COMPARISON OF GOES MAGNETOSPHERE MAGNETIC FIELD MEASUREMENTS WITH IMECH MAGNETOSPHERE MAGNETOSHEATH MODEL PREDICTIONS *

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1 11 th National Congress on Theoretical and Applied Mechanics, 2-5 Sept. 2009, Borovets, Bulgaria COMPARISON OF GOES MAGNETOSPHERE MAGNETIC FIELD MEASUREMENTS WITH IMECH MAGNETOSPHERE MAGNETOSHEATH MODEL PREDICTIONS * P. DOBREVA, M. KARTALEV Institute of Mechanics, Bulgarian Academy of Sciences, Block 4, Akad. G. Bontchev Str., Sofia 1113, Bulgaria polya@geospace4.imbm.bas.bg N. BORODKOVA, G. ZASTENKER Space Research Institute, RAN, Profsousnaya 84/32, Moscow , Russia nlbor@mail.ru ABSTRACT. We report first comparison of the measurements of GOES magnetospheric magnetic field from geosynchronous orbit with the predictions of the magnetosphere module of the new IMECH magnetosphere - magnetosheath model. The magnetosphere module of the IMECH complex model could be considered as a modification of the Tsyganenko magnetosphere magnetic field statistical model with more realistic 3D magnetopause shape and position, obtained self-consistently together with the solution of the 3D magnetosheath problem in gasdynamic approach. The pressure balance condition on the magnetopause is satisfied in this solution and the corresponding magnetopause shielding field is computed, solving the Chapmen-Ferraro problem by finite element numerical method. Thus, the resulting magnetosphere model depends on the solar wind parameters not only through the Tsyganenko's current systems, but via the shape and the position of so obtained more realistic magnetopause and shielding field. A good coincidence of the measured and predicted magnetic field values are demonstrated under real solar wind conditions. KEY WORDS: magnetosheath, magnetosphere, finite elements, gas dynamics, Chapman-Ferraro problem. * This research was partially supported under Project INTAS No

2 Dobreva, Borodkova, Kartalev, Zastenker 1. Introduction The magnetosphere models could be conventionally classified into two groups: physical models and the empirical ones. The physical models are based on the theoretical assumptions. Examples of such models are magnetosphere model of Voigt 1972, 1981 [14,15] which magnetopause consist of hemisphere and infinite cylinder, and the paraboloid model of Stern 1985 [7]. Some models are based on the numerical solution of Chapman-Ferraro problem - Toffoleto 1994 [8], Klouchek and Toffoleto [4]. The model, developed by Kartalev 1995 [2] and Koitchev 1999 [5], appeared independently of those of Toffoletto. The Chapman-Ferraro boundary value problem for the sought shielding field is solved using of non-conforming finite elements. The initial variant, concerning the two-dimensional problem - Kartalev 1995, is thereafter elaborated to the 3D variant - Koitchev 1999, but the magnetosphere boundary, consisting of a hemisphere and a cylinder, still remains fixed. Many magnetosphere model, based on statistical treatment of magnetic field data, were developed in the resent decades. Tsyganenko models are the most polular - Tsyganenko and Usmanov 1982 [9], Tsyganenko 87 [10] and Tsyganeko 1989 [11]. The more comprehensive variants - Tsyganenko 1995 [12] and Tsyganenko 2001 [13] are based on the better mathematical description of each current source and it was incorporated a real data-based megnetopause form. The experimental models have the serious shortcoming to approximate the magnetopshere boundary with an axisymmetric surface, while the theoretical models are not applicable for practical purposes, because they do not relate to the real measurements. In order to avoid the above mentioned circumstances and to match the advantages of the theoretical and the data-based models, the Imech magnetosphere-magnetosheath model was created in Geospace Hydrodynamics Laboratory. On one side, it provides a good description of the physical processes in the magnetosphere. On the other side, as a data-based model, it is adequate for practical purposes, such as comparison with experimental data. This paper presents a first attempt to compare the magnetosphere modul of the composite Imech model with real measurements of the magnetic field, obtained from GOES satellites. 2. Model description 2.1. The self-consistent model The composite IMech model incorporates two modules, working together, and calculating the numerical solution in the whole magnetosphere-magnetosheath region. For the given input data, the gas-dynamic parameters distribution and the magnetic field in the magnetosphere are received. The positions of the boundaries - bow shock and magnetopause, are also received in the process of the solution. The interaction between the two regions is attained through the boundary conditions, posed at the common boundary - the magnetopause. The construction of the

3 Comparison of GOES measurements with IMech model composite model is based on the modular approach conception, allowing separate description of each region with models of quite different types. An ideal gasdynamic model is applied in the magnetosheath region. The module could be considered as a development of the earlier axisymmetric model - Kartalev 1996 [3], approved to 3D in the present variant for a better depiction of the real flow distribution in the magnetosheath. The Euler equations are solved by an application of the grid-characteristic method, developed by Magomedov and Holodov 1988 [6]. The bow shock location is obtained as a result of the satisfaction of Renkin-Hugoniot relationships. The two regions interact through their common boundary, where the pressure balance equation is imposed - the gasdynamic pressure from magnetosheath side and the magnetic pressure from the magnetosphere side could be equalized. The magnetic pressure: 2 Bτ (2.1) p M = 8π is finding knowing the magnetic field distribution, calculated from the magnetosphere model The magnetosphere model The model is a generalization of the earlier created in Geospace Hydrodynamic Laboratory finite elements model - Koitchev 1999, developed now to an arbitrary magnetopause form, which is received as a result of pressure equilibrium. In the present variant the magnetic fields of the following sources are included: the Earth's dipole B d, the tail B t, ring B r and Birkeland B b currents, and the sought shielding field B s. The field of B r and B b are calculated, using the Tsyganenko T96 model, while B t is from Tsyganenko T01. For the sough B s field, it is supposed, that: (2.2) divu = 0, rotu = 0 and hence the field potential - a harmonic scalar function U exists: (2.3) Δ U = 0, Bs = U. The distribution of the normal magnetic field component is given at the boundary points. Standard algorithm, using 20 points serendipity finite elements, is applied - Koitchev The potential distribution in the magnetosphere region is obtained as a result of the algorithm, and the magnetic field is a gradient of the founded potential - equation 2.3. The magnetic field values, computed exactly in such a way, are used in the comparison with the experimental data. 3. The comparison algorithm GOES - Geostationary Operational Environmental Satellite, circles the Earth in a geosynchronous orbit (6.6 R E ) over the equator, thus observing the Earth from the exact same place all the time. They were launched to monitor the atmosphere for severe weather development such as tornadoes, flash floods, hailstorms, and

4 Dobreva, Borodkova, Kartalev, Zastenker hurricanes. The magnetic field is measured by the twin-fluxgate spinning sensor on board the satellite. Vx, km/sec Temp, ev Dens, n/sm WIND Plasma Data, 23 May, :30 16:45 17:00 17:15 UT Fig. 1. Input data for the case 23 May 2000 density, velocity and temperature, measured by WIND satellite. Table 1. Input data for the case 23 May, 2000: time moment, density ρ in sm -3, velocity V x in km/s, temperature in K, B y and B z Interplanetary magnetic field components (in nt in GSE coordinates ), Dst index and the dipole tilt angle (in radians). UT ρ V x T B y B z Dst Tilt 16: : We consider the case 23 May, 2000, and the period 16:15-17:20 UT along the orbit of GOES satellites. The input for the Imech model data - density, velocity and temperature, shown in fig. 1, are taken from WIND satellite and appropriately shifted in time. It can be seen at the figure, that at 16:55 UT all the input parameters change, as the density and temperature increase, while the velocity decreases. The standard algorithm - Dobreva 2005 [1], is applied for the choice of the input parameters and the model calculation. Namely, the interval is divided into two subintervals with relatively permanent values of the parameters. Average parameters values are chosen for each of the intervals - the data are given in table 1.

5 Comparison of GOES measurements with IMech model Table 2. Location (in GSM coordinate system) of GOES 10 for the above mentioned time moments from the trajectory of the satellite on 23 May, UT X gsm Y gsm Z gsm 16: : Model calculations are performed for each of the intervals. It is obtained the magnetic field distribution in the whole magnetosphere region. Particularly, the magnetic field at the points of the satellite location can be calculated. 60 Bx (GSM) By (GSM) GOES 10 Magnetic field, 23 May, Bz (GSM) UT 16:15 16:30 16:45 17:00 17:15 17:30 Fig. 2. Comparison between measured by GOES (solid line), numerically calculated (asterisks) and Tsyganenko 96 (circles) magnetic field for the case 23 May, The coordinates of the GOES 10, corresponding to the two time moments (16:50 and 17:10 Ut) are given in table 2. The results between measured and model received values are presented in fig. 2. The magnetic field variation between 16:50 and 17:10 UT, caused by corresponding variations in the solar wind data, could be observed also in the model results. 4. Summary Capabilities of the magnetosphere module of the IMech model are tested. It is observed a good coincidence between measured and computed magnetic field at the geostationary orbit. Magnetic field changes, caused by solar wind variation, are also registered by the model. This is a preliminary test and further investigations needed.

6 Dobreva, Borodkova, Kartalev, Zastenker R E F E R E N C E S [1] DOBREVA, P. S., M. D. KARTALEV, N. N. SHEVYREV, G. N. ZASTENKER. Compassion of a new magnetosphere-magnetosheath model with Interball-1 magnetosheath plasma measurements, Planet. Space Sci., 53, , [2] KARTALEV, M. D., M. S. KASCHIEV, D. K. KOITCHEV. Finite element numerical modeling of stationary two-dimensional magnetosphere with defined boundary, J. Comput. Phys., 119, , [3] KARTALEV, M. D., V. I. NIKOLOVA, V. F. KAMENETSKY, I. P. MASTIKOV. On the self-consistent determination of dayside magnetopause shape and position, Planet. Space Sci., 44, , [4] KLOUCEK, P., F. R. TOFFOLETTO. The three dimensional non-conforming finite element solution of the Chapman-Ferraro problem, J. Comp. Phys., 150, , [5] KOITCHEV, D. K., M. S. KASCHIEV, M. D. KARTALEV. Simplified 3D magnetospheric magnetic field, In Finite Difference Methods: Theory and Applications, , Nova Science Publishers, [6] MAGOMEDOV, K. M., A. S. HOLODOV. Grid-Characteristic Numerical Methods, Nauka, Moscow, [7] STERN, D. P. Parabolic harmonics in magnetospheric modeling: The main dipole and the ring current, J. Geophys. Res., 90, , [8] TOFFOLETTO, F. R., R. V. HILMER, T. W. HILL, G.-H. VOIGT. Solution of the Chapman-Ferraro problem with an arbitrary magnetopause, Geophys. Res. Lett., 21, , [9] TSYGANENKO, N. A., A. V. USMANOV. Determination of the magnetospheric current system parameters and development of experimental geomagnetic field models based on data from IMP and HEOS satellites, Planet. Space Sci., 30, , [10] TSYGANENKO, N. A. Global quantitative models of the geomagnetic field in the cislunar magnetosphere for different disturbance levels, Planet. Space Sci., 35, , [11] TSYGANENKO, N. A. A magnetospheric magnetic field model with a warped tail current sheet, Planet. Space Sci., 37, 5-20, [12] TSYGANENKO, N. A. A model of the near magnetosphere with a dawn-dusk asymmetry 1.Mathematical structure, J. Geophys. Res., 107, 1179, [13] TSYGANENKO, N. A. Modeling the Earth's magnetospheric magnetic field confined within a realistic magnetopause, J. Geophys. Res., 100, , [14] VOIGT, G.-H. A three dimensional analytical magnetospheric model with defined magnetopause, Z. Geophys., 38, , [15] VOIGT, G.-H. A mathematical magnetospheric field model with independent physical parameters, Planet. Space Sci., 29, 1-20, 1981.