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matt-pharr merged 1 commit into from
Oct 28, 2026
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PerturbedEquilibrium - DOCS - Identify the surface displacement and correct Glasser citations #540

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4 changes: 2 additions & 2 deletions docs/development/references.md
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Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@ The ForceFreeStates module (ideal MHD stability analysis) implements methods fro

- **Glasser (2016)**: "The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma"
- Location: `docs/resources/2016-Glasser-The_direct_criterion_of_Newcomb_for_the_ideal_MHD_stability_of_an_axisymmetric_toroidal_plasma.pdf`
- Published: Physics of Plasmas **23**, 112506 (2016)
- Published: Physics of Plasmas **23**, 072505 (2016)
- **Describes: FUNDAMENTAL PAPER - Newcomb's criterion for ideal MHD stability (current implementation)**

- **Glasser (2018)**: "A Riccati solution for the ideal MHD plasma response with applications to real-time stability control"
Expand Down Expand Up @@ -97,7 +97,7 @@ GPEC will eventually implement resistive MHD stability analysis based on:

- **Glasser (2016)**: "Computation of resistive instabilities by matched asymptotic expansions"
- Location: `docs/resources/2016-Glasser-Computation_of_resistive_instabilities_by_matched_asymptotic_expansions-compressed.pdf`
- Published: Physics of Plasmas **23**, 072505 (2016)
- Published: Physics of Plasmas **23**, 112506 (2016)
- Describes: Resistive stability analysis and Δ' calculation via matched asymptotic expansions

- **Glasser (2018)**: "A robust solution for the resistive MHD toroidal Δ′ matrix in near real-time"
Expand Down
16 changes: 9 additions & 7 deletions src/PerturbedEquilibrium/FieldReconstruction.jl
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Expand Up @@ -7,7 +7,9 @@ field perturbations in mode space, following the GPEC gpeq module approach.
Displacement components from ODE integration (u_store/du_store/xi_s_store):
- ξ_ψ: radial displacement (u_store[:,:,1,:])
- dξ_ψ/dψ: radial derivative (du_store)
- ξ_s: toroidal displacement (xi_s_store, Glasser 2016 eq. 18)
- ξ_s: surface displacement ξ_s = J(ξ×B)·(∇θ×∇ζ) = χ₁(q ξ^θ - ξ^ζ), the in-surface
displacement across B (binormal Clebsch component); it is not a toroidal displacement
(xi_s_store; Glasser 2016 Phys. Plasmas 23, 072505, eqs. 9 and 18)

Contravariant perturbed field from ideal MHD (matches Fortran gpeq_sol):
b^ψ = χ₁·(m - n·q)·2πi·ξ_ψ
Expand Down Expand Up @@ -227,13 +229,13 @@ alpha = flux_matrix \\ response_vector
Then sum eigenmode contributions at each radial point (matches Fortran gpeq_sol):
xi_psi[ipsi, :] = u_store[:, :, 1, ipsi] * alpha # Ξ_ψ
xi_psi1[ipsi, :] = du_store[:, :, ipsi] * alpha # dΞ_ψ/dψ
xi_s[ipsi, :] = xi_s_store[:, :, ipsi] * alpha # Ξ_s (toroidal, Glasser 2016 eq. 18)
xi_s[ipsi, :] = xi_s_store[:, :, ipsi] * alpha # Ξ_s (surface displacement, Glasser 2016 eqs. 9, 18)

# Returns

- `xi_psi_modes`: Radial displacement ξ_ψ(ψ, m) [npsi, numpert_total]
- `xi_psi1_modes`: Radial derivative dξ_ψ/dψ(ψ, m) [npsi, numpert_total]
- `xi_s_modes`: Toroidal displacement ξ_s(ψ, m) = -A⁻¹(B·dξ_ψ/dψ + C·ξ_ψ) [npsi, numpert_total]
- `xi_s_modes`: Surface displacement ξ_s(ψ, m) = χ₁(q ξ^θ - ξ^ζ) = -A⁻¹(B·dξ_ψ/dψ + C·ξ_ψ) [npsi, numpert_total]
"""
function sum_eigenmode_contributions(
response_vector::Vector{ComplexF64},
Expand Down Expand Up @@ -262,7 +264,7 @@ function sum_eigenmode_contributions(
mul!(view(xi_psi1_modes, ipsi, :),
@view(solution.du_store[:, :, ipsi]),
alpha)
# xi_s_store = Ξ_s = -A⁻¹(B·Ξ'_ψ + C·Ξ_ψ) (toroidal displacement, Glasser 2016 eq. 18)
# xi_s_store = Ξ_s = -A⁻¹(B·Ξ'_ψ + C·Ξ_ψ) (surface displacement, Glasser 2016 eqs. 9, 18)
mul!(view(xi_s_modes, ipsi, :),
@view(solution.xi_s_store[:, :, ipsi]),
alpha)
Expand Down Expand Up @@ -422,7 +424,7 @@ function compute_clebsch_displacements(
# xms = -(A\B)*xmp1 - (A\C)*xsp
xsp_vec = view(xi_psi_modes, ipsi, :)
mul!(xms_vec, bmat, xmp1_vec) # xms = B*xmp1
mul!(xms_vec, cmat_buf, xsp_vec, 1.0+0.0im, 1.0+0.0im) # xms += C*xsp
mul!(xms_vec, cmat_buf, xsp_vec, 1.0 + 0.0im, 1.0 + 0.0im) # xms += C*xsp
# ideal A only; the kinetic A is non-Hermitian and is treated separately above
amat_fact = cholesky!(Hermitian(amat, :L))
ldiv!(amat_fact, xms_vec) # xms = A\(B*xmp1 + C*xsp)
Expand Down Expand Up @@ -831,7 +833,7 @@ function compute_b_n_xi_n_modes(
jd = jacs .* delpsis

for in in 1:npert
blk = ((in - 1) * mpert + 1):(in * mpert)
blk = ((in-1)*mpert+1):(in*mpert)
# IDFT: mode space → theta space
bwp_fun = phase_fwd * b_psi_modes[ipsi, blk] # [mthsurf] — b^ψ (not J-weighted)
xwp_fun = phase_fwd * xwp_modes[ipsi, blk] # [mthsurf] — J·ξ^ψ (J-weighted from gpeq_contra)
Expand Down Expand Up @@ -1020,7 +1022,7 @@ function _apply_rzphi_transform(
zeta_fn = buf.ze

for in in 1:npert
blk = ((in - 1) * mpert + 1):(in * mpert)
blk = ((in-1)*mpert+1):(in*mpert)
# Inverse DFT: modes → theta-space (in place)
Utilities.FourierTransforms.inverse_transform!(psi_fun, ft, view(psi_input, ipsi, blk))
Utilities.FourierTransforms.inverse_transform!(theta_fn, ft, view(theta_input, ipsi, blk))
Expand Down
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