Large amounts of data, like one or more time series from some spacecraft carried instruments, have to be reduced and presented in understandable quantities. As physical theories and models often are formulated in terms of frequency rather than time, it is often useful to transform the data from the time domain into the frequency domain. The transformation to frequency domain and application of statistics on the result is known as spectral analysis. The literature on spectral analysis is voluminous. In most cases, it is written by experts in signal processing, which means that there are many texts available outlining the fundamental mathematics and elaborating the fine points. However, this is not the only background needed for a space physicist who is put to the task of actually analysing spacecraft plasma data. Simple questions on normalisation, physical interpretation, and how to actually use the methods in practical situations are sometimes forgotten in spectral analysis texts. This chapter aims at conveying some information of that sort, offering a complement to the textbooks rather than a substitute for them. The discussion is illustrated with idealised examples as well as real satellite data. In order not to expand the chapter into a book in itself, we concentrate on the application of basic Fourier and wavelet methods, not treating interesting topics in time series analysis like stationarity tests, filtering, correlation functions, and nonlinear analysis methods. Higher order methods like bispectral analysis are also neglected. Fundamentals of such items are covered by many of the references to this chapter, and methods particularly suited for multipoint measurements are of course found throughout this book. Other introductions with multi-spacecraft applications in mind can be found in the paper by Glassmeier and Motschmann [1995] and in other papers in the same publication. The disposition of the chapter is as follows. First, we introduce the basic concepts in Section1.2, where we also discuss time-frequency methods for the analysis of nonstationary signals. The practical implementation of classical Fourier techniques is treated in Section1.3, while the implementation of Morlet wavelet analysis is discussed in Section 1.4. In Section1.5, we turn to the simultaneous analysis of two or more signals by the cross spectrum technique, particularly relevant for the analysis of multipoint measurements. Finally, we touch upon the use of parametric spectral methods in Section 1.6.

Analysis methods for multi-spacecraft data

[1] We describe several newly developed methods for propagation analysis of electromagnetic plasma waves. We make use of singular value decomposition (SVD) technique and we determine the wave vector direction, ellipticity and directions of axes of the polarization ellipse, wave refractive index, transfer function of electric antennas, estimators of the planarity of polarization, and electromagnetic planarity. Simulations of Z-mode waves, which simultaneously propagate with different wave vectors, indicate that the SVD methods give reasonable results even if the assumption on the presence of a single plane wave is invalid. Simulations of whistler mode waves show that these methods can be used to recognize cases when the waves simultaneously propagate with wave vectors in two opposite hemispheres. Finally, we show an example of analysis of natural whistler mode and Z-mode emissions measured in the high-altitude auroral region by the MEMO experiment onboard the INTERBALL spacecraft.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2000RS002523

Singular value decomposition methods for wave propagation analysis

The Cassini Plasma Spectrometer (CAPS) will make comprehensive three-dimensional mass-resolved measurements of the full variety of plasma phenomena found in Saturn’s magnetosphere. Our fundamental scientific goals are to understand the nature of saturnian plasmas primarily their sources of ionization, and the means by which they are accelerated, transported, and lost. In so doing the CAPS investigation will contribute to understanding Saturn’s magnetosphere and its complex interactions with Titan, the icy satellites and rings, Saturn’s ionosphere and aurora, and the solar wind. Our design approach meets these goals by emphasizing two complementary types of measurements: high-time resolution velocity distributions of electrons and all major ion species; and lower-time resolution, high-mass resolution spectra of all ion species. The CAPS instrument is made up of three sensors: the Electron Spectrometer (ELS), the Ion Beam Spectrometer (IBS), and the Ion Mass Spectrometer (IMS). The ELS measures the velocity distribution of electrons from 0.6 eV to 28,250 keV, a range that permits coverage of thermal electrons found at Titan and near the ring plane as well as more energetic trapped electrons and auroral particles. The IBS measures ion velocity distributions with very high angular and energy resolution from 1 eV to 49,800 keV. It is specially designed

Cassini plasma spectrometer investigation

We discuss chorus emissions measured by the four Cluster spacecraft at close separations during a geomagnetically disturbed period on 18 April 2002. We analyze the lower band of chorus below one half of the electron cyclotron frequency, measured at a radial distance of 4.4 Earth's radii, within a 2000 km long source region located close to the equator. The characteristic wave vector directions in this region are nearly parallel to the field lines and the multipoint measurement demonstrates the dynamic character of the chorus source region, changing the Poynting flux direction at time scales shorter than a few seconds. The electric field waveforms of the chorus wave packets (forming separate chorus elements on power spectrograms) show a fine structure consisting of subpackets with a maximum amplitude above 30 mV/m. To study this fine structure we have used a sine-wave parametric model with a variable amplitude. The subpackets typically start with an exponential growth phase, and after reaching the saturation amplitude they often show an exponential decay phase. The duration of subpackets is variable from a few milliseconds to a few tens of milliseconds, and they appear in the waveform randomly, with no clear periodicity. The obtained growth rate (ratio of the imaginary part to the real part of the wave frequency) is highly variable from case to case with values obtained between a few thousandths and a few hundredths. The same chorus wave packets simultaneously observed on the different closely separated spacecraft appear to have a different internal subpacket structure. The characteristic scale of the subpackets can thus be lower than tens of kilometers in the plane perpendicular to the field line, or hundreds of kilometers parallel to the field line (corresponding to a characteristic time scale of few milliseconds during the propagation of the entire wave packet). Using delays of time-frequency curves obtained on different spacecraft, we have found the same propagation direction as obtained from the simultaneous Poynting flux calculations. The delays roughly correspond to the whistler-mode group velocity estimated from the cold plasma theory. We have also observed delays corresponding to antiparallel propagation directions for two neighboring chorus wave packets, less than 0.1 s apart.

https://hal-insu.archives-ouvertes.fr/insu-01409763/document

Spatio-temporal structure of storm-time chorus

This paper introduces and describes the radio and plasma wave investigation on the STEREO Mission: STEREO/WAVES or S/WAVES. The S/WAVES instrument includes a suite of state-of-the-art experiments that provide comprehensive measurements of the three components of the fluctuating electric field from a fraction of a hertz up to 16 MHz, plus a single frequency channel near 30 MHz. The instrument has a direction finding or goniopolarimetry capability to perform 3D localization and tracking of radio emissions associated with streams of energetic electrons and shock waves associated with Coronal Mass Ejections (CMEs). The scientific objectives include: (i) remote observation and measurement of radio waves excited by energetic particles throughout the 3D heliosphere that are associated with the CMEs and with solar flare phenomena, and (ii) in-situ measurement of the properties of CMEs and interplanetary shocks, such as their electron density and temperature and the associated plasma waves near 1 Astronomical Unit (AU). Two companion papers provide details on specific aspects of the S/WAVES instrument, namely the electric antenna system (Bale et al., Space Sci. Rev., 2007) and the direction finding technique (Cecconi et al., Space Sci. Rev., 2007).

/pdf/s-waves-the-radio-and-plasma-wave-investigation-on-the-1z7xu9woo0.pdf

S/WAVES: The radio and plasma wave investigation on the STEREO Mission

The Cassini radio and plasma wave investigation is designed to study radio emissions, plasma waves, thermal plasma, and dust in the vicinity of Saturn. Three nearly orthogonal electric field antennas are used to detect electric fields over a frequency range from 1 Hz to 16 MHz, and three orthogonal search coil magnetic antennas are used to detect magnetic fields over a frequency range from 1 Hz to 12 kHz. A Langmuir probe is used to measure the electron density and temperature. Signals from the electric and magnetic antennas are processed by five receiver systems: a high frequency receiver that covers the frequency range from 3.5 kHz to 16 MHz, a medium frequency receiver that covers the frequency range from 24 Hz to 12 kHz, a low frequency receiver that covers the frequency range from 1 Hz to 26 Hz, a five-channel waveform receiver that covers the frequency range from 1 Hz to 2.5 kHz in two bands, 1 Hz to 26 Hz and 3 Hz to 2.5 kHz, and a wideband receiver that has two frequency bands, 60 Hz to 10.5 kHz and 800 Hz to 75 kHz. In addition, a sounder transmitter can be used to stimulate plasma resonances over a frequency range from 3.6 kHz to 115.2 kHz. Fluxes of micron-sized dust particles can be counted and approximate masses of the dust particles can be determined using the same techniques as Voyager. Compared to Voyagers 1 and 2, which are the only spacecraft that have made radio and plasma wave measurements in the vicinity of Saturn, the Cassini radio and plasma wave instrument has several new capabilities. These include (1) greatly improved sensitivity and dynamic range, (2) the ability to perform direction-finding measurements of remotely generated radio emissions and wave normal measurements of plasma waves, (3) both active and passive measurements of plasma resonances in order to give precise measurements of the local electron density, and (4) Langmuir probe measurements of the local electron density and temperature. With these new capabilities, it will be possible to perform a broad range of studies of radio emissions, wave-particle interactions, thermal plasmas and dust in the vicinity of Saturn.

http://lasp.colorado.edu/~horanyi/graduate_seminar/Radio_Plasma_Wave.pdf

The Cassini Radio and Plasma Wave Investigation

The Spatio-Temporal Analysis of Field Fluctuations (STAFF) experiment is one of five experiments which together comprise the Wave Experiment Consortium (WEC). STAFF consists of a three-axis search coil magnetometer to measure magnetic fluctuations at frequencies up to 4 kHz, and a spectrum analyser to calculate in near-real time aboard the spacecraft, the complete auto- and cross-spectral matrices using the three magnetic and two electric components of the electromagnetic field. The magnetic waveform at frequencies below either 10 Hz or 180 Hz is also transmitted. The sensitivity of the search coil is adapted to the phenomena theo be studied: the values 3 × 10-3 nT Hz-1/2 and 3 × 10-5 nT Hz-1/2 are achieved respectively at 1 Hz and 100 Hz. The dynamic range of the STAFF instruments is about 96 dB in both waveform and spectral power, so as to allow the study of waves near plasma boundaries. Scientific objectives of the STAFF investigations, particularly those requiring four point measurements, are discussed. Methods by which the wave data will be characterised are described with emphasis on those specific to four-point measurements, including the use of the Field Energy Distribution function.

A. Meyer

Papers

The Cassini Radio and Plasma Wave Investigation

The Cluster Spatio-Temporal Analysis of Field Fluctuations (STAFF) Experiment

STAFF (Spatio-Temporal Analysis of Field Fluctuations) experiment for the Cluster mission