A Dynamical Bridge from Tearing-Mode Torque Balance to Forced Kuramoto Dynamics: Implications for Aperiodic Phase Structure and Mode Locking

Paper 12 in The Geometry of the Critical Line programme. Mode locking — the loss of rotation of a magnetohydrodynamic (MHD) instability relative to the laboratory frame — is a dominant precursor to major disruptions in tokamak plasmas. We show that the overdamped torque balance governing a tearing mode interacting with an error field reduces exactly to the Adler equation, the canonical first-order phase-locking model that is itself the single-oscillator limit of the forced Kuramoto network. This establishes a precise dynamical bridge between plasma mode-locking physics and the theory of coupled oscillator synchronisation. Using this bridge, we reinterpret a recent computational result: deterministic aperiodic…