ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-35-117-2017Spin axis offset calibration on THEMIS using mirror modesFrühauffDennisd.fruehauff@tu-bs.dehttps://orcid.org/0000-0003-0092-8979PlaschkeFerdinandhttps://orcid.org/0000-0002-5104-6282GlassmeierKarl-HeinzInstitut für Geophysik und extraterrestrische Physik, Braunschweig, GermanySpace Research Institute, Austrian Academy of Sciences, Graz, AustriaDennis Frühauff (d.fruehauff@tu-bs.de)19January201735111712128November20166January20176January2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/35/117/2017/angeo-35-117-2017.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/35/117/2017/angeo-35-117-2017.pdf
A newly developed method for determining spin axis offsets of magnetic field
instruments on spacecraft is applied to THEMIS. The formerly used
determination method, relying on solar wind Alfvénic fluctuations, was
rarely applicable due to the orbital restrictions of the mission. With the
new procedure, based on magnetic field observation of mirror modes in the
magnetosheath, updated spin axis offsets can be estimated approximately once
per year. Retrospective calibration of all THEMIS magnetic field measurements
is thereby made possible. Since, up to this point, spin axis offsets could
hardly ever be calculated due to the mission's orbits, this update represents
a substantial improvement to the data. The approximate offset stability is
estimated to be < 0.75 nT year-1 for the complete course of the
mission.
Magnetospheric physics (magnetosheath; MHD waves and instabilities; planetary magnetospheres)Introduction
Accurate in-flight calibration of magnetic field instruments has always been
an important prerequisite in space physics. On ground, proper calibration can
be easily realized using defined reference setups. In space, reference fields
are rarely available and additional disturbances and non-stationary magnetic
field profiles make calibration difficult. In case of a spinning spacecraft,
such as CLUSTER , THEMIS , and MMS
, the calibration of components perpendicular to the spin
axis can be performed to a very high degree of accuracy. The determination of
the spin axis component's offset, though, suffers from the aforementioned
difficulties. Obviously, the situation is the same for three-axis-stabilized
spacecraft, such as Rosetta and, prospectively,
BepiColombo's Mercury Planetary Orbiter (MPO) . So far,
only few methods have been developed to determine fixed-axis component
offsets. Among these are the Hedgecock method (i.e., calibration using
Alfvénic fluctuations in the solar wind; see , and
) and the electron drift method
. The first method requires the presence of
solar wind measurements, while the latter needs an electron drift instrument
aboard the probe.
The THEMIS (Time History of Events and Macroscale Interactions During
Substorms) and ARTEMIS (Acceleration, Reconnection,
Turbulence, and Electrodynamics of the Moon's Interaction with the Sun)
missions consist of a total of five identical
spinning spacecraft, of which none features electron drift instruments.
Therefore, calibration of the spin axis components has been consistently
possible only for the two probes orbiting the Moon (spacecraft THB and THC),
since the solar wind is seen very frequently and calibration through the
detection of Alfvénic waves is possible. Figure shows the
behavior the spin axis offset since the beginning of the scientific mission
in 2008. The ARTEMIS probes (lower panel) were monthly calibrated using solar
wind data. The Earth-orbiting satellites (probes THA, THD, and THE) were only
calibrated occasionally, with only one calibration instance during the last
5 years of the mission. While probes THB and THC show an offset stability
of around 0.1 nT year-1, it is likely that the other probes face
larger offset drifts. Due to their orbits, the spacecraft are exposed to
stronger temperature changes and enhanced radiation in the Van Allen belts,
advancing the sensors' and electronics' aging processes (THA, THD, THE).
These effects are currently not incorporated in the routine instrument
calibration procedures. The reason for the nonavailability of solar wind
encounters can be attributed to the probes' orbits. Figure
illustrates the range of maximum X distance of the probes on the Earth–Sun
line (i.e., in geocentric solar ecliptic coordinates, GSE). Using a simple
model for magnetopause and bow shock position on the Earth–Sun line
, and smoothed solar wind data from OMNI database the
magnetospheric coverage upstream Earth can be visualized. On average, the
three THEMIS probes have never seen solar wind data. Of course, variations on
shorter timescales might have occasionally pushed the magnetospheric
boundaries inwards, thereby making a few short calibration intervals
possible. In total, though, offset determination using solar wind methods is
not an adequate method for probes orbiting only inside the magnetosphere.
Offset stability of THEMIS (upper panel) and ARTEMIS (lower panel)
for the complete mission. After 2012 no updates on the spin axis offsets were
calculated but for a single occasion on THA in 2015.
Recently, have presented a method using mirror mode
observations during magnetosheath passages. Figure also indicates
that sheath encounters are much more likely than solar wind observations.
Therefore, the mirror mode method appears to be a good candidate to catch up
on spin axis offset calibrations for THEMIS.
Brief summary of the mirror mode method
The mirror mode method is based on the assumption that mirror modes are
highly compressible fluctuations .
Consequently, the direction of maximum variance is
expected to be parallel to the mean magnetic field direction. If analyzed in
a non-rotating, spin-axis-oriented coordinate system, this assumption leads
to an equation containing the remaining spin axis offset. The method is
outlined in detail in . It consists of four basic steps:
THEMIS (THA, THD, THE)
GSE-X distance upstream Earth and magnetopause and bow shock models. The
magnetosheath is shaded gray.
Identify magnetosheath passages using THEMIS data from the electrostatic
analyzer (ESA) at ≈3 s resolution and OMNI
solar wind density data .
For each subinterval, calculate an estimate for the spin axis offset,
Ozi, and its uncertainty, ΔOzi, using maximum
variance analysis and the equations presented in .
Since not all of the subintervals represent mirror mode structures,
select those fulfilling the criteria and thresholds in ,
, and .
For all remaining offset estimates within a certain interval (e.g., a
month, a science phase), calculate an estimate for the final spin axis offset,
Ozf, using a kernel density estimator (KDE) with a Gaussian
kernel . This final offset will be the value for
which the probability density function maximizes. Since the selection of data
points is influenced by the magnetic field measurements, and, hence, their
offset value, an iterative repetition of these steps is necessary until the
method converges to a final estimate.
To enhance the accuracy of the KDE method, we have incorporated weights,
wi, for each measurement computed from their uncertainties, ΔOzi:
wi=exp-(ΔOzi)22σ2,
where the width of the error distribution function, σ, is determined
by the maximum of the probability density distribution of all ΔOzi. The probability density distribution for the offsets,
Ozi, is then computed as
P(Õz)=12πNh∑iN1wiexp-(Õz-Ozi)22h2,
with the number of observations, N, and the bandwidth, h, which is
determined adaptively by the procedure (see, e.g., ). An
example distribution is shown in Fig. . used
uniform weights and a fixed bandwidth of h=1 nT. For comparison, the
resulting density functions for both the unweighted and weighted calculations
are shown. While the differences in the maximum position are generally small,
the THEMIS data have shown that the use of individual weights and an
auto-determined bandwidth can severely influence the offset calculations:
The weight distribution prevents the algorithm from repetitively
micro-adjusting the result to nonphysically large values.
Through the
adaptive bandwidth the overall shape of the distribution is improved, thereby
especially pronouncing the maximum, making the position estimate more
accurate.
Histogram of mirror mode offset estimates for THE in the sixth
sheath interval and KDE probability distribution functions (first
iteration).
Results and discussion
The identification of magnetosheath encounters results in a database
visualized in Fig. . For the three THEMIS probes it can be seen
that the major part of the observations will be made when the spacecraft are
in their dayside conjunction . As a comparison, the
number of possible observations for the two ARTEMIS probes is shown in the
lower panel. Obviously, in the first 2 years of the mission, when the
spacecraft were still in orbit around Earth, a fair amount of data is
available (yet, THB and THC did also see solar wind due to their greater
apogee distance). Then, when lifted into orbit around the Moon, the probes
only rarely encountered mirror modes in the Earth's magnetosheath.
As a first criterion intervals are selected when the probes' apogee
projection onto the X–Y plane (in GSE coordinates) is not more than
30∘ away from the Earth–Sun line: the spacecraft are in a
subsolar region where mirror mode observations are expected to be observed
frequently . These intervals are depicted by the black lines
in Fig. .
Sheath encounters of THEMIS (upper panel) and ARTEMIS (lower panel)
probes. The designated offset determination intervals are marked by black
lines. The histogram bin size is 2 months.
From Fig. the following strategy for implementing new spin axis offsets can be deduced:
For probes THA, THD, and THE a new Ozf will be estimated for
all data during each of the aforementioned intervals. This will lead to a
single updated spin axis offset value approximately once per year. The
determined value will be kept constant until a new estimate is available.
Spacecraft THB and THC did and still do see solar wind frequently. To
prevent any discontinuity in the determination method, these two probes will
continue to be calibrated using solar wind data .
The complete set of results is displayed in Fig. . For spacecraft
THA, THD, and THE the new spin axis offsets are shown together with the past
results from spurious solar wind calibrations. As suspected earlier, the
total offset drift of the three Earth-orbiting probes is stronger than the
offset drift of THB and THC. The overall drift is in the range of
0.5–0.75 nT year-1 while each of the probes show a similar trend in
the offset data. As indicated by the dashed lines, which display the past
calibration values, the updated data compare within < 2 nT to the
previous parameters (during the time when past updates were actually
calculated, i.e., until 2012).
The possibility to update spin axis offsets on the THEMIS probes constitutes
a major improvement to the previous approach. While relative changes of a few
nanoteslas do not make a big difference in the high field regions of the
magnetosphere, they will certainly have an influence on scientific studies in
high-beta regions, such as the plasma sheet in the near-Earth magnetotail.
With the publication of this work, the new offsets will be incorporated into
the THEMIS database.
Full spin axis offsets of the three THEMIS spacecraft as
recalculated by the mirror mode method. Dashed lines indicate the past
results. With the beginning of each sheath interval, a new value becomes
effective.
Data availability
THEMIS data and the latest calibration files are publicly available at
http://themis.ssl.berkeley.edu/ or via the SPEDAS software. Solar wind
data are available at https://omniweb.gsfc.nasa.gov/, and auroral
electrojet data can be found at http://wdc.kugi.kyoto-u.ac.jp/.
The authors declare that they have no conflict of
interest.
Acknowledgements
We acknowledge NASA contract NAS5-02099 and V. Angelopoulos for use of data
from the THEMIS Mission – specifically, C. W. Carlson and J. P. McFadden for
use of ESA data. This project is financially supported by the German
Ministerium für Wirtschaft und Energie and the Deutsches Zentrum für
Luft- und Raumfahrt under contract 50 OC 1403. The topical editor, Y. Miyoshi, thanks A. Matsuoka and
C. Smith for help in evaluating this paper.
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