  Magnetic separators, which lie on the boundary between four
topologically-distinct flux domains, are prime locations in three-dimensional
magnetic fields for reconnection, especially in the magnetosphere between the
planetary and interplanetary magnetic field and also in the solar atmosphere.
Little is known about the details of separator reconnection and so the aim of
this paper, which is the first of two, is to study the properties of magnetic
reconnection at a single separator. Three-dimensional, resistive
magnetohydrodynamic numerical experiments are run to study separator
reconnection starting from a magnetohydrostatic equilibrium which contains a
twisted current layer along a single separator linking a pair of
opposite-polarity null points. The resulting reconnection occurs in two phases.
The first is short involving rapid-reconnection in which the current at the
separator is reduced by a factor of around 2.3. Most ($75\%$) of the magnetic
energy is converted during this phase, via Ohmic dissipation, directly into
internal energy, with just $0.1\%$ going into kinetic energy. During this phase
the reconnection occurs along most of the separator away from its ends (the
nulls), but in an asymmetric manner which changes both spatially and temporally
over time. The second phase is much longer and involves slow impulsive-bursty
reconnection. Again Ohmic heating dominates over viscous damping. Here, the
reconnection occurs in small localised bursts at random anywhere along the
separator.
