The China Seismo-Electromagnetic Satellite (CSES) was
launched in February 2018 into a polar, sun-synchronous, low Earth orbit. It
provides the first demonstration of the Coupled Dark State Magnetometer
(CDSM) measurement principle in space. The CDSM is an optical scalar
magnetometer based on the coherent population trapping (CPT) effect and
measures the scalar field with the lowest absolute error aboard CSES.
Therefore, it serves as the reference instrument for the measurements done
by the fluxgate sensors within the High Precision Magnetometer instrument
package.
In this paper several correction steps are discussed in order to improve the
accuracy of the CDSM data. This includes the extraction of valid 1 Hz data,
the application of the sensor heading characteristic, the handling of
discontinuities, which occur when switching between the CPT resonance
superpositions, and the removal of fluxgate and satellite
interferences.
The in-orbit performance is compared to the Absolute Scalar Magnetometer
aboard the Swarm satellite Bravo via the CHAOS magnetic field model.
Additionally, an uncertainty of the magnetic field measurement is derived
from unexpected parametric changes of the CDSM in orbit in combination with
performance measurements on the ground.
Introduction
The China Seismo-Electromagnetic Satellite (CSES), also known as
Zhangheng-1, investigates natural electromagnetic phenomena and possible
applications for earthquake monitoring from space (Shen et al.,
2018). CSES was launched in February 2018 into a polar, sun-synchronous, low
Earth orbit with an inclination of approximately 97∘ and a period of
approximately 95 min. The High Precision Magnetometer (HPM) instrument package
(Cheng et al., 2018) consists of two fluxgate magnetometers
(FGMs) in a gradiometer configuration and the Coupled Dark State
Magnetometer (CDSM). The CDSM measures the magnetic field strength with the
lowest absolute error of the instruments aboard CSES and serves as the
reference instrument for the measurements done by the fluxgate sensors. The
suitability of the CDSM for the in-flight calibration of the fluxgate
magnetometers is discussed in Zhou et al. (2019).
The CDSM is an optical scalar magnetometer based on a quantum interference
effect called coherent population trapping (CPT)
(Arimondo, 1996; Wynands and Nagel, 1999),
which inherently enables omnidirectional measurements
(Lammegger,
2008; Pollinger et al., 2012) and an all-optical sensor design without
double cell units, excitation coils or active electronics parts
(Pollinger et al., 2018).
Laser excitation scheme within the D1-line hyperfine
structure of 87Rb.
The instrument simultaneously probes several CPT resonances which are
established within the D1-line hyperfine structure (HFS) of 87Rb
shown in Fig. 1. Here, the total angular momentum
quantum numbers and the magnetic quantum numbers of the 52S1/2
ground states are denoted by F̃ and correspondingly by
mF̃, while for the 52P1/2 excited states the labels are
primed. The wavelength λFS corresponds to the fine structure
transition 52S1/2→52P1/2. The HFS ground state
splitting frequency is denoted by νHFS. The energy shift
introduced by the magnetic field is expressed by νF. For the
excitation of each CPT resonance, a Λ-shaped excitation scheme is
prepared in the HFS, which consists of three energy levels interacting with
two light fields indicated by the arrowed lines in Fig. 1.
In order to create the necessary light fields, a vertical-cavity
surface-emitting laser (VCSEL) diode (vacuum wavelength λLaser=λFS≈794.978 nm) is frequency-modulated (FM)
by a microwave oscillator signal (fMW=1/2⋅νHFS≈3.417 GHz). The CPT resonance n=0 is excited by the two light
fields denoted by the black dashed arrowed lines in Fig. 1 and occurs under certain conditions when the
frequency difference of both first-order sidebands of this FM spectrum fits
the energy difference of the 52S1/2 ground states
F̃=1, mF̃=0 and F̃=2,
mF̃=0. This resonance is used to adjust the microwave
oscillator frequency to changes in νHFS and to compensate for a
temperature-dependent drift of the electronics.
An additional modulation of the microwave oscillator signal probes the
first-order Zeeman splitting of HFS ground states via the superposition of
the CPT resonances n=+2 and -2 or n=+3 and -3, which are
indicated by the red and blue arrowed lines in Fig. 1, respectively. The differential probing of the
magnetic-field-induced energy shifts, with one of the two CPT resonance
pairs, cancels or at least mitigates the influence of sensor temperature
variations on the magnetic field measurement
(Lammegger, 2008; Pollinger et al.,
2018).
The instrument consists of a mixed signal electronics board and a laser
unit, which are mounted in an instrument box inside the spacecraft body, as
well as a sensor unit which is located outside the satellite at the tip
of a boom. Additionally, the instrument box and the sensor unit are
connected with two optical fibres and two twisted pair cables to guide the
light field to and from the sensor unit and to control the sensor
temperature (Pollinger et al., 2018).
Magnetic field strength measured by the CDSM within ±65∘ of geocentric latitude for the reoccurrence period of
5 d. Credit for the background image: Reto Stöckli, NASA Earth Observatory.
The CDSM development started in 2007, and the instrument measured the
magnetic field in space for the first time in March 2018 aboard CSES. As far
as we know, this was also the first time a magnetometer based on the CPT
effect was launched into space. Since then, the instrument has been
operational and orbited Earth more than 12 000 times until April 2020. The
main scientific objective of the CSES mission is within ±65∘ of geocentric latitude, and most of the attitude control
activities are moved outside this area to the polar regions
(Shen et al., 2018; Zhou et al., 2019). The data transfer
is separated into a 1 Hz channel for all latitudes and a channel with higher
instrument update rates for the area within ±65∘ of geocentric
latitude. The 1 Hz channel is mainly used for housekeeping purposes and is
not accessible for the CDSM team. Figure 2 shows the
magnetic field strength measured by the CDSM along the CSES orbit tracks
within ±65∘ of geocentric latitude for the 5 d
reoccurrence period of 3–8 January 2019.
Minimum and maximum optical power detected at the photodiode
during individual orbit segments.
All available housekeeping data are within the nominal operational limits
throughout the elapsed mission time. As an example, the minimum and
maximum optical power detected at the photodiode on the electronics board
are shown for individual orbit segments in Fig. 3.
The light is generated in the laser unit and guided through two optical
fibres to and from the sensor unit where it interacts with the rubidium
atoms and derives information on the surrounding magnetic field. The optical
power received at the photodiode is an indicator for the health of the VCSEL
diode (Ellmeier et al., 2018), the fibres, the
optical components in the sensor and the photodiode. The graph in Fig. 3 shows gaps since not all data were made available
to the CDSM team or the satellite was in safe mode in which the scientific
instruments were switched off. The optical power varies due to the design of
the CDSM (Pollinger et al., 2018). It is assumed that the
different exposures to sunlight cause thermal stress in the multimode
outbound fibre, which results in a variation of the polarization state at the
sensor input. Behind the polarizer in the sensor unit a defined linear
polarization state is re-established with the consequence that the optical
power varies. No trend is visible in Fig. 3, and the
minimum optical power was above the operational limit of 5 µW
throughout the available data for the elapsed mission time.
Each orbit is divided into two orbit segments, and data are stored separately
in Hierarchical Data Format 5 (HDF5) files for each orbit segment. Dayside
and nightside orbit segments are marked with the suffixes 0 and 1,
respectively. For example, 44270 is the identifier for the daytime
ascending segment of orbit 4427.
Correction of in-orbit data
Several correction steps are required in order to improve the accuracy of
the CDSM data. This includes the extraction of valid 1 Hz data, the
application of the sensor heading characteristic, the handling of
discontinuities, which occur when switching between the CPT resonance
superpositions, and the removal of fluxgate and satellite
interferences. Table 1 lists these steps and
introduces data product labels. L1a, L1b and L1c are not official data
products.
CDSM data products and correction steps.
Data productDescriptionSectionL1Valid 1 Hz data extracted2.1L1aSensor heading corrected2.2L1bResidual discontinuity jumps when switching between2.3the CPT resonance superpositions removedL1cFluxgate feedback fields cleaned2.4L2Satellite interferences cleaned – final data product2.5Extraction of valid 1 Hz data
The raw data rate of the CDSM is 30 Hz. However, every second is divided in
three subsequent parts: the first third of each second is reserved for the
sensor heating, the second third of each second for adjusting the microwave
oscillator to track the CPT resonance n=0 and the last third of each
second for the actual magnetic field measurement by tracking the CPT
resonance superposition n=±2 or n=±3.
The CPT resonances n=0, n=+2, n=-2, n=+3 and n=-3
depend differently on the magnetic strength in second order (57.515 kHz mT-2 for n=0, 43.136 kHz mT-2 for n=±2 and
21.568 kHz mT-2 for n=±3). As a consequence, the CPT
resonance n=0 is not in the centre of the single CPT resonances n=+2 and n=-2 or n=+3 and n=-3 used for magnetic field measurement. Thus,
the modulation of the microwave oscillator signal would not probe the single
CPT resonances n=+2 and -2 or n=+3 and -3 at the same time. With
the fact that individual single CPT resonances can have different line
shapes, this might cause a deviation of the magnetic field measurement
(Pollinger et al., 2018). This cannot be ignored for CSES
where the magnetic field strength is between 18 and 52 µT.
Therefore, during the last third of every second, the microwave oscillator
control loop for tracking the CPT resonance n=0 is paused and the latest
microwave oscillator control value is corrected by an offset in order to
re-centre the microwave oscillator signal with respect to the single CPT
resonances n=+2 and n=-2 or n=+3 and n=-3. Details are
discussed in Sect. 3.2 and Pollinger et al. (2018).
An additional control loop tracks the CPT resonance superposition n=±2 or n=±3 and continuously delivers magnetic field
values. However, only the last seven samples of every second are considered
to be unaffected by the influence of the sensor heater current, by deviations
due to the second-order magnetic field dependence or by those linked to
transients in the magnetic field strength read-out. Every second the mean
value of these last seven samples is tagged with the time stamp of the
fourth of the last seven samples. The mean values serve as 1 Hz raw data for the
CDSM instrument.
Application of sensor heading characteristic
The CDSM read-out has a deviation of the actual magnetic field strength,
which depends on the angle between the light propagation direction through
the sensor and the magnetic field vector (from here on called the sensor
angle). This heading is characteristic for the flight model and was
determined during performance tests in the assembled HPM configuration at
the Fragment Mountain Weak Magnetic Laboratory of the National Institute of
Metrology in China (Pollinger et al., 2018). The 1 Hz raw data
are corrected by this heading characteristic according to the magnetic field
direction derived from the HPM fluxgate data.
As an example Fig. 4a shows the magnetic field
strength measured by the CDSM during orbit segment 44270. In order to show
details on the correction process, the magnetic field strength calculated
with CHAOS-6 (Finlay et al., 2016; Olsen et al.,
2006), a geomagnetic Earth field model derived from the Swarm, CHAMP,
Ørsted and SAC-C satellites as well as ground observatory data, was
subtracted.
Figure 4b displays sign-changed heading
measurements derived from Pollinger et al. (2018) and the
angular-dependent heading correction applied for the orbit segment 44270.
The heading correction pattern is not continuous over an orbit segment. The
CDSM uses one of the two CPT resonance superpositions n=±2 or n=±3 to enable omnidirectional magnetic field measurements
(Pollinger et al., 2012). The selection
depends on the sensor angle. For angles between approximately 0 and
60∘ as well as 120 and 180∘ the signal
amplitude of the CPT resonance superposition n=±2 is large enough
to be used, while for angles between approximately 60 and 120∘
only the superposition n=±3 is applicable. In flight, the CDSM
gets HPM fluxgate data to switch between these two resonance superpositions
at 60 and 120∘ with an intended hysteresis of approximately
2∘. The actual switching angles vary with ±1∘
due to a basic on-board fluxgate correction. For the descending orbit
segment 44270 shown in Fig. 4a, the sensor angle
changed from approximately 165 to 27∘. The instrument
switched from the CPT resonance superposition n=±2 to n=±3 at approximately 117∘ and from the CPT resonance superposition
n=±3 to n=±2 at approximately 58∘. The heading
correction for the CPT resonance superposition n=±2 was refined
compared to the linear fit in Pollinger et al. (2018) to better
represent the characteristic seen during various measurements on the ground.
Now, measurements with the CPT resonance superposition n=±2 are
corrected with a second-order polynomial fit. The origin of the heading
characteristic is still under investigation.
Example for applying the sensor heading characteristic and the
corresponding correction pattern derived from measurements on the ground.
Removal of residual discontinuity jumps when switching CPT resonance
superpositions
After the sensor heading correction, the magnetic field values are not
continuous when the resonance superpositions n=±2 and
n=±3 are switched. For example, Fig. 5a shows the magnetic field strength measured by the CDSM during the orbit
segment 44270 with the CHAOS-6 calculation subtracted. When switching from
the CPT resonance superposition n=±2 to n=±3 a jump of
the magnetic field strength of approximately -0.71 nT is observable in the CDSM
read-out, while for the change from CPT resonance superposition n=±3 to n=±2 the step is approximately -0.66 nT. These discontinuity jumps
vary with each orbit segment and are further discussed in Sect. 3.2.
In order to avoid a misinterpretation by the scientific user, the
discontinuity jumps are removed individually for each orbit segment by
adjusting the magnetic field data derived with the CPT resonance
superposition n=±3 to measurements with the CPT resonance
superposition n=±2.
When switching from CPT resonance superposition n=±2 to n=±3 the signal amplitude of the CPT resonance n=0 is also small
and the microwave oscillator control loop is paused (Pollinger
et al., 2018). For the subsequent measurements with the CPT resonance
superposition n=±3 the last microwave oscillator control value is
re-centred as discussed in Sect. 2.1. When switching from the CPT resonance
superposition n=±3 to n=±2 the signal of the CPT
resonance n=0 is large enough to re-activate the control loop.
Consequently, for measurements with the CPT resonance superposition n=±2 the microwave oscillator control loop is active. Then it can
compensate for a possible temperature drift of the electronics and can follow a
change in the HFS ground state splitting due to e.g. a sensor temperature
drift.
For each orbit segment the two discontinuity jumps at the resonance
transitions are used to calculate a linear ramp. The ramp is added to the
magnetic field strength measured with CPT resonance superposition n=±3. As an example this correction pattern is shown for the orbit
segment 44270 in Fig. 5b.
Example for removing residual discontinuity jumps, which occur
when switching CPT resonance superpositions, and the corresponding
correction pattern.
Removal of fluxgate interferences
The HPM sensor configuration consists of the CDSM sensor mounted at the tip
of a 4.7 m long boom, while the FGM 2 and FGM 1 sensors are located 0.367
and 0.767 m inwardly.
Fluxgates are inherently zero field detection devices with which an artificial
magnetic field is applied to cancel the environmental magnetic field in the
sensor (Auster, 2008). For CSES this field can significantly
influence the magnetic field measurement of the other sensors. The cross
interferences were characterized with the sensors mounted on a dummy boom in
a µ-metal chamber (Zhou et al., 2018). The FGM 1 and
FGM 2 sensors were located at the correct distances and orientation with
respect to the CDSM position. The CDSM was replaced by a third fluxgate
sensor for this test. The influence of the FGM 2 feedback field FFG2 at
the CDSM sensor position is
FFG2,xFG2FFG2,yFG2FFG2,zFG2=IFxFG2FyFG2FzFG2=10-55.341.970.671.33-7.820.000.001.902.76FxFG2FyFG2FzFG2,
where I is the matrix characteristic of the FGM 2 feedback field influence,
which depends on the Earth's magnetic field vector F. The FGM 2 sensor
coordinates xFG2, yFG2, and zFG2 correspond to the satellite
coordinates ysat, zsat and xsat, respectively, where
xsat is approximately the flight direction and zsat points approximately to
the centre of Earth. The matrix characteristic of the FGM 1 feedback field
influence is not available from ground tests. Nevertheless, with the
same sensor design, orientation and given location, the influence of the
FGM 1 feedback field FFG1 at the CDSM sensor position can be estimated
as
FFG1,xFG2FFG1,yFG2FFG1,zFG2≈0.11FFG2,xFG2FFG2,yFG2FFG2,zFG2,
where FFG2 is the influence of the FGM 2 feedback field at the CDSM
sensor position and xFG2, yFG2 and zFG2 are the FGM 2 sensor
coordinates. The CDSM scalar measurement is transformed into a vector as a
function of F derived by FGM 2 and is corrected by FFG1 and FFG2.
In orbit the impact of the fluxgate sensors is up to 4.4 nT at the CDSM
position, and it depends on the magnetic field direction and strength. As an
example the influence of the fluxgates during orbit segment 44270 is shown
in Fig. 6.
Example for the influence of the fluxgate feedback fields and the
corresponding correction pattern.
Removal of satellite interferences
Although there was a magnetic cleanliness programme carried out by the
satellite developer, some magnetic disturbances remain visible to the
magnetometers. In order to be able to remove these interferences from the
scientific data the whole satellite was installed in a coil system and
different operation modes were magnetically measured. The influence of the
satellite Fsat at the CDSM sensor position was published in
Xiao et al. (2018) as
Fsat,xsatFsat,ysatFsat,zsat=AFxsatFysatFzsat+F0+CMxsatMysatMzsat=10-5-1.1080.0250.725-0.350-2.808-1.1001.225-1.1584.658FxsatFysatFzsat+-0.16-0.260.29+0.200.010.000.030.56-0.01-0.080.07-0.47MxsatMysatMzsat,
where A is the matrix characteristic of the soft magnetic influences, which
depends on the Earth's magnetic field vector F, F0 is the remanence of
hard magnetic materials and C is the matrix characteristic of the
magnetorquer influence which depends on the torque states M. The coordinates
xsat, ysat and zsat correspond to the satellite where
xsat is approximately the flight direction and zsat points approximately to
the centre of Earth. The CDSM scalar measurement is transformed into a
vector as a function of F derived by FGM 2 and is corrected by Fsat. As
an example, the influence of the satellite during the orbit segment 44270 is
shown in Fig. 7.
Example of the satellite interferences and the corresponding
correction pattern.
In-orbit performance
The CDSM is the magnetometer with the lowest absolute error aboard CSES.
Therefore, the in-orbit performance of the CDSM can solely be obtained by
comparing its measurements to magnetic field models, measurements from other
satellite missions or through a study of the integrity of its own data.
Comparison to CHAOS model and Swarm data
The CDSM data were compared to the CHAOS-6 model
(Finlay et al., 2016; Olsen et al., 2006). The
CHAOS model is optimized for the nightside, which means that the CHAOS
coefficients are determined in such a way as to minimize the difference
between the CHAOS model and Earth's magnetic field on the nightside. These
residuals are dominated by a magnetospheric ring-current contribution, which
is not included in the CHAOS model and which shows a minimum scatter at around
±35∘ of dipole latitude. Therefore, the mean values and
standard deviations, which are calculated for the dipole latitude ranges of
-40 to -30∘ (southern evaluation interval) and
30 to 40∘ (northern evaluation interval), are an
indicator for the magnetometer's data quality.
Additionally, only data with a Kp index smaller than 1 have been selected
for this evaluation. The Kp index quantifies disturbances in the horizontal
component of the Earth's magnetic field (Bartels et
al., 1939).
With an ascending node at approximately 02:00 and an inclination of approximately 97∘, the actual local time of CSES nightside orbit segments is
between approximately 01:00 and 03:00. Swarm is a three-satellite low Earth orbit
mission of the European Space Agency launched in 2013 to study the Earth's
magnetic field. Each satellite contains an Absolute Scalar Magnetometer
(ASM) as a reference instrument. The Swarm satellite Bravo has an inclination
of approximately 88∘, and the ascending and descending nodes drift.
Between 15 and 30 November 2018 the ascending nodes of Swarm Bravo were between
02:38 and 01:19 and 48–42 min after the ascending nodes of CSES. The
local time ranges overlapped for the Swarm and CSES nightside orbit
segments. Data for this time interval have been selected for the comparison.
The altitude of the Swarm satellite Bravo was between 501 and 518 km, while
CSES orbited at 500–511 km during the selected time interval.
Magnetic field strength measured by CDSM compared to Swarm Bravo
ASM via the CHAOS-6 Earth field model for nightside and dayside orbit
segments.
Figure 8a shows the difference between CDSM
measurements and the CHAOS-6 model for the 135 selected night-time orbit
segments, while Fig. 8b displays the equivalent
analysis for the ASM aboard Swarm satellite Bravo. The mean values
ΔF‾ and standard deviations σ of the differences to the
CHAOS model were calculated with a 10∘ resolution of the dipole
latitude. These values are shown as error bars for each individual
instrument in Fig. 8c.
The mean values of both instrument deviations are consistent in the magnetic
dipole latitude range of -40 to -30∘ (ΔF‾=1.5 nT, σ=1.8 nT for CDSM and ΔF‾=0.9 nT,
σ=1.9 nT for ASM). One can see that the 1σ error bars
of both instruments match in size and mean values widely but start to
separate at dipole latitudes greater than 20∘. For the dipole
latitude range of 30 to 40∘ the mean values of both
instruments differ by 1.9 nT (ΔF‾=2.7 nT for CDSM and
ΔF‾=0.8 nT for ASM). Similar differences between the CDSM
and the ASM mean values can also be observed for dayside orbit segments in
Fig. 8d, e and f.
Discussion of data integrity
For the analysis in this section data from 9387 of 13 058 possible orbit
segments between 16 November 2018 and 19 January 2020 were available. As
already discussed in Sect. 2.3 the magnetic field values are not continuous
when the resonance superpositions n=±2 and n=±3 are
switched. Histograms of these discontinuity jumps are presented in Sect. 3.2.1. All available instrument parameters, especially the microwave
oscillator frequency controller adjustment, are investigated in detail. The
sensitivity of the magnetic field measurement as a function of a microwave
oscillator frequency detuning is derived in Sect. 3.2.2. The variations of
housekeeping parameters, such as the optical power received at the photodiode as well as the sensor and printed circuit board (PCB) temperatures,
are discussed in Sect. 3.3.3, 3.3.4 and 3.3.5, respectively. In Sect. 3.3.6,
an angular-dependent adjustment of the microwave oscillator frequency is
presented, which could be observed for measurements with the CPT resonance
superposition n=±2 during ground tests with the flight model.
Some influences are understood and can be subtracted from the actual
in-orbit microwave oscillator controller adjustment. The unknown residual
microwave oscillator adjustment is used in Sect. 3.3.7 to derive the
uncertainty of the magnetic field measurement.
Histograms of the discontinuity jumps when switching the CPT
resonance superpositions.
Discontinuity jumps when switching CPT resonance superpositions
Figure 9 shows the histograms for the discontinuity
jumps for the entire available data set. The blue histogram in Fig. 9a describes the changes in the magnetic field
strength read-out introduced by switching from the CPT resonance
superposition n=±2 to n=±3 at sensor angles of approximately
62∘ during nightside orbit segments. The blue histogram in Fig. 9b shows the discontinuity jumps when switching
from the CPT resonance superposition n=±3 to n=±2 for
nightside orbit segments which occur at sensor angles of approximately 122∘. The red histogram in Fig. 9b
describes the discontinuity jumps when switching from the CPT resonance
superposition n=±2 to n=±3 at sensor angles of approximately 118∘ during dayside orbit segments. The red histogram in Fig. 9a shows the discontinuity jumps when switching
from the CPT resonance superposition n=±3 to n=±2 for
dayside orbit segments which occur at sensor angles of approximately 58∘. The sign of the values for the dayside orbit segments was changed to make
them comparable to the nightside orbit segments for similar sensor angles.
Ideally, each of the four medians should be zero. There is no significant
difference between the medians of 0.34 and 0.23 nT when switching CPT resonance superpositions at approximately 58 and 62∘,
respectively. However, a significant difference exists when
switching CPT resonance superpositions at approximately 118
and 122∘ (0.72 and 0.15 nT, respectively).
Microwave oscillator detuning sensitivity of the magnetic field
measurement
The sensitivity of the magnetic field measurement as a function of a
microwave oscillator frequency detuning (from here on called detuning
sensitivity) can be determined in orbit for measurements with the CPT
resonance superposition n=±2. As discussed in Sect. 2.1 every
second is divided in three subsequent parts. During the second third of each
second, the microwave oscillator frequency controller tracks the HFS ground
state splitting. In the last third of each second, this controller is paused
and the latest control value is adjusted by an offset in order to re-centre
the microwave oscillator frequency with respect to the single CPT resonances
n=+2 and n=-2. The CPT resonance n=0 and the CPT resonance
superposition n=±2 depend differently on the magnetic field
strength in second order. The applied offset is half of this frequency
difference and thus a function of the magnetic field strength. The control
loop for the magnetic field measurement is active at all times, and read-outs can
be derived during the microwave oscillator tracking and offset parts
separately. In orbit the magnetic field strength changes with up to 40 nT s-1, and therefore measurements done during the tracking part of each
second have been interpolated to make them comparable with the offset part
of each second. The impact on the magnetic field measurement as a function
of the applied microwave controller offset can be used to calculate the
detuning sensitivity.
Detuning sensitivity of the magnetic field measurement.
The blue and red dots in Fig. 10 show the calculated
detuning sensitivity for in-orbit measurements with the CPT resonance
superposition n=±2. The detuning sensitivity depends on the
sensor angle. Apart from data artefacts, the scatter of the measured
detuning sensitivity is a function of the magnetic field strength. It is
dominated by the division through the microwave oscillator controller offset
and increases with decreasing magnetic field values and thus smaller offset
values. This can be observed via the South Atlantic Anomaly, which keeps the
noise level quite high towards lower sensor angles in the Southern
Hemisphere during many orbits. It also explains the step-like drop of the
noise at a sensor angle of 25∘. The black solid lines are a fit
of the in-orbit measurements whose shape was confirmed with the flight spare
model on the ground.
For the measurements with the CPT resonance superposition n=±3
the detuning sensitivity cannot be calculated from in-orbit data. The
microwave oscillator controller cannot track the HFS ground state splitting,
and the latest control value during measurements with the CPT resonance
superposition n=±2 is always adjusted by an offset as a function
of the current magnetic field strength. The detuning sensitivity for
measurements with the CPT resonance superposition n=±3 shown in
Fig. 10 was derived from measurements with the
flight spare model.
The detuning sensitivity crosses zero at 53 and 127∘
for measurements with the CPT resonance superposition n=±2 and at
90∘ for measurements with the CPT resonance superposition n=±3. At these sensor angles the magnetic field measurement is not
sensitive to the (offset) detuning of the microwave oscillator frequency
with respect to the centre of the single CPT resonances n=+2 and n=-2 or n=+3 and n=-3.
Optical power during orbit segments.
Histograms of the optical power when switching the CPT resonance
superpositions.
Optical power
The black lines in Fig. 11 show the envelope of the
optical power received at the photodiode for the entire available data set.
It is proportional to the optical power in the sensor and varies between 17
and 36 µW due to the instrument design, as described in the
Introduction. A major part of this variation occurs every orbit, which can
be observed with the sample orbit segments 44261 and 44270. For
completeness, Fig. 12 shows the histograms of the
optical power when the CDSM switches between the resonance superpositions n=±2 and n=±3. As an example and similar to Fig. 9, the blue histogram in Fig. 12a describes the optical power when switching
from the CPT resonance superposition n=±2 to n=±3 at
sensor angles of approximately 62∘ during nightside orbit segments.
Sensor temperature during orbit segments.
Sensor temperature
The black lines in Fig. 13 show the envelope of the
sensor temperature for the entire available data set. The major part of the
variation between 26.2 and 32.7 ∘C is seasonal. The
controller is not active and constant power heats the sensor unit. The same
approach was used during the sensor heading characterization of the magnetic
field measurement with the flight model on the ground (Pollinger
et al., 2018) where the environmental temperature was settled within
0.1 ∘C for each run. The in-orbit sensor temperature measurement
experiences step-like interferences which can be observed with the sample
orbit segments 44261 and 44270. These are likely caused by the unshielded
twisted pair cable along the boom in combination with the high gain of the
measurement circuit in order to minimize the current through the platinum
resistance temperature detector close to the sensor cell. For further
analysis the data were filtered.
Sensor-temperature-dependent microwave oscillator variation and
magnetic field deviation.
The HFS ground state splitting frequency depends on the sensor temperature
with 13 Hz K-1 (Pollinger et al., 2018).
Figure 14a and c show the sensor-temperature-dependent variations of the microwave oscillator for the entire available
data set. The variations are offset with respect to the reference points
when switching from CPT resonance superposition n=±2 to n=±3, which occurs at the sensor angles of approximately 62 and
118∘ for nightside and dayside orbit segments, respectively. For
measurements with the CPT resonance superposition n=±2 the
microwave oscillator controller is active and can compensate for the sensor-temperature-dependent frequency changes in the HFS ground state splitting
via the CPT resonance n=0. The adjustment values are shown as blue
lines. For measurements with the CPT resonance superposition n=±3
the microwave oscillator controller is paused and does not track the sensor-temperature-dependent frequency changes in the HFS ground state splitting. A
temperature change leads to a detuning of the microwave oscillator frequency
with respect to the centre of the single CPT resonances n=+3 and n=-3. This detuning is shown in Fig. 14a and c as
red lines with a maximum detuning of 3.3 and -2.1 Hz for nightside and
dayside orbit segments, respectively. In combination with the detuning
sensitivity discussed in Fig. 10 the detuning can
cause a deviation of the magnetic field measurement with the CPT resonance
superposition n=±3. The derived magnetic field deviation is shown
in Fig. 14b and d with a maximum deviation of
the magnetic field strength of -0.16 and -0.10 nT for nightside and
dayside orbit segments, respectively. A sensor temperature change can
contribute to the discontinuity jumps when switching from CPT resonance
superposition n=±3 to n=±2 in Fig. 9 but cannot affect the discontinuity jumps when
switching from CPT resonance superposition n=±2 to n=±3.
Reoccurring PCB temperature pattern during orbit segments.
PCB temperature and noise of the microwave oscillator control loop
The temperature of the printed circuit board (PCB) is between
46.2 and 49.7 ∘C for the entire available data set.
It has a reoccurring pattern which is displayed for 1.5 d in Fig. 15. The maximum temperature change is 0.03 K min-1, which occurs during specific dayside orbit segments.
The impact of the PCB temperature variations in space was investigated with
the flight spare model on the ground. The microwave generator is realized by a
phase-locked loop which consists of a voltage-controlled microwave
oscillator and a fractional-N counter frequency divider
(Pollinger et al., 2018). The time base for the microwave
oscillator is an adjustable reference oscillator which is tuned via a
voltage input by the actuating variable of the microwave oscillator
controller. The reference oscillator is temperature-compensated and
autonomously adjusts the output as a function of the environmental
temperature in order to mitigate the temperature dependence of the
oscillator.
Temperature dependence of the microwave oscillator output
frequency.
The temperature dependence of the reference oscillator was evaluated with
the instrument box of the flight spare model located in the
thermally controlled environment of a vacuum chamber. The output frequency
was measured with a HP5335A counter and a SRS FS725 rubidium frequency
standard. The instrument box and the counter were connected via an
electrical vacuum feedthrough. The reference oscillator temperature was
derived from the CDSM housekeeping data since the PCB temperature
measurement is within 0.5 cm on the electronics board. The reoccurring
pattern of the in-orbit PCB temperature cannot be reproduced exactly with
the available test facilities. Figure 16 shows the
frequency change for a temperature variation of 1.4 K within an orbit period
of approximately 95 min and a maximum temperature change of 0.07 K min-1.
The reference oscillator frequency varies, which is equivalent to a change in
the microwave oscillator frequency of -14.8 Hz K-1.
The noise of the microwave oscillator control loop was evaluated with the
instrument box of the flight spare model located in the thermally controlled
environment of a vacuum chamber and the sensor unit positioned outside in a
µ-metal shielding can. The instrument box and the sensor unit were
connected via optical and electrical vacuum feedthroughs. The maximum
duration of measurements with the CPT resonance superposition n=±3 is 13 min during each orbit segment for the entire available data set.
This is longer than each of the two measurement intervals with the CPT
resonance superposition n=±2 during each orbit segment for the
entire available data set. The sensor temperature was controlled by the CDSM
electronics, and the CDSM housekeeping read-out varied within 0.01 ∘C for the evaluation period of 13 min. The PCB temperature was kept
constant by the vacuum chamber, and the CDSM housekeeping read-out varied
within 0.05 ∘C for the evaluation period of 13 min. An
artificial magnetic field was generated in the µ-metal shielding can
with a Keithley 6221 current source and a coil. The generated magnetic field
strength can be assumed to be sufficiently constant for this evaluation. The
microwave oscillator controller tracked the CPT resonance n=0, and the
actuating variable is a measure for the adjustment of the microwave
oscillator output frequency. The standard deviation σ of the
calculated microwave oscillator output frequency is 0.6 Hz for the
evaluation period of 13 min.
PCB-temperature-dependent microwave oscillator variation and
magnetic field deviation.
Figure 17a and c show PCB-temperature-dependent
variations of the microwave oscillator for the entire available data set.
The analysis for the adjustment and detuning values is identical to the
sensor temperature. The variations are offset with respect to the reference
points when switching from CPT resonance superposition n=±2 to n=±3. The adjustment for measurements with the CPT resonance
superposition n=±2 is shown as blue lines, while the detuning for
measurements with the CPT resonance superposition n=±3 is
displayed as red lines. The derived magnetic field deviation for
measurements with the CPT resonance superposition n=±3 is shown
in Fig. 17b and d. The maximum detuning of 1.0
and -2.1 Hz leads with the angular-dependent detuning sensitivity to a
maximum deviation of the magnetic field values of -0.05 and -0.10 nT for
nightside and dayside orbit segments, respectively. A PCB temperature change
can contribute to the discontinuity jumps when switching from CPT resonance
superposition n=±3 to n=±2 in Fig. 9 but cannot affect the discontinuity jumps when
switching from CPT resonance superposition n=±2 to n=±3.
Angular-dependent microwave oscillator adjustment during ground
tests.
Angular-dependent microwave oscillator adjustment during ground tests
An angular-dependent adjustment of the microwave oscillator frequency could
be observed for measurements with the CPT resonance superposition n=±2. The data in Fig. 18 were derived during
the sensor heading characterization of the magnetic field measurement with
the flight model on the ground. The blue lines show individual measurements at
the Conrad Observatory (COBS) of the Zentralanstalt für Meteorologie und
Geodynamik in Lower Austria and in the coil systems of the Technical
University Braunschweig (TU-BS) in Germany as well as the Fragment Mountain
Weak Magnetic Laboratory of the National Institute of Metrology (NIM) in
China (see Fig. 4b). The microwave oscillator
variations are referenced to the sensor angles of 60 and
120∘ in order to make them comparable. The black dashed lines show
the envelope of these measurements. The microwave oscillator adjustment
varies between -5 and -24 Hz. The sensor and PCB temperatures were
settled within 0.1 ∘C for each run, which would lead to an
adjustment of the microwave oscillator frequency of only 0.7 and 1.5 Hz,
respectively. The magnetic field strength was artificially controlled for
the measurements at TU-BS and NIM. A magnetic field variation of 20 nT at an
Earth field of 48 550 nT would lead to an adjustment of the microwave
oscillator frequency of just 0.06 Hz during the COBS measurements. Thus, the
reason for the angular-dependent behaviour cannot be explained so far.
Microwave oscillator variation during measurements with the CPT
resonance superposition n=±2 for individual orbit segments.
Unknown residual microwave oscillator adjustment and derived
uncertainty of magnetic field measurement
Figure 19 shows two examples of microwave oscillator
variations during measurements with the CPT resonance superposition n=±2 in orbit. The blue curves display the actual microwave oscillator
controller adjustment required to track the CPT resonance n=0 with the
microwave oscillator frequency. The re-centring as described in Sect. 2.1
is not displayed for simplicity. The output frequency is offset to the last
microwave oscillator controller value before it was paused when switching
from CPT resonance superposition n=±2 to n=±3. For the
ascending nightside orbit segment 44261 in Fig. 19a and the descending dayside orbit segment 44270 in Fig. 19b this occurred at 62 and
118∘, respectively. The brown and orange lines are the calculated
microwave oscillator adjustments needed to compensate for the sensor and PCB
temperature changes with respect to the reference point when switching from
CPT resonance superposition n=±2 to n=±3. The black
solid lines are the expected frequency change in the CPT resonance n=0
as a function of the magnetic field strength in second order. Their vertical
offset was obtained by nonlinear least-squares fitting to the actual
microwave oscillator controller adjustment for each individual orbit
segment. The envelope of the angular-dependent microwave oscillator
adjustment discovered during ground tests is shown as black dashed lines.
The influences of the magnetic field strength in second order, the sensor
temperature and the PCB temperature are understood and can be subtracted
from the actual microwave oscillator controller adjustment. The residuals
between the actual and understood microwave oscillator adjustments are
plotted as red lines in Fig. 19 and show the same
sensor angular-dependent trend as the ground measurements in Fig. 18.
Residual microwave oscillator adjustment for measurements with
the CPT resonance superposition n=±2.
The residual microwave oscillator controller adjustments vary with each
orbit segment. Figure 20 shows the residuals for the
entire available data set. The maximum residual microwave oscillator
adjustment is 17.3 Hz and occurs during nightside orbit segments.
Derived uncertainty of magnetic field measurement as a function
of the sensor angle.
For measurements with the CPT resonance superposition n=±2 it can
be assumed that the controller adjusts the microwave oscillator frequency
correctly to the CPT resonance n=0 with the limit of the control loop
noise discussed above. Since the cause of the residual microwave oscillator
adjustment in Fig. 20 is unknown, it cannot be
assumed that the offset-adjusted light field matches the centre of the
single CPT resonances n=+2 and n=-2 for measurements with the CPT
resonance superposition n=±2. A theoretical magnetic field
deviation associated with the residual microwave oscillator adjustment can be
calculated via the detuning sensitivity for measurements with the CPT
resonance superposition n=±2 in Fig. 10.
This deviation is shown as blue and red dots in Fig. 21. Taking the maximum residual microwave oscillator
adjustment and the detuning sensitivity for measurements with the CPT
resonance superposition n=±2, one can derive an uncertainty for
the magnetic field measurements with the CPT resonance superposition n=±2 for the available 9387 orbit segments. In Fig. 21 this uncertainty is visualized with solid black
lines and grey areas below for sensor angles between approximately 6
and 62∘ as well as 118 and 169∘. The maximum
derived uncertainty for measurements with the CPT resonance superposition
n=±2 is ±0.8 nT.
As mentioned above, for the measurements with the CPT resonance
superposition n=±3 the microwave oscillator control loop is
paused when switching from CPT resonance superposition n=±2 to n=±3, and the last control value is offset as a function of the
current magnetic field strength. The influence of the sensor and PCB
temperature changes during measurements with the CPT resonance superposition
n=±3 could be mitigated with correction curves. Temperature-dependent correction terms could be additionally applied to the last control
value in order to compensate for a change in the HFS ground state splitting or a
temperature drift of the microwave oscillator frequency. This is implemented
in the flight model but would require a regular update of certain parameters,
which is not applicable for this mission. The uncertainties of the magnetic
field measurement caused by sensor and PCB temperature changes without
correction terms are shown in Fig. 21 as brown and
orange areas, respectively. The uncertainties were defined as the absolute
maximum deviations in Fig. 14b and d as well as Fig. 17b and d as a function of the sensor
angle.
With the observed residual microwave oscillator adjustment during
measurements with the CPT resonance superposition n=±2 it can be
assumed that similar additional adjustments would be required to re-centre
the light field with respect to the single CPT resonances n=+3 and n=-3 during measurements with the CPT resonance superposition n=±3. Taking the maximum residual microwave oscillator adjustment
during measurements with the CPT resonance superposition n=±2 and
the expected detuning sensitivity for measurements with the CPT resonance
superposition n=±3 one can calculate a theoretical uncertainty
associated with the expected microwave oscillator detuning during
measurements with the CPT resonance superposition n=±3. In Fig. 21 this uncertainty is visualized as grey areas for
sensor angles between approximately 58 and 122∘ .
The sum of the sensor-temperature-dependent uncertainty, the PCB-temperature-dependent uncertainty and the uncertainty derived from the expected
microwave oscillator detuning during measurements with the CPT resonance
superposition n=±3 can be interpreted as the uncertainty of the
magnetic field measurement with the CPT resonance superposition n=±3. The derived uncertainty does not exceed ±1.1 nT and is
displayed in Fig. 21 with black dashed lines. The
derived uncertainty of the magnetic field measurement as a function of
geomagnetic coordinates is shown in Fig. 22.
Derived uncertainty of the magnetic field measurement as a
function of geomagnetic coordinates.
With the results of Fig. 21 one can calculate the
sum of the derived uncertainties for the magnetic field measurement with the
CPT resonance superpositions n=±2 and n=±3 for sensor
angles when the CPT resonance superpositions n=±2 and n=±3 are switched (see Sect. 3.2.1). The combined uncertainties for the
magnetic field measurement are approximately ±1.4, ±1.4,
±1.5 and ±1.4 nT at the sensor angles of approximately 58, 62, 118 and 122∘,
respectively; 99.3 %, 99.3 %, 99.5 % and 99.8 % of the corresponding
discontinuity jumps are within the combined derived uncertainties for the
magnetic field measurement with the CPT resonance superpositions n=±2 and n=±3.
Conclusions
The China Seismo-Electromagnetic Satellite (CSES) mission provides the first
demonstration of the Coupled Dark State Magnetometer (CDSM) measurement
principle in space. The CDSM is operational and all available housekeeping
data have been nominal throughout the elapsed mission time.
Data correction processes were established in order to improve the accuracy
of the CDSM data. This includes the extraction of valid 1 Hz data, the
application of the sensor heading characteristic, the handling of
discontinuities, which occur when switching between the coherent population
trapping (CPT) resonance superpositions, and the removal of fluxgate
and satellite interferences. The sum of all corrections applied to the CDSM
L1 data is between -2.4 and 3.6 nT.
The CDSM measurements were compared to the Absolute Scalar Magnetometer
(ASM) measurements aboard the Swarm satellite Bravo via the CHAOS-6 Earth
field model between 15 and 30 November 2018. In this period the ascending nodes
of the Swarm satellite Bravo were between 02:38 and 01:19 and 48–42 min
after the ascending nodes of CSES at 02:00. The local time ranges
overlapped. For nightside orbit segments the mean values of both instrument
deviations compared to the CHAOS-6 model were ΔF‾=1.5 nT
for CDSM and ΔF‾=0.9 nT for ASM in the magnetic dipole
latitude range of -40 to -30∘ (southern evaluation
interval). For the dipole latitude range of 30 to 40∘
(northern evaluation interval) the mean values of both instruments differed
by 1.9 nT (ΔF‾=2.7 nT for CDSM and ΔF‾=0.8 nT for ASM). Similar differences between the CDSM and the ASM mean values
were also observed for dayside orbit segments.
For the available data set of 9387 orbit segments, discontinuity jumps with
a median up to 0.72 nT were observed in the magnetic field strength read-out
when the CDSM switched between the CPT resonance superpositions n=±2 and n=±3. All available instrument parameters,
especially the microwave oscillator frequency controller adjustment, were
investigated in detail. The frequency of the microwave oscillator is used to
track the hyperfine structure (HFS) ground state splitting via the CPT
resonance n=0 and is part of the light field to track the CPT resonance
superposition n=±2 or n=±3 for the magnetic field
measurement. The sensitivity of the magnetic field measurement on a
microwave oscillator frequency detuning was calculated from in-orbit
measurements with the CPT resonance superposition n=±2. For
measurements with the CPT resonance superposition n=±3 this
detuning sensitivity was determined with the flight spare model on the ground.
During measurements with the CPT resonance superposition n=±3,
the microwave oscillator control loop is paused and cannot track changes in
the sensor and PCB temperatures. The maximum deviations of the magnetic
field measurement caused by sensor and PCB temperature changes during
measurements with the CPT resonance superposition n=±3 were
absolute 0.16 and 0.10 nT, respectively, for the available data set in
orbit.
During measurements with the CPT resonance superposition n=±2,
the microwave oscillator control loop tracks changes in the HFS ground state
splitting caused by variations of the magnetic field strength in second
order or the sensor temperature, and it compensates for a possible temperature-dependent drift of the electronics. These influences are understood and can
be subtracted from the actual microwave oscillator controller adjustment. A
residual microwave controller adjustment up to 17.3 Hz could be observed for
the available data set of 9387 orbit segments. With the maximum of this
residual microwave oscillator adjustment and the calculated detuning
sensitivity one can derive an uncertainty of the magnetic field measurement,
which depends on the sensor angle between the light propagation direction
through the sensor and the magnetic field vector. This derived uncertainty
does not exceed ±0.8 nT for measurements with the CPT resonance
superposition n=±2 and ±1.1 nT for measurements with the
CPT resonance superposition n=±3. It is zero at sensor angles of
53, 90 and 127∘. At these angles the
magnetic field measurement is not sensitive to a moderate detuning of the
microwave oscillator frequency with respect to the centre of the single CPT
resonances n=+2 and n=-2 or n=+3 and n=-3.
For future missions a new sensor design is under development with which the light
field passes the Rb-filled glass cell twice but with opposite helicities of
the circular polarization state (Ellmeier,
2019). This reduces the sensitivity of the magnetic field measurement to the
microwave oscillator frequency detuning.
Data availability
A limited set of raw and L2 data was made available to the instrument developer for this analysis. The China Earthquake Administration is responsible for the distribution of CSES data to the scientific community (https://www.leos.ac.cn, last access: 24 October 2019). Data from the Swarm mission are publicly available at https://swarm-diss.eo.esa.int (last access: 9 July 2020). The CHAOS-6 model is publicly available at https://www.spacecenter.dk/files/magnetic-models/CHAOS-6 (last access: 9 July 2020). All figures are available as vector
graphics on the journal home page.
Author contributions
AP conceived the study and prepared the paper. WM supervised the whole
project. BC and BZ carried out ground tests to characterize the fluxgate
feedback coil interference; CA and ME provided expertise on the detuning
sensitivity for measurements with the CPT resonance superposition n=±3. AB, ME, CH, IJ, RL, WM and AP contributed to the instrument
development. All authors have read and approved the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The authors would like to thank Nils Olsen of the Technical University of
Denmark for his support and expertise on the CHAOS magnetic field model.
Financial support
The China Seismo-Electromagnetic Satellite mission is a project organized
and mainly funded by the China National Space Administration. The work of
the Space Research Institute and the Institute of Experimental Physics was
co-funded by the Austrian Space Applications Programme (project no. 859716),
which is managed by the Austrian Research Promotion Agency. The work of the
National Space Science Center was funded by the National Key Research and
Development Program of China, which is managed the Ministry of Science and
Technology (project no. 2016YFB0501503).
Review statement
This paper was edited by Valery Korepanov and reviewed by two anonymous referees.
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