A Deterministic Limit for Magnetic Reconnection: Deriving the Critical Tearing Radius via Plasma Diffusion

The prediction of catastrophic magnetic reconnection in high-energy plasmas—governing phenomena such as solar flare eruptions and Tokamak disruption events—relies heavily on empirical Lundquist numbers and Sweet-Parker scaling heuristics. These magnetohydrodynamic (MHD) frameworks estimate tearing mode instabilities but fail to deterministically define the spatial boundary where localized resistive tearing triggers irreversible magnetic field snapping. This paper introduces a continuum framework for macroscopic plasma containment, where the current sheet is modeled as a dynamic balance between magnetic diffusion and localized resistive tearing. We derive a critical reconnection radius (Rreconnect), showing that magnetic snapping is not a probabilistic instability, but a deterministic limit where localized X-point tearing strictly overpowers the plasma's ability to smooth flux. The proposed approach offers a potential breakthrough for fusion reactors, using Active Containment Telemetry (ACT) with Electron Cyclotron Resonance Heating (ECRH) to provide real-time prediction and stabilization before catastrophic plasma loss.