A reconstruction method for the reconnection rate applied to Cluster magnetotail measurements

We apply a theoretical model to describe the behavior of nightside flux transfer events (NFTEs) measured by Cluster satellites in the Earth magnetotail. Based on the Cagniard–deHoop method we calculate the magnetic field and plasma flow time series observed by a satellite. Our aim is to solve an inverse problem to obtain the reconnection rate from the measured plasma data. The ill-posed inverse problem is treated with the method of regularization, since the solution of the Cagniard–deHoop method is given in the form of a convolution integral, which is well known in the theory of inverse problems. This method is applied to Cluster measurements from September 8th, 2002, where a series of Earthward propagating 1-min scale magnetic field and plasma flow variations were observed outside of the plasma sheet, which are consistent with the theoretical picture of NFTEs. Estimations of the satellite position with respect to the reconnection site and of the Alfvén velocity are made because they are necessary parameters for the model. The reconnection rate is found to be in the range of 1–2 mV/m and the reconnection site at about 29 R e tailwards.