[tomneiser]

Summary

Two fixes to the Luce shape functions.

1. luce_squareness inner-quadrant labels swapped

luce_squareness computes the four quadrant squareness values in the order (ou, ol, iu, il) (see the names/POs/PEs tuples), but the unpack after the loop read zetaou, zetaol, zetail, zetaiu = z, assigning the upper-inner value to zetail and the lower-inner value to zetaiu. Since the function returns (zetaou, zetaol, zetail, zetaiu) and miller_R_a_κ_δ_ζ / flux_surfaces consume it in that documented order, squareness_upper_inner and squareness_lower_inner were exchanged on output. Outer quadrants were unaffected.

Verified numerically against an independent implementation on five DIII-D boundaries: outer quadrants agree to 1e-16, inner quadrants agree only after exchanging the labels. A lower-single-null shape (δ_lower = 0.67) had its strongly negative X-point squareness reported as squareness_upper_inner.

2. boundary_shape lower half reflected about the wrong axis

The lower quadrants of boundary_shape were built by negating the upper-half Z after zoffset had already been added, so for any nonzero zoffset the lower half was mirrored about Z = 0 instead of Z = zoffset and displaced vertically by twice the offset. Found while regenerating the sample DIII-D boundary from its extracted parameters (outboard extremum at Z = -0.05 m, lower half 0.10 m too high). No callers in IMAS or FUSE pass a nonzero zoffset today.

Changes

• One-line fix to the unpack in luce_squareness (src/physics/fluxsurfaces.jl). Return order, docstring, and quadrant geometry are unchanged.
• Mirror the lower half of boundary_shape about zoffset (src/physics/boundary.jl).
• New testset luce_squareness quadrant labels in test/runtests_fluxsurfaces.jl: builds a boundary from Luce's superellipse parameterisation (PPCF 55 (2013) 095009) with four distinct per-quadrant squareness values and checks each is recovered in the right quadrant. A mirror-symmetric test cannot catch this bug; this one fails before the fix with the two inner values exchanged and passes after.
• New testset boundary_shape zoffset: a nonzero zoffset must be a pure vertical translation of the zoffset = 0 shape, with and without X-points. Fails 9 of 18 before the fix.

Downstream impact

Consumers of squareness_lower_inner / squareness_upper_inner (e.g. FUSE pulse_schedule initialisation, shape-control targets, any stored references derived from earlier IMAS output) will see the two inner values exchange after this fix.

Test plan

• luce_squareness quadrant labels fails before the fix (ζil gets -0.20, ζiu gets 0.25) and passes after
• boundary_shape zoffset fails before the fix (9/18) and passes after
• Full Pkg.test("IMAS") passes

🤖 Generated with Claude Code

[smithsp]

I would appreciate a diagram here.

[tomneiser]

Two figures to illustrate the bugs and the fixes.

Figure 1: luce_squareness geometry. Left is the Luce superellipse boundary used in the new test, with four distinct prescribed squareness values. Right is the sample DIII-D LCFS from IMASdd. Dashed lines are the PO→PE diagonals, green dots the ζ=0 reference point PC, orange dots the boundary crossing PD. Outer quadrants are unchanged by this PR. On master the two inner quadrants report each other's value; after the fix each quadrant reports its own. For the sample DIII-D shape, the strongly negative upper-inner value (-0.62) was being reported as squareness_lower_inner.

Figure 2: regenerating a boundary from the extracted parameters. Shape parameters are extracted with miller_R_a_κ_δ_ζ and fed back to boundary_shape, with no X-point treatment. Orange is master: swapped inner labels and the old lower-half mirror. Green has the squareness fix only. Blue has both fixes.

• The label swap puts the pinched inboard corner on the wrong side of the midplane (orange vs green/blue).
• The old boundary_shape mirror reflected the lower half about Z = 0 instead of Z = zoffset, so with zoffset = -0.05 m on the DIII-D case the lower half sits 0.10 m too high (green vs blue). On the test boundary zoffset = 0, so green and blue coincide.

With both fixes the test boundary is reproduced exactly. The residual mismatch on the DIII-D case, at the inboard midplane and at the X-point corner on top, is a limitation of the Luce form with a single zoffset and no null, not of this PR.

(Figures are hosted on the pr-318-figures branch.)