A simple method for obtaining a three-dimensional proton distribution function from Voyager plasma data

The main sensor of the Vogager plasma experiment consists of a cluster of three, modulated-grid Faraday cups whose normals are arranged symmetrically about the symmetry axis of the cluster at an angle of 20 degrees to that axis. In interplanetary space, each cup explores the positive ion distribution by accepting particles from contiguous slices in velocity space. The slices are narrow in the direction of the normal to the modulating grid but are broad in planes parallel to that grid. The resulting three sets of measurements can be combined to yield the three-dimensional distribution function in the following way: the distribution function is assumed to be gyrotropic. For each value of speed in a frame of reference moving with the bulk velocity of the solar wind, the variation of the distribution function with angle from the field direction is represented by a series of Legendre polynomials. Effects such as double-streaming and heat flow can be well represented by using only the first three terms of the series which are fully specified by the measurements. Examples of the use of this method in the analysis of Voyager data are shown.