This is the real 2D object a tearing mode lives in: the poloidal cross-section of the tokamak — the plane you'd see slicing straight through the donut. Nothing about the reconnection physics needs the toroidal direction, so this view solves and draws the whole mode directly in that plane instead of decorating a 3D torus with points.
q(r) = q0 + (qa − q0)(r/a)² safety-factor profile
q(r_s) = m/n resonant surface
ψ(x,θ) = ½ψ0″x² − δψs·cos(mθ) helical flux, x = r − r_s
W = 4·√(δψs / ψ0″) island full width (separatrix)
The colour field is a rasterised map of ψ itself (not a discrete point sample): every pixel inside the plasma boundary gets its own ψ value converted straight to a colour band, so the cat's-eye island structure and the surrounding nested surfaces both appear as continuous regions. The white separatrix curve and the O/X points on top of it are found analytically and numerically for the same ψ, so the two never disagree by construction. Small arrows show the local perturbed poloidal field B ≈ (r⁻¹∂ψ/∂θ, −∂ψ/∂r), computed by central finite differences — you can see it circulate around each O-point and reverse across each X-point.
Growth follows the same simplified Rutherford equation as the physics, but is now integrated with a proper 4th-order Runge–Kutta step each frame rather than a single Euler step, which matters most right at the Δ′ > 0 → saturation transition:
τ_R · dW/dt = r_s · Δ′ · (1 − W / W_sat)
- Δ′ > 0 — linearly unstable: the island grows, then saturates nonlinearly at W_sat.
- Δ′ < 0 — linearly stable: any seed island decays back toward zero width.
- q(a) slider — reshapes the whole q-profile (see the live q(r) chart, top right) and moves r_s and the local shear.
- The m O-points and m X-points are located by a direct numeric scan of ψ along the resonant circle, not just placed by formula — their count always matches the mode number m you selected.