This browser-side companion to the resistive-interchange lecture organizes the local story around the cylindrical drive parameter Ds, finite-compressibility parameter Γβ, geometric stabilization 𝒮, and outer tearing index Δ′. The goal is not to replace the full CGJ shooting calculation, but to make the lecture’s parity competition visible: the interchange-like branch reacts strongly to finite pressure and geometric stabilization, while the tearing-like branch remains the natural island-forming continuation when pressure drive is present in a low-shear layer.
Switch between the lecture’s finite-pressure branch splitting and the nearly degenerate low-β benchmark.
Scales the local bad-curvature pressure drive entering Ds.
Larger local shear suppresses Ds through the usual Suydam denominator.
The lecture’s representative finite-pressure case uses Γβ = 1/6.
This is the stabilizing geometric term that pushes the even branch down much more strongly.
Negative values are classically tearing-stable, but the odd parity can still survive on pressure-gradient free energy.
Ds = 3/16, Γβ ≈ 1/6, and 𝒮 ≈ 1.
The large panel shows the branch growth proxies Q = γ/γR as the pressure-gradient scale is varied at fixed shear. The small panels then show how the same two parity branches respond to shear and what their local basis functions look like right at the resonant layer.
At fixed pressure drive, both branches feel shear stabilization, but the tearing-like branch remains much more robust.
Ξ(0) ≠ 0, Ψ(0) = 0: finite radial displacement at the surface, but no leading-order island.
Ξ(0) = 0, Ψ(0) ≠ 0: the odd branch carries finite helical flux and is the island-forming one.
The explorer uses the lecture’s organizing variables
Ds ∝ gp / gs2,
Q = γ/γR,
and parity-resolved finite-pressure corrections anchored to the low-β Coppi benchmark
Q ≈ 0.39685 at Ds = 3/16.
The absolute numbers should be read as lecture-faithful branch proxies, not as a replacement for the full CGJ boundary-value solve. The pedagogical point is the branch ordering: once finite pressure and weak shear are present, the tearing-like parity tends to remain the dominant island-forming continuation.