Disentangling the Tangled Linkages of Relative Magnetic Helicity

Magnetic helicity is a topological property that is believed to be key to understanding solar eruptions. Relative magnetic helicity is a generalization that is appropriate for plasmas in a magnetically open volume of interest. This quantity is defined relative to an arbitrary reference magnetic field, B_R, that matches the measured normal component, B_n, on the boundary of the system. New insights based on Gauss’ 1839 work imply that this normal component originates with current systems both interior to and exterior to the volume of interest. We revisit relative helicity and reveal its complexity for understanding the linkages between the magnetic fields produced by current systems inside and outside the volume of interest. This new approach can potentially reveal new and important interactions between the internal and external universe in simulations and NLFFF modeling.