A Scaling Study of Single X-point Hall MHD Reconnection with System Size

Magnetic reconnection is a fundamental process that enables rapid energy conversion in plasmas, but how its rate scales in large-scale systems remains a key question. We present a study using a Hall magnetohydrodynamics (MHD) model to investigate how reconnection properties depend on the system size relative to the ion skin depth (dᵢ). We perform a series of two-dimensional numerical simulations of a single X-point using a Hall MHD model with a hyper-resistive dissipation term to break the frozen-in condition. The study focuses on a systematic scan of the global system size, L, normalized to the ion skin depth, dᵢ, over a wide range of values. Our simulations demonstrate that both the reconnection rate and the opening angle of the exhaust region exhibit a weak but clear dependence on the system size. Specifically, the reconnection rate becomes slower, and the opening angle decreases as the system size increases relative to dᵢ. This scaling implies that in vast space and astrophysical plasmas, where the system size is many orders of magnitude larger than the ion skin depth, the reconnection rate may be noticeably lower than the rate obtained from small-scale simulations.