Magnetic Reconnection on a Klein Bottle

What is it about?

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.

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Photo by Maximalfocus on Unsplash

Photo by Maximalfocus on Unsplash

Why is it important?

We have shown that a novel boundary condition based on the topology of a Klein bottle can be used in numerical simulations of magnetic reconnection. The new boundary condition combines the advantages of other common options by being both self-reinforcing (as in systems with doubly periodic boundary conditions) and computationally compact (as seen in the single current sheet of the GEM Challenge boundaries).