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Proper Frame Determination and Walen Test

Sonnerup, Bengt U. O.; Paschmann, Gotz

To study structures, such as current sheets, flux ropes, or fully three-dimensional configurations, it is desirable to examine them in their proper (co-moving) frame, in which they appear as time stationary as the data permit. And it is important to establish the frame velocity so that their physical dimensions can be determined. In the present ch…

Multi-Spacecraft Methods of Wave Field Characterisation

Glassmeier, Karl-Heinz; Pinçon, Jean-Louis

Space plasmas are collisionless and thus waves play a major role in the collective interaction between particles. Also, space plasmas are subject to a variety of instabilities, generating a plethora of different plasma wave modes. Thus, for many physical processes the role of waves and turbulence is likely to be predominant. The simultaneous four-…

Reciprocal Vectors

Vogt, Joachim; Paschmann, Gotz; Chanteur, Gérard

Reciprocal vectors and barycentric coordinates are well-established concepts in various scientific fields, where lattices and grids are essential, e.g., in solid state physics, crystallography, in the numerical analysis of partial differential equations using finite elements, and also in computer graphics and visualisation. In preparation of the C…

The Curlometer and Other Gradient Based Methods

Eastwood, Jonathan P.; Dunlop, Malcolm W.

The magnetic field measurements on the four Cluster spacecraft can be combined to produce a determination of the electric current density, j, point by point in time, from Ampere's law, i.e., through an estimate of the curl of the magnetic field, B, assuming the displacement current may be neglected (an assumption nearly always true in space plasma…

Empirical Reconstruction

de Keyser, Johan

Empirical reconstruction methods attempt to interpret in situ observations of the magnetospheric boundary in terms of time-stationary structures that are convected past the spacecraft. The ever-changing position of the boundary is considered an unknown of the problem. Once the motion of the boundary is found, empirical reconstruction produces spat…

Discontinuity Orientation, Motion, and Thickness

Sonnerup, Bengt U. O.; Haaland, Stein E.; Paschmann, Gotz

Grad-Shafranov and MHD Reconstructions

Hasegawa, Hiroshi; Sonnerup, Bengt U. O.; Teh, Wai-Leong

Since the publication of the multi-spacecraft data analysis book ISSI SR-001, new methods have been developed that allow field and plasma structures traversed by one or more spacecraft to be reconstructed in a region surrounding the spacecraft path from the measured data. Maps of field and plasma properties are created with the aid of various vers…

Multi-Spacecraft Turbulence Analysis Methods

Osman, Kareem T.; Horbury, Tim S.

Turbulence is ubiquitous in space plasmas, from the solar wind to supernova remnants, and on scales from the electron gyroradius to interstellar separations. Turbulence is responsible for transporting energy across space and between scales and plays a key role in plasma heating, particle acceleration and thermalisation downstream of shocks. Just a…

Geometrical Structure Analysis of the Magnetic Field

Shen, Chao; Dunlop, Malcolm W.

The geometrical configuration of the magnetic field underpins important research top- ics in magnetospheric physics. The magnetic field is the skeleton of the magnetosphere and plays a crucial role in determining the plasma distribution of particles, the occurrences of various macro and micro instabilities, the triggering and evolution of substorm…

Plasma Kinetics

Schwartz, Steven J.; Daly, Patrick W.; Lefebvre, Betrand

In Chapter 7 of ISSI SR-001, Schwartz et al. [1998] explain the basic ideas of analysis by means of plasma kinetics: Liouville mapping and finite gyroradius effects. Liouville mapping can be used to relate features of distribution functions such as heating, anisotropies or beams, to the field variations. It is based on the conservation of phase sp…