Magnetic Reconnection on a Klein Bottle

TL;DR

This paper introduces a novel boundary condition for magnetic reconnection simulations using Klein bottle topology, offering computational efficiency and improved flux reconnection, with limitations in asymmetric plasma systems.

Contribution

It proposes a new Klein bottle-based boundary condition that enhances simulation efficiency and flux reconnection without external assumptions.

Findings

The new boundary condition is computationally cheaper than fully periodic boundaries.

It reconnects more flux than systems with conducting boundaries.

It reproduces expected reconnection features but has limitations with asymmetric plasmas.

Abstract

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.