1. Investigation of Field-aligned Currents Onboard of Interkosmos Bulgaria-1300 Satellite Dimitar Danov Solar-Terrestrial Influences Laboratory, Bulgarian academy of sciences

2. Introduction BULGARIA-1300 SATELLITE Launch date: 07-08-1981 Termination date: Termination date: 17-02-1983 Perigee (km): 825 Apogee (km): 906 Inclination (°): Inclination (°): 81.2 Eccentricity: 0.005 Spin rate (rpm): 0

3. Introduction BULGARIA-1300 SATELLITE Triaxial Fluxgate Magnetometer Triaxial Fluxgate Magnetometer Magnetic field components B x, B y, B z Dynamic range ±64000 nT Sensitivity 5 nT 5 nT Time sampling 80 or 320 ms Number of Fine scales 256 Fine scale (Dynamic range) ~500 nT

4. Introduction Reason for … The statistical picture of large-scale field-aligned current (FAC) distribution has been obtained by Iijima and Potemra [1976] and by many satellite observations including latest Iridium results (Waters et al. [2001]). At the same time it is well known that large-scale field aligned current sheets are frequently stratified on multiple sheets (see Kamide and Rostoker [1977]). Antonova et al. [1998] discussed the mechanisms of such stratification.

5. Investigations of the stratifications of large-scale field-aligned current bands on multiple field-aligned current sheets were limited by the assumption of the existence of infinite homogeneous current sheets. However, this assumption is valid when the width of the current sheet in longitudinal direction exceeds significantly its size along the meridian. Investigations of the stratifications of large-scale field-aligned current bands on multiple field-aligned current sheets were limited by the assumption of the existence of infinite homogeneous current sheets. However, this assumption is valid when the width of the current sheet in longitudinal direction exceeds significantly its size along the meridian. This allowed reducing the three-dimensional problem to one- dimensional one and deriving FAC’s structure from one-satellite measurements This allowed reducing the three-dimensional problem to one- dimensional one and deriving FAC’s structure from one-satellite measurements. Introduction Reason for … We try to evaluate the corrections considering a finite size of the sheet in the longitudinal direction and show the efficiency of our methodology using Interkosmos–Bulgaria-1300 magnetic field measurements.

6. We identify current sheets in magnetic field data “manually” by the following algorithm: 1.Process the telemetry and obtain three magnetic components in satellite coordinate system 2.Subtract the model IGRF geomagnetic field from the measured field 3.Transform the magnetic vector to three components in spherical Solar Magnetic (SM) coordinate system 4.Analyse the graphs of these components to identify the sheets 5.The value (and sign) of the current density is evaluated by a simple program In the past we have done all these steps automatically, but we obtained many false currents.

7. Whenever the current density is estimated from the curl(B) the following approximation is very popular curl(B) ~  B y /  x ~  By/V x  t Sources of errors ??

8. MODELS SELECTED We use two models of current sheets, to understand possible errors : 1.Model of a finite plane current sheet current sheet in X,Y directions with a rectangular form and constant current density inside the rectangular: j=const if a1  x  a2, b1  y  b2 and j=0 outside this interval. 2.Conical model (used by Tsyganenko 2001) current sheet is defined inside the spherical cone : j=const if a1   a2 and j=0 outside this cone.

9. Model of a finite current sheet The normal (meridional) component of the magnetic field disturbance for such configuration is symmetric with respect to the tangential surface of symmetry and antysymmetric with respect to the normal one. The tangential (zonal) component is antysymmetrical with respect to the tangential surface of symmetry and symmetrical with respect to the normal one.

10. Model of a finite current sheet Model of a finite current sheet One sheet, s/c trajectories are normal to it Changes in the tangential and normal components of the magnetic field corresponding to the field-aligned current sheet shown at the top, the satellite orbit is perpendicular to the sheet. Trace - 1 near the ‘center’ of current sheet Trace - 3 near the ‘termination’ of current sheet As seen from graphs on this slide,  B y /  x approximation and the possible limited size of the current in Y-direction can be a cause for the appearance of ‘false’ currents.

11. Model of a finite current sheet Model of a finite current sheet One sheet, s/c trajectories are normal to it Trace - 1 near the ‘center’ of current sheet Trace - 3 near the ‘termination’ of current sheet  the current sheet  False current sheet with  B y /  x >0 Another false current sheet  B y /  x >0

12. Model of a finite current sheet Model of a finite current sheet Two sheets, trajectories are normal to it Trace - 1 Trace - 2 Trace - 3 The value of the current density is equal in both sheets, but their directions are opposite. In case of TRACE 1 & 2 one can estimate equivalent (and opposite) current densities. NO false currents In case of TRACE 3 one can estimate different (and opposite) current densities. AS WELL false currents

13. Model of a finite current sheet Model of a finite current sheet Very complicated case It is good that B-1300 satellite has such Inclination, and cuts across FAC sheets near it’s normal. Cross with fair approach to normal Cross with fair approach to tangent Cross with big angle

14. Obtaining of ‘false’ currents sheets can be demonstrated also with the conikal model.

15. Conical model ( used by Tsyganenko in his work from 2001) This model is defined in spherical coordinate system. It is complicated but self consistent. outside the interval a1    a2 and where in the interval a1    a2

16. Conical model ( used by Tsiganenko 2001) Formulas for meridional and zonal components of the magnetic field are to long, for that reason we will show only graphs. Trajectory provisionally parallel to 5 MLT zonal meridional  the current sheet  False current sheet with  B y /  x <0 False current sheet with  B y /  x <0

17. The X-axis represents the distance (in percents) from satellite trajectory to symmetry surface (100%) 1.The calculated current density is always less than the real one; the  B y /  x approximation works well only in case when s/c crosses the sheet near its middle; 2.There are cases when the satellite does not cross the sheet, but the change in the tangential component is significant – one can obtain false current. In the model of finite current sheet we evaluate the difference between the value of the modeled tangential component of the magnetic field at both edges of the sheet.

18. Magnetic data & Field Aligned Currents The procedure we use to avoid obtaining false currents: We calculate the currents only for those measurements which: longitudinal 1. The graph of the longitudinal component B   is linear;  B  between both edges of the linear interval is greater than 50nT;  max(B  ) – min(B  ) < 30nT (for the meridional component); 4. The correlation coefficient between B  and  is greater 0.9 5. j =  0 -1  B      coefficient of the linear regression B  to 

19. Magnetic data & Field Aligned Currents Seance 217. Midnight satellite trajectory. Series of FACs are present. Tsyganenko-2001 model field is plotted with symbols. Tsy-2001 c/ sheet  Tsy-2001 c/ sheet 

20. Magnetic data & Field Aligned Currents Seance 183. Midnight satellite trajectory. FAC is directed into ionosphere. Tsyganenko-2001 model field is plotted with symbols. Tsy-2001 c/ sheet  Tsy- 2001 c/ sheet 

21. Statistics of current sheets FAC density thickness distribution measured aboard ICB-1300 satellite It is possible to see that more than 60% of observed current sheets have thickness less than 1.5 0.

22. Conclusions and discussion The conducted analysis shows that both components (meridional and zonal) of the magnetic field must be taken into account when estimating the FAC density and position, to eliminate the false groups of sheets. Estimated from measurements FAC density is always smaller than the real one, up to 25% at the end of the sheet. The FAC density is greater and thickness is smaller than usually accepted. We compared the results of our analysis with Tsyganenko [2002] and Papitashvili et al. [2001] models and results of Lukianova et al. [2001]. It is possible to mention that Intercosmos-Bulgaria-1300 observations show that FAC density is greater and thickness is usually smaller, than in these works. Unfortunately we have no sufficient data to investigate the dependence of FAC's density or thickness on other parameters like Kp, Dst or Solar Wind parameters

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