Estimation of electron temperature at sub-spin time resolution 

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Magnetic Field Measurements

The magnetic eld is measured by two instruments on board Cluster, a ux-gate magnetometer (FGM) (Figure 3.4) and a search-coil magnetometer (STAFF)(Figure 3.5). FGM focuses on DC eld measurements while STAFF measures uctuations of the magnetic eld.

Flux-gate magnetometer

A ux-gate magnetometer consists of two coils wrapped around a ferromagnetic core. Alternating current is applied to the primary coil creating an induced current in the secondary coil. If there is no external magnetic eld the current induced in the secondary coil will be the same as the current applied in the primary coil.
An external magnetic eld will create an oset between two currents which yield a measurement of the magnetic eld.
The FGM instrument on board Cluster consists of two tri-axial sensors measuring the three components of the magnetic eld [51]. One sensor is placed at the end of a 5.2 meter boom while the other is placed on the same boom 1.5 meter away from the spacecraft body, in order to control the magnetic interference from the spacecraft. The ux-gate sensors are nominally sensitive in the range 0Hz to 10Hz, although in practice the instrument noise level is such that the sensitivity degrades signicantly above 1Hz. For the DC eld the accuracy of the instrument is 0:1nT. The sampling rate in Burst Mode operation is 67Hz.

Search-coil magnetometer

STAFF consists of a magnetic waveform unit (STAFF-SC) and a spectrum analyzer (STAFF-SA). The rst measures uctuations of the magnetic eld from 0:1Hz up to 4kHz while the second computes spectra of the magnetic and electric eld from 8Hz up to 4kHz. It consists of a coil wrapped around a ferromagnetic core. In the presence of a varying external magnetic eld, the variation of the magnetic ux induced by the eld is proportional to the voltage induced in the coil. The STAFF instrument has a tri-axial search-coil sensor operating at frequencies between 0:1Hz and 4kHz. Given the transfer function of the instrument noise, the measurements are less sensitive than FGM below 1Hz. STAFF-SC provides waveforms of the 3 components of the magnetic eld with a sampling frequency of up to 450Hz in Burst Mode. STAFF-SA provides spectral matrices and power spectral densities for each of the 3 components of the magnetic eld (Bx;By;Bz) and for two components of the electric eld (Ex;Ey) at dierent time resolutions for frequencies from 8Hzup to 4kHz. Those quantities are calculated on board using measurements by the magnetic eld sensors (STAFF) and electric eld probes (EFW). In Burst mode, spectral matrices are provided in the frequency range of 64Hz to 4kHz with 1s resolution, while the power spectral densities are provided
for the same frequency range but at higher time resolution (0:125s or 0:25s).

Electric Field Measurements

 The electric eld is measured by the EFW instrument [50] using four spherical probes located at the end of thin wire booms extending outwards from the spacecraft in the spacecraft spin plane and phased by 90o in that plane [110]. Two probes in each pair are kept at a distance of about 88m from each other by the rotation of the spacecraft around its axis. The requirement for a relatively long distance between the probes and the spacecraft comes from the necessity to overcome the eects of the Debye shielding as well as the photoelectron cloud around the spacecraft. Additionally, the larger distance between the probes results in a larger potential dierence, which is easier to measure. The potential dierence between two opposed probes yields a measurement of the electric eld in the direction along the axis dened by the two probes (Figure 3.7). The use of the 4 probes allows an estimation of two orthogonal components of the electric eld in the plane of the spacecraft spin. There is no antenna to measure the component of the electric eld along the spin axis, that can only be estimated from the two components measured in the plane. Such third component is deduced by using the assumption ~E ~B = 0. This assumption leads to signicant errors when the angle between the magnetic and the electric eld is small and cannot be used at all when they are aligned since it degenerates. In the case of EFW the third component is usually not calculated if the angle between the magnetic and the electric eld is below 15o. More recent missions such as MMS are equipped with a rigid antenna and directly measure the component of the electric eld along the spin axis. For Cluster, the probe to probe potential and the subsequent electric eld measurement are given at a sampling rate of up to 450Hz in when operating in Burst Mode.

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Table of contents :

List of Figures
List of Tables
1 Introduction 
2 Theoretical Background 
2.1 Magnetic Reconnection
2.2 Turbulence
2.3 Magnetic Reconnection in Turbulence
3 Instruments and Data Products 
3.1 Cluster Mission Overview
3.2 Magnetic Field Measurements
3.2.1 Flux-gate magnetometer
3.2.2 Search-coil magnetometer
3.3 Electric Field Measurements
3.4 Spacecraft Potential
3.5 Electron Measurements
3.5.1 Instrument Operation
3.5.2 Data Products
3.5.3 Main issues
4 Methods of data analysis 
4.1 Methods for the detection of current sheets
4.1.1 Partial Variance of Increments
4.1.2 Magnetic Shear Angle
4.1.3 Curlometer technique
4.2 Orientation and motion of current sheets
4.2.1 Minimum Variance Analysis
4.2.2 Timing Analysis
4.3 Estimation of electron temperature at sub-spin time resolution
4.3.1 Implementation
4.3.2 Diagnostics
4.3.3 Instrumental Limitations
5 Results 
5.1 Statistics of thin current sheets
5.1.1 Detection of current sheets
5.1.2 Properties of current sheets
5.1.3 Electron heating
5.1.4 Energy partition
5.2 Electron heating within reconnecting current sheet
5.2.1 Electron heating and acceleration mechanisms
5.2.2 Evidence of reconnection
5.2.3 Electron distributions and heating
5.2.4 Wave measurements
6 Conclusion and future work 
6.1 Conclusion
6.2 Future Work


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