Quantifying Gyrotropy in Magnetic Reconnection

A new scalar measure of the gyrotropy of a pressure tensor is defined. Previously suggested measures are shown to be incomplete by means of examples for which they give unphysical results. To demonstrate its usefulness as an indicator of magnetic topology, the new measure is calculated for electron data taken from numerical simulations of magnetic reconnection, shown to peak at separatrices and X-points, and compared to the other measures. The new diagnostic has potential uses in analyzing spacecraft observations and so a method for calculating it from measurements performed in an arbitrary coordinate system is derived.