Vector Calculator
Contents:
Overview
The Cluster/MMS vector calculator returns the curl, gradient, divergence and barycentric average of a vector quantity.
The vector quantity along with the spacecraft position from four spacecraft must
be supplied. The vector quantities are based on a linear approximation of the spatial gradients, and should
be used with care if the four spacecraft are located in very different plasma regimes. A particular useful
application may be the Curlometer to determine electric current density from
Amperes law.
Input data
Required inputs are a vector quantity (e.g. magnetic field, electric field, plasma velocity etc.) and the
spacecraft sepration vector. In addition, a time interval and a normalization factor can be given.
The inputs are automatically joined to the timetags of the input vector from Spacecraft C3
Outputs
The outputs, curl, gradient, divergence and barycentric average of the input vectors are returned
to the worklist. Additionally, the curl is also returned in an a MVA system (curl rotated by the
rotations matrix from a minimum variance of the curl time series). When used as a curlometer, this
MVA rotated curl represents the current in a current sheet aligned system.
A special application of the PlugIn is to directly calculate current density from
magnetic field gradients. 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 nA/m^2 as unit.
For magnetic fields, the ration |div|/|curl| provides an estimate of the quality of the
current estimate. This unitless ratio is stored as QUALITYRATIO in the metadata of the curl output.
Bugs/Caveats
None known.
SEH, 16 Mar, 2016