Analysis of multiple current layers in the magnetopause region with Cluster

1. Analysis of multiple current layers in the magnetopause region with Cluster A. Blăgău (1, 2), B. Klecker (1), G. Paschmann (1), M. Scholer (1), B. U. Ö. Sonnerup (3), S. Haaland (1, 4), O. Marghitu (2, 1), I. Dandouras (5), L. M. Kistler (6) and E. A. Lucek (7) (1) Max-Planck-Institut für extraterrestrische Physik, Garching, Germany (2) Institute for Space Sciences, Bucharest, Romania (3) Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA (4) Department of Physics, University of Bergen, Norway (5) CESR-CNRS, Toulouse, France (6) Space Science Center, University of New Hampshire, Durham, USA (7) Imperial College, London, UK

2. Abstract The current system in the magnetopause (MP) region often presents itself as a multiple layer structure. We have investigated two such cases seen by the Cluster satellites during dayside out-bound traversals: one having a well-defined two-step boundary layer and the other with a pronounced overshoot in the magnetic signature located on the magnetospheric side. By timing analysis (TA) and making use of the multipoint character of the mission one can determine the MP orientation and velocity along the normal as well as the thickness of each individual layer. For both cases the normals obtained in this way are in good agreement with those provided by the single spacecraft minimum variance method, which adds confidence to our results. The nature of the finer, super-imposed magnetic fluctuations seen during the MP crossing in one of the cases is investigated.

3. Minimum variance analysis (MVA) of the magnetic field • Gives n, no V • Single satellite method • Assumes the MP is a planar, time-stationary, 1-D discontinuity • Finds the direction in space along which the magnetic variation has a minimum and associates it with the MP normal • Sometimes the simple, un-constrained MVA gives false results (i.e Bn unreasonable large) • It is better to do both constrained (by imposing Bn=0) and unconstrained MVA and to compare the results • (Sonnerup, B. and Scheible, M., ISSI Report, 1998)

4. Timing analysis from the four Cluster satellites • Gives n and V • Relies on all 4 spacecraft measurements and on the assumption that the MP is locally planar • We have the task of determining the orientation and velocity of a plane that moves over the Cluster configuration. For solving it the 4 crossing times and the satellites position at the time of crossing are sufficient • For assigning the 4 moments of time we fitted the magnetic data corresponding to the transition and pick representative points of the fit (e.g. central points). In addition, from the duration of the transition we compute the discontinuity thickness • We could assume that the velocity of the discontinuity is constant (Constant Velocity Approach, CVA) or that it has a constant thickness (Constant Thickness Approach, CTA) • (Haaland, S. et. al. AnnGeo, 22, 4, 2004)

5. Minimum variance analysis of the current density • gives n and V • Appropriate when the spacecraft separation is small compared with the scale-length of the discontinuity • It is a multi-spacecraft method • The current density is first obtained from the curlometer technique (by using Ampere’s law) • For determining the normal a constrained MVA analysis on the current density is performed (relies on ‹Jn› = 0 assumption) • Assuming a constant velocity for the discontinuity we could find V by integrating the components of Ampere’s law in the barycentric reference frame • (Haaland, S. et. al. GRL, 31, 10, 2004)

6. DeHoffmann-Teller frame method • Gives the velocity of the discontinuity as a whole, no n • Single-spacecraft method • Applicable when the MP possesses a good deHoffmann-Teller frame • Search for the existence of a reference system in which the convection electric field is zero (search whether the data corresponding to a discontinuity could be interpreted as produced by time-stationary structure, without an intrinsic electric field, that moves across the spacecraft) • We compared the projection of deH-T velocity along the normal direction (obtained from other method) with the velocity obtained from the timing analysis • (Khrabrov, A. and Sonnerup, B., ISSI Report, 1998)

7. Cluster trajectory and configuration at 2002-04-13 Cluster constellation projected on MP plane and in a plane containing the MP normal (at 21:51:30) Cluster orbit in GSE • Crossing in the dayside northern hemisphere • Separation distance around 100 km (ideal for curlometer) • The sequence of crossings is Cluster1, 4, 3 and 2

8. Cluster1 ions (HIA) and magnetic field (FGM) data sets • Particularly interesting is the step-like variation seen in magnetic field max-var component, density, temperature and pressure • We have a complex transition, with a two-step boundary layer followed by the magnetopause crossing • The total pressure (magnetic + plasma) is in approx. equilibrium in the boundary layers but not at the magnetopause • The limits of the inner and outer boundary layer show a well-defined magnetic rotation, allowing us to determine the orientation, velocity and thickness for all layers

9. MP interval: fit for max-var component of B field • Fitting function: superposition of two displaced tanh functions • Magnetopause definition: the interval where most of the magnetic change occurs (approx. 76% of the total jump) • From fit we obtained the central time T_middle (to be used for timing) and dT (for thickness calculation)

10. Normals for the magnetopause interval • The center of the polar plot represents a reference direction in space, which we took as the average over the four normals from the constrained MVA on B • There is one normal given by the un-constrained MVA on B (with the corresponding error ellipsis) and one normal given by constrained MVA on B (with error segment) at each satellite level • There are two normals from timing analysis (CTA and CVA methods) and one from MVA for J • We conclude that the constrained MVA algorithm offers a better estimate for the normal because: • the Walen test for the MP failed (therefore it behaves like a tangential discontinuity) • in the planar case, the normal for the MP interval should be very close to the normal corresponding to the outer BL margin and this condition is fulfilled when using the constrained method • If we neglect the un-constrained normals, the remaining ones are within a cone of approx. 5 deg.

11. Normals for outer boundary layer margin • Fitting function: difference of two displaced tanh (to account for the overshoot) • The origin of the plot is the same as for the MP interval • In this case the constrained and un-constrained normals are well separated • The timing analysis and the MVA on J are very close to the normals obtained by constrained MVA on B (within a cone of approx. 3 deg.) • We have a tangential discontinuity between inner and outer boundary layer

12. Normals for boundary layer margin • Fitting function: difference of two displaced tanh (to account for the overshoot) • In this case the normals are more spread in direction, possibly because we have a small, low-shear transition • The uncertainties are higher but still within approx. 12 deg. • The origin of the plot is different by approx. 12 deg (MP normal direction is indicated by the violet square)

13. Velocities and thicknesses Fit between the convection electric field Ei=Vi X Bi and the VdHT X Bi • From TA we obtained for each discontinuity a velocity (shown in blue) and a thickness (in km and scaled to gyro-radius) • In the plateau regions the thicknesses were computed by using averaged velocity • For the MP we identified a good deHT reference frame (cc 0.9947 and slope of 1.0024) • The deHT velocity perpendicular to the MP (in violet) is in good agreement with the one from timing • If we search for an accelerated deHT frame we obtain an inward acceleration (shown in red), consistent with our timing velocities at MP and outer boundary layer • In this case the MVA on J failed to provide reasonable results for the normal velocity

14. Cluster trajectory and configuration at 2003-03-20 Cluster constellation projected on MP plane and in a plane containing the MP normal (at 04:44:30) Cluster orbit in GSE • Crossing in the dayside northern hemisphere • Separation distance around 5000 km (not suitable for curlometer technique) • The sequence of crossings is Cluster1, 2, 4 and 3

15. Cluster 1 and 3 ions and magnetic field data sets • The large scale conditions for this event are very stable. A finer superimposed oscillation in the exterior plasma parameters is observed and how it penetrates into the magnetosphere • We have the case of clear and regular MP transitions at all satellites levels which is ideal for the timing analysis

16. Fit for max-var component of B field • There is a large overshoot in the max-var component of the magnetic field at the magnetosphere edge • Fitting function: superposition of two displaced tanh functions, corresponding to anti-parallel current sheets • If the asymptotic levels are Bsphere and Bsheath than we considered the MP to be the region where the fit is between Bsheath + tanh(1)*(Bsphere - Bsheath) and Bsphere - tanh(1)*(Bsphere - Bsheath) i.e approx 76% of the total jump between the asymptotic levels • If the peak of the fit is Bmax than we consider the left overshoot margin to be at Bsphere + tanh(1)*(Bmax -Bsphere) • The central times and durations for both regions are used in a TA

17. Normals, thicknesses and velocities • From TA (CVA method) the average MP thickness is around 1770 km (~12 RL) and the average overshoot region is around 2400 km (~ 16 RL) • The inward velocity for the MP region obtained from TA is around 152 km/sec and the one for the overshoot region around 181 km/sec. We identified a good deHT frame and this technique, applied on the whole interval (MP + overshoot), gives an inward velocity of 194 km/sec • From TA applied on the MP region we obtain a normal of approx. 10 deg. from the average normal provided by the constrained MVA on B. Given the large inter-spacecraft separation and the expected non-constancy of MP velocity, there is a good agreement between the two methods • In this case there are indications suggesting a 2D MP shape, which prevents the use of CTA method

18. Superimposed oscillations • When substracting the general trend (described by a double anti-parallel curent layer) from the actual data we obtain the smaller-scale oscillations with a time-period of around 7 sec. • Inside the MP (left from the dotted vertical line) the oscillations are damped. The attenuation constants, obtained by fitting with a damped sine function, are ~ 2787 km (~16 RL) for Cluster3 and ~1193 km (~10 RL) in case of Cluster4

19. Summary and conclusions • We studied two magnetopause crossing events that show a multiple layer structure of the current system in that region • By applying a timing analysis on the magnetic profiles of each of these layers we determined their thicknesses and normal velocities. In both cases a ‘good’ DeHoffmann-Teller frame was identified. By comparing the results provided by both methods a reasonable agreement was found • Several methods were used for inferring the normal orientation (i.e. constrained and un-constrained MVA on B, timing analysis and MVA on J in case of small satellite separation). We found that the results are in good agreement when the constrained MVA algorithm is used • In the first case, the timing analysis supports the interpretation of a three layer structure (MP plus a two-step BL) • In the same case, the various methods for normal determination are consistent with the idea that between the inner and outer boundary layer there is a tangential discontinuity. This also explains why the two regions do not mix, keeping that two-step profile • In the second case a large overshoot region is present, whose thickness is even larger than that of the MP. In this event we showed how the small-scale superimposed oscillations in the magnetic field are damped as they enter the magnetosphere

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