Chirped Plasmoid Instability in 3D Torsional Spine Reconnection

Abstract

Magnetic reconnection at three-dimensional (3D) magnetic null points is fundamental to solar flares and magnetospheric substorms. While the plasmoid instability in two-dimensional current sheets is well understood, its analytical treatment in intrinsically 3D null-point geometries is lacking. We present a reduced magnetohydrodynamic (RMHD) formulation for the torsional spine null, where a cylindrical current channel around the spine drives reconnection. The guide field component varies linearly along the spine, causing the local Alfvén speed to increase with distance from the null and breaking translational symmetry. This gives rise to the chirped plasmoid instability: a chain of magnetic islands whose normalized growth rate varies inversely with axial distance, quantified by a dimensionless chirp parameter significantly larger than unity. A multiple-scale WKB analysis yields an axial-coordinate-dependent tearing dispersion relation, confirming the continuous spatial variation of growth rate and wavenumber. We also analyze magnetic helicity evolution, showing that the helicity injection rate increases linearly with axial distance, resulting in a geometric enhancement of the total plasmoid helicity relative to two-dimensional estimates. The helicity flux from the spine into the fan plane via torsional Alfvén waves is derived, providing a quantitative criterion for cross-null plasmoid seeding. This work constitutes the first analytical theory of the 3D plasmoid instability in a torsional spine geometry, with direct implications for interpreting high-resolution solar observations.