Tearing Mode Poloidal Cross-Section — 2D Magnetic Island Map

A tearing mode is fundamentally a phenomenon of the tokamak's poloidal plane: wherever the safety factor q(r) crosses a low-order rational m/n, resistive reconnection at that rational surface opens a chain of m magnetic islands with no help from the toroidal direction at all. This simulator works directly in that plane — rasterising the helical flux function ψ(r,θ) into a continuous colour field, tracing its separatrix analytically, locating every O-point and X-point with a numeric scan, and drawing the local perturbed magnetic field as a vector quiver — while a proper Runge–Kutta integrator grows or decays the island width from your chosen tearing stability index Δ′ according to the Rutherford equation. A live q(r) profile chart shows exactly where the resonant surface sits and how the q(a) slider moves it.