In space plasma physics, the knowledge of the magnetic field is of primary importance. Space plasmas are almost always magnetized and the plasma dynamics are significantly dependent on the ambient fields via the Lorentz force. Consequently, measuring the magnetic field in space has been a primary goal since the beginning of the space era. Therefore, fluxgate magnetometers (FGM) have usually been used due to their small size, mass, and power consumption paired with robustness and measurement accuracy. Early examples of scientific space missions carrying FGMs are the Explorer 6 mission from 1959 and the Voyager 1 and 2 missions, both launched in 1977 . The Pioneer Venus Orbiter mission launched into space in 1978 had a FGM on board as well . Newer multi-spacecraft missions carrying FGMs around the Earth's magnetosphere are the Cluster mission , the Time-History of Events and Macroscale Interactions during Substorms (THEMIS) mission and the Magnetospheric Multi-Scale (MMS) mission . FGMs are also on their way to Jupiter on the JUICE (Jupiter Icy Moons Explorer) mission and flying to Mercury onboard BepiColombo . The diversity of these missions and their profiles, exploring planetery magnetospheres, measuring the solar wind (SW), and even venturing into interstellar space, shows the versatility of FGM instruments.

However, magnetometers of fluxgate type are not the only ones being used on scientific spacecraft. Over the last decades, different magnetometers have been flown on missions to various parts of the solar system. Anisotropic magnetoresistive (AMR) magnetometers were used on the TRIO CINEMA mission in low Earth orbit (LEO) for space weather investigations. The benefit of such magnetometers is their low weight and robustness, whereas the offset stability and overall measurement accuracy is diminished compared to scientific FGMs . Another example for the applicaton of AMR magnetometers is the so-called Service Oriented Space Magnetometer (SOSMAG); it has been part of the Korean GEO-KOMPSAT–2A spacecraft launched in 2018 into geostationary orbit (GEO) . SOSMAG consists of two AMRs inside the spacecraft and two FGMs mounted on a one meter long boom, which is very short in comparison to the spacecraft dimensions . Here, the AMR magnetometers are used to measure high intensity magnetic disturbances generated inside the spacecraft in order to be able to correct for them in the more precise FGM measurements.

An Overhauser magnetometer (or proton precession magnetometer) was used in the Danish Ørsted mission to newly measure Earth's magnetic field . This kind of magnetometer features high accuracy and stability. However, it can only perform scalar measurements, the sampling rate is low, requires a high ambient field to operate at all, and is rather heavy in comparison to AMR and FGMs.

Another group of magnetometers falls into the category of optically pumped magnetometers, of which the vector helium magnetometer (VHM) is a flight-proven example. The Ulysses mission launched in 1990 used a VHM together with an FGM . The VHM combines a high offset stability with the ability to measure the absolute magnetic field. Thus, the VHM can be used to calibrate the FGM with very high accuracy, also deep within planetary magnetospheres. The same measurement principle was also applied in the Cassini mission targeting the Saturnian system . VHMs are also flying on the three-satellite mission Swarm in LEO to study Earth's magnetic field . Here, vector FGMs were also used in combination on each satellite.

The coupled dark state magnetometer (CDSM) is a new optically pumped magnetometer that is part of the JUICE mission on its way to Jupiter. Furthermore, it has been launched on the China Seismo-Electromagnetic Satellite (CSES) and is now investigating natural electromagnetic phenomena in LEO . The CDSM is a scalar magnetometer that is able to measure the magnetic field modulus irrespective of the field direction with respect to the sensor cell. It measures the magnetic field using the Zeeman effect of rubidium in a small glass cell filled with an additional buffer gas . The shifting and splitting of the hyperfine structure energy levels as a function of the ambient magnetic field is combined with coherent population trapping. This leads to narrow resonance features and also enables omni-directional measurement. Other magnetometers are also under development, for example on the basis of nitrogen vacancies in diamond , though these are not space-ready yet .

As stated, the various magnetometers all have different characteristics that can be compared, among others: noise (frequency dependent), ability to perform scalar vs. vector measurements, stability with respect to calibration parameters (offsets, gains, direction of magnetic axes) and their linearity, system complexity, robustness, power consumption, price, and size. Depending on the mission or spacecraft constraints, the mission's scientific objectives and duration, and the visited space region's characteristics, a specific magnetometer type has to be chosen. While FGMs have been the traditonal choice, it shall be investigated whether other types might also be suitable for certain regions or conditions. This work is a first step to systemetically look for required and realized noise levels in near-Earth space environments. All of the magnetometers mentioned above measure space phenomena in the frequency range from DC to tens of Hz. For higher frequencies search coil magnetometers (SCM) are used e.g.. For a comparison of search coil vs. FGMs and a merging of their observations, see . It is important to note that the measurement performance of the satellite missions considered is not limited by the magnetometers themselves, but rather by the magnetic properties of the satellite. The satellites generate significant DC and AC magnetic disturbances – particularly evident in later sections – which are detected by magnetometers mounted on short booms. Consequently, ensuring magnetic cleanliness, especially in the AC regime, is more critical than further improvements in instrument sensitivity or accuracy.

In this paper we investigate the noise levels of one FGM and one AMR magnetometer in a magnetically quiet environment. These are then compared to fluxgate measurements from GEO inside the Earth's magnetosphere (from SOSMAG), from the magnetosheath (MSH) and from the pristine solar wind upstream (both from THEMIS). Data from GEO represent mostly undisturbed measurements inside the magnetosphere. To contrast these, we also included Cluster measurements from a polar orbit taken during times of electromagnetic ion cyclotron (EMIC) wave activity. These are common waves in the magnetosphere that are produced by anisotropic proton distributions in the 0.1–5 Hz frequency range. They are usually transverse left-hand polarized waves .

In this paper, six data sets are investigated: (a) fluxgate magnetic field measurements in a magnetically quiet laboratory environment, (b) AMR measurements also in a magnetically quiet laboratory environment, (c) Cluster FGM measurements of EMIC waves in Earth's magnetosphere, (d) SOSMAG measurements in GEO, (e) THEMIS FGM measurements in the terrestrial magnetosheath, and (f) THEMIS FGM measurements in the solar wind: a.

A state-of-the-art science grade FGM similar to the ones used on Rosetta see, THEMIS see, and JUICE see is put in a magnetically shielded environment on the ground. Its ring cores have a diameter of 13 mm (for XZ direction) and 18 mm diameter (for YZ direction), respectively . The magnetic field is measured overnight with a data rate of 4 Hz. The whole data series is 9 h and 12 s long. In order to remove disturbing trends from external effects at the beginning and the end, only data between 5000–25 000 s (about 83 min to 7 h) were used .

The random picking of 1000 intervals for data sets (d) to (f) and 500 for data set (c) has been chosen to get statistical significance while limiting the computation time. Additionally, this lets small variations of individual measurements fade into the background noise level, so all disturbances seen are either from the spacecraft or a result of general space phenomena (as seen in Sect. ). It has been checked in several runs for each data set that the overall results do not depend on the exact combination of chosen intervals. For the selected intervals of data sets (c) to (f), the average power spectral density (PSD) per component is calculated with a discrete Fourier transform according to: 1P(fk)=13∑xyz2ΔtN∑m=0N-1Bxyz,mexp⁡-2πimkN2 where P(fk) is the PSD at frequency fk=k/(NΔt), Δt denotes the sampling period, N is the number of sampling points per interval and Bxyz,m represents the magnetic field measurement observation in one component (x, y, or z) at position m within the interval. For each data set and frequency, the 5th, 10th, 25th, 50th, 75th, 90th, and 95th percentiles of the square roots of the PSDs (P(f)1/2, also called the amplitude spectral density) are calculated. Here, the 5th percentile corresponds to the value that is equal to 5 % of the maximum value at each frequency, the 10th percentile corresponds to the value that is equal to 10 % of the maximum value at each frequency and so forth. This approach with percentiles is used to see the range at each frequency and will be quantified in Sect. . For the two magnetometers, as seen in data sets (a) and (b), the average PSD of the whole data set is computed using Welch's method . First, the data set is split into intervals of a length of 4000 (FGM) and 2000 (AMR) points, then the overlap is defined to be half of the segment length. The difference in the number of points is due to the different data rates of the magnetometers, it leads to a resolution of 1 mHz in both cases. Second, the data is detrended linearly. Third, the overlapping data intervals are windowed with a Hamming window. Fourth, the discrete Fourier transform is calculated for each window according to Eq. (). The averaging of the calculated periodograms is done by using the mean. This is done for each component of the magnetic field indiviudally, then they are all summed up and divided by three to get the amplitude spectral density per component.

Results pertaining to the data sets (a) through (f) are shown in the corresponding panels (a) through (f) of Fig. . The square roots of the PSDs of each of the random intervals is calculated and then, the percentiles thereof are shown in Fig. . Note that the axis scalings are different for the lab measurements and space measurements.

The values of the 50th percentiles of the amplitude spectral densities P(f)1/2 of each data set at 3.3 mHz, 0.1, and 1 Hz (for GEO at 0.5 Hz) as shown in panels (a) through (f) of Fig.  are listed in Table . For the FGM and AMR data sets, the values are given at 1 mHz, 0.1, and 1 Hz. The values at 0.1 Hz are included as an extra point of comparison, because the standard point of comparison at 1 Hz used in literature is in this case quite near to the Nyquist frequency. This might lead to effects on the measured values due to the internal filters of the instrument.

All the panels in Fig.  show a downward slope of the spectrum. The spectral slope α in the log-log scale is given by 2α=log⁡P(f2)nT2/Hz-log⁡P(f1)nT2/Hzlog⁡f2Hz-log⁡f1Hz=log⁡P(f2)P(f1)log⁡f2f1 where P is the value of the spectrum, f is the frequency and the indices 1 and 2 denote two different points on the spectrum. The spectral slope is often used as a measure of turbulence . All the spectral slopes α are listed in Table . Note that the slope is calculated without taking the square root of the spectrum. Therefore, the slopes taken from the spectra (e.g. in Fig. ) must be multiplied by 2 to match the values listed in Table . For the AMR and the magnetosheath data sets, there are two slopes. The first slope of the AMR data set is calculated from the second data point until 3×10-2 Hz. The second slope was calculated between 0.1–1 Hz. For the magnetosheath data set, the corner frequency of 0.2 Hz was used. There are two distinct regions in the corresponding panels, as can be seen in Fig. b and e. For all other data sets, the second and the second to last data points were used.

A second characteristic is the variation V of P(f)1/2 of the data sets, which is given by V=1N/2∑k=1N/2log⁡P951/2(fk)nTHz-1/2-log⁡P51/2(fk)nTHz-1/23=1N/2∑k=1N/2log⁡P951/2(fk)P51/2(fk) where N is the number of sampling points, P95 is the 95th percentile of PSDs, P5 is the 5th percentile of PSDs, and fk is the frequency. The variation is a measure for the variability of the data set: the larger the variation, the more different in spectral power the individual intervals are. The variation of the percentiles of the data sets is also listed in Table .

With slope and variation defined, we can now evaluate the data sets. The least steep slope over a complete data set can be seen in Fig. a, where the FGM data set is shown. The next higher slope is exhibited by the amplitude spectral density of the AMR shown in Fig. b with at first α=-1.02. It can be seen to flatten at 3×10-2 Hz to α=-0.23 (see Table ). At low frequencies, the overall values of the amplitude spectral densities are one order of magnitude higher for the AMR compared to the FGM. At 0.5 Hz the amplitude spectral density of the AMR is a factor of more than 12 higher than the FGM's (see Table ).

The GEO data set shown in Fig. d exhibits an average slope of α=-1.72 with values of the amplitude spectral density between 3843 pTHz-1/2 at 3.3 mHz and 52 pTHz-1/2 at 0.5 Hz.

The EMIC wave data set shown in Fig. c behaves similarly to the GEO data set collected in Earth's magnetosphere. The spectrum has higher values of the amplitude spectral density at low frequencies (see Table ). It exhibits a slightly higher slope of α=-1.81 than GEO that leads to higher values of the amplitude spectral density at 0.5 Hz, but continues to decrease to 49 pTHz-1/2 at 1 Hz. The amplitude spectral density of the EMIC wave data set also features a slight bump above 0.2 Hz. The magnetosheath data set featured in Fig. e shows a less steep slope of α=-1.37 compared to EMIC and GEO in the lower frequencies up to 0.2 Hz. A break in the slope is observed at this point, with the slope value of α=-2.56 being the steepest among all data sets (see Table ). In the last panel of Fig. , the solar wind data set is shown with a slope of α=-1.68.

The variation V of the data sets can only be given for data sets (c) through (f) of Fig. , since only for those several amplitude spectral densities were available. The biggest variation V with 1.2 can be seen in the EMIC data set in Fig. c. The magnetosheath data set in Fig. e also exhibits a large variation with V=1.11. The GEO and solar wind data sets in panels (d) and (f) have very similar, smaller variations with V=0.8 and V=0.78, respectively. Some of the data sets also exhibit distinct spikes in their PSDs. In the AMR data set in Fig. b, those are at 0.25 and 0.5 Hz caused by housekeeping transmission. The EMIC data set in Fig. c has a spike at 0.24 Hz which is close to the spin frequency of 0.25 Hz of the spacecraft (Cluster has a spin period of 4 s, ). In Fig. d, a spike at 0.166 Hz is visible in the GEO data set. This spike has been attributed to a disturbance source located in the spacecraft . In Fig. f, the solar wind data features several spikes at 0.33 Hz and multiples thereof. These can be attributed to the spacecraft's spin frequency and its harmonics.

To assess the suitability of the two magnetometer types to make sensible measurements in the respective regions of space, we have to compare the maximum noise floor of their lab environment spectra with the lowest PSD values (5 % percentiles) of the space spectra. In Fig.  exactly this comparison is shown. The spectra pertaining to the magnetometers are plotted in light and dark blue; the spectra pertaining to the other data sets are depicted in other colors. Plots likes this with the 50th and 95th percentiles for the space data sets are available in the Appendix. If the magnetometer's spectra are below those of the space environments, this means it is possible to use the magnetometer to measure all of the phenomena of interest in those environments. If half of the spectra of the space environments were higher than the magnetometer's spectra, half of the phenomena would be invisible. It can be seen that the AMR magnetometer can only be used to measure in regions with higher values of the amplitude spectral density, i.e. continuously above 200 pTHz-1/2. This is for example given in the magnetosheath until 0.5 Hz. In all other regions, at frequencies up to a maximum of 2.5×10-2 Hz, the AMR noise floor is above the phenomena of interest. In contrast, the FGM spectrum remains below, or at the same level as, the others across the entire frequency range.

Turbulence describes the process of energy transport between varying magnetic fields and motions from larger to smaller spatial scales . The spectral slope α is an important feature of turbulent plasmas. It changes in distinct regions of frequencies . In Fig. , the amplitude spectral densities of all data sets are shown. Since all the spectra were obtained from space plasmas, they generally follow Kolmogorov's law for turbulent spectra f-5/3 . Comparing the slope of the solar wind data set shown in Fig. f, which in our case was at α=-1.68 (see Table ), it is very similar to other values reported in literature. In , the reported spectral slope (sometimes also called spectral index) of the solar wind is α=-1.62, in it is at α=-1.7 for the respective frequency range of 10-3 to 1 Hz, and in , it is reported at α=-1.49 from 10-3 to 0.2 Hz. Compared to the other data sets of regions and phenomena included in this paper, the solar wind data set has the lowest amplitude spectral density. It includes only pristine upstream solar wind (no foreshock) with structures continually evolving in the plasma on small scales. Other phenomena adding to the spectrum could be e.g. corotating and stream interaction regions, or mesoscale structures .

Two of the data sets were collected inside Earth's magnetosphere: the GEO dataset and the EMIC data set. As described in the last section, the EMIC data set has higher values of the amplitude spectral density than the GEO data set. This might be due to the fact that for that data set, specifically times with wave activity were included, whereas for the GEO data set calm times with low wave activity are predominantly present in the data set. Both panels (c) and (d) of Fig.  show a spike: for EMIC it is due to the spin frequency of the spacecraft, for GEO the spike is due to a disturbance as explained in the last section. In the EMIC data set, a bump appears between 0.2–1 Hz. This bump can be attributed to the EMIC waves: in Earth's magnetosphere, these narrowband (few 100 smHz) emissions can occur in a wider frequency range (0.1–2.5 Hz in the present study) . The amplitude spectral densities of three single EMIC events are shown in Fig. . They have one or more distinct peaks, but at different frequencies in the cited range. This holds true for all the individual events. When all events are averaged, the individual peaks are smoothed in the overall spectrum, as they are averaged with the flat portions of the spectra from other events. This averaging effect leads to the observed bump within the overall frequency range of EMIC wave occurrences. Note that the different background levels are due to different range modes used: event #25 used mode 2, event #351 used mode 3 (both low background levels), and event #37 used mode 4 (higher background level). Each range mode has a different digital resolution.

The magnetosheath data set shown in Fig. e features a spectral break at 0.2 Hz, which is in the transition region of inertial ranges between ion and electron scales . Below 0.2 Hz, the spectral slope was less than Kolmogorov's law for turbulent spectra with α=-1.37. Above, it has the largest slope exhibited in all the data sets with α=-2.56. This is due to a broad enhancement of the spectrum in the frequency range of 3×10-2 to 1 Hz. In this frequency range, several different phenomena may contribute to the higher amplitude spectral density. In the magnetosheath, the turbulence levels depend on the measurement position and on how the interplanetary magnetic field (IMF) is aligned with the upstream bow shock segment: at a quasi-parallel shock, where the angle between IMF and bow shock normal vector is below 45°, plasma turbulence is strong . Foreshock waves such as 30 s waves and 3 s waves play an important role as well as so-called magnetosheath jets . Short Large Amplitude Magnetic Structures (SLAMS) also transmit into the magnetosheath at the quasi-parallel bow shock and might add to the enhancement seen in the data set. Mirror modes may be locally generated downstream of the quasi-perpendicular shock and there-by contribute to the overall fluctuating levels in this region of space.

The results obtained thus far can now be compared with the FGM and AMR measurements. The amplitude spectral density of the FGM is shown in Fig. a. It has a spectral slope of α=-0.75, approximately following a 1/f noise spectrum as is expected in this frequency range . It exhibits the lowest values of all data sets, going down to 9 pTHz-1/2 at 1 Hz. This means the FGM is well suited for measurements in all the listed space regions and of all phenomena occuring therein (also see Fig. ). If a magnetometer with a higher data rate is chosen, it can also measure at higher frequencies; the FGM used in the MMS mission, for instance, can measure up to 128 Hz (burst mode) although above 16 Hz for the merged data product the SCM data is used exclusively on MMS .

The spectrum of the AMR magnetometer as shown in Fig. b has a slope of α=-1.02 due to 1/f noise, as seen in other AMR magnetometers . A spectral break occurs at 0.05 Hz, above 0.1 Hz the sensor exhibits only frequency independent thermal noise . However, the general noise level is significantly higher with 217 pTHz-1/2 at 1 Hz compared to the FGM as already seen in the last section. Since this is at quite a high level, this AMR magnetometer is not suitable for scientific measurements at frequencies below 1 Hz, since the noise floor is higher than the lowest expected signals. There exist other AMRs with lower noise floors as described in . This finding is also well illustrated in Fig. : all amplitude spectral densities except for the one pertaining to the magnetosheath data set mostly lie below the AMR's spectrum, thus making measurements with the AMR in these regions not reasonable.

The variation as listed in Table  shows that the regions and/or phenomena with more wave activity and turbulence also exhibit a higher variation in the amplitude spectral densities. This means that the individual intervals are quite diverse, some with high values of the spectrum due to possibly higher wave activity and turbulence, others with lower values of the spectrum that likely have less wave activity and turbulence. The calculated variations are averaged over the whole spectrum. This is why the variation of the solar wind is seemingly not fitting to the plot: the variation at low frequencies is quite different for this data set compared to the variation at higher frequencies.

Overall, as shown in Fig. , the lowest spectrum pertains to the solar wind. EMIC and GEO have similar values of their respective amplitude spectral densities, underlining that the data sets were collected in the same region of Earth's magnetosphere. The magnetosheath data set shows a turbulent magnetic field, which is mirrored in the corresponding higher values of the spectrum going up to 4.7×104 pTHz-1/2 at 3.3 mHz. The difference of values in the amplitude spectral densities between the lowest and highest frequencies of each data set is more than 2 orders of magnitude for the solar wind, magnetosheath, GEO, and EMIC data sets, but only 1 order of magnitude for the magnetometer data sets. One also has to keep in mind that the noise levels seen are also depending on the instrument itself and not only the ambient conditions. The digital resolution decreases with increasing ranges of the instrument (or the range mode used), so the general noise level accordingly increases with increasing range. This was explicitly shown in Fig.  for the different range modes in Cluster. Thus, the FGMs have limitations concerning the amount of telemetry (reflected e.g. in ranges). These limits increase instrument noise levels artificially and are also reflected in the statistics used for this work.

We've compared the amplitude spectral densities of a FGM and an AMR in a shielded lab environment with spectra obtained in different regions of space (magnetosphere, magnetosheath, solar wind). The spectral slopes are generally higher in space than in shielded environments. The highest amplitude spectral density values are measured in the magnetosheath. In sum, for all of the measured phenomena and regions, an FGM will be able to measure the fields and resolve the natural fluctuations within a frequency range of 1 mHz to 2.5 Hz. Higher frequencies are achievable with higher data rates, but were not analyzed here. The AMR magnetometer is only suitable for more turbulent regions such as the magnetosheath. Alternatively, it can be used in combination with an FGM to clean the latter's data as was done in SOSMAG.

The selection of a magnetometer depends on the expected phenomena to be measured, with an additional margin in measurement capabilities to ensure robustness and accommodate the need to detect unforeseen events. Furthermore, there is an inherent trade-off between selecting a highly sensitive magnetometer for optimal scientific measurements and the associated costs and system complexities. This paper aims to quantify this noise-related trade-off when choosing a magnetometer for a mission. Based on noise levels and frequency ranges covered, the data sets presented here favor the FGM over the AMR, which exhibits more limited applicability.

However, only two magnetometer types were considered here. As mentioned in the introduction, there are other types of magnetometers that might be suitable depending on the mission. For some applications, e.g. measurements in the solar wind, the stability of offsets (especially over time) or other calibration parameters () might be of utmost importance. Future works could also consider mass and size (of the sensor and the electronics), power consumption, complexity, and price. Different choices in magnetometer types might emerge depending on the exact application. Although similar findings are to be expected in other planetary magnetospheres, future works could explicitly compare this as well as other regions in Earth's magnetosphere such as LEO measurements.