Magnetic Reconnection on a Klein Bottle

We present a new boundary condition for simulations of magnetic reconnection based on the topology of a Klein bottle. When applicable, the new condition is computationally cheaper than fully periodic boundary conditions, reconnects more flux than systems with conducting boundaries, and does not require assumptions about regions external to the simulation as is necessary for open boundaries. The new condition reproduces the expected features of reconnection, but cannot be straightforwardly applied in systems with asymmetric upstream plasmas.