Data from magnetometers on spacecraft are typically used for one, or both, of two purposes: for the determination of the spacecraft attitude and for the measurement of physical processes local to, or indeed far from, the spacecraft. No measurement is perfect, and the measurement of magnetic fields is particularly challenging given their low values and the particularly small nature of the variations that must be detected for some applications; see, e.g., for a historical description of space magnetometer techniques. All sensor and spacecraft environments have different capabilities, and every application of magnetometer data has different requirements in terms of cadence, accuracy, noise, etc.; thus, the intended use cannot be isolated from the methods used to recover accurate magnetic field measurements since one drives the other.

Attitude control knowledge often results in rather coarse requirements of just a few degrees e.g., corresponding to an absolute accuracy in a given field component of ∼ 2000 nT or greater at low Earth orbit (LEO), equivalent to at least ∼ 4 %. In contrast, for scientific applications the requirements are more stringent and depend on the precise goal: for example the ESA Swarm mission aims for sub-nT absolute precision . However, if the scientific requirement is to be able to detect transient signals in magnetometer data at LEO, such as field-aligned currents at the auroral oval e.g. the review of, then such absolute precision in the overall magnetic field is not required. It is therefore important to assess what it is possible to achieve with a magnetometer, given the quality of the sensor and the environment it is in.

CubeSats offer the possibility of low-cost spacecraft in orbit around the Earth equipped with scientific instruments, e.g. for space weather monitoring purposes cf.. The CubeSat specification, however, constrains both dimensions (a three-unit CubeSat is 10 cm × 10 cm × 30 cm with no protuberant parts at launch) and total mass (≲ 4 kg for 3U) e.g.. Furthermore, the dimensions restrict the amount of available power from solar cells to ≲ 2 W per unit e.g.. In terms of magnetic field measurements, typical fluxgate magnetometer instruments used for space plasma physics applications e.g. are thus unsuitable for use on CubeSats since they exceed all of these constraints. Additionally, a full magnetic cleanliness program e.g. is not possible with CubeSats; thus, the raw data will be contaminated to some degree with fields of spacecraft origin. Therefore, in designing magnetometers (or indeed any scientific instrument) for CubeSat platforms, there must be a trade-off in mass, power and/or precision levels which will affect the instruments' capabilities.

Magnetometers flown on CubeSats thus far have typically been used for attitude purposes e.g.. However, there may also be potential science applications for magnetometers on such spacecraft: QuakeSat's single-axis search-coil AC magnetometer has detected lightning-generated whistler mode waves (10–1000 Hz) and ELF bursts (10–150 Hz), simultaneously observed on the ground, which were possibly due to earthquakes ; and DICE's (Dynamic Ionosphere CubeSat Experiment) DC vector magnetometer has detected ∼ 200 nT magnetic deflections due to field-aligned currents at the auroral oval during a marginally geomagnetically active period . The scientific capabilities that such lower-quality sensors (necessitated by the constraints of CubeSats) offer are as yet not entirely clear. In this paper we assess one such example from the first CINEMA (CubeSat for Ions, Neutrals, Electrons and MAgnetic fields) spacecraft.

CINEMA is a 3U CubeSat equipped with avionics and science instruments launched into low Earth orbit (LEO) on 13 September 2012, with orbital elements shown in Table , as a secondary payload from a P-POD (Poly Picosat Orbital Deployer) dispenser. Two additional near-identical CINEMA CubeSats were launched on 3 November 2013 which we do not discuss in this paper. The spacecraft's science instrumentation includes MAGIC (MAGnetometer from Imperial College), two novel miniaturised vector DC magnetometers using anisotropic magnetoresistive (AMR) sensors . One sensor, the inboard (IB), is contained within the spacecraft, whereas the other, the outboard (OB), is on the end of a 1 m stacer boom in order to reduce the effect of spacecraft fields on the measurements. The two sensors and their relative axes are illustrated in Fig. . provide a summary of the modes of operation of the instrument. The requirements of the MAGIC instrument are twofold. Firstly, the sensors (in particular the inboard) should provide measurements of Earth's magnetic field at a level of accuracy suitable for attitude-determination purposes . Secondly, the outboard sensor should be capable of detecting transient science signals in addition to Earth's field, e.g. magnetic perturbations associated with magnetospheric current systems, important for space weather monitoring cf..

Unfortunately, there have been a number of problems with the spacecraft's systems hence only a limited amount of data has been retrieved from the first CINEMA spacecraft. In this paper we present the first in-flight MAGIC results from the two longest time intervals of MAGIC data obtained for which the onboard clock was reliable. In Sect.  we describe the attitude-independent calibration procedure used on the raw data, through the use of the International Geomagnetic Reference Field (IGRF). Following calibration, the attitude of the sensors is estimated using a simple magnetometer-only method as described in Sect. . Finally, Sect.  discusses the small-amplitude (∼ 20–60 nT), transient (> 21 mHz) science signals detected by MAGIC in science mode. These are revealed to be field-aligned currents at the auroral oval, which are corroborated by measurements from the DMSP (Defense Meteorological Satellite Program) and POES (Polar-orbiting Operational Environmental Satellites) spacecraft. We, therefore, assess the science capabilities of the MAGIC sensors flown on CINEMA through the use of simple magnetometer-only methods and discuss the possibilities of utilising sensors similar to MAGIC for science purposes in the future.

Following the attitude-independent calibration of MAGIC, we wish to use the magnetometer data to estimate the spacecraft and sensor attitude at each datapoint.

While we have shown that attitude information can be extracted by comparing the MAGIC data with IGRF, the requirements of the instrument additionally included the ability to detect transient physical signals in the time series due to either spatially or temporally confined phenomena. We transformed the despun MAGIC science mode data in a field-aligned system (ν, ϕ, μ), where μ is aligned with IGRF, ν is perpendicular to IGRF pointing radially outwards and ϕ is the usual azimuthal direction; subsequently, we band-pass filtered the data to reveal transients. A lower cutoff of 21 mHz was used to remove spin tones due to errors in calibration, and the upper cutoff was set at 1.8 Hz in order to reduce noise and remove quasi-periodic spikes in the data of spacecraft origin.

The two perpendicular components of the magnetic field are shown in Fig. , revealing transient signals of ∼ 20–60 nT in amplitude, particularly at the start of the interval, when CINEMA was at high magnetic latitudes in the Southern Hemisphere. Through the Ampère–Maxwell law j=∇×B/μ0, the field-aligned currents (FACs) associated with these magnetic perturbations can be estimated using the method of , namely j∥=1μ0v⟂ddtB⟂⋅n^, where v⟂ is the spacecraft orbital speed perpendicular to IGRF and n^=μ×v/μ×v is a unit vector perpendicular to both IGRF and the orbital velocity. This method can lead to a factor-of-2 underestimation of the current density due to the finite extent of the (assumed infinite) current sheets . The calculated FACs are displayed in the second panel of Fig. , showing currents of up to a few µAm-2. We highlight (grey areas) the times of the two periods of FACs between 16:35 and 16:50 UT when CINEMA was traversing the polar cap, where the S=log⁡10j∥2‾ parameter (not shown) of was used to identify the boundaries. The FACs are qualitatively similar and of similar amplitude to those determined from CHAMP (Challenging Minisatellite Payload) magnetic field data at the auroral oval .

To check whether these field-aligned currents are consistent with the location of the auroral oval, we use Total Energy Detector (TED) data from the NOAA POES and SSJ/5 precipitating particle sensor data from the DMSP spacecraft. Figure  displays auroral oval crossings of these spacecraft 45 min either side of the FACs observed by CINEMA, where the tracks have been coloured by the observed total energy fluxes. The POES TED instrument measures energy fluxes into the atmosphere of both ions and electrons in the range 50–20 000 eV, whereas for DMSP we display only the electron fluxes in the range 30–30 000 eV from SSJ/5. CINEMA's trajectory is shown as the black lines, and the two periods of field-aligned currents identified in Fig.  are also highlighted. The locations of these FACs are in fairly good agreement with the position of the auroral oval as evidenced from the precipitating particle data; thus, we are confident that MAGIC did indeed detect field-aligned currents at the auroral oval.

A further period of FACs was detected by MAGIC between 17:04:40 and 17:12:20 UT with amplitudes of typically ∼ 0.5 µA m-2. During this time CINEMA was near the magnetic equator and only a few degrees eastward of the dawn day–night terminator on the ground. Given this location, we suggest that these could be due to equatorial plasma bubbles, the FAC signatures of which have been detected by CHAMP , revealing similar amplitudes to those presented here. Unfortunately, there is no independent measurement to confirm this interpretation.

In the calibration of the MAGIC data, as presented in Sect. , we used an attitude-independent method e.g.. In the case of attitude mode, this has assumed constant calibration parameters, whereas for science mode we have added a linear temperature dependence cf.. also employed attitude-independent calibration to a commercial off-the-shelf PNI Sensor Corporation MicroMag3 vector magnetometer flown on the RAX-1 (Radio Aurora Explorer) CubeSat in LEO. They found residuals with IGRF of ∼ 900 nT, larger than those reported here for MAGIC. However, they subsequently allowed for time-varying biases by modelling (through the Biot–Savart law) telemetered spacecraft currents, reducing the RMSD to 174 nT. Such a procedure could be implemented for MAGIC in future flight opportunities as the next step in calibration. Furthermore, following attitude estimation it may be possible to apply attitude-dependent calibration, e.g. by taking into account the induced currents in solar panels due to their illumination.

Our method of attitude estimation (Sect. ) can be applied to CINEMA only because its tumbling motion is suitably slow. Had CINEMA successfully detumbled and spun up, then the method described here would not have been required since sun sensor data could have been combined with that from MAGIC to uniquely define the spacecraft attitude . On the other hand, more sophisticated methods of magnetometer-only attitude determination do exist . These methods would necessitate further modelling than is possible for CINEMA since they require measures of the spacecraft inertia tensor and any external torques (such as gravity gradients and drags) acting upon it. It is possible that such attitude modelling could be implemented in the future to better constrain spacecraft attitude.

At present, the determination of physical signals in the MAGIC data (Sect. ) is limited by a number of factors since both calibration and attitude are all determined through the magnetometer only. The main limiting factor is the period of CINEMA's rotation, precession and nutation. The cutoff in our filtering is chosen such that the low-pass filter will retain these frequencies, whereas the band-pass filter will reduce them. This serves as a limitation on the timescales (corresponding to equivalent length scales here of ∼ 4–360 km) of the physical signals which can currently be achieved and could in fact be affecting the determined physical signals and corresponding FACs presented here to some degree. It is possible that a further developed attitude model may reduce these effects.

Both the magnetometer-only calibration and attitude estimation methods used here rely on the real physical magnetic field being, on average, well represented by the International Geomagnetic Reference Field (IGRF) cf.. While this is certainly the case in low Earth orbit, it is of course not true in general. Nonetheless, AMR sensors similar to MAGIC could be used in other environments, though the methods used to recover accurate magnetic field measurements would have to be tailored to the unique environment and requirements of the instrument.

We have presented the first in-flight science results from MAGIC (MAGnetometer from Imperial College), a novel miniaturised vector DC magnetometer using anisotropic magnetoresistive (AMR) sensors, aboard the CINEMA (CubeSat for Ions, Neutrals, Electrons and MAgnetic fields) spacecraft in low Earth orbit. We have detailed our attitude-independent (and temperature-dependent, in the case of science mode) calibration procedures, which result in root mean squared deviations in field magnitude from IGRF of 1.95 and 1.23 % respectively for the inboard (in attitude mode) and outboard (science mode) sensors respectively. Such levels of accuracy in the overall magnetic field are certainly sufficient for attitude estimation cf.. Indeed, through the use of magnetometer data only, we estimate CINEMA's attitude to within a few degrees using a simple method, thus characterising the spacecraft's spin, nutation and precession and successfully satisfying the first requirement of the MAGIC instrument.

Furthermore, we have presented evidence that MAGIC is capable of detecting transient physical signals (∼ 20–60 nT) in addition to simply IGRF, thereby accomplishing the other requirement. These signals were 1 order of magnitude smaller than those detected by the science AMR on the DICE CubeSat during a marginally geomagnetically active period . Indeed, MAGIC has a resolution and noise floor that are 1 order of magnitude superior to those of the DICE SciMag instrument. The determined field-aligned currents observed by MAGIC (∼ 0.5–2 µA m-2) show qualitative agreement with previous observations from the CHAMP spacecraft , and those detected at the auroral oval are consistent in location with other available data sets, namely DMSP and POES. Therefore, to our knowledge, MAGIC is the highest-sensitivity vector DC magnetometer flown on a CubeSat to date for which conducting scientific studies is feasible. While AMR sensors cannot achieve the absolute precision of magnetic field measurements at LEO, such as Swarm , certain scientific applications do not require such high levels of precision for which sensors similar to MAGIC could play a role. Indeed we have demonstrated that simple methods applied to only the magnetometer data can yield useful scientific results, such as the locations of field-aligned currents, even during geomagnetically quiet times. The relatively low cost of CubeSats offers the possibility in the future of employing a constellation of spacecraft with MAGIC sensors, e.g. for the purposes of space weather monitoring.