QSAS Index Eugen's VectorCalculus Plug-in

Contents:

Overview

The plug-in computes gradients of scalar data as well as gradient, curl and divergence of vectorial data from three- or four- spacecrafts measurements. This plug-in is an enhancement of the ISSI_ClusterVectorCalc plug-in, which was written by Stein Haaland, and many of comments to his plug-in apply to this one as well. Parts of his documentation are marked in italics below. The 4-spacecraft estimation was used from the previous plug-in. The 3-spacecraft estimation is an implementation of Joachim Vogt's algorithm. For more information on the 3-spacecraft estimation, please see the article: Vogt, J., Albert, A. and Marghitu, O. "Analysis of three-spacecraft data using planar reciprocal vectors: methodological framework and spatial gradient estimation", Annales Geophysicae, Volume 27, Issue 8, 2009, pp. 3249 - 3273.

The vector quantities are based on a linear approximation of the spatial gradients, and should be used with care if the [...] spacecrafts are located in very different plasma regimes.



Input data

The time series inputs above are automatically joined to the timetags of the input vector from Spacecraft C3 . Note that either all of the input data must be scalar or all of them must be vectorial. Positions can be relative to Earth, relative to one of satellites or relative to any point of origin. If input data are vectors then it is required that the measured vectors are in the same frame as the position vectors of satellites.



Outputs

Estimation of the gradient of the vector field, the gradient of the magnitude of the field intensity, curl and divergence is given for vectorial data, while only the estimation of gradient is given for scalar input data. For both types of data the worklist (WL) will also have the normal component to the plane formed by the first three satellites and the volume of the tetrahedron formed by the 4 satellites. The former can be used to estimate the quality of the gradient computation. If only 3 satellites are given, the VolumeTetrahedron variable will actually be the area of a triangle formed by satellites.

The plug-in will also compute the predicted value of the field at the barycentre and the position of barycentre itself. These values can be used, for example, in the featherPlot plug-in.



Curlometer

A special application of the PlugIn is to calculate current density according to the so-called curlometer technique: Current density can be expressed from Ampere's law as
  J = curl (B) / mu_0

If the input vector quantity is a magnetic field, and the CurlNormalize slot contains mu0 (magnetic permeability = see QSAS constants), the curl output represents a current density and has A m^-2 as unit.



Minimum Variance analysis of current density

When used as a Curlometer, a minimum variance of the current density is performed. A set of eigenvalues and eigenvectors from the minimum variance of the curl quantity as well as a velocity are also printed in the output field of the PlugIn. Under certain conditions, (e.g. 1D current sheet appproximation) the eigenvector corresponding to the lowest eigenvalue can be used as an estimate of the current sheet normal. An approximate velocity of the current sheet motion is also given.



Bugs/Caveats

If you find a bug, please inform me by email: e.sorbalo (at) jacobs-university.de


History


Eugen, 12 January 2012