InnerLayer.SLAYER - API - Choose one default radial label for the Fitzpatrick layer formalism

[d-burg]

Question

SLAYER's entire layer stack — rs, the r-based shear sval_r, S (Lundquist), tau_R, tau_E, W_d, the Delta-prime reference-length factor k_ref (PR #403), and the new resistive-layer-width overlap criterion (layer-overlap psihigh cap, PR to follow) — is expressed in a radial label r selected by the programmatic rs_method option. The default is :midplane (outboard axis-to-edge chord), kept for continuity. Should the default move to the flux label?

Evidence, from two independent investigations

Non-covariance (layer-overlap work). Fitzpatrick's diffusive-resistive width, Nucl. Fusion 2025 Eq. (100), scales as (q/|dq/dr|)^(1/2) and picks up J^(1/2) under a change of radial variable — the formula is anchored to the coordinate it was derived in, which is the Eq. (30) flux label r = sqrt(2*psi_t/B0). Evaluated on the DIII-D-like deck the label choice moves the overlap cut by one rational surface (:midplane 0.99752 vs :flux 0.99939). The flux label reduces to the geometric minor radius on a circular LAR equilibrium (r/a = 0.99–1.05) and supplies a systematic shape correction on the shaped deck (r/a = 1.20–1.45), so it is shape-general by construction. The same non-covariance argument applies to the layer dispersion that the r_s-referenced Delta-prime feeds.

TJ cross-validation (Delta-prime convention work, PR #403). In the four-arm radial-label comparison on the shaped DIII-D-like equilibrium, the flux-type labels (:halfwidth, :fsa, :volume) reproduce TJ's circular flux label to <= 1.2 percent while :midplane is the outlier (the Shafranov shift compresses the outboard chord). The 2/1 growth rate moves about +/- 3 percent across labels at defaults, growing to O(1) sensitivity at q >~ 4 on shaped surfaces.

Both lines of evidence, obtained independently, agree: the geometric midplane chord is the odd label out for Fitzpatrick-formalism quantities, and the Eq. (30) flux label is the theoretically anchored choice.

Why this is not being flipped inside either PR

Changing the default moves rs, sval_r, lu, tau_R and the Delta-prime normalization everywhere at once — a results-moving change that needs the regression harness, a !-tagged PR of its own, and its own argument. Both in-flight PRs therefore keep :midplane as the default and scope their label usage explicitly (PR #403 exposes the labels programmatically only, not via TOML; the overlap-cap work evaluates its criterion in :flux internally).

Caveats on record

• :fsa and other geometric labels lose their Jacobian near a separatrix (da/dpsi collapses as the surfaces converge to the separatrix shape); this is edge-specific — at interior rational surfaces the geometric labels are well-behaved and validated.
• The flux label's own value saturates at the separatrix (toroidal flux is finite) but its derivative dr/dpsi ~ q keeps growing, which is what the width conversions need.

Decision needed

After PR #403 and the layer-overlap cap PR land: pick the long-term default (:flux being the theory-anchored candidate), run the harness on the flip, and ship it as a single !-tagged change.

[d-burg]

Reconciliation of the two evidence sets, after cross-checking where each was measured — this sharpens the decision this issue should make.

The two validations sampled different regimes and do not contradict each other:

• The TJ cross-validation's "flux-type labels reproduce TJ's label to <= 1.2 percent" was measured on the circular TJ eps = 0.15 benchmark (K^(2mu) conversion factors at the q = 2 and q = 3 surfaces: halfwidth 0.38 percent, fsa 0.46 percent, volume 0.30 percent off TJ's reference, vs midplane 1.9 percent off). On a circular equilibrium all flux-type labels coincide to O(eps^2), so this certifies the family but cannot discriminate within it.
• The layer-overlap investigation's per-surface label table on the shaped DIII-D-like deck is the discriminator: :fsa tracks the Eq. (30) :flux label to ~1 percent at psi = 0.5, degrading to ~12 percent by psi = 0.99, while :halfwidth sits ~16 percent below :flux in the core — on shaped equilibria :halfwidth is a genuinely different label, not an approximation to Eq. (30).

Consequence — this issue should make two decisions, not one:

1. Edge overlap criterion (layer widths near the separatrix): no freedom. Eq. (100) is non-covariant and the geometric labels lose their Jacobian approaching the separatrix (they converge to the separatrix shape, so da/dpsi collapses and surfaces past psi ~ 0.99 cannot be scored at all). The criterion must be evaluated in the Eq. (30) flux label. This part is effectively settled and the overlap-cap PR implements it that way internally.
2. Interior Delta-prime conversion / layer-stack default: a convention choice with real but bounded spread (labels agree to ~1-5 percent in r at interior rational surfaces on the shaped deck; ~ +/- 3 percent in the 2/1 growth rate). :flux remains the theory-anchored candidate for consistency with (1), but flipping it is the results-moving !-tagged change described above, and :fsa is the closest geometric stand-in if a geometric label is ever preferred for diagnostic comparison.

One correction to the caveats section: the earlier statement that :halfwidth is "the closest stand-in for the circular flux label" holds only on circular equilibria; on shaped decks :fsa is the closest geometric approximation to Eq. (30) and :halfwidth should be treated as its own convention (shift-free midplane half-chord), useful for comparison with midplane diagnostics rather than as a flux-label proxy.