. .. Event-overview, 67 7.4 Determination of the local coordinate system, p.70

. .. , 71 7.5.1 Computing the distance spacecraft-reconnection site with the FOTE method

. .. Electron-scale-structuring-of-the-edr, , p.75

C. .. Discussion, , p.78

.. .. Future,

, A Supplemental material about the determination of the local coordinate system

?. G. Cozzani, A. Retinò, F. Califano, A. Alexandrova, O. L. Contel et al., In situ spacecraft observations of a structured electron diffusion region during magnetopause reconnection, Phys. Rev. E, vol.99, p.43204, 2019.
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?. O. Pezzi, G. Cozzani, F. Califano, F. Valentini, M. Guarrasi et al., ViDA: a Vlasov-DArwin solver for plasma physics at electron scales, Journal of Plasma Physics, vol.85, issue.5, p.905850506, 2019.

?. H. Breuillard, O. L. Contel, T. Chust, M. Berthomier, A. Retinò et al., The properties of lion roars and electron dynamics in mirror mode waves observed by the Magnetospheric MultiScale mission, Journal of Geophysical Research: Space Physics, vol.123, pp.93-103, 2018.
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?. J. Webster, J. L. Burch, P. H. Reiff, A. G. Daou, K. J. Genestreti et al., Magnetospheric Multiscale Dayside Reconnection Electron Diffusion Region Events, Journal of Geophysical Research: Space Physics, vol.123, pp.4858-4878, 2018.

?. Z. Wang, H. S. Fu, C. M. Liu, Y. Y. Liu, G. Cozzani et al., Electron distribution functions around a reconnection X-line resolved by the FOTE method, Geophysical Research Letters, vol.46, pp.1195-1204, 2019.

?. Z. Chen, H. S. Fu, C. M. Liu, T. Y. Wang, R. E. Ergun et al., Electron-driven dissipation in a tailward flow burst, vol.46, pp.5698-5706, 2019.

, Schematic picture of magnetic field merging

, At time t, prior to reconnection, the fluid element A and B (C and D) are frozen to the same field line (left panel)

, Reconnection electric field, magnetic field, and in/outflow velocities, are shown in orange, black, and red/blue respectively, p.16, 2002.

, Schematic rapresentation of the explanation for the out-of-plane quadrupolar magnetic field

, A schematic representation of the stretching of the reconnected magnetic field lines in the z direction caused by the non uniform v e,z across the current sheet. The loop represents the magnetic field line initially lying the xy plane. The arrows directed along z represent the electron velocity which is larger in the center of the current sheet, 1994.

, Ion and electron orbit within the current sheet. The magnetic field is B = bx ? x/?? and the electric field is E = ?a?, 1965.

]. .. Yamada, 19 2.10 Schematic diagram of the diffusion region. Ions are decoupled from the electrons and from the magnetic field in the ion diffusion region. The Hall magnetic and electric field patterns are present in the IDR. Electrons are demagnetized in the electron diffusion region, Schematic representation of the crescent-shaped distribution function in the velocity space and the corresponding orbit in the xz plane, 2015.

, The Earth's magnetosphere with (a) southward IMF and (b) and northward IMF obtained with simulations with no dipole tilt. The white lines are the magnetic field lines. Earth is the white sphere at the origin and the Sun is to the right. The background color represents the out-ofplane current density

. .. Adapted-from-komar-;-], , 2015.

P. .. Gonzalez, Density n, magnetic field strength B, ion temperature T i , ion Alfvén speed c A , and plasma beta ? are reported. The parameters on the magnetosheath side are computed from observations in the solar wind with the assumptions that across the bow shock the density and magnetic field strength increase by a factor of 4, the solar wind ion temperature increases by a factor of 10 across the bow shock and that there is no further change in the shocked solar wind plasma as it convects from downstream of the bow shock to the subsolar magnetopause. a The Alfvén speeds in parenthesis are derived assuming anti-correlation between the solar wind density and interplanetary magnetic field strength, Typical plasma parameters at the magnetospheric side (top) and at the magnetosheath side (bottom) of the Earth's subsolar magnetopause, vol.27, 2016.

E. Shay, The red solid lines indicates where the cuts shown in the other panels were taken (L = 6.35 d i ). (k) Three components of the magnetic field; (l) three components of the electric field; (m) ion and electron number density; (n) parallel and perpendicular (to the magnetic field) electron temperature; (o) three components of the electron velocity; (p) three components of the ion velocity, 2016.

. .. , 2 MMS orbit during (left) Phase 0 and 1, (center) the transition from Phase 1 (apogee of 12 R E ) to Phase 2 (apogee of 25 R E ), (right) Phase 3. The orbits are shown in the x-y plane (GSE coordinates), p.34

, Ecliptic-plane scheme of MMS orbit (red dashed). The ROI is the blue orbital segment while the burst segments are in yellow, p.35

, SDP booms and probes in the x-y plane, p.38

, Schematic description of the Field Of View (FOV) of the top hat electrostatic analyzers (ESA) used in the FPI instrument, p.39

, The DES (or DIS) locations are indicated with the numbers from 1 to 8 on the spacecraft. Each spectrometer exercises four deflected fields of view with a maximum deflection of ? 17 ?

, Schematic representation of the current densities computed with the Curlometer method

V. .. Cs, Schematic representation of MMS tetrahedron encountering a planar discontinuity moving with a constant velocity, vol.46

, Schematic representation of a A-type radial magnetic null (left) and of a As-type spiral magnetic null (right)

, The reconnected magnetic flux versus time from a variety of simulation models as shown in Birn et al, 2001.

, (a) Magnetic field components as measured by WIND and propagated to the magnetopause; (b) MMS1 magnetic field components; (c) MMS1 ion density and (d) MMS1 ion velocity components; (e) Zoom-in of the MMS1 magnetic field components and strength; (f) Zoom-in of the electron velocity components. Data are shown in GSE. The yellow shaded region in panels (a)-(d) indicates the EDR crossing, MMS location relative to Earth and the average magnetopause boundary, shown in GSE, in units of Earth radii

, components of the solar wind velocity measured by WIND on the day of the EDR encounter

, Four spacecraft measurements of (a) B L ; (b) B M ; (c) B N ; (d) J L

J. M. , Since the velocity of the magnetopause is much larger than the spacecraft velocities, the MMS path shown is produced entirely by the motion of the magnetopause in the LN plane. The three tetrahedra represent MMS location at different times along the trajectory; (h) Projection of the MMS tetrahedron in the LN and in the MN plane

, 5 (a) Four spacecraft magnetic field strenght; (b) |r CM ? r null | where r CM is the position of the center of mass of MMS tetrahedron and r null is the position of the magnetic null point

, (a) Magnetic field components and strength; (b) electron velocity components; (c) current density components; (d) M component of electric field (30 ms resolution), (v e × B) M (30 ms resolution), (v i × B) M (150 ms resolution); (e) agyrotropy parameter ? Q; (f) parallel and perpendicular electron temperature, The yellow shaded region include the interval of the EDR encounter and it corresponds to the time interval of Figure 7.7

E. ·j, E. , M. , E. , and N. , The ?, ? and ? lines correspond to the times of the ?, ? and ? distribution functions in panels (l)-(t) shifted accordingly to the timing method. (k) Cartoon of J M and of the energy conversion, Four spacecraft (a) B L ; (b) Time-shifted B L . (c) Time-shifted J M ; (d) Time-shifted J N ; (e) Time-shifted E M

E. Adapted and . Swisdak, , 2018.

, / E rec where E rec is the is the time average of the reconnection electric field for the period where reconnection is ongoing. The magenta lines are electrons trajectories. The three white arrows show the direction of the electron flow, Contours of f M / E rec = (E+v×B) M, 2018.

, MMS location relative to Earth, shown in GSE, in units of Earth radii. The magenta lines represents the magnetic field lines. The orbit of MMS is in black and the Region Of Interest (ROI) of the orbit is colored in yellow. The light blue diamond represents MMS at the time of the EDR encounter, vol.9

. .. E-n-j-n-;(h)-e-·-j, 11 (a) B z and B L magnetic field components in the GSE (black), LMN (blue) and LMN rotated (red) coordinate systems; (b) B y and ?B M magnetic field components in the GSE (black), LMN (blue) and LMN rotated (red) coordinate systems; (c) J z and J L, vol.7, p.85

, associated maximum error for the four spacecraft; (Bottom left) E N J N and its associated maximum error for the four spacecraft; (Bottom right) E · J and its associated maximum error for the four spacecraft, Illustration of the magnetopause crossing as inferred from the data shown in the LMN (green line) or in the LMN rotated coordinate systems, vol.87

. ?-?1-c,p-;-(c)-t-*-=-15, 27 ? ?1 c,p ; (d) t * = 18.61 ? ?1 c,p . The domain sheets. The contour lines of the magnetic flux ? are superposed

. .. , Time evolution of the reconnected magnetic flux ??, p.102

, Contour plots of B z (a); out-of-plane electron current density j e,z (b)

, The contour lines of the magnetic flux ? are superposed. 103 8.4 (a) x component of the electron velocity u e (black line) and of the proton velocity u p (red line) at x * = 3.00 d p and (b) at x * = 10.52 d p . The quantities are shown at the time t * = 18.13 ? ?1 c, p.103

. Jara-almonte, In this simulation, the z direction is the outflow direction and the x direction is normal to the current sheet, 2014.

, 2 Profiles of the magnetic field and density for the Harris kinetic equilibrium

. .. , Initial unperturbed profiles of (a) the magnetic field B x (y); (b) the density n(y) (n e = n p = n); (c) the current density j z (y), p.110

, 4 (top) Time evolution of the reconnected magnetic flux ??; (bottom) time evolution of the normalized reconnection electric field cE z /B 0 V A,p at the X-point

, Contour plot of (a) the reconnecting magnetic field component B x ; (b) the out-of-plane magnetic field B z ; (c) the reconnection electric field E z . All quantities are shown at time t * = 3752 ? ?1 p,e and zoomed in y in the interval [0, 35] d e . The contour lines of the magnetic flux ? are superposed

, ) the proton outflow velocity v p,x ; (c) the out-of-plane electron current density j e,z ; (d) the electron density n e . All quantities are shown at time t * = 3752 ? ?1 p,e and zoomed in y in the interval [0, 35] d e . The contour lines of the magnetic flux ? are superposed

, The contour lines of the magnetic flux ? are superposed, Contour plot of the out-of-plane electron current density at time t * = 3752 ? ?1 p,e and zoomed in y in the interval

, The contour lines of the magnetic flux ? are superposed, p.116

, 10 Contour plot of the out-of-plane magnetic field B z at different times (a) t * = 0 ? ?1 p,e

A. , 1 (a) Schematic rapresentation of the Earth in the GSE coordinate system. µ indicates the Earth's dipole. (b) Schematic representation of the reconnecting magnetopause current sheet in the boundary local coordinate system, p.126, 2016.

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