Scientific Data Analysis

The instruments onboard THOR take the next technological steps to further increase the time resolution over existing magnetospheric satellite missions. In comparison to earlier and other upcoming missions key major improvements include: 
  • accuracy/sensitivity of electric and magnetic field measurements,
  • temporal resolution of mass resolved ions (H+, He++), 
  • temporal/angular resolution of pristine solar wind ions
  • temporal resolution of electrons. 
A vital part of the THOR proposal is the combination of excellent, high resolution measurements and a comprehensive box of analysis methods and tools to exploit the measurements. An extensive set of analysis methods exist for studying structures, waves and turbulence in space. Many of them has been develop for use by a single spacecraft but has been validated using four spacecraft mission such as Cluster and MMS. THOR also has the capability of serving as multi-point measurements using multiple probes at different locations of the spacecraft. 

Waves and turbulence

In a wave or structure where the ions are unmagnetised and the electrons are magnetised, a current associated with the ExB drift will be associated with a magnetic field. By comparing the electrostatic potential obtained by integrating the electric field assuming different phase velocities (blue) and the electrostatic potential estimated from the magnetic field (red), the phase velocity can be found [Norgren et al. (2012)].  
Particle heating and acceleration happen both in quasi-monochromatic waves and in turbulent fluctuations. While the quasi-monochromatic waves have discrete frequencies and wavevectors and appear as clear peaks in the energy spectrum, the turbulent fields no longer have clear spatial or temporal structures and appear as a continuous spectrum.

Properties of the quasi-monochromatic waves are studied using a variety of analysis methods. Using the magnetic field data, one may determine the energy spectra for different fluctuation components, the compressibility of magnetic field, the field rotation sense around the mean magnetic field, and the wavevector direction by minimum variance analysis. When combining with the electric field and the plasma data, one may determine the phase speed, the Poynting flux, the helicity quantities, the wave distribution function, and the wavevectors. 

For the studies of turbulent fluctuations, the slope and the shape (flattening or steepening) of the energy spectrum are determined not only in the frequency domain (in the spacecraft frame) but also in the streamwise wavenumber domain using Taylor's frozen-in flow hypothesis. The spectra of the helicity quantities can also be determined. Wave-wave and wave-particle interactions are studied, e.g., for the detection of Landau and cyclotron resonances, pitch angle scattering, and three-wave couplings (bispectrum). Statistical behavior, in particular non-Gaussian nature of the turbulent fluctuations are studied using the method of phase coherence, probability density function, and local intermittency measure. 

Structures and discontinuities

Turbulent fields are closely associated with coherent structures and discontinuities. Shock waves, for example, are a major driver of turbulence. In order to investigate one dimensional plasma structures such as current sheets or two and tree dimensional structures such as magnetic islands and flux ropes, it is often useful to transform them into a proper, co-moving reference frame. Often, it is also necessary to establish the orientation of plasma structures. Experience based on multi-spacecraft missions like Cluster and MMS has shown that a well equipped single spacecraft platform, like the proposed THOR mission, is capable of providing the required resolution and can resolve the inherent space-time ambiguities without the need for a full constellation of spacecraft. 

To achieve this, a number of methods are available. In particular, variance analysis and residue methods have  proven to be very robust and useful for this purpose. Residue methods are typically based on simple conservation laws for example conservation of energy, mass or flux. The most commonly used method is probably minimum variance of the magnetic field to establish the orientation of a one-dimensional current sheet [Sonnerup & Scheible, (1998)]. A unified approach to variance analysis and residue methods, applicable to any measured quantity (both vector fields and scalars) which obeys classical conservation laws was presented in Sonnerup et al, (2006). In its simplest form, the unified approach only takes the B-field as input. More refined variants take the electric field, density, plasma flow or higher order moments such as pressure or heat flux as inputs. An advantage of residue methods is that they can provide error estimates both for the frame velocity and for the boundary normal of the structure. An overview of the methods and their application can be found in Paschmann and Daly (2008).

Visualization of magnetic field and plasma structures

Magnetic field maps recovered from reconstruction based on ACE measurements from the solar wind. Colors show the out-of-plane magnetic field component, and white arrows at points along y = 0 show the transverse velocities obtained from the reconstruction. After Hasegawa et al., JGR, (2014)
During the last decade, various methods to reconstruct the topology of the magnetic field and plasma properties in a region around the spacecraft have been developed. Plasma and field parameters can be visualized by two dimensional maps as shown in the figure to the right. The reconstruction is based on MHD equations and under the assumption that structures can be treated as 2D structures and are nearly time-independent in their proper reference frame. The proper frame and invariant axis are typically established using one of the structure analysis methods mentioned above.

Reconstruction has been tested extensively in a number of plasma regimes and scale sizes ranging large flux ropes in the solar wind to the electron diffusion region in a reconnection region. The high time resolution of THOR opens for new possibilities to investigate the topology of small scale structures.

Data Analysis Tools

(Solar system plasma Turbulence: Observations, inteRmittency and Multifractals) is an European FP7 project that investigates solar system plasma turbulence through a thorough survey of the existing data bases  (e.g. Ulysses, Cluster, Venus Express). One of the goals of the project and one of its major deliverables is to build and test an integrated software library for nonlinear data analysis (INA) that cumulates analysis methods able to reveal the structure and topology of turbulent fluctuations. The library is versatile enough to ingest data from various missions and to apply a full package of analysis methods, ranging from lower order analysis, like the Power Spectral Density analysis, to higher order analyses like the Probability Distribution Functions and their moments (e.g. flatness), wavelet analysis and multifractals. The integrated library is equipped with a graphical user interface that enables an interactive analysis and a full control of the analysis parameters. The library is extensively tested with ESA missions data (e.g. Cluster, Ulysses, Venus Express). More detailed description is in the attachment. 

IRFU-MATLAB ( This is a MATLAB package that includes many different type of routines allowing to analyse both multi-spacecraft and single spacecraft data. Some of the important parts include:
  • General plasma physics: estimates of different plasma parameters, plasma wave dispersion relations for cold and hot plasma, plasma wave visualisation, different space plasma models,...
  • General time series analysis routines
  • Single spacecraft analysis methods: Minimum Variance of B, deHoffmann-Teller analysis, Walén analysis, SVD, Means, EMHD reconstruction, multi-probe interferometry,...
  • Multi-spacecraft analysis methods: Discontinuity Analyser, gradient methods (e.g. curlometer).
  • Data reading supports: Cluster Science Archive, OMNI, MMS, different cdf sources.
  • Plotting routines of publishing quality figures: time series, spectrograms, spacecraft location, models,...
) is a powerful tool for manipulating, analyzing and plotting data from spacecraft missions. QSAS can read a variety of data files (cdf,cef, ASCII etc) and should be applicable to THOR data without any special adaptations. Many of the structure analysis methods above are implemented in QSAS and have been extensively tested on Cluster and MMS data. 

3D view of THOR orbit, Bow-shock and Magnetopause modelsO
rbit Visualization Tool - OVT ( is a software for visualization of satellite orbits in the Earth's and interplanetary 
magnetic field. The program can display satellite orbits in five coordinate systems (GEI, GEO, GSM, SMC, GSE), satellite footprints projected on the Earth's surface and shown in either geographic (GEO) or geomagnetic (SMC) coordinates. In addition to satellite orbits the software computes and displays various models of magnetospheric structures, magnetopause, bow shock and foreshock, and interplanetary field conditions. The models are time-dependent on the solar wind, IMF and geomagnetic activity levels. OVT will be particularly useful for planning of THOR operations.

Andris Vaivads,
Jan 6, 2015, 11:35 AM