Magnetic Reconnection on a Klein Bottle

Magnetic reconnection is a process in plasma physics where magnetic field lines from different regions come together, reconfigure, and release stored magnetic energy. The phenomena is thought to explain solar flares, geomagnetic storms, coronal mass ejections, astrophysical jets, magnetotail dynamics, and more. Currently, computational simulations of magnetic reconnection involving the PIC (particle in cell) method use boundary conditions that come with certain drawbacks. One popular method based on a famous test problem includes hard walls at the top and bottom edges that unnaturally limit the time that the simulation can be run. Another common option with fully periodic boundary conditions effectively requires doubling the size of the simulation domain, hence increasing its computational cost. We investigate a novel periodic boundary condition that topologically maps from a 2-dimensional rectangular sheet to a Klein bottle, or from a 3-D rectangular prism to a 3-D manifold analogous to a higher-dimensional Klein Bottle. We show that these boundary conditions conserve energy and preserve the important properties of magnetic reconnection. Furthermore, these boundary conditions do not involve unnatural hard boundaries and decrease the computational power compared to the double sheet while maintaining the desired periodicity.