RDCON - BUGFIX - Galerkin vacuum matrix keeps its imaginary part

[StuartBenjamin]

Stacked on #295 (this PR's base branch): merge after it.

RDCON's Galerkin Δ′ uses a real vacuum matrix. free_get_wvac calls mscvac with complex_flag=.FALSE., so the Galerkin edge condition sees only Re(W_v). On an up-down asymmetric equilibrium Im(W_v) is not small, and the free-boundary Δ′ comes out wrong. This is the Galerkin counterpart of the STRIDE complex_flag change in #295, and it builds on #295's conjugation (without it, the imaginary part would enter in the wrong frame). It is a one-line change.

Evidence (TokaMaker DIII-D-like H-mode i-file, n = 1, mpsi 512, mtheta 512, no wall):

	Δ′(2/1)	Δ′(3/1)
RDCON, develop + #295	8.139	−3.988
RDCON, this PR	8.167	−3.935
STRIDE, develop + #295 (reference)	8.172	−3.936

• STRIDE with DCON/RDCON/STRIDE: put the vacuum matrix and norm in the plasma's Fourier frame #295 is the correct reference: DCON/RDCON/STRIDE: put the vacuum matrix and norm in the plasma's Fourier frame #295 puts its complex W_v in the plasma frame, and at the same harmonic range STRIDE agrees with Julia GPEC's independent Riccati solver (with Vacuum/ForceFreeStates - BUGFIX! - Put the vacuum and norm matrices in the plasma's Fourier frame OpenFUSIONToolkit/GPEC#503) to 0.06 % on 2/1 and 0.3 % on 3/1.
• RDCON before this PR is the mean of STRIDE with W_v (8.172, −3.936) and STRIDE with conj(W_v) (8.118, −4.030), i.e. Re(W_v).
• With this PR, RDCON and STRIDE agree to 0.06 % (2/1) and 0.03 % (3/1). They differed by 0.5 % and 1.9 % before.
• With the same harmonic range (mpert 35), RDCON, STRIDE and Julia GPEC (with Vacuum/ForceFreeStates - BUGFIX! - Put the vacuum and norm matrices in the plasma's Fourier frame OpenFUSIONToolkit/GPEC#503, Galerkin and Riccati) agree to ≤ 0.12 % on 2/1.

Stock examples: solovev_resistive (up-down symmetric, so Im(W_v) = 0) gives a byte-identical delta_gw.out. DIIID_resistive runs with rpec_flag, which replaces the vacuum edge, so its outputs are unchanged as well.

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🤖 Generated with Claude Code

[matt-pharr]

Just for the record, not using an i-file does not produce quite as clean agreement between rdcon and stride, though this PR does move us monotonically towards stride:

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Δ′ results (DIII-D resistive example, rpec_flag=f, mpsi=512, mtheta=512; STRIDE with dmlim and mthvac matched to RDCON)

	q=2	q=3
RDCON before, LU	7.031 (−2.04 %)	−3.774 (−16.5 %)
RDCON PR, LU	7.060 (−1.63 %)	−3.729 (−15.1 %)
RDCON before, Cholesky	7.038 (−1.94 %)	−3.431 (−5.9 %)
RDCON PR, Cholesky	7.065 (−1.57 %)	−3.397 (−4.9 %)
STRIDE (reference)	7.178	−3.239

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However, this is a correct change and I do not see anything downstream that this might break so I am going to approve + merge to develop.