How is helicity (and twist) partitioned in magnetohydrodynamic simulations of reconnecting magnetic flux tubes?

Magnetic helicity conservation provides a convenient way to analyze specific properties (namely, the linkage and twist) of reconnecting flux tubes and yield additional insight into the pre- and post-reconnection states of magnetic structures in the solar atmosphere. A previous study considered two flux tubes with footpoints anchored in two parallel planes. They showed that reconnection would add self-helicity equivalent to a half turn of twist to each flux tube. We address a related and fundamental question here: if two flux tubes anchored in a single plane reconnect, what are the resulting twists imparted to each of the reconnected tubes? Are they equal and do they have a simple exact value independent of footpoint location? To do this, we employ a new (computationally efficient) method which subdivides each flux tube into distinct elements and calculates the mutual helicity of many elemental pairs, the sum of which determines the self-helicity of the overall flux tube. Having tested the method using a simple analytical model, we apply the technique to a magnetohydrodynamic simulation where initially untwisted magnetic flux tubes are sheared and allowed to reconnect (based on a previous reconnection model). We recover values of self-helicity and twist in the final end state of the simulations which show excellent agreement with theoretical predictions.