[matt-pharr]

Summary

The kinetic Euler-Lagrange matrices built in torque.F90 (the op_wmats path that DCON uses for kin_flag runs) bounce-average the W vectors with the opposite complex pairing from PENTRC's scalar torque. As a result the self-consistent kinetic matrices encode the drift-kinetic action of the up-down-mirrored perturbation rather than the actual one. This PR conjugates the bounce-averaged wmmt/wemt (two lines), so W^T Ξ is exactly the projection the scalar route computes.

What was wrong

In tpsi, the scalar route forms bj = ∫ conj(jvtheta)·(pl + (1−σ)/pl), where jvtheta = Σ_m D_m e^{+2πi(m−nq)θ} is the perturbation along the field line. Its magnitude is |∫ jvtheta·conj(pl)|: the real perturbation projected onto the orbit phase.

The matrix route bounce-averaged conjg(wmu_mt)·pl and then contracted with the unconjugated D_m. That gives Σ_m D_m ∫ e^{−2πi(m−nq)θ}·pl, which pairs D_m with conjugated phases. It is neither the perturbation nor its conjugate; it is the mirrored perturbation. Conjugating the bounce integrals gives Σ_m D_m ∫ e^{+2πi(m−nq)θ}·conj(pl) = ∫ jvtheta·conj(pl), identical to the scalar route's δJ as a complex number.

On up-down-symmetric equilibria the mirrored and actual perturbations coincide, so nothing changes. On asymmetric ones, the self-consistent kinetic matrices, and everything built on them (kinetic DCON eigenfunctions, the GPEC response, the self-consistent torque gpec_dw_profile), were affected. PENTRC's scalar methods (fgar etc.) evaluated on a given perturbation were already correct.

Evidence

Logan's thesis (ch. 7, App. C) requires the self-consistent torque from DCON's boundary term and PENTRC's fgar to agree pointwise in ψ. Before this fix they don't on asymmetric equilibria; after it they do.

Fortran, DIII-D-like docs/examples/run_kinetic_example (up-down asymmetric), mpsi = 256:

build	GPEC ∫T_φ [N·m]	PENTRC fgar [N·m]	fgar ÷ GPEC
develop	0.15447	0.1537	0.995
this PR	0.15046	0.1507	1.0016

Pointwise at mpsi = 128, away from resonances, PENTRC's and GPEC's torque densities disagree by 15–20% on develop and agree to 0.1–0.5% with this PR. On develop the total torques happen to agree (0.07%) only because those regional errors cancel.

Fortran, docs/examples/solovev_kinetic_example (up-down symmetric): develop and this PR give identical output to every printed digit (DCON energies, ∫T_φ = 3.93793e−6, fgar = 3.954e−6), as expected for a symmetric equilibrium.

Julia GPEC (a faithful port with the same pairing), TokaMaker up-down-asymmetry family: 11 fixed-boundary shapes, R₀ = 1.7 m, a = 0.6 m, κ = 1.7, mean δ = 0.35, with Δδ = δ_upper − δ_lower from 0 to 0.5 at fixed q₀ = 1.13, q_edge = 5.0 and β_N = 1.5%. Each was run on 26 radial grids from mpsi 128 to 1024, with and without the fix. In the converged-grid figure (mpsi ≥ 576), the unpatched gap between the two torque routes grows with asymmetry (up to −0.57% and +1.09%), while with the fix it stays at the discretization floor (+0.01–0.05%) for every shape. At Δδ = 0 the builds agree with each other.

Notes for review

• Unchanged convention: both routes still use conj(pl) as the orbit weight. That matters only for passing particles and predates this PR. A mirror-symmetry test that checks it independently is planned as a follow-up.
• Downstream impact: kinetic DCON / GPEC results on asymmetric equilibria (DIII-D, ITER, …) will move. Results on symmetric (Solovev) equilibria do not.

🤖 Generated with Claude Code

[logan-nc]

Very convincing tests. Thanks for the catch!