The magnetic ®eld experiment onboard Equator-S and its scienti®c possibilities

The special feature of the ringcore ¯uxgate magnetometer on EquatorS is the high time and ®eld resolution. The scienti®c aim of the experiment is the investigation of waves in the 10±100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the in¯uence of the spacecraft on the magnetic ®eld measurement will be discussed. The work shows that the applied pre-and in¯ight calibration techniques are sucient to suppress spacecraft interferences. The oset in spin axis direction was determined for the ®rst time with an independent ®eld measurement by the EquatorS Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.


Introduction
The Equator-S magnetometer experiment (MAM) was built to provide: 1. Magnetic ®eld data in the frequency range up to 64 Hz 2. Online magnetic ®eld data for the Electron Drift Instrument (EDI) experiment 3. Near-Earth magnetic ®eld data for the attitude determination In comparison to former magnetic ®eld measurements in the magnetosphere, the¯uxgate magnetometer on Equator-S has an improved measurement accuracy (better than 5 pT/ p Hz) in the frequency range between 0.1 and 64 Hz. Fluxgate magnetometers of other ISTP mission like Wind (11 Hz) and Geotail (16 Hz) have lower sampling rates or less ®eld resolution. The same is valid for several magnetometers on the Interball spacecrafts. Some experiments try to overcome this shortcoming by using measurement ranges with band characteristics (e.g., the magnetometer on Freja; Zanetti et al., 1994). But those data must be processed with the help of a transformation into the Laplace domain, dierent channels must be weighted and ®tted together, and retransformed into the frequency range. The Equator-S¯uxgate magnetometer works with a dierent concept. The frequency range is not switched, only the dynamic range is adapted to the external ®eld, dependent on the orbit position. To achieve the high ®eld resolution near apogee (11 Earth radii) and to measure the Earth dipole ®eld near perigee (500 km), the instrument ranges must be switched between 250 nT and 50000 nT. Errors of sensor and electronics (noise and oset drift) must be small enough to correspond with the 8 pT resolution in the 250 nT range. The noise of the AD-converter was suppressed by an oversampling factor of up to eight. With a sampling rate of 128 Hz, a resolution of 8 pT and a low noise sensor the magnetic ®eld could be investigated to frequencies up to 64 Hz.
To determine the magnetic ®eld direction to better than one degree, as required by EDI to accurately inject its electron beam perpendicular to the magnetic ®eld, at a spin rate of 40 rpm a timing to better than 1 ms is required. Therefore the bandwidth of the analogue electronics of all ranges was ®xed to 100 Hz (see Fig. 2). That was a compromise between delay time requirements and aliasing error suppression. The delay time of about 10 ms at a 100 Hz bandwidth was stable enough to ful®l the 1 ms requirement. The risk of making aliasing errors caused by frequencies between 64 Hz and 200 Hz is low because former measurements with search coil magnetometers have shown no large ®eld amplitudes in this frequency region.
Another problem for the magnetic ®eld measurement onboard Equator-S was the vicinity of the magnetometer sensors to the main spacecraft, which included a torquer system with four iron-®lled coils (together 4 kg soft magnetic material). This was used for spin up and two air coils have been used for changing the spin axis of the spacecraft. Compared with magnetometer booms on other spacecraft (Cluster 5 m, Interball 13 m, Wind 12 m, Geotail and Polar 6 m) the 1.8-m booms of Equator-S are small. Therefore the investigation of the interaction between torquer coils and magnetometer were one of the most important pre-¯ight measurement tasks.

Instrument description
The Equator-S spacecraft carries two dual¯uxgate magnetometers in cold redundancy (main and redundant system). Each magnetometer consists of two threecomponent ringcore sensors (outboard and inboard), its analogue electronics, a 16 bit ADC, a data processing unit, and a DC/DC converter.
Electronics and sensors were manufactured by MPE and Magson GmbH, and the DC/DC converter by Imperial College, London. The block diagram of one of these systems is shown in Fig. 1 and the main technical parameters are listed in Table 1.
In order to detect and correct for the changing magnetic background of the spacecraft, outboard sensors are mounted at the tips of the two 1.8-m radial booms and inboard sensors are located 50 cm inward from the end of the boom. The Y components of the sensors are aligned in the boom direction. Two operation modes are installed in the onboard software. In dual mode, data of both sensors (OS and IS) are transmitted at a rate of 64 Hz. In single mode data from only the primary sensor is transmitted at a rate of 128 Hz. Either sensor can be con®gured as the primary sensor. The sampling process will be triggered with the transmission of the Z-component of the primary sensor for all components at the same time.
The following hard-and software tools are implemented: 1. An oversampling factor of 1 to 8 can be chosen by command. 2. The ranges can be switched automatically, depending on the magnitude of the external ®eld. The con®guration for auto ranging is programmable. Free parameters are the upper and lower thresholds for range switching, the number of vectors which have to exceed the threshold before the range will be switched, and the start range.  3. Compensation ®elds can be generated to reduce spacecraft generated oset. Maximum compensation ®elds in the 256-nT and in the 1000-nT range are 100 nT and in the upper ranges 5000 nT. 4. A test cycle using a sequence of compensation ®elds is implemented onboard.

Pre¯ight calibration
The magnetometer for Equator-S was tested over more than two years in test facilities of the following institutions and companies: Geomagnetic Observatory Niemegk, Germany, Technical University Braunschweig, Magnetsrode, Germany, Centre National Researche Geophysique National Garchy, France, Magson GmbH, JeserigerhuÈ tten, Germany, and IABG, Ottobrunn, Germany. The time delay between the measurement and the moment of writing into the telemetry frame was calculated and experimentally determined. The time delay depends on both the analogue time delay (dominated by the bandwidth) and the operation mode of the instrument. Dependent on range and mode the time delay was between 8 and 10 ms. The accuracy of its determination and its stability was better than 0.5 ms.
The sensor oset and its time and temperature stability was determined at many times during the pre¯ight calibration phase. In the 256-nT and 1000-nT range the osets of all sensors were always less than 1 nT at room temperature. The dependency from the sensor temperature (tested between A55°C to 45°C) was less than 4 nT total. The dependency from the electronics temperature (tested between A20°C to 60°C) was less than 0.5 nT total. The output of the oset determination is a vector, O MAG , which is dependent on the selected range.
Scale factors and orthogonality of the sensor system were determined in JeserigerhuÈ tten (JH) and Magnetsrode with the help of two dierent measurement concepts. In JH the sensor was rotated in the homogeneous Earth ®eld. The ®eld magnitude calculated from the three¯uxgate components was ®tted to the measurement result of a proton magnetometer by varying scale factors and orthogonality of the¯uxgate components. Using the coil facilities in Magnetsrode we could show that the orthogonality does not depend on the measurement range. The nonlinearity was less than 0.1% in all ranges. The non-linear in¯uence of a transverse ®eld was not detectable. The output of both calibration procedures is a matrix, M MAG , which also depends on the selected range.
The measurement of the magnetic properties of the satellite was performed at the IABG Ottobrunn. The main disturbance source was the magnetorquer system. The core material of the coils is a soft magnetic Permenorm alloy from Vacuumschmelze Hanau. If we assume that the material is completely saturated the magnetic moment could be calculated as follows: w M w f Sat mal 0 q 1 Using a density, q = 8.2 g/cm 3 , and a saturation induction, B Sat = 1.5 T, for Permenorm, we have the following relation between the weight of the soft magnetic material and magnetic moment: This means that 1 kg of soft magnetic materials per coil are necessary to generate a magnetic moment of 150 Am 2 . A low coercivity of less than 40 mA/cm corresponds to a low rest magnetisation. The rest magnetisation after switching o the torquer generates a ®eld on the position of the outboard sensor of 5 nT. To reduce this in¯uence, demagnetisation procedures were introduced into the onboard software. After demagnetisation the oset generated by the torquer, O SC , was less than 1 nT (outboard) and 2 nT (inboard sensor).
To estimate the induced in¯uence we have to calculate the equivalent magnetic moment for an external ®eld using the eective permeability, l e , of the torquer coil. The eective permeability for a iron rod could be estimated with the following equation (Boll, 1990;Sommerfeld, 1961): At a length/diameter ratio, p, of about 90 and a permeability, l a , of 9000, the eective permeability of a torquer coil is about 1800. Introducing the eective permeability in Eq. (1) the following relation between induced magnetic moment and external ®eld is: The coils are eective only in Y and Z directions (simpli®ed two of them in each direction). Therefore the following relation for the components of the induced magnetic moment is: Using the geometry, given in Fig. 3, we can calculate the magnetic ®eld on the i xY yY z sensor positions as follow: f Ti l 0 a4p3iw x x w y y w z za 5 À w i a 3 7 The calculated in¯uence is given in the following matrix: OS: 1X0000 0X0018 0X0000 0X0000 0X9960 0X0000 0X0000 0X0000 1X0022 The in¯uence of the soft magnetic material on orthogonality and scale factor was also tested in the IABG. The IABG coil system was used to generate well known ®elds in all direction. Additional sensors are located on the nominal position of the deployed Equator-S sensor booms. The measurement has been performed with and without spacecraft.
The following spacecraft matrices, M SC , are the results of these measurements: The comparison between calculated in¯uences, based on material parameters and dimensions, and the measured results shows only dierences smaller than 10 A3 . The main in¯uence on scale factor of about 0.5% is in boom direction. The orthogonality is in¯uenced in the angle between boom and rotation axis with 0.2°.
The ®nal calibration matrix was calculated from sensor osets and sensor matrix (both depends from range) and from spacecraft oset and spacecraft matrix: These four sources are the basis for the in¯ight calibration.

In¯ight calibration
The main and the redundant magnetometer system were tested successfully during the commissioning phase. All hard and software parts were faultless in operation. The magnetometer was working during the commissioning phase from 11 December, 1997, to 20 January, 1998, in dual mode and from 20 January to 30 April, 1998 in single mode. The sensor works in a temperature range between 3°C to 23°C. The electronics temperature varied between 18°C and 36°C. The osets of the components perpendicular to the spin axis (Y, Z) were determined with the help of the spacecraft rotation. Figure 4 shows the oset behaviour of the Y and Z-components of the outboard sensor over a¯ight time of four month in 1998. The oset determination was made each orbit in a time interval of 3 h relative to apogee. The oset variation of both components was less than 1 nT.
The spin axis oset (X) could be determined only with the help of ®eld magnitudes measured by EDI, because due to the orbit (distance <11 R E ) statistical methods gave only poor results. The X oset changed between A2.5 and A3.3 nT (Paschmann et al., 1998).
The in¯uence of the torquer on the oset is shown in Fig. 5a, b. Figure 5a shows the oset behaviour after perigee without any torquing manoeuvre on 6 January 1998. Figure 5b shows the same orbit interval after a torquing manoeuvre on 15 January. The time axis is relative to apogee. In the top panels the absolute osets of the Y and Z components are drawn. In the second panels the dierences of inboard and outboard sensor for all three components are drawn. The osets will be in¯uenced by the sensor temperature (panel 3) and the external ®eld (bottom panels). The in¯uence is independent of the torquing manoeuvre at less than 0.5 nT.
5 Evaluation of the data quality Figure 6 shows two spectrograms during smooth magnetic ®eld conditions over a 1 min interval on 30 January, 1998 from 19:13:26 to 19:14:30 UT Earthward of the magnetopause. The magnitude is in the order of 90 nT. The noise level in components and magnitude is Fig. 6. Amplitude spectrum of a component perpendicular to the spin axis (upper) and amplitude spectrum of the ®eld magnitude (lower) less than 2 pT/ÖHz in the frequency band between 0.1 and 64 Hz. The rotation frequency part and the scale of its upper harmonics give an impression concerning the accuracy of the determination of osets, scale factors, and orthogonality. The low levels at rotation frequency and its upper harmonics in the Y and Z components demonstrate the accuracy of the instrument's linearity, timing and despinning.
Magnetic ®eld measurements in the magnetosheath on 24 January from 23:20:50 to 23:21:20 UT are shown in Fig. 7. The upper panel shows the magnitude and the polar and azimuth angles of the magnetic ®eld in GSE coordinates for a time interval of 30 s. The deep magnetic trough of a mirror wave can clearly be seen. Also seen are three intervals, where the angles show strong variations, indicating higher frequency shear Fig. 7. Magnetic trough inside a magnetosheath mirror wave (upper panel in GSE) and Lion Roar signal wave form perpendicular to the mean ®eld (lower panels) waves, namely electron whistler waves ®rst detected by Smith and Tsurutani (1976) and named Lion Roars.
The middle panel shows one of the components transverse to the mean ®eld of these electron whistlers and a zoomed-in interval of only 3 s is shown in the lower panel. The Lion Roar wave forms are clearly visible, for the ®rst time in¯uxgate magnetometer measurements. The ®rst has a higher frequency but a lower amplitude (40 Hz with about 0.3 nT) and the second has lower frequency but a higher amplitude (24 Hz with about 0.5 nT). A detailed description of Lion Roars observations with Equator-S can be found in the companion paper by Baumjohann et al. (1999).

Summary
Magnetic ®eld measurements on Equator-S demonstrates that both high oset stability and low noise level could be realised although the boom length was limited and the spacecraft was contaminated with magnetic materials. Interference could be calculated theoretically, tested on the ground and could be veri®ed in space. Its in¯uence on the magnetometer sensors was stable enough so that the overall accuracy was still limited by the sensor itself. The oset variation was less than 1nT over the whole¯ight time and the noise less than 2 pT/ ÖHz in the frequency band between 0.1 and 64 Hz. A forecast of the oset could be made independently from the torquing history with an accuracy of 0.5 nT. The spin-axis oset could be determined the ®rst time by comparing on the ®eld magnitude measured by EDI and the magnetometer. Measurements in a frequency range up to 64 Hz could be made perfectly.