A Transport Theory of Turbulent Coronal Heating in General Geometry

Magnetic geometry shapes how turbulence transports and dissipates energy in strongly magnetized plasmas. The solar corona, a maze of open and closed flux tubes with sharp transverse gradients, is a prominent example, yet most wave-turbulence models of coronal heating assume symmetric flux tubes or add geometric effects in ad hoc ways. Here we develop a geometry-complete multiscale transport theory for reduced-magnetohydrodynamic turbulence in an arbitrary background field, retaining squashing (magnetic shear), transverse gradients, curvature, and gravity at the same order as standard expansion-driven reflection, and coupling fast, anisotropic fluctuations to slow background evolution through conservation laws. Applied to the corona, it recovers the standard reflection-driven turbulent cascade in smooth regions such as coronal-hole interiors, but predicts that in structured regions geometry-driven channels can dominate: squashing drives reflection even when parallel Alfv'en-speed gradients are weak; curvature and non-radial geometry drive compressive heating channels; and waves catalyze the relaxation of velocity shear into heat. The same dynamics drive cross-field transport of mass, composition, momentum, and heat across open-closed interfaces, at rates rivaling the field-parallel supply from the base. These effects bias heating to low altitudes in structured regions, giving a physical basis for the coronal-hole--boundary corrections used in empirical wind-speed predictors. Additionally, the framework's slow-timescale transport equations could be evolved in time, providing a route to a global, geometry-aware model of a structured wave-driven corona and wind. More broadly, the theory provides an energy-consistent account of turbulence, geometry, and transport effects relevant to various astrophysical and terrestrial settings, from magnetospheres and accretion flows to fusion experiments.