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Axially magnetised (AMF) diffuse vacuum arcs are the heart of a major part of power distribution switchgears in the medium voltage range, and are gaining increasing interest in the high voltage sector. Although there is a good qualitative understanding of the behaviour of AMF vacuum arcs based on empirical experimental results, there is still a lack of understanding of the details of the plasma-contact interaction in high-current switching arcs. A number of different arc models has been developed by different groups, in order to investigate the behaviour of AMF arcs by means of FEM simulation models. We report on a three-dimensional, transient FEM model that is currently being developed. It is based on a magneto-hydrodynamic approach of the magnetised plasma with temperature-dependent material properties. The model is presented in detail, and first results concerning the plasma behaviour are reported.