ForceFreeStates - BUGFIX! - Trigger the Gaussian reduction on the conditioning of U₁ and factor U₁ in the plasma response matrix

examples/DIIID-like_SLAYER_example/gpec.toml

@@ -49,7 +49,7 @@ kinetic_factor = 0.0           # Scaling of kinetic matrices (0 = ideal path; >0
 eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations
 save_interval = 1              # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
 integrator            = "riccati" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/DIIID-like_error_field_example/gpec.toml

@@ -52,7 +52,7 @@ kinetic_factor = 0.0           # Scaling of kinetic matrices (0 = ideal path; >0
 eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
 save_interval = 1              # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
 integrator            = "forward" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/DIIID-like_gal_resistive_example/gpec.toml

@@ -48,7 +48,7 @@ kinetic_factor = 0.0           # Scaling of kinetic matrices (0 = ideal path; >0
 eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations
 save_interval = 1              # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
 integrator          = "galerkin" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/DIIID-like_gal_resistive_pe_example/gpec.toml

@@ -48,7 +48,7 @@ kinetic_factor = 0.0           # Scaling of kinetic matrices (0 = ideal path; >0
 eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations
 save_interval = 1              # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
 integrator          = "galerkin" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/DIIID-like_ideal_example/gpec.toml

@@ -47,7 +47,7 @@ kinetic_factor = 0.0           # Scaling of kinetic matrices (0 = ideal path; >0
 eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
 save_interval = 1              # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
 integrator            = "forward" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/DIIID-like_ideal_multi_n_example/gpec.toml

@@ -49,7 +49,7 @@ kinetic_factor = 0.0           # Scaling of kinetic matrices (0 = ideal path; >0
 eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
 save_interval = 1              # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
 integrator            = "forward" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/DIIID-like_riccati_deltaprime_example/gpec.toml

@@ -49,7 +49,7 @@ kinetic_factor = 0.0           # Scaling of kinetic matrices (0 = ideal path; >0
 eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
 save_interval = 1              # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
 integrator            = "riccati" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/LAR_beta_scan/gpec.toml

@@ -49,7 +49,7 @@ mthvac       = 960             # Number of points used in splines over poloidal
 
 eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min             = 1e-4 # Fractional distance from rational q at which ideal jump enforced
-ucrit                   = 1e3  # Column-norm threshold that triggers solution renormalization
+ucrit                   = 1e3  # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 sing_order              = 6    # Order of the singular-surface (Frobenius) series expansion
 
 integrator            = "riccati" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/LAR_epsilon_scan/gpec.toml

@@ -50,7 +50,7 @@ mthvac       = 960             # Number of points used in splines over poloidal
 
 eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min             = 1e-4 # Fractional distance from rational q at which ideal jump enforced
-ucrit                   = 1e3  # Column-norm threshold that triggers solution renormalization
+ucrit                   = 1e3  # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 sing_order              = 6    # Order of the singular-surface (Frobenius) series expansion
 
 integrator            = "riccati" # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)

examples/LAR_ideal_match_test/gpec.toml

@@ -46,7 +46,7 @@ mthvac      = 960              # Number of points used in splines over poloidal
 
 eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min             = 1e-4  # Fractional distance from rational q at which ideal jump enforced
-ucrit                   = 1e3   # Column-norm threshold that triggers solution renormalization
+ucrit                   = 1e3   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 sing_order              = 6     # Power-series order for the singular-surface asymptotics
 save_interval           = 1     # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 

examples/LAR_resistive_match_test/gpec.toml

@@ -47,7 +47,7 @@ mthvac      = 960              # Number of points used in splines over poloidal
 
 eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min             = 1e-4  # Fractional distance from rational q at which ideal jump enforced
-ucrit                   = 1e3   # Column-norm threshold that triggers solution renormalization
+ucrit                   = 1e3   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 sing_order              = 6     # Power-series order for the singular-surface asymptotics
 save_interval           = 1     # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 

examples/Solovev_ideal_example/gpec.toml

@@ -68,7 +68,7 @@ kinetic_source = "fixed"      # Kinetic matrix source: "fixed" test matrices, or
 kinetic_factor = 0.0          # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 save_interval = 1             # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)

examples/Solovev_ideal_example_3D/gpec.toml

@@ -34,7 +34,7 @@ kinetic_source = "fixed"      # Kinetic matrix source: "fixed" test matrices, or
 kinetic_factor = 0.0          # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 save_interval = 1             # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)

examples/Solovev_ideal_example_multi_n/gpec.toml

@@ -45,7 +45,7 @@ kinetic_source = "fixed"      # Kinetic matrix source: "fixed" test matrices, or
 kinetic_factor = 0.0          # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details).
 # The multi-n Δ' matrix has open issues and is skipped with a warning; the energies stay valid.

examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml

@@ -44,7 +44,7 @@ kinetic_source = "fixed"      # Kinetic matrix source: "fixed" test matrices, or
 kinetic_factor = 0.0          # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 write_outputs_to_HDF5 = true  # Write outputs to the HDF5 file
 HDF5_filename = "euler_n1.h5" # Output HDF5 filename
 # Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium.

examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml

@@ -44,7 +44,7 @@ kinetic_source = "fixed"      # Kinetic matrix source: "fixed" test matrices, or
 kinetic_factor = 0.0          # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 write_outputs_to_HDF5 = true  # Write outputs to the HDF5 file
 HDF5_filename = "euler_n2.h5" # Output HDF5 filename
 # Solovev analytic equilibrium parameters (eq_type = "sol"); see SolovevConfig in src/Equilibrium.

examples/Solovev_kinetic_NTV_example/gpec.toml

@@ -65,7 +65,7 @@ kinetic_source = "fixed"      # Kinetic matrix source: "fixed" test matrices, or
 kinetic_factor = 0.0          # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 save_interval = 1             # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 
 # Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)

examples/Solovev_kinetic_calculated_example/gpec.toml

@@ -61,7 +61,7 @@ kinetic_factor = 1.0          # Full-strength kinetic matrices (the "calculated"
 integrator = "forward"        # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 write_outputs_to_HDF5 = true  # Write outputs to the HDF5 file
 verbose = false               # Enable verbose logging
 

examples/Solovev_kinetic_multiion_example/gpec.toml

@@ -66,7 +66,7 @@ kinetic_source = "fixed"      # Kinetic matrix source: "fixed" test matrices, or
 kinetic_factor = 0.0          # Scaling of kinetic matrices (0 = ideal path; >0 enables kinetic mode)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4            # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                   # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                   # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 save_interval = 1             # Save every Nth ODE step (1=all). Always saves near rational surfaces.
 
 # Integration-range truncation (see ForceFreeStatesControl docstring for details)

examples/a10_kinetic_example/gpec.toml

@@ -42,7 +42,7 @@ kinetic_factor = 1.0           # Scaling of kinetic matrices (0 = ideal path; >0
 integrator = "forward"         # Integration formalism: "forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "galerkin" (RDCON outer-region singular Galerkin Δ′, with the optional RPEC inner-layer match)
 eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
 singfac_min = 1e-4             # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3                    # Column-norm threshold that triggers solution renormalization
+ucrit = 1e3                    # Forward: U₁ condition number that triggers Gaussian reduction; Riccati: entry size that triggers renormalization
 write_outputs_to_HDF5 = true   # Write outputs to the HDF5 file
 force_termination = true       # Stop after force-free states — the kinetic stability eigenvalues are the result of interest