Abstract
The cold, linear, resistive, magnetohydrodynamic (MHD) equations are used to study the dynamics of current accumulation at a three-dimensional magnetic null. The particular null under study is axisymmetric about its so-called spine axis, allowing a decomposition into azimuthal modes labeled by mode number m. Analysis shows that the axisymmetric perturbations (m=0) can lead to a current parallel to the spine axis at the null, while the m=1 mode produces currents orthogonal to the spine axis at the null (in the so-called fan plane). For all the modes with m > 1, there is no current accumulation at the null. The dynamic processes involved in producing these currents are revealed using numerical simulations. In particular, it is found that the m=1 mode leads to motions across both the fan plane and the spine axis regardless of whether the initially imposed disturbances are restricted to be across either the fan plane or the spine axis. The m=1 mode efficiently focuses the excess magnetic energy in toward the null, and therefore we consider it to be the prime reconnective mode in three dimensions. In attempting to understand magnetic reconnection at a three-dimensional null, it is clearly important to detail the currents that can be produced. This we have done within the framework of the linear theory. We discuss the implications of these results for reconnection in the solar corona in the presence of finite-amplitude fields and flows.