1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.

/pdf/wavelet-methods-for-time-series-analysis-1m2hg2nm53.pdf

Wavelet Methods for Time Series Analysis

. The accurate measurement of the magnetic field along the orbits of the four Cluster spacecraft is a primary objective of the mission. The magnetic field is a key constituent of the plasma in and around the magnetosphere, and it plays an active role in all physical processes that define the structure and dynamics of magnetospheric phenomena on all scales. With the four-point measurements on Cluster, it has become possible to study the three-dimensional aspects of space plasma phenomena on scales commeasurable with the size of the spacecraft constellation, and to distinguish temporal and spatial dependences of small-scale processes. We present an overview of the instrumentation used to measure the magnetic field on the four Cluster spacecraft and an overview the performance of the operational modes used in flight. We also report on the results of the preliminary in-orbit calibration of the magnetometers; these results show that all components of the magnetic field are measured with an accuracy approaching 0.1 nT. Further data analysis is expected to bring an even more accurate determination of the calibration parameters. Several examples of the capabilities of the investigation are presented from the commissioning phase of the mission, and from the different regions visited by the spacecraft to date: the tail current sheet, the dusk side magnetopause and magnetosheath, the bow shock and the cusp. We also describe the data processing flow and the implementation of data distribution to other Cluster investigations and to the scientific community in general. Key words. Interplanetary physics (instruments and techniques) – magnetospheric physics (magnetospheric configuration and dynamics) – space plasma physics (shock waves)

/pdf/the-cluster-magnetic-field-investigation-overview-of-in-16rqb5qjp6.pdf

The Cluster Magnetic Field Investigation: overview of in-flight performance and initial results

In this review we will focus on a topic of fundamental importance for both plasma physics and astrophysics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Ulysses’ high latitude observations and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

/pdf/the-solar-wind-as-a-turbulence-laboratory-4mad4q4xdr.pdf

The Solar Wind as a Turbulence Laboratory

Solar Probe Plus (SPP) will be the first spacecraft to fly into the low solar corona. SPP’s main science goal is to determine the structure and dynamics of the Sun’s coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Understanding these fundamental phenomena has been a top-priority science goal for over five decades, dating back to the 1958 Simpson Committee Report. The scale and concept of such a mission has been revised at intervals since that time, yet the core has always been a close encounter with the Sun. The mission design and the technology and engineering developments enable SPP to meet its science objectives to: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles. The SPP mission was confirmed in March 2014 and is under development as a part of NASA’s Living with a Star (LWS) Program. SPP is scheduled for launch in mid-2018, and will perform 24 orbits over a 7-year nominal mission duration. Seven Venus gravity assists gradually reduce SPP’s perihelion from 35 solar radii (
 $R_{S}$
 ) for the first orbit to ${<}10~R_{S}$
 for the final three orbits. In this paper we present the science, mission concept and the baseline vehicle for SPP, and examine how the mission will address the key science questions

/pdf/the-solar-probe-plus-mission-humanity-s-first-visit-to-our-e2fb5pur3z.pdf

The Solar Probe Plus Mission: Humanity’s First Visit to Our Star

Energetic particles are accelerated in rich profusion at sites throughout the heliosphere. They come from solar flares in the low corona, from shock waves driven outward by coronal mass ejections (CMEs), from planetary magnetospheres and bow shocks. They come from corotating interaction regions (CIRs) produced by high-speed streams in the solar wind, and from the heliospheric termination shock at the outer edge of the heliospheric cavity. We sample all these populations near Earth, but can distinguish them readily by their element and isotope abundances, ionization states, energy spectra, angular distributions and time behavior. Remote spacecraft have probed the spatial distributions of the particles and examined new sources in situ. Most acceleration sources can be "seen" only by direct observation of the particles; few photons are produced at these sites. Wave-particle interactions are an essential feature in acceleration sources and, for shock acceleration, new evidence of energetic-proton-generated waves has come from abundance variations and from local cross-field scattering. Element abundances often tell us the physics the source plasma itself, prior to acceleration. By comparing different populations, we learn more about the sources, and about the physics of acceleration and transport, than we can possibly learn from one source alone.

/pdf/particle-acceleration-at-the-sun-and-in-the-heliosphere-2yha5t1u73.pdf

Particle Acceleration at the Sun and in the Heliosphere

Magnetic field measurements from the Ulysses space mission overthe south polar regions of the sun showed that the structure and properties of the three-dimensional heliosphere were determined by the fast solar wind flow and magnetic fields from the large coronal holes in the polar regions of the sun. This conclusion applies at the current, minimum phase of the 11-year solar activity cycle. Unexpectedly, the radial component of the magnetic field was independent of latitude. The high-latitude magnetic field deviated significantly from the expected Parker geometry, probably because of large amplitude transverse fluctuations. Low-frequency fluctuations had a high level of variance. The rate of occurrence of discontinuities also increased significantly at high latitudes.

https://science.sciencemag.org/content/sci/268/5213/1007.full.pdf

The heliospheric magnetic field over the South polar region of the sun.

The Ulysses mission provides an opportunity to study the evolution of magnetohydrodynamic (MHD) turbulence in pure high-speed solar wind streams. The absence at high heliocentric latitudes of the strong shears in solar wind velocity generally present near the heliocentric current sheet allows investigation of how fluctuations in the magnetic field and plasma relax and evolve in the radially expanding solar wind. We report results of an analysis of the radial and latitudinal variation of the turbulence properties of the fluctuations, especially various plasma-field correlations, in high latitude regions. The results constrain current theories of the evolution of MHD turbulence in the solar wind. Compared to similar observations at 0.3 AU by Helios, we find spectra that are similar in having a large frequency band with an f¹ power spectrum in the outward traveling component of the waves, followed at higher frequencies by a steeper spectrum. Ulysses observations establish that at high latitudes the turbulence is less evolved (i.e., has a smaller inertial range) than it is in the ecliptic at the same heliocentric distance, apparently due to the absence of strong velocity shear. Once Ulysses is in the polar coronal hole, properties of the turbulence appear to be determined by the heliocentric distance of the spacecraft rather than by its helio-latitude.

Properties of magnetohydrodynamic turbulence in the solar wind as observed by Ulysses at high heliographic latitudes

Properties of Magnetohydrodynamic Turbulence in the Solar Wind as Observed

Observations of solar wind magnetic field discontinuities using 3 spacecraft allow their orientations to be estimated. During 5 days when Geotail, Wind and IMP 8 were between 6 × 104 and 4 × 105 km apart, 35 events identified using the Tsurutani-Smith method were detected in all 3 magnetic field data sets. Normals estimated from inter-spacecraft timings showed that very few were unambiguous rotational discontinuities, with 77% likely to be tangential, with < 20% of the magnetic field at the discontinuity threading the normal plane. However, previous single spacecraft studies using minimum variance suggest that most discontinuities are rotational. Minimum variance analysis resulted in many normal estimates lying far from the timing-derived normals. While some of this discrepancy is likely to be due to random errors in minimum variance vectors, there appears to be a class of events with small field magnitude changes where the minimum variance directions and discontinuity normals are approximately perpendicular, probably due to surface waves on the discontinuities.

/pdf/three-spacecraft-observations-of-solar-wind-discontinuities-kix8bbwjj1.pdf

Three spacecraft observations of solar wind discontinuities

The heliospheric magnetic field over the poles of the sun has been examined to identify intervals when the polarity of the magnetic field deviates significantly from the calculated Parker spiral, using Ulysses observations in 1994 and 1995, near solar minimum Intervals with deviation > 90° have been identified, corresponding to magnetic field vectors pointing in the hemisphere opposite to that of the dominant polarity in the high speed solar wind originating in the polar coronal holes The number of inversion periods decreases as the averaging period is increased from 1 to 12 hours Their distribution was found to vary in time over the northern solar pole, where the average direction also deviated from the Parker direction The propagation direction of waves during polarity inversions show that these are caused by large-scale folds in the magnetic field, rather than by opposite polarity magnetic flux tubes originating near the sun

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999GL900061

T. S. Horbury

Papers

The heliospheric magnetic field over the South polar region of the sun.

Properties of magnetohydrodynamic turbulence in the solar wind as observed by Ulysses at high heliographic latitudes

Properties of Magnetohydrodynamic Turbulence in the Solar Wind as Observed

Three spacecraft observations of solar wind discontinuities

Heliospheric magnetic field polarity inversions at high heliographic latitudes