This browser-side companion follows the external-kink lecture directly. It keeps the lecture’s
exact constant-q wall bands, then replaces the analytic interior with a smooth tokamak current
profile built from the same family used in the tearing explorer. The edge safety factor qa,
core value q0, and wall ratio b/a then feed a numerical Newcomb solve for the
edge logarithmic derivative aξ′(a)/ξ(a), which is inserted back into the surface-energy
formula for the external mode.
Choose one low-order external-kink branch at a time, then inspect the resulting q(r), f(r), g(r), and the two Newcomb plasma solutions directly.
Together with qa, this sets the smooth current profile jz(r) ∝ (1-r²/a²)ν through ν = qa/q0 - 1.
Sets a simple dimensionless peaked pressure profile in the large-aspect-ratio g(r) term. Here the reduced model uses a smooth edge-vanishing gradient, so pressure changes g(r) directly while f(r) remains the magnetic line-bending coefficient.
Sets αm = (a/b)2m. Bringing the wall in widens the classic ideal-wall stabilization strip below each rational edge value qa = m/n.
Awaiting solve.
Awaiting solve.
Awaiting solve.
Awaiting solve.
δW ∼ [ (F²/k₀²)(aξ′/ξ) + FF†/k₀² + (a²F²/m)Λm ]a.
The interior solution comes from the reduced Euler–Lagrange form
(fξ′)′ - gξ = 0, integrated from the axis to the edge with the smooth
current profile set by q0 and qa. The exterior segment is the
ideal-wall vacuum continuation that matches the edge displacement and vanishes at r=b.
When a rational surface lies inside the plasma, the explorer now follows Newcomb’s logic more explicitly:
one solution is regular at the axis, a second is regular at the edge/vacuum side, and their small-solution
behavior is compared across F=0. The side-by-side panels separate the line-bending coefficient
f(r) from the total g(r), including the added pressure contribution.
q(r)=m/n occurs inside the plasma, the explorer now switches
to a piecewise Newcomb construction and shows the axis-regular and edge-regular plasma branches separately.
The first panel shows the smooth q(r) profile for the chosen current profile and selected rational level. The second panel now shows the two plasma-side Newcomb solutions: one regular at the axis and one regular at the outer boundary. The matching panel below shows the normalized radial magnetic perturbation br, which is the quantity naturally continued through the vacuum out to the ideal wall. The lower pair separates the reduced coefficients f(r) and g(r), making the magnetic and pressure weighting behind the mode structure easier to read.