Propagation characteristics of electromagnetic waves recorded by the four
LPCE/CNRS, 3A Avenue de la Recherche Scientifique, 45071 Orléans cedex 2, France
Dept. of Physics and Astronomy, Univ. of Iowa, Iowa City, Iowa 52242, USA
CETP/UVSQ, 10/12 Avenue de L'Europe, 78140 Velizy, France
DESPA, Place Janssen, 92195 Meudon Principal Cedex, France
CESR, 9 Avenue du Colonel Roche, 31029 Toulouse, France
This paper will describe the methods we use to determine the propagation characteristics of electromagnetic
waves observed by the four CLUSTER satellites. The data is recorded aboard CLUSTER by the STAFF ( Spatio-
Temporal Analysis of Field Fluctuations) spectrum analyser. This instrument has several modes of operation, and can
provide the spectral matrix of three magnetic and two electric components. This spectral matrix is processed by a
dedicated software (PRASSADCO: PRopagation Analysis of STAFF-SA Data with Coherency Tests) in order to
determine the wave normal directions with respect to the DC magnetic field. PRASSADCO also provides a number of
alternative methods to estimate wave polarisation and propagation parameters, such as the Poynting vector, and the
refractive index. It is therefore possible to detect the source extension of various electromagnetic waves using the 4
satellites. Results of this data processing will be shown here for one event observed by one satellite.
The four CLUSTER 2 spacecraft are in a tetrahedral configuration on an orbit which allows the
study of the frontiers between the solar wind and the Earth's magnetosphere. This paper will present
propagation characteristics of waves observed close to perigee. We will show the data of only one
satellite in order to stay within the page limit. Section 2 will shortly describes the STAFF ( Spatio-
Temporal Analysis of Field Fluctuations) experiment whereas the dedicated software PRASSADCO
(PRopagation Analysis of STAFF-SA Data with COherency tests) is presented in Section 3. One event
recorded by the four CLUSTER satellites is described in Section 4. Conclusions are given in Section 5.
2. The experiment
STAFF is a part of the Wave Experiment Consortium ( WEC) onboard the four CLUSTER 2
satellites [1,2]. STAFF consists of three magnetic search coils linked to a processing unit. The
processing unit has two parts in order to obtain on one hand waveforms of the three components of the
magnetic field up to 10 Hz (180 Hz in the burst mode), and on the other hand the spectral matrix of five
components of the electromagnetic field up to 4 kHz (the two electric components are from the Electric
Field and Wave experiment EFW). The latter will be used in the following. This 5x5 spectral matrix has
27 frequencies distributed logarithmically between 8 Hz and 4 kHz. The time resolution varies between
125 ms and 4 s.
3. The data processing software
PRASSADCO is a computer program designed to analyze multicomponent measurements of
electromagnetic waves. It implements a number of methods used to estimate polarization and
propagation parameters, such as the degree of polarization, sense of elliptic polarization and axes of
polarization ellipse, the wave vector direction, the Poynting vector, and the refractive index . The main
purpose of PRASSADCO is to facilitate scientific analysis of spectral matrix obtained by the STAFF-
SA instruments onboard the four satellites. The inputs of this software are the CLUSTER data CD-
roms provided by ESA, the CSDS Prime Parameters of FGM, and the CSDS Summary Parameters of
auxiliary data. The results can be represented in different visual and numerical formats. Tests have been
made with simulated data and with ground test data of STAFF-SA. The program was also used to
analyze data of previous satellites [4,5,6].
4. Detailed analysis of one event recorded by CLUSTER
The Figure represents data recorded by the spacecraft 2 on March 31, 2001 between 06.44 and
08.29 UT. The satellite is at the perigee around 07.20 UT and crosses the magnetic equator at 07.12
UT. The first and second panels show the magnetic and electric power-spectral densities, respectively.
The power-spectral densities are average values which take into account all available electric and
magnetic components. An intense electrostatic noise is observed at low frequencies (< 200 Hz) except
close to the equator. A banded electromagnetic emission is seen between 1 kHz and 3 kHz, the
maximum frequency being close to the equator. The following panels present propagation characteristics
of this latter emission in frequency-time plots similar to spectrograms with intensities color-coded
according to the scale on the right. The third panel shows the degree of polarization obtained from the
eigenvalues of the magnetic spectral matrix. The value corresponding to the banded emission is between
0.8 and 0.9. A value close to 1.0 corresponds to the presence of a single plane wave. The fourth panel
indicates that the sense of polarization of the emission is right-hand polarized. The fifth panel represents
the ellipticity of polarization. The sixth and seventh panel represent the polar and the azimuthal angles of
the wave normal direction relatively to the Earth's magnetic field, respectively. These angles are obtained
from the magnetic spectral matrix with the method of . It is shown that the emission propagates with
an angle of ~40° relatively to the magnetic field except close to the equator where this angle decreases.
The eighth panel gives an estimation of the parallel component of the Poynting vector and the ninth
presents phase shift between the electric signal and a projected magnetic component (see explanations in
. These two last panels give similar indication concerning the direction of the emission relatively to the
magnetic field. A phase shift around ±180° corresponds to a positive z-component of the Poynting
vector. A value near 0° corresponds to a negative z-component. The change at the equator indicates
that the waves propagate away from the equator. The tenth panel gives an estimation of the refractive
index . Theoretical values of this refractive index allow to evaluate the transfer function between the
plasma and the electric antenna by comparison.
Then the eleventh panel represents the phase shift due to this transfer function. This value also gives the
sign of the z-component of the wave normal direction, and it is observed that the values agree with those
in the panels 8 and 9.
It has been shown that PRASSADCO is a powerful tool for wave propagation analysis. This
software is particularly adapted to the CLUSTER data. In the future, it will be used to detect the
extension of various electromagnetic wave sources using the 4 satellites. The calculation of the wave
normal directions relatively to the Earth's magnetic field will be done for the 4 satellites at different times
and different frequencies according to the event we are looking at. All these wave normal directions will
be the input to a ray tracing program used to trace back to the source. Prime parameters from other
CLUSTER experiments obtained from the Cluster Science Data System: FGM (local magnetic field),
WHISPER (local electron density), and auxiliary data will be used. Considering the 4 satellite results, a
minimum ray separation criterium will be used to stop the calculation, and then to determine the source
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