) to estimate the magnetic energy of the geomagnetic field variations on the ground from observations or model distribution of these variations (the IZMEM model). Then, it will be possible to introduce a geomagnetic activity index that is more precise than the classic ones and which can be used for more realistic classification of geomagnetic activity level. The energy of the ground geomagnetic variations during October and November, 2003 major magnetic storms has been estimated using the IZMEM model.

Abstract. The magnetospheric energy budget is calculated as Us = Uj + Uc + U

1. Introduction
Any large-scale physical phenomenon in the Earth's environment occurs either with energy injection or energy dissipation. The solar wind is the main energy source for the electromagnetic processes in the magnetosphere. The energy is delivered from the solar wind to the magnetosphere and distributed within different magnetospheric regions, providing the energetics of large-scale current systems in the Earth's magnetosphere. The magnetic fields of these current systems superposing on the geomagnetic dipole field cause the magnetosphere formation in the space region where there is geomagnetic field. Today it is generally recognized that the Bz component of the interplanetary magnetic field (IMF), to a large extent, controls the energy input to the magnetosphere. Once the IMF turns southward, the rate of reconnection at the subsolar magnetopause is enhanced, leading to an increase of open magnetic flux in the magnetosphere. This corresponds to more effective coupling of the magnetosphere to the solar wind dynamo and an increase in the magnetospheric electric field, driving a more intense convection. An increase in the lobe flux due to dayside magnetic field erosion leads to the development of a more tail-like magnetospheric configuration and to an increase of the cross-tail current. The surface currents on the magnetopause shield the space outside the magnetosphere from the magnetic fields of the dipole and all current systems. In the nightside, the magnetospheric magnetic field is stretched, forming a comet-like tail, the dawn-to-dusk current in the central part of the tail being closed via the magnetopause. On the magnetopause, a MHD-generator, which is the source of the large-scale field-aligned current system, arises as a result of the interaction of the solar wind plasma with the magnetosphere. The field-aligned currents flow from the magnetosphere into the ionospheric altitudes on the dawnside and out of the ionosphere on the duskside. During magnetic storms, the ring current generated by hydrogen and oxygen ions with energies of tens keV arises in the inner magnetosphere between the plasma sheet and plasmasphere due to solar wind energy input. Accelerated ions of both plasma sheet and ionospheric origin are sources of this current. The energy of the large-scale current system, stored in the magnetic fields generated by the currents, dissipates through upper atmosphere Joule heating by the ionospheric currents, energetic charged particles injections, ejection

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of plasma, energetic particles and magnetic field via the remote part of the magnetotail to the solar wind, chargeexchange interaction of the ring current ions with the neutral particles of the exosphere, energetic ions ejection across the dayside magnetopause in the course of the curvature/gradient drift around the Earth. In this paper we estimate the accuracy of computational procedures for calculation of magnetospheric energy budget taken in the form Us = Uj (Joule heating in the high-latitude ionosphere) + Uc (power of auroral precipitation) + UDR (ring current energization) + UT (plasma sheet energization). Besides, we present the results of our budget calculations for four magnetic storms in 1998: on March (Dst = -116 nT), May (Dst = -205 nT), August (Dst = -205 nT), September (Dst = -207 nT). After that, we discuss the most widely used energy input function, the so-called parameter of Akasofu, characterizing the power incoming to the Earth's magnetosphere from interplanetary medium. Based on the correlation of Uj, Uc, UDR, UT, Us with solar wind parameters, we propose a new function ' which is similar to , but has a more transparent physical meaning.

2. Calculation of magnetospheric energy budget for magnetic storms
The global energy deposition during magnetic storm and Akasofu, 1978; Akasofu, 1981; Ahn et al., 1983; 1995; Lu et al., 1998; Feldstein et al., 2003 and investigations, with concentrating on computational pr budget. Possible errors of these computational procedur has previously been investigated in many studies [Perreault Monreal Mac-Mahon and Gonzales, 1997; Cooper et al., references therein]. We show some examples of these ocedures used in calculations of the magnetospheric energy es are discussed.

2.1. Computation procedures for the energy budget Through solar wind-magnetosphere-ionosphere interaction, a part of incoming solar wind energy is released in Joule heating Uj of the high-latitude ionosphere, auroral precipitation Uc, ring current energization UDR in the inner magnetosphere, plasma sheet particle heating UT, plasmoid ejection in the magnetotail UPL. 2.2.1. Computation of Uj The current system connecting the Earth's ionosphere with space consists of the magnetospheric currents, field aligned currents (FACs), and closure currents in the ionosphere. The distributions in time and space of these currents depend not only on FAC driving mechanism but also on the ionospheric conditions, particularly on the ionospheric conductivity. A change in the conductivity may be caused by the electric current as well as by other parameters such as the electric field. Therefore, the ionosphere conductivity and the electric field are related to each other in various current systems. The FACs are a part of the system which transfers the energy and momentum from the magnetosphere to the ionosphere. While it is clear that the system is driven ultimately by the solar wind, the direct physical mechanism providing energy and momentum and initiating their transfer into the ionosphere is still not well understood. Nor we have detailed knowledge as to whether and how these driving physical mechanisms are influenced by ionospheric conditions, which are variable in time and in space. In early investigations the relationship Uj = constâ(AE-index) was suggested for computation of Joule heating. In [Akasofu, 1981], const = 2 for Uj in Watts and AE in nT. It is obvious, that the accuracy of such a relationship is not high enough. The discrepancies in estimating of Uj taken in this form by different authors can be attributed to several causes: a) not the same AE index is used in different studies, i.e. the utilization of AE(12 stations), AE(10), etc. can lead to a discrepancy of factor ~ 1.5; b) AE index is different in the northern and southern hemispheres which is likely to cause differences in the estimates as high as ~ 1.5 times; c) the relation between AE and various electrodynamic quantities is nonlinear, and the cross-polar cap potential drop tends to saturate the estimates for AE > 1000 nT. The power function fits of AE versus Uj are a significant improvement over the linear fitting in terms of reducing the standard deviation. In other words, calculation of Uj = Uj(AE) is not accurate and the difference between the estimates obtained and real values may be as large as an order. Another method of calculation uses the relation of Uj to the ionospheric electric field E and ionospheric conductivity in the form Uj = (JE) = (p)E2, where J = E is the ionospheric current, is the tensor of integral conductivity of the ionosphere and p is Pedersen part of this conductivity. In [Manreal Mac-Mahon, 1997] the relationship Uj = pE2(Re + h)2Sindd was used for this aim, where changes from 0° to the geomagnetic colatitude for the equatorward boundaries of the auroral zone and is the geomagnetic longitude. The auroral zone boundaries were determined using the database on the total energy flux of electrons from the NOAA satellite. The electric field in the polar ionosphere was estimated in a sort of hybrid way using both ionospheric and interplanetary (ISEE-3 satellite) data. This method was used in [Lu et al., 1998], where the electric potential (E= -) and p were calculated by AMIE procedure [Richmond and Kamide, 1988; Richmond et al., 1990] on the basis of geomagnetic data and 5-min snapshots, auroral electron energy flux derived by combining various observations (DMSP F10, F12, F13; NOAA12 and 14 satellites, auroral UVI images from the Polar satellite, ion drift measurements from 6 SuperDARN radars, Millstone Hill and Sonderstrom radars; 119 ground magnetometers). Such an approach was also used in [Feldstein et al., 2003], where and J were obtained from the IZMEM model which gives these values for high latitudes as a function of solar wind parameters [Feldstein and Levitin, 1986].

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The discrepancies in the estimates of Uj by these methods can be attributed to several causes (in addition to those mentioned above). First of all, when calculating the height-integrated Joule heating rate Q = pE2, there is an error associated with the estimated large-scale electric field E at each grid point. This error depends on the manner of calculation of the electric potential from geomagnetic field variations and conductivity of the ionosphere. When using geomagnetic variation, it is necessary to set a basic level but actually this level is not known, especially in the period of magnetic storm. The points of registration of geomagnetic variations are not uniformly distributed over the surface, so that using spherical harmonic presentation for geomagnetic disturbances may be incorrect. As for the ionospheric conductivity, it is known very poorly in the period of storms. Secondly, some postulates using for calculation of the high-latitude current system from geomagnetic data (such as equipotentiality of geomagnetic field lines, the condition E= -, etc.) can be violated [Feldstein and Levitin, 1986]. Therefore, any method for Uj calculation contains non-controllable errors, so that the differences between the estimates and real values can reach an order of magnitude. 2.2.2. Computation of Uc In early investigations to calculate the power of auroral precipitation Uc the following expressions were used: Uc = 108AE [Akasofu, 1981] and Uc = [1.75â(AE/100 + 1.6]â1010 [Spiro et al., 1982], where Uc is in Watt and AE is in nT. Some other relationships were also proposed: Uc = 1.6108âAL; Uc = (4.4âAL1/2 ­ 7.6)â109. It is clear that for the reasons mentioned in 2.2.1 these expressions can also lead up to an order of magnitude discrepancy between the estimates and real values. 2.2.3. Computation of UDR According to the Dessler-Parker-Schopke relationship [Sckopke, 1966], B/B0 = -KR/KM, where KM = 8â1024 ergs, the total energy of the particles of the ring current being equal to KR = 4â1020âD, where D is the pressurecorrected Dst index in nT (Dst*). The energy injection rate is obtained from the energy balance equation: UDR = 4â1024(dDst*/dt + Dst*/), where is the particle lifetime in the ring current. The magnitude of the ring current energy rate strongly depends on parameter. Several models were proposed to estimate this parameter. In earlier studies the same for all possible Dst values was assumed [Buton et al., 1975]. Later, the necessity to introduce different values of for different Dst ranges was emphasized [Prigancova and Feldstein, 1992; Feldstein, 1992]. In [Feldstein et al., 2003], the equation UDR = -0.74â1010(dDR/dt + DR/) was used for DR, which is the ring current magnetic field on the Earth's surface determined by AMPTE/CCE ion measurements in the magnetosphere. The values are often chosen to provide the overall balance between the input solar wind energy and total magnetospheric energy consumption. Since the real is unknown, UDR estimates can differ from the real values by factor 2 - 5 or by an order of magnitude. 2.2.4. Computation of UT UT computation is a very hard task and the accuracy of UT calculation can not be determined at present. In [Feldstein et al., 2003] UT was calculated with the use of the paraboloid model [Alexeev and Feldstein, 2001] according to the relation UT = ET/dt ­ ET/, in which the tail energy ET = (ET1)exp{(t ­ t1)/lT, where ET1 = (2F02/µR1) â AâB; A = (2R2/R1 + 1)1/2; B = Ln[2Rk/R1 + 1)1/2/(2R2/R1 + 1)1/2], R1 being the distance to the magnetopause subsolar point, R2 the distance to the inner edge of the current sheet and Rk = 60Re. What is the accuracy of such an approximation? UT estimates can differ from the real values by factor 2 - 5 or up to an order of magnitude, as it is for Uj, Uc and UDR. 2.2.5. Computation of UP Computation of UP is also very difficult. In [Leda et al., 1998], based on statistical analysis of plasmoid evolution, it was suggested that the energy carried by each plasmoid is ~2â104 J in the middle tail, and this energy is lost on the way from the middle to the distant tail. This value was derived for the plasmoid dimensions of 10Re(length)â 40Re(width)â10Re(height). Accordingly, the energy, ejected tailward in the course of substorm, was roughly estimated to be 1015 J. It is comparable to the energy released to the auroral region and to the ring current. It is unclear what the accuracy of such an approximation is. The estimates for UP can differ from the real values by factor 2 - 5 or up to an order of magnitude, as it is for Uj, Uc and UDR and UT. Thus the estimates for the sum Us = Uj + Uc + UDR + UT + UP can from 2 to 5 times (or up to an order of magnitude) differ from the real values. Energetics of the solar wind At present, there are no direct observational means capable to determine the energy transfer from the solar wind into the magnetosphere. In fact, we do not even know the details of how and where the transfer takes place. It is known that the efficiency of transferring is strongly coupled to the IMF southward component.

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In [Feldstein et al., 2003] a quantitative estimation is presented of the energy transferred by the plasma flux and solar wind electromagnetic field into the magnetosphere with a cross section S. The rate of kinetic energy transfer is Ukin(W) = 8.35â10-7N(particles cm-3)â(V(km s-1)/100)3âS, while the rate of electromagnetic energy transfer onto the surface S is Uemag = 7.9â10-8[V(km s-1)/100]â[B(nT)]2xS. The cross section along the dawn-dusk meridian of the magnetopause with the paraboloid shape can be found as S = (1.5R1)2, where R1 is the distance to the magnetopause subsolar point. For quantitative description of solar wind energy input into the magnetosphere Akasofu compiled a so-called function: = VBsin4(/2)x(L0)2 [Perreault and Akasofu, 1978; Akasofu, 1981]. This function has identical correlation properties with respect to the Uj, Uc, Udr, Ut, as well as to the Us. The parameter L0 = 7Re enables to calibrate to the order of Us magnitude (for -function relation to the Poynting flux see [Kan and Akasofu, 1982]). While in practice it has been shown that is a very useful parameter, there is no convincing evidence of its superiority over other known coupling parameters. We have performed correlation analysis of the amplitudes of Uj, Uc, UDR, UT and of their sum for four magnetic storms with the solar wind parameters. Depending on the dataset used, underlying assumptions, and time-scales considered, different functions turned out to exhibit better or worse correlations in different events or under different statistical approaches. The parameter is one of the proper parameters (along with Bs, VBs etc.) that exhibit a good correlation with Uj, Uc, UDR, UT and with their sum. But the physical meaning of is questionable. As a new energy input parameter, we propose P = V(Bs)2âS, where Bs = 0.5 for Bz > 0, Bs = -Bz for Bz < 0, S = (1.5R1)2, and R1 is calculated using the paraboloid model [Dremukhina et al., 1999; Alexeev and Feldstein, 2001]. In Tables 4-7 the coefficients of Uj, Uc, Udr, Ut and Us correlation with different combinations of IMF components and solar wind parameters are presented.

3. Calculation of energetics for particular magnetic storms
To study the magnetospheric energy budget, four magnetic storms of 1998 were selected. Table 1 shows the main characteristics of the storms. Table 1 Characteristics of the magnetic storms N Date Dst minim, nT Main phase: day, UT Recovery phase: day, UT 1 March, 1998 -116 nT 10.03, 13 ­ 10.03, 22 10.03, 23 ­ 11.03, 09 2 May, 1998 -205 04.05, 00 ­ 04.05, 05 04.05, 06 ­ 05.05, 00 3 August, 1998 -155 26.08, 08 ­ 27.08, 14 27.08, 15! 4 September, 1998 -207 25.09, 00 ! .28.08, 12 . 25.09, 09 25.09, 10 ! .25.09, 19 3.1. Computation of the magnetospheric energy budget for four magnetic storms For each of the storms we calculated Us = Uj + Uc + UDR + UT, in which Uc = 2â{4.4(AL) ½ - 7.6)}â109; UDR = 0.74â1010(dDR/dt + DR/ ), where = 2.4 x exp{9.74/(4.69 + VâBs)} and Bs = -Bz for Bz < 0, Bs = 0.5 for Bz 0 [O'Brain and McPherron, 2000]. To calculate Joule heating, we used the relation Uj = Uj(steady-state current) + Uj(substorm), in which Uj(substorm) = 0.32â109(AE) [Baumjohann and Kamide, 1984]. In calculating UT, we used the relations from [Feldstein et al., 2003] presented in section 2.2.4. The hourly values of Uj, Uc, UT, UDR, Us, as well as their maximum values, are presented in Table 2 (for the storms in March and in May) and in Table 3 (for the storms in August and in September). As the storm in May included two disturbed periods, all data in Table 2 are given for two days: May, 2 (the first disturbance), and May, 4 (the second disturbance).

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Table 2 Hourly means and maximum values of Uj, Uc, UT, UDR, Us for the magnetic storms in March and in May March storm, mean (W) Uj Uc UT UDR Us 2 1 4 2 0 ­ 30 0 ­ 15 0 ­ 60 0 ­ 30 120 170 March storm, max(W) 45 20 100 45 190 275 May storm, mean (W) May, 02 20 ­ 40 15 ­ 20 40 ­ 80 20 ­ 30 100 ­ 150 150 ­180 May, 04 60 25 145 35 240 240 May storm, max (W) May, 02 May, 04 50 ! . 60 100 20 ­ 30 35 150 ­ 200 380 40 ­ 60 90 150 ­ 300 480 900 2000



Table 3 Hourly means and maximum values of Uj, Uc, UT, UDR, Us for the magnetic storms in August and in September August mean 30 ­ 15 ­ 120 ­ 30 ­ 150 ­ 200 ­ storm, (W) 50 20 150 50 450 260 August storm, max (W) 75 30 220 60 370 340 September storm, mean (W) 40 ­ 60 15 ­ 25 100 ­ 150 40 ­ 50 150 ­ 250 350 ­ 400 September storm, max (W) 85 30 410 65 565 520

Uj Uc UT UDR Us



The coefficients of correlation between the hourly values of Uj , Uc, UT, UDR, Us and , Bs, VBs, BsNV2, Bs/B, BT/B for the main phase of the storms (for all four magnetic storms) are presented in Table 4. Here V is the solar wind velocity, N is the solar wind density, B is the IMF magnitude, BT = [(Bz)2 + (By)2]1/2. The same correlation coefficients for the recovery phase are presented in Table 5. Table 4 Main phase of the storms. Correlation coefficients between hourly means Uj, Uc, UT, UDR, Us and , Bs, VBs, BsNV2, Bs/B, BT/B. Uj Uc UT UDR Us 0.64 0.55 0.60 0.47 0.72 Bs 0.54 0.50 0.51 0.54 0.65 BsâV 0.55 0.51 0.55 0.59 0.69 BsâNV2 0.51 0.43 0.62 0.43 0.68 Bs/B 0.37 0.40 0.31 0.47 0.45 BT/B 0.12 0.16 0.09 0.09 0.08

Table 5 Recovery phase of the storms. Correlation coefficients between Uj , Uc, UT, UDR, Us and , Bs, VBs, BsNV2, Bs/B, BT/B. Uj Uc UT UDR Us 0.74 0.67 0.60 0.57 0.54 Bs 0.78 0.75 0.31 0.34 0.67 BsâV 0.81 0.77 0.27 0.37 0.66 BsâNV2 0.56 0.50 0.18 0.53 0.50 Bs/B 0.58 0.59 0.50 0.05 0.64 BT/B 0.64 0.64 0.37 0.09 0.56

As one can see, , VBs and Bs have identical correlation properties with respect to Uj, Uc, UDR, Ut. Good correlation of with the parameters of geomagnetic activity is due to the term Vâ[Sin(/2)]4, which is proportional to VBs.

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We analyzed a multi-parameter correlation assuming U = U0 + KB â() + KBsâ(Bs) + KBsVâ(BsV) + KBsNV2â(BsNV2). Table 6 (Table 7) presents correlation coefficients (R) and parameters for the main phase of the magnetic storms (for the crecovery phase). Table 6 Main phase of the storms. Correlation coefficients R and parameters U0, K, KBs, KBsV,KBsNV2. U Uj Uc UT UDR Us R 0.66 0.57 0.63 0.64 0.73 U0 26.23 15.95 34.39 12.05 88.62 K 0.11 0.03 0.10 -0.07 0.17 KBs 1.44 0.41 0.23 -1.44 0.63 KBsV - 0.33 - 0.06 - 0.20 0.73 0.13 KBsNV2 -0.12 -0.16 0.65 0.01 0.49 Table 7 Recovery phase of the storms. Correlation coefficients R and parameters U0, K, KBs, KBsV,KBsNV2. U Uj Uc UT UDR Us R 0.81 0.77 0.47 0.68 0.68 U0 12.26 10.23 23.91 19.97 66.37 KB 0.04 0.01 -0.23 0.10 - 0.08 KBs -0.60 0.27 2.01 3.21 4.90 KBsV 0.53 0.12 0.47 -0.73 0.39 KBsNV2 - 0.41 - 0.21 1.54 0.28 1.21

The correlation coefficients of multi-parameter regression for the main phases of the storms are equal to those in Tables 4 and 5 but for the recovery phases the correlation coefficients of multi-parameter regression are larger than in Tables 4 and 5. One can see that the correlation coefficients of Us with the solar wind parameters are equal to ~ 0.7. The new parameter that we propose (P = V(Bs)2S, where S = (1.5R1)2 and Bs = -Bz for Bz < 0 and Bs = 0.5 for Bz 0) has more transparent physical meaning than . It can be interpreted as a product of the electric field E = VBs and vertical component of the interplanetary magnetic field Bs. S is the area of the section of the magnetosphere of the paraboloid form. It is equal to the area of the circle with the radius of 1.5R1, where R1 is the distance to the magnetopause subsolar point. We calculated R1 using the paraboloid model [Alexeev and Feldstein, 2001]. The coefficient of correlation of the new parameter P with for the four storms chosen is equal to 0.91 for the storm main phases and 0.81 for the recovery phases. The coefficient of P to Us correlation is equal to 0.66 for the main phases of the storms (the coefficient of to Us correlation is 0.72 for the storm main phases) and 0.54 for the recovery phases (the same coefficient for is equal to 0.54). But, unlike calculating, it is not necessary to introduce L0 = 7Re for calculating P.

4. Summary
The adequate calculation of the magnetospheric energy budget has not been accomplished yet. All known calculation procedures are based on rough approximations, so that the reported estimations of Uj (Joule heating in the high-latitude ionosphere), Uc (power of auroral precipitation), UDR (ring current energization) and UT (plasma sheet enegization) may differ several times from the real values. All the equations for Uj, Uc, UDR, UT contain terms parameterized by the solar wind parameters, therefore, they correlate rather well with the main geoeffective parameters such as Bs, VBs, etc.. Accordingly, a number of expressions similar to that for have been proposed. Those correlate with Uj, Uc, UDR, UT quite well (the correlation coefficients are about 0.7). Parameter is not really a measure of energy input into the magnetosphere, and we have proposed a new function ' similar to . The new parameter ' and of Akasofu have identical correlation properties with respect to the Uj, Uc, UDR, Ut, Us but ' has more transparent physical meaning.

Acknowledgments. The research was supported by INTAS grant N 03-51-5359 and RFBR grant N 05-05-65196. We are grateful to the staff of the International Space Science Institute, Bern, Switzerland, for their support. References
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