Test of methods to infer the magnetic reconnection geometry from spacecraft data

When analyzing data from a cluster of spacecraft (such as Cluster or MMS) crossing a site of magnetic reconnection, it is desirable to be able to determine the orientation of the reconnection site. If the reconnection is quasi-two dimensional, there are three key directions, the direction of inhomogeneity (direction across the reconnection site), the direction of the reconnecting component of the magnetic field, and the direction of rough invariance (the out of plane direction). Using simulated spacecraft observations of an MHD simulation of magnetic reconnection in the geomagnetic tail, we test a direction-finding method based on the gradient of the vector magnetic field and find that the directions can be well determined. The results from this method, however, can be in error if there are systematic calibration errors in the magnetic field measurements. We show that the effect of these errors can be eliminated if an average gradient is subtracted from a time series of gradient values before they are used for the analysis. We also test a method to determine the velocity of the reconnecting structure relative to the spacecraft using the time derivative and gradient of the magnetic field and show that this velocity can be well determined. Calibration errors can be eliminated in this case also if an average time derivative and gradient are subtracted from the time series of values before they are used for the analysis.