Motivation
While implementing the layer-overlap truncation (#298), the general two-fluid Riccati width
(riccati_del_s, the 2023 book's model — validated against its figs 6.2/6.3) and the closed-form
diffusive-resistive width of Fitzpatrick 2025 Eq. (100) (arXiv:2511.07666; the width the truncation
criterion is calibrated with) were compared on the DIII-D-like deck. They differ by a near-uniform
factor: Eq. (100) ≈ 0.47–0.59 × the ODE width across m = 2–10, surfaces spanning very different
parameters.
A near-constant ratio suggests a width-definition offset, not a physics disagreement: the ODE width
is defined through the dispersion relation (the equivalent resistive-sheet thickness, book Eq. 6.24,
extracted via the small-q limit of Eq. 6.41), while Eq. (100) is the spatial decay scale of the
layer solution (the |G|^(-1/4) p-space thickness of the paper's Eq. 97, converted to radius).
Those are inequivalent definitions of "width" for the same layer and should differ by a derivable
O(1) constant. But this is currently a hypothesis fit to one deck, and the ~20% drift in the ratio
is unexplained (model differences are plausible: four-field at Q = Q_e vs the paper's three-field
static-RMP response at Q_E + Q_e; compressibility/semi-collisional terms in one and not the other).
The check
In the deep diffusive-resistive corner (book regime map fig 6.1: Q̂*, P̂ → 0), either
- extract a spatial-decay width from the general Riccati solve (the analogue of
|G|^(-ν)), or
- derive the book model's DR asymptote analytically,
and compare against Eq. (100) under a single width definition. The DIII-D 2/1 surface sits in that
corner (Q̂ ≈ 0.007, P̂ ≈ 0.009), so the existing slayer_dels_fitzpatrick harness fixture covers
the right parameter range for a regression pin once the constant is derived.
Acceptance
- The ratio is explained by a derived constant (with the residual drift attributed), or a real model
discrepancy is identified and its consequence for the truncation criterion stated.
- The result is recorded where the two widths are documented (workflow docs page /
references.md one-liner), and pinned in the harness if a clean identity exists.
Why it matters
The truncation criterion (#298) uses Eq. (100) because the paper's ε_c values and its fig 9
cross-validation are calibrated in that convention. On the DIII-D deck the factor ~2 between the two
widths is exactly the difference between truncating at ψ = 0.9971 (keep q ≤ 6) and ψ = 0.9892
(keep q ≤ 5), so knowing whether the offset is definitional or physical bounds the systematic
uncertainty of the domain choice. Not a blocker for #298.
Motivation
While implementing the layer-overlap truncation (#298), the general two-fluid Riccati width
(
riccati_del_s, the 2023 book's model — validated against its figs 6.2/6.3) and the closed-formdiffusive-resistive width of Fitzpatrick 2025 Eq. (100) (arXiv:2511.07666; the width the truncation
criterion is calibrated with) were compared on the DIII-D-like deck. They differ by a near-uniform
factor: Eq. (100) ≈ 0.47–0.59 × the ODE width across m = 2–10, surfaces spanning very different
parameters.
A near-constant ratio suggests a width-definition offset, not a physics disagreement: the ODE width
is defined through the dispersion relation (the equivalent resistive-sheet thickness, book Eq. 6.24,
extracted via the small-q limit of Eq. 6.41), while Eq. (100) is the spatial decay scale of the
layer solution (the
|G|^(-1/4)p-space thickness of the paper's Eq. 97, converted to radius).Those are inequivalent definitions of "width" for the same layer and should differ by a derivable
O(1) constant. But this is currently a hypothesis fit to one deck, and the ~20% drift in the ratio
is unexplained (model differences are plausible: four-field at Q = Q_e vs the paper's three-field
static-RMP response at Q_E + Q_e; compressibility/semi-collisional terms in one and not the other).
The check
In the deep diffusive-resistive corner (book regime map fig 6.1: Q̂*, P̂ → 0), either
|G|^(-ν)), orand compare against Eq. (100) under a single width definition. The DIII-D 2/1 surface sits in that
corner (Q̂ ≈ 0.007, P̂ ≈ 0.009), so the existing
slayer_dels_fitzpatrickharness fixture coversthe right parameter range for a regression pin once the constant is derived.
Acceptance
discrepancy is identified and its consequence for the truncation criterion stated.
references.mdone-liner), and pinned in the harness if a clean identity exists.Why it matters
The truncation criterion (#298) uses Eq. (100) because the paper's ε_c values and its fig 9
cross-validation are calibrated in that convention. On the DIII-D deck the factor ~2 between the two
widths is exactly the difference between truncating at ψ = 0.9971 (keep q ≤ 6) and ψ = 0.9892
(keep q ≤ 5), so knowing whether the offset is definitional or physical bounds the systematic
uncertainty of the domain choice. Not a blocker for #298.