Analysis Software for The Cluster Mission: The Spatial Gradient of Density

All physically observable field parameters within the magnetosphere, such as particle densities and electric and magnetic fields, vary in both space and time. Understanding the underlying physical processes requires knowledge of both temporal and spatial variations of these parameters. Analysing data acquired simultaneously from two satellites allows determination of the component of the spatial gradient in the direction of their separation. However, to determine all three components of the spatial gradient, data from at least four spacecraft is required. This is the main objective of the Cluster mission: four identical spacecraft forming a tetrahedron in space. We present here the least square method as a means of calculating the spatial gradient of plasma density from data gathered using Cluster’s WHISPER (Waves of High frequency and Sounder for Probing of Electron density by Relaxation) experiment. Also presented here is software developed for the calculation and visualisation of the density gradient. The software plots the trajectory of the centre of mass of the four spacecraft, showing the density measured at each of the four spacecraft and the gradient density at the centre of mass along the trajectory. This work is included in preparation of the Cluster mission, developing methods and tools for the analysis of the subsequent multipoint measurements.