Determination of Flux rope axis for GS reconstruction

It is important to give the axis direction and velocity of a magnetic flux ropes before employing Grad-Shafranov reconstruction. The ability of single-satellite based MVA (MVAB and CMVA) and multi-satellite based MDD methods in finding the invariant axis are tested by a model. The choice of principal axis given by MVA along the aimed direction is dependent on the distance of the path from the flux-rope axis. The MDD results are influenced by the ratio of Noise level/separation to the gradient of the structure. An accurate axial direction will be obtained when the ratio is less than 1. By a model, an example with failed HT method is displayed indicating the importance of the STD method in obtaining the velocity of such a structure. The applicability of trial and error method by Hu and Sonnerup(2012) was also used and discussed. Finally, all above methods were applied to a flux-rope observed by Cluster. It shows that the GS method can be easily carried out in the case of clearly known dimensionality and velocity.