diff --git a/CLAUDE.md b/CLAUDE.md index 447f8e8e..4cde0ee8 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -200,6 +200,10 @@ julia benchmarks/benchmark_git_branches.jl \ - Tool requires HDF5.jl for reading euler.h5 output - Each benchmark run takes several minutes per branch (includes compilation + warm runs) +**Benchmark plot output convention:** +- Benchmark scripts save PNG plots to `benchmarks/` or a dedicated subdirectory within it (e.g. `benchmarks/plots/`, `benchmarks/scan_edge_layer_width/`) +- **Never save benchmark plots to `examples/`** — example directories are for inputs and reference outputs only, not diagnostic plots + ## Architecture diff --git a/Project.toml b/Project.toml index 7d74e308..19b241e4 100644 --- a/Project.toml +++ b/Project.toml @@ -17,7 +17,6 @@ JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" -PlotlyJS = "f0f68f2c-4968-5e81-91da-67840de0976a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" @@ -42,7 +41,6 @@ JLD2 = "0.6.3" LinearAlgebra = "1" OrdinaryDiffEq = "6.102.0" Pkg = "1" -PlotlyJS = "0.18.17" Plots = "1.40.15" Printf = "1" SparseArrays = "1" diff --git a/benchmarks/DIIID_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk b/benchmarks/DIIID_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk deleted file mode 100644 index 41a07c2d..00000000 --- a/benchmarks/DIIID_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk +++ /dev/null @@ -1,13741 +0,0 @@ -tMaker: 0 257 257 - 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0.224462295E+01-0.289018273E+00 0.224922132E+01-0.275459528E+00 0.225362110E+01 --0.261929035E+00 0.225783205E+01-0.248426318E+00 0.226185131E+01-0.234944105E+00 - 0.226570511E+01-0.221488416E+00 0.226933742E+01-0.208030954E+00 0.227280116E+01 --0.194588959E+00 0.227608490E+01-0.181152895E+00 0.227917290E+01-0.167713836E+00 - 0.228207445E+01-0.154271290E+00 0.228478599E+01-0.140821084E+00 0.228730273E+01 --0.127359256E+00 0.228962564E+01-0.113883540E+00 0.229175735E+01-0.100392126E+00 - 0.229369068E+01-0.868815407E-01 0.229543734E+01-0.733513758E-01 0.229696774E+01 --0.597961098E-01 0.229830122E+01-0.462167524E-01 0.229941940E+01-0.326105431E-01 - 0.230032253E+01-0.189770106E-01 0.230101657E+01-0.531557994E-02 - 0.949999988E+00-0.129999995E+01 0.949999988E+00-0.127999997E+01 0.949999988E+00 --0.125999999E+01 0.949999988E+00-0.124000001E+01 0.949999988E+00-0.122000003E+01 - 0.949999988E+00-0.120000005E+01 0.949999988E+00-0.117999995E+01 0.949999988E+00 --0.115999997E+01 0.949999988E+00-0.113999999E+01 0.949999988E+00-0.112000000E+01 - 0.949999988E+00-0.110000002E+01 0.949999988E+00-0.108000004E+01 0.949999988E+00 --0.105999994E+01 0.949999988E+00-0.103999996E+01 0.949999988E+00-0.101999998E+01 - 0.949999988E+00-0.100000000E+01 0.949999988E+00-0.980000019E+00 0.949999988E+00 --0.959999979E+00 0.949999988E+00-0.939999998E+00 0.949999988E+00-0.920000017E+00 - 0.949999988E+00-0.899999976E+00 0.949999988E+00-0.879999995E+00 0.949999988E+00 --0.860000014E+00 0.949999988E+00-0.839999974E+00 0.949999988E+00-0.819999993E+00 - 0.949999988E+00-0.800000012E+00 0.949999988E+00-0.779999971E+00 0.949999988E+00 --0.759999990E+00 0.949999988E+00-0.740000010E+00 0.949999988E+00-0.720000029E+00 - 0.949999988E+00-0.699999988E+00 0.949999988E+00-0.680000007E+00 0.949999988E+00 --0.660000026E+00 0.949999988E+00-0.639999986E+00 0.949999988E+00-0.620000005E+00 - 0.949999988E+00-0.600000024E+00 0.949999988E+00-0.579999983E+00 0.949999988E+00 --0.560000002E+00 0.949999988E+00-0.540000021E+00 0.949999988E+00-0.519999981E+00 - 0.949999988E+00-0.500000000E+00 0.949999988E+00-0.479999989E+00 0.949999988E+00 --0.460000008E+00 0.949999988E+00-0.439999998E+00 0.949999988E+00-0.419999987E+00 - 0.949999988E+00-0.400000006E+00 0.949999988E+00-0.379999995E+00 0.949999988E+00 --0.360000014E+00 0.949999988E+00-0.340000004E+00 0.949999988E+00-0.319999993E+00 - 0.949999988E+00-0.300000012E+00 0.949999988E+00-0.280000001E+00 0.949999988E+00 --0.259999990E+00 0.949999988E+00-0.239999995E+00 0.949999988E+00-0.219999999E+00 - 0.949999988E+00-0.200000003E+00 0.949999988E+00-0.180000007E+00 0.949999988E+00 --0.159999996E+00 0.949999988E+00-0.140000001E+00 0.949999988E+00-0.119999997E+00 - 0.949999988E+00-0.100000001E+00 0.949999988E+00-0.799999982E-01 0.949999988E+00 --0.599999987E-01 0.949999988E+00-0.399999991E-01 0.949999988E+00-0.199999996E-01 - 0.949999988E+00 0.000000000E+00 0.949999988E+00 0.199999996E-01 0.949999988E+00 - 0.399999991E-01 0.949999988E+00 0.599999987E-01 0.949999988E+00 0.799999982E-01 - 0.949999988E+00 0.100000001E+00 0.949999988E+00 0.119999997E+00 0.949999988E+00 - 0.140000001E+00 0.949999988E+00 0.159999996E+00 0.949999988E+00 0.180000007E+00 - 0.949999988E+00 0.200000003E+00 0.949999988E+00 0.219999999E+00 0.949999988E+00 - 0.239999995E+00 0.949999988E+00 0.259999990E+00 0.949999988E+00 0.280000001E+00 - 0.949999988E+00 0.300000012E+00 0.949999988E+00 0.319999993E+00 0.949999988E+00 - 0.340000004E+00 0.949999988E+00 0.360000014E+00 0.949999988E+00 0.379999995E+00 - 0.949999988E+00 0.400000006E+00 0.949999988E+00 0.419999987E+00 0.949999988E+00 - 0.439999998E+00 0.949999988E+00 0.460000008E+00 0.949999988E+00 0.479999989E+00 - 0.949999988E+00 0.500000000E+00 0.949999988E+00 0.519999981E+00 0.949999988E+00 - 0.540000021E+00 0.949999988E+00 0.560000002E+00 0.949999988E+00 0.579999983E+00 - 0.949999988E+00 0.600000024E+00 0.949999988E+00 0.620000005E+00 0.949999988E+00 - 0.639999986E+00 0.949999988E+00 0.660000026E+00 0.949999988E+00 0.680000007E+00 - 0.949999988E+00 0.699999988E+00 0.949999988E+00 0.720000029E+00 0.949999988E+00 - 0.740000010E+00 0.949999988E+00 0.759999990E+00 0.949999988E+00 0.779999971E+00 - 0.949999988E+00 0.800000012E+00 0.949999988E+00 0.819999993E+00 0.949999988E+00 - 0.839999974E+00 0.949999988E+00 0.860000014E+00 0.949999988E+00 0.879999995E+00 - 0.949999988E+00 0.899999976E+00 0.949999988E+00 0.920000017E+00 0.949999988E+00 - 0.939999998E+00 0.949999988E+00 0.959999979E+00 0.949999988E+00 0.980000019E+00 - 0.949999988E+00 0.100000000E+01 0.949999988E+00 0.101999998E+01 0.949999988E+00 - 0.103999996E+01 0.949999988E+00 0.105999994E+01 0.949999988E+00 0.108000004E+01 - 0.949999988E+00 0.110000002E+01 0.949999988E+00 0.112000000E+01 0.949999988E+00 - 0.113999999E+01 0.949999988E+00 0.115999997E+01 0.949999988E+00 0.117999995E+01 - 0.949999988E+00 0.120000005E+01 0.949999988E+00 0.122000003E+01 0.949999988E+00 - 0.124000001E+01 0.949999988E+00 0.125999999E+01 0.949999988E+00 0.127999997E+01 - 0.949999988E+00 0.129999995E+01 0.970138907E+00 0.129999995E+01 0.990277767E+00 - 0.129999995E+01 0.101041663E+01 0.129999995E+01 0.103055561E+01 0.129999995E+01 - 0.105069447E+01 0.129999995E+01 0.107083333E+01 0.129999995E+01 0.109097219E+01 - 0.129999995E+01 0.111111116E+01 0.129999995E+01 0.113125002E+01 0.129999995E+01 - 0.115138888E+01 0.129999995E+01 0.117152774E+01 0.129999995E+01 0.119166672E+01 - 0.129999995E+01 0.121180558E+01 0.129999995E+01 0.123194444E+01 0.129999995E+01 - 0.125208330E+01 0.129999995E+01 0.127222228E+01 0.129999995E+01 0.129236114E+01 - 0.129999995E+01 0.131250000E+01 0.129999995E+01 0.133263886E+01 0.129999995E+01 - 0.135277772E+01 0.129999995E+01 0.137291670E+01 0.129999995E+01 0.139305556E+01 - 0.129999995E+01 0.141319442E+01 0.129999995E+01 0.143333328E+01 0.129999995E+01 - 0.145347226E+01 0.129999995E+01 0.147361112E+01 0.129999995E+01 0.149374998E+01 - 0.129999995E+01 0.151388884E+01 0.129999995E+01 0.153402781E+01 0.129999995E+01 - 0.155416667E+01 0.129999995E+01 0.157430553E+01 0.129999995E+01 0.159444439E+01 - 0.129999995E+01 0.161458337E+01 0.129999995E+01 0.163472223E+01 0.129999995E+01 - 0.165486109E+01 0.129999995E+01 0.167499995E+01 0.129999995E+01 0.169513893E+01 - 0.129999995E+01 0.171527779E+01 0.129999995E+01 0.173541665E+01 0.129999995E+01 - 0.175555551E+01 0.129999995E+01 0.177569449E+01 0.129999995E+01 0.179583335E+01 - 0.129999995E+01 0.181597221E+01 0.129999995E+01 0.183611107E+01 0.129999995E+01 - 0.185625005E+01 0.129999995E+01 0.187638891E+01 0.129999995E+01 0.189652777E+01 - 0.129999995E+01 0.191666663E+01 0.129999995E+01 0.193680561E+01 0.129999995E+01 - 0.195694447E+01 0.129999995E+01 0.197708333E+01 0.129999995E+01 0.199722219E+01 - 0.129999995E+01 0.201736116E+01 0.129999995E+01 0.203749990E+01 0.129999995E+01 - 0.205763888E+01 0.129999995E+01 0.207777786E+01 0.129999995E+01 0.209791660E+01 - 0.129999995E+01 0.211805558E+01 0.129999995E+01 0.213819456E+01 0.129999995E+01 - 0.215833330E+01 0.129999995E+01 0.217847228E+01 0.129999995E+01 0.219861102E+01 - 0.129999995E+01 0.221875000E+01 0.129999995E+01 0.223888898E+01 0.129999995E+01 - 0.225902772E+01 0.129999995E+01 0.227916670E+01 0.129999995E+01 0.229930544E+01 - 0.129999995E+01 0.231944442E+01 0.129999995E+01 0.233958340E+01 0.129999995E+01 - 0.235972214E+01 0.129999995E+01 0.237986112E+01 0.129999995E+01 0.240000010E+01 - 0.129999995E+01 0.240000010E+01 0.127999997E+01 0.240000010E+01 0.125999999E+01 - 0.240000010E+01 0.124000001E+01 0.240000010E+01 0.122000003E+01 0.240000010E+01 - 0.120000005E+01 0.240000010E+01 0.117999995E+01 0.240000010E+01 0.115999997E+01 - 0.240000010E+01 0.113999999E+01 0.240000010E+01 0.112000000E+01 0.240000010E+01 - 0.110000002E+01 0.240000010E+01 0.108000004E+01 0.240000010E+01 0.105999994E+01 - 0.240000010E+01 0.103999996E+01 0.240000010E+01 0.101999998E+01 0.240000010E+01 - 0.100000000E+01 0.240000010E+01 0.980000019E+00 0.240000010E+01 0.959999979E+00 - 0.240000010E+01 0.939999998E+00 0.240000010E+01 0.920000017E+00 0.240000010E+01 - 0.899999976E+00 0.240000010E+01 0.879999995E+00 0.240000010E+01 0.860000014E+00 - 0.240000010E+01 0.839999974E+00 0.240000010E+01 0.819999993E+00 0.240000010E+01 - 0.800000012E+00 0.240000010E+01 0.779999971E+00 0.240000010E+01 0.759999990E+00 - 0.240000010E+01 0.740000010E+00 0.240000010E+01 0.720000029E+00 0.240000010E+01 - 0.699999988E+00 0.240000010E+01 0.680000007E+00 0.240000010E+01 0.660000026E+00 - 0.240000010E+01 0.639999986E+00 0.240000010E+01 0.620000005E+00 0.240000010E+01 - 0.600000024E+00 0.240000010E+01 0.579999983E+00 0.240000010E+01 0.560000002E+00 - 0.240000010E+01 0.540000021E+00 0.240000010E+01 0.519999981E+00 0.240000010E+01 - 0.500000000E+00 0.240000010E+01 0.479999989E+00 0.240000010E+01 0.460000008E+00 - 0.240000010E+01 0.439999998E+00 0.240000010E+01 0.419999987E+00 0.240000010E+01 - 0.400000006E+00 0.240000010E+01 0.379999995E+00 0.240000010E+01 0.360000014E+00 - 0.240000010E+01 0.340000004E+00 0.240000010E+01 0.319999993E+00 0.240000010E+01 - 0.300000012E+00 0.240000010E+01 0.280000001E+00 0.240000010E+01 0.259999990E+00 - 0.240000010E+01 0.239999995E+00 0.240000010E+01 0.219999999E+00 0.240000010E+01 - 0.200000003E+00 0.240000010E+01 0.180000007E+00 0.240000010E+01 0.159999996E+00 - 0.240000010E+01 0.140000001E+00 0.240000010E+01 0.119999997E+00 0.240000010E+01 - 0.100000001E+00 0.240000010E+01 0.799999982E-01 0.240000010E+01 0.599999987E-01 - 0.240000010E+01 0.399999991E-01 0.240000010E+01 0.199999996E-01 0.240000010E+01 - 0.000000000E+00 0.240000010E+01-0.199999996E-01 0.240000010E+01-0.399999991E-01 - 0.240000010E+01-0.599999987E-01 0.240000010E+01-0.799999982E-01 0.240000010E+01 --0.100000001E+00 0.240000010E+01-0.119999997E+00 0.240000010E+01-0.140000001E+00 - 0.240000010E+01-0.159999996E+00 0.240000010E+01-0.180000007E+00 0.240000010E+01 --0.200000003E+00 0.240000010E+01-0.219999999E+00 0.240000010E+01-0.239999995E+00 - 0.240000010E+01-0.259999990E+00 0.240000010E+01-0.280000001E+00 0.240000010E+01 --0.300000012E+00 0.240000010E+01-0.319999993E+00 0.240000010E+01-0.340000004E+00 - 0.240000010E+01-0.360000014E+00 0.240000010E+01-0.379999995E+00 0.240000010E+01 --0.400000006E+00 0.240000010E+01-0.419999987E+00 0.240000010E+01-0.439999998E+00 - 0.240000010E+01-0.460000008E+00 0.240000010E+01-0.479999989E+00 0.240000010E+01 --0.500000000E+00 0.240000010E+01-0.519999981E+00 0.240000010E+01-0.540000021E+00 - 0.240000010E+01-0.560000002E+00 0.240000010E+01-0.579999983E+00 0.240000010E+01 --0.600000024E+00 0.240000010E+01-0.620000005E+00 0.240000010E+01-0.639999986E+00 - 0.240000010E+01-0.660000026E+00 0.240000010E+01-0.680000007E+00 0.240000010E+01 --0.699999988E+00 0.240000010E+01-0.720000029E+00 0.240000010E+01-0.740000010E+00 - 0.240000010E+01-0.759999990E+00 0.240000010E+01-0.779999971E+00 0.240000010E+01 --0.800000012E+00 0.240000010E+01-0.819999993E+00 0.240000010E+01-0.839999974E+00 - 0.240000010E+01-0.860000014E+00 0.240000010E+01-0.879999995E+00 0.240000010E+01 --0.899999976E+00 0.240000010E+01-0.920000017E+00 0.240000010E+01-0.939999998E+00 - 0.240000010E+01-0.959999979E+00 0.240000010E+01-0.980000019E+00 0.240000010E+01 --0.100000000E+01 0.240000010E+01-0.101999998E+01 0.240000010E+01-0.103999996E+01 - 0.240000010E+01-0.105999994E+01 0.240000010E+01-0.108000004E+01 0.240000010E+01 --0.110000002E+01 0.240000010E+01-0.112000000E+01 0.240000010E+01-0.113999999E+01 - 0.240000010E+01-0.115999997E+01 0.240000010E+01-0.117999995E+01 0.240000010E+01 --0.120000005E+01 0.240000010E+01-0.122000003E+01 0.240000010E+01-0.124000001E+01 - 0.240000010E+01-0.125999999E+01 0.240000010E+01-0.127999997E+01 0.240000010E+01 --0.129999995E+01 0.237986112E+01-0.129999995E+01 0.235972214E+01-0.129999995E+01 - 0.233958340E+01-0.129999995E+01 0.231944442E+01-0.129999995E+01 0.229930544E+01 --0.129999995E+01 0.227916670E+01-0.129999995E+01 0.225902772E+01-0.129999995E+01 - 0.223888898E+01-0.129999995E+01 0.221875000E+01-0.129999995E+01 0.219861102E+01 --0.129999995E+01 0.217847228E+01-0.129999995E+01 0.215833330E+01-0.129999995E+01 - 0.213819456E+01-0.129999995E+01 0.211805558E+01-0.129999995E+01 0.209791660E+01 --0.129999995E+01 0.207777786E+01-0.129999995E+01 0.205763888E+01-0.129999995E+01 - 0.203749990E+01-0.129999995E+01 0.201736116E+01-0.129999995E+01 0.199722219E+01 --0.129999995E+01 0.197708333E+01-0.129999995E+01 0.195694447E+01-0.129999995E+01 - 0.193680561E+01-0.129999995E+01 0.191666663E+01-0.129999995E+01 0.189652777E+01 --0.129999995E+01 0.187638891E+01-0.129999995E+01 0.185625005E+01-0.129999995E+01 - 0.183611107E+01-0.129999995E+01 0.181597221E+01-0.129999995E+01 0.179583335E+01 --0.129999995E+01 0.177569449E+01-0.129999995E+01 0.175555551E+01-0.129999995E+01 - 0.173541665E+01-0.129999995E+01 0.171527779E+01-0.129999995E+01 0.169513893E+01 --0.129999995E+01 0.167499995E+01-0.129999995E+01 0.165486109E+01-0.129999995E+01 - 0.163472223E+01-0.129999995E+01 0.161458337E+01-0.129999995E+01 0.159444439E+01 --0.129999995E+01 0.157430553E+01-0.129999995E+01 0.155416667E+01-0.129999995E+01 - 0.153402781E+01-0.129999995E+01 0.151388884E+01-0.129999995E+01 0.149374998E+01 --0.129999995E+01 0.147361112E+01-0.129999995E+01 0.145347226E+01-0.129999995E+01 - 0.143333328E+01-0.129999995E+01 0.141319442E+01-0.129999995E+01 0.139305556E+01 --0.129999995E+01 0.137291670E+01-0.129999995E+01 0.135277772E+01-0.129999995E+01 - 0.133263886E+01-0.129999995E+01 0.131250000E+01-0.129999995E+01 0.129236114E+01 --0.129999995E+01 0.127222228E+01-0.129999995E+01 0.125208330E+01-0.129999995E+01 - 0.123194444E+01-0.129999995E+01 0.121180558E+01-0.129999995E+01 0.119166672E+01 --0.129999995E+01 0.117152774E+01-0.129999995E+01 0.115138888E+01-0.129999995E+01 - 0.113125002E+01-0.129999995E+01 0.111111116E+01-0.129999995E+01 0.109097219E+01 --0.129999995E+01 0.107083333E+01-0.129999995E+01 0.105069447E+01-0.129999995E+01 - 0.103055561E+01-0.129999995E+01 0.101041663E+01-0.129999995E+01 0.990277767E+00 --0.129999995E+01 0.970138907E+00-0.129999995E+01 0.949999988E+00-0.129999995E+01 diff --git a/benchmarks/DIIID_ideal_example/euler.bin b/benchmarks/DIIID_ideal_example/euler.bin deleted file mode 100644 index f634e860..00000000 Binary files a/benchmarks/DIIID_ideal_example/euler.bin and /dev/null differ diff --git a/benchmarks/DIIID_ideal_example/gpec.toml b/benchmarks/DIIID_ideal_example/gpec.toml deleted file mode 100644 index ceb57869..00000000 --- a/benchmarks/DIIID_ideal_example/gpec.toml +++ /dev/null @@ -1,67 +0,0 @@ -[Equilibrium] -eq_type = "efit" # Type of the input 2D equilibrium file -eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file -jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) -power_bp = 0 # Poloidal field power exponent for Jacobian -power_b = 0 # Toroidal field power exponent for Jacobian -power_r = 0 # Major radius power exponent for Jacobian -grid_type = "ldp" # Radial grid packing type -psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.993 # Upper limit of normalized flux coordinate -mpsi = 128 # Number of radial grid points -mtheta = 256 # Number of poloidal grid points -newq0 = 0 # Override for on-axis safety factor (0 = use input value) -etol = 1e-7 # Error tolerance for equilibrium solver -force_termination = false # Terminate after equilibrium setup (skip stability calculations) - - -[ForceFreeStates] -bal_flag = false # Ideal MHD ballooning criterion for short wavelengths -mat_flag = true # Construct coefficient matrices for diagnostic purposes -ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) -vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes -mer_flag = true # Evaluate the Mercier criterian - -set_psilim_via_dmlim = true # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See set_psilim_via_dmlim -psiedge = 1.00 # If less then psilim, calculates dW(psi)... -qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... -qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... -sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) - -nn_low = 1 # Smallest toroidal mode number to include -nn_high = 1 # Largest toroidal mode number to include -delta_mlow = 8 # Expands lower bound of Fourier harmonics -delta_mhigh = 8 # Expands upper bound of Fourier harmonics -delta_mband = 0 # Integration keeps only this wide a band... -mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. -thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds - -kin_flag = false # Kinetic EL equation (default: false) -con_flag = false # Continue integration through layers (default: false) -kinfac1 = 1.0 # Scale factor for energy contribution (default: 1.0) -kinfac2 = 1.0 # Scale factor for torque contribution (default: 1.0) -kingridtype = 0 # Regular grid method (default: 0) -passing_flag = true # Includes passing particle effects (default: false) -ktanh_flag = true # Ignore kinetic effects in the core smoothly (default: false) -ktc = 0.1 # Parameter for ktanh_flag (default: 0.1) -ktw = 50.0 # Parameter for ktanh_flag (default: 50.0) -ion_flag = true # Include ion dW_k when kin_flag is true -electron_flag = false # Include electron dW_k when kin_flag is true - -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 = 1e4 # Maximum fraction of solutions allowed before re-normalized - -[WALL] -shape = "nowall" -aw = 0.05 -bw = 1.5 -cw = 0 -dw = 0.5 -tw = 0.05 -equal_arc_wall = 0 -a = 0.2415 - -[DEBUG] -output_benchmark_data = true # Output benchmark data for comparison between codes diff --git a/benchmarks/DIIID_ideal_example/vac.in b/benchmarks/DIIID_ideal_example/vac.in deleted file mode 100644 index 68e91e03..00000000 --- a/benchmarks/DIIID_ideal_example/vac.in +++ /dev/null @@ -1,99 +0,0 @@ -! **** Running DCON's input *** -&MODES - mth = 480 - xiin(1:9) = 0 0 0 0 0 0 0 1 0 - lsymz = .TRUE. - leqarcw = 1 - lzio = 0 - lgato = 0 - lrgato = 0 -/ -&DEBUGS - checkd = .FALSE. - check1 = .FALSE. - check2 = .FALSE. - checke = .FALSE. - checks = .FALSE. - wall = .FALSE. - lkplt = 0 - verbose_timer_output = f -/ -&VACDAT - ishape = 6 - aw = 0.05 - bw = 1.5 - cw = 0 - dw = 0.5 - tw = 0.05 - nsing = 500 - epsq = 1e-05 - noutv = 37 - idgt = 6 - idot = 0 - idsk = 0 - delg = 15.01 - delfac = 0.001 - cn0 = 1 -/ -&SHAPE - ipshp = 0 - xpl = 100 - apl = 1 - a = 20 - b = 170 - bpl = 1 - dpl = 0 - r = 1 - abulg = 0.932 - bbulg = 17.0 - tbulg = 0.02 - qain = 2.5 -/ -&DIAGNS - lkdis = .FALSE. - ieig = 0 - iloop = 0 - lpsub = 1 - nloop = 128 - nloopr = 0 - nphil = 3 - nphse = 1 - xofsl = 0 - ntloop = 32 - aloop = 0.01 - bloop = 1.6 - dloop = 0.5 - rloop = 1.0 - deloop = 0.001 - mx = 21 - mz = 21 - nph = 0 - nxlpin = 6 - nzlpin = 11 - epslp = 0.02 - xlpmin = 0.7 - xlpmax = 2.7 - zlpmin = -1.5 - zlpmax = 1.5 - linterior = 2 -/ -&SPRK - nminus = 0 - nplus = 0 - mphi = 16 - lwrt11 = 0 - civ = 0.0 - sp2sgn1 = 1 - sp2sgn2 = 1 - sp2sgn3 = 1 - sp2sgn4 = 1 - sp2sgn5 = 1 - sp3sgn1 = -1 - sp3sgn2 = -1 - sp3sgn3 = -1 - sp3sgn4 = 1 - sp3sgn5 = 1 - lff = 0 - ff = 1.6 - fv = 1.6 1.6 1.6 1.6 1.6 1.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 -/ diff --git a/benchmarks/Solovev_ideal_example/vac.in b/benchmarks/Solovev_ideal_example/vac.in deleted file mode 100644 index 0f17d7c6..00000000 --- a/benchmarks/Solovev_ideal_example/vac.in +++ /dev/null @@ -1,99 +0,0 @@ -! **** Running DCON's input *** - -&MODES - mth = 480 - xiin(1:9) = 0 0 0 0 0 0 0 1 0 - lsymz = .TRUE. - leqarcw = 1 - lzio = 0 - lgato = 0 - lrgato = 0 -/ -&DEBUGS - checkd = .FALSE. - check1 = .FALSE. - check2 = .FALSE. - checke = .FALSE. - checks = .FALSE. - wall = .FALSE. - lkplt = 0 -/ -&VACDAT - ishape = 6 - aw = 0.05 - bw = 1.5 - cw = 0 - dw = 0.5 - tw = 0.05 - nsing = 500 - epsq = 1e-05 - noutv = 37 - idgt = 6 - idot = 0 - idsk = 0 - delg = 15.01 - delfac = 0.001 - cn0 = 1 -/ -&SHAPE - ipshp = 0 - xpl = 100 - apl = 1 - a = 0.2415 - b = 170 - bpl = 1 - dpl = 0 - r = 1 - abulg = 0.932 - bbulg = 17.0 - tbulg = 0.02 - qain = 2.5 -/ -&DIAGNS - lkdis = .FALSE. - ieig = 0 - iloop = 0 - lpsub = 1 - nloop = 128 - nloopr = 0 - nphil = 3 - nphse = 1 - xofsl = 0 - ntloop = 32 - aloop = 0.01 - bloop = 1.6 - dloop = 0.5 - rloop = 1.0 - deloop = 0.001 - mx = 21 - mz = 21 - nph = 0 - nxlpin = 6 - nzlpin = 11 - epslp = 0.02 - xlpmin = 0.7 - xlpmax = 2.7 - zlpmin = -1.5 - zlpmax = 1.5 - linterior = 2 -/ -&SPRK - nminus = 0 - nplus = 0 - mphi = 16 - lwrt11 = 0 - civ = 0.0 - sp2sgn1 = 1 - sp2sgn2 = 1 - sp2sgn3 = 1 - sp2sgn4 = 1 - sp2sgn5 = 1 - sp3sgn1 = -1 - sp3sgn2 = -1 - sp3sgn3 = -1 - sp3sgn4 = 1 - sp3sgn5 = 1 - lff = 0 - ff = 1.6 - fv = 1.6 1.6 1.6 1.6 1.6 1.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 -/ diff --git a/benchmarks/benchmark_edge_splines.jl b/benchmarks/benchmark_edge_splines.jl new file mode 100644 index 00000000..b75b91c7 --- /dev/null +++ b/benchmarks/benchmark_edge_splines.jl @@ -0,0 +1,749 @@ +""" +Benchmark and visualization script for edge inverse splines (near-separatrix extension). + +This script demonstrates the edge inverse spline construction introduced for diverted +plasmas, allowing GPEC to integrate beyond psihigh toward the separatrix. + +For a diverted plasma, it produces the following plots saved alongside the input toml: + 1. iota (= 1/q) vs psin: shows the iota inner spline descending smoothly to 0 at psin=1 + 2. q vs psin: compares the direct spline (ExtendExtrap) vs the edge inverse spline + 3. dV/dψ vs psin: same comparison + 4. R(psin) and Z(psin) for fixed poloidal angles toward the edge + 5. Flux surface cross-section with x-point marked + 6. Rational surface density in the edge zone + 7. et[1] vs psi in the edge zone (stability diagnostic, requires a prior gpec.h5 output) + +For a limited plasma (no x-point), the script prints a summary and exits since no +edge inverse splines are built. + +Usage: + julia --project=. benchmarks/benchmark_edge_splines.jl [path/to/gpec.toml] + +If no path is given, defaults to examples/DIIID-like_ideal_example/gpec.toml. +""" + +using GeneralizedPerturbedEquilibrium +using GeneralizedPerturbedEquilibrium.Equilibrium: eval_q +using FastInterpolations +using HDF5 +using Roots +using Plots +using TOML +using Printf + +# --- Configuration --- +toml_path = length(ARGS) > 0 ? ARGS[1] : joinpath(@__DIR__, "..", "examples", "DIIID-like_ideal_example", "gpec.toml") +toml_path = abspath(toml_path) +example_dir = dirname(toml_path) # where GPEC input/output files live (geqdsk, gpec.h5, etc.) +output_dir = joinpath(@__DIR__, "edge_splines") # where benchmark PNGs are saved +mkpath(output_dir) + +println("="^70) +println("Edge Spline Benchmark") +println("="^70) +println("Input: $toml_path") +println() + +# --- Load equilibrium --- +println("Loading equilibrium...") +inputs = TOML.parsefile(toml_path) +eq_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], example_dir) +pe = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(eq_config) +edge_layer_width = get(get(inputs, "ForceFreeStates", Dict()), "edge_layer_width", 1e-4) +profiles = pe.profiles +params = pe.params +psihigh = pe.config.psihigh + +println(@sprintf(" psihigh = %.4f", psihigh)) +println(@sprintf(" is_diverted = %s", string(params.is_diverted))) +if !isnothing(params.r_xpoint) + println(@sprintf(" X-point: R = %.4f m, Z = %.4f m", params.r_xpoint, params.z_xpoint)) +end +println() + +# --- Check diverted topology --- +if isnothing(params.is_diverted) || !params.is_diverted + println("Plasma is LIMITED (no x-point detected). No edge inverse splines were built.") + println("Re-run with a diverted equilibrium to see edge spline diagnostics.") + exit(0) +end + +if isnothing(profiles.iota_spline) + println("ERROR: is_diverted=true but iota_spline is nothing. Check equilibrium_solver.") + exit(1) +end + +# Grid from the direct spline +psi_core = profiles.xs + +# --- Build dense evaluation grids (completed after rzphi extension below) --- +psi_plot_core = range(psi_core[1], psihigh, length=500) + +# Key reference values at psihigh +q_at_psihigh_direct = profiles.q_spline(psihigh) +q_at_psihigh_edge = eval_q(profiles, psihigh) +dV_at_psihigh_direct = profiles.dVdpsi_spline(psihigh) +dV_at_psihigh_edge = 1.0 / profiles.dVdpsi_inv_spline(psihigh) + +# --- Scan for edge rational surfaces and extend rzphi geometry --- +# Must happen before psi_plot_edge is built so the edge grid has nonzero width. +# Uses the same check-before-push logic as sing_find!. +iota_inner = profiles.iota_spline +println("Scanning rational surfaces in edge zone [psihigh, 0.9999]...") +nn = 1 +m_start = trunc(Int, q_at_psihigh_direct) + 1 +m_end = trunc(Int, min(q_at_psihigh_direct * 5, 500.0)) +edge_surfaces = Float64[] +let hint = Ref(1) + for m in m_start:m_end + iota_target = nn / m + iota_at_start = iota_inner(psihigh; hint=hint) + iota_target >= iota_at_start && continue + psi_bracket_hi = 1.0 - 1e-8 + try + psi_surf = find_zero( + psi -> iota_inner(psi; hint=hint) - iota_target, + (psihigh, psi_bracket_hi), Roots.Brent(); xatol=1e-8 + ) + psi_last = isempty(edge_surfaces) ? psihigh : edge_surfaces[end] + psi_surf - psi_last < edge_layer_width && break + push!(edge_surfaces, psi_surf) + catch + end + end +end +println(@sprintf(" Found %d rational surfaces (n=%d) in edge zone before density cutoff", + length(edge_surfaces), nn)) + +if !isempty(edge_surfaces) + GeneralizedPerturbedEquilibrium.Equilibrium.equilibrium_extend_rzphi!(pe, edge_surfaces) +end + +# Edge grid now spans [psihigh, pe.rzphi_xs[end]] after extension. +psi_plot_edge = range(psihigh, pe.rzphi_xs[end], length=500) +psi_plot_all = vcat(collect(psi_plot_core), collect(psi_plot_edge)[2:end]) + +# Direct spline evaluated everywhere (extrapolates linearly beyond psihigh) +q_direct = profiles.q_spline.(psi_plot_all) +dV_direct = profiles.dVdpsi_spline.(psi_plot_all) + +# Edge inverse spline (only valid in edge zone) +hint_q = Ref(1) +hint_dV = Ref(1) +q_edge_vals = [1.0 / iota_inner(psi; hint=hint_q) for psi in psi_plot_edge] +dV_edge_vals = [1.0 / profiles.dVdpsi_inv_spline(psi) for psi in psi_plot_edge] +iota_edge_plot = [iota_inner(psi; hint=hint_q) for psi in psi_plot_edge] + +# --- Print key diagnostics --- +println("Continuity check at psihigh:") +println(@sprintf(" q: direct = %.5f, edge = %.5f, |Δ| = %.2e", + q_at_psihigh_direct, q_at_psihigh_edge, abs(q_at_psihigh_direct - q_at_psihigh_edge))) +println(@sprintf(" dV/dψ: direct = %.5f, edge = %.5f, |Δ| = %.2e", + dV_at_psihigh_direct, dV_at_psihigh_edge, abs(dV_at_psihigh_direct - dV_at_psihigh_edge))) +println() + +# --- q vs psin --- +# Compute q derivatives for the junction check. +# Focus on a window around psihigh to show continuity (or lack thereof). +psi_junc = psi_plot_all[psi_plot_all .>= psihigh - 0.02] + +# Direct spline: q, q', q'', q''' (only valid up to psihigh; ExtendExtrap beyond) +q_d0_dir = profiles.q_spline.(psi_junc) +q_d1_dir = profiles.q_deriv.(psi_junc) +_deriv2_q = deriv2(profiles.q_spline) +_deriv3_q = deriv3(profiles.q_spline) +q_d2_dir = _deriv2_q.(psi_junc) +q_d3_dir = _deriv3_q.(psi_junc) + +# Edge inverse spline: compute via chain rule from iota inner spline +# q = 1/iota, q' = -iota'/iota², q'' = (2iota'²-iota·iota'')/iota³, etc. +_iota_inner = profiles.iota_spline +_d1_iota = deriv1(_iota_inner) +_d2_iota = deriv2(_iota_inner) +_d3_iota = deriv3(_iota_inner) +q_d0_edge = [1.0 / _iota_inner(p) for p in psi_junc] +q_d1_edge = map(psi_junc) do p + ι = _iota_inner(p); ι1 = _d1_iota(p) + -ι1 / ι^2 +end +q_d2_edge = map(psi_junc) do p + ι = _iota_inner(p); ι1 = _d1_iota(p); ι2 = _d2_iota(p) + (2*ι1^2 - ι*ι2) / ι^3 +end +q_d3_edge = map(psi_junc) do p + ι = _iota_inner(p); ι1 = _d1_iota(p); ι2 = _d2_iota(p); ι3 = _d3_iota(p) + (-6*ι1^3 + 6*ι*ι1*ι2 - ι^2*ι3) / ι^4 +end + +function make_deriv_panel(ylabel_str, title_str, dir_vals, edge_vals) + p = plot(; xlabel="ψₙ", ylabel=ylabel_str, title=title_str, legend=:topleft) + plot!(p, psi_junc, dir_vals; + label="Direct", lw=2, color=:orange, ls=:dash) + plot!(p, psi_junc, edge_vals; + label="Edge inverse", lw=2, color=:blue) + vline!(p, [psihigh]; label=@sprintf("psihigh=%.4f", psihigh), ls=:dash, color=:gray, lw=1) + return p +end + +p2a = make_deriv_panel("q", "q: direct vs edge inverse", q_d0_dir, q_d0_edge) +p2b = make_deriv_panel("dq/dψ", "q' (1st deriv): junction match", q_d1_dir, q_d1_edge) +p2c = make_deriv_panel("d²q/dψ²","q'' (2nd deriv): junction match", q_d2_dir, q_d2_edge) +p2d = make_deriv_panel("d³q/dψ³","q''' (3rd deriv): junction match", q_d3_dir, q_d3_edge) +p2 = plot(p2a, p2b, p2c, p2d; layout=(4,1), size=(900, 1100), bottom_margin=4Plots.mm) +savefig(p2, joinpath(output_dir, "edge_spline_q.png")) +println("Saved: edge_spline_q.png") + +# --- dV/dψ vs psin --- +dV_cap = 2.5 * dV_at_psihigh_direct +dV_direct_plot = min.(dV_direct, dV_cap) +dV_edge_plot = min.(dV_edge_vals, dV_cap) + +p3 = plot( + psi_plot_all, dV_direct_plot; + xlabel = "ψₙ", + ylabel = "dV/dψ", + title = "Volume gradient dV/dψ: direct vs edge inverse spline", + label = "Direct spline (ExtendExtrap beyond psihigh)", + lw = 2, color = :orange, ls = :dash, + ylims = (0.0, dV_cap * 1.05) +) +plot!(p3, collect(psi_plot_edge), dV_edge_plot; + label = "Edge inverse spline", lw = 2, color = :blue) +vline!(p3, [psihigh]; label = @sprintf("psihigh = %.3f", psihigh), ls = :dash, color = :gray) +savefig(p3, joinpath(output_dir, "edge_spline_dVdpsi.png")) +println("Saved: edge_spline_dVdpsi.png") + +# --- Helper: reconstruct (R, Z) from stored rzphi 2D splines --- +# rzphi_rsquared stores rfac² = (R-ro)² + (Z-zo)² +# rzphi_offset stores η/(2π) - θ, where η is the geometric poloidal angle +# R = ro + rfac * cos(η), Z = zo + rfac * sin(η) +function RZ_at(pe, psi, theta) + rsq = pe.rzphi_rsquared((psi, theta)) + offset = pe.rzphi_offset((psi, theta)) + rfac = sqrt(max(0.0, rsq)) + eta = 2π * (theta + offset) + R = pe.ro + rfac * cos(eta) + Z = pe.zo + rfac * sin(eta) + return R, Z +end + +# --- Plot 4: R(psin) and Z(psin) for several fixed theta values toward the edge --- +theta_vals = [0.0, 0.25, 0.5, 0.75] # outboard, top, inboard, bottom +theta_names = ["θ=0 (outboard)", "θ=0.25 (top)", "θ=0.5 (inboard)", "θ=0.75 (bottom)"] +psi_rz_plot = range(psi_core[1], psihigh, length=150) # only in valid spline domain + +p4a = plot(; xlabel="ψₙ", ylabel="R [m]", + title="Major radius R(ψₙ) for fixed poloidal angles", legend=:topright) +p4b = plot(; xlabel="ψₙ", ylabel="Z [m]", + title="Vertical position Z(ψₙ) for fixed poloidal angles", legend=:topright) + +for (theta, name) in zip(theta_vals, theta_names) + R_vals = [RZ_at(pe, psi, theta)[1] for psi in psi_rz_plot] + Z_vals = [RZ_at(pe, psi, theta)[2] for psi in psi_rz_plot] + plot!(p4a, collect(psi_rz_plot), R_vals; label=name, lw=2) + plot!(p4b, collect(psi_rz_plot), Z_vals; label=name, lw=2) +end +vline!(p4a, [psihigh]; label=@sprintf("psihigh=%.3f", psihigh), ls=:dash, color=:gray) +vline!(p4b, [psihigh]; label=@sprintf("psihigh=%.3f", psihigh), ls=:dash, color=:gray) + +p4 = plot(p4a, p4b; layout=(1, 2), size=(900, 400)) +savefig(p4, joinpath(output_dir, "edge_spline_RZ_vs_psin.png")) +println("Saved: edge_spline_RZ_vs_psin.png") + +# --- Plot 5: Flux surface cross-section with x-point --- +theta_fs = range(0.0, 1.0, length=200) # full poloidal circuit +psin_surfaces = [0.5, 0.7, 0.85, 0.93, 0.97, psihigh] # core → edge + +p5 = plot(; xlabel="R [m]", ylabel="Z [m]", + title="Flux surface cross-section", + aspect_ratio=:equal, legend=:topright) + +colors = cgrad(:blues, length(psin_surfaces); rev=false) +for (i, psin_val) in enumerate(psin_surfaces) + R_fs = [RZ_at(pe, psin_val, th)[1] for th in theta_fs] + Z_fs = [RZ_at(pe, psin_val, th)[2] for th in theta_fs] + lbl = @sprintf("ψₙ = %.3f%s", psin_val, psin_val == psihigh ? " (LCFS)" : "") + plot!(p5, R_fs, Z_fs; label=lbl, lw=1.5, color=colors[i]) +end + +# Mark magnetic axis and x-point +scatter!(p5, [pe.ro], [pe.zo]; label="Axis", marker=:cross, ms=8, color=:black) +scatter!(p5, [params.r_xpoint], [params.z_xpoint]; + label=@sprintf("X-point (R=%.3f, Z=%.3f)", params.r_xpoint, params.z_xpoint), + marker=:x, ms=10, color=:red, markerstrokewidth=2) + +savefig(p5, joinpath(output_dir, "edge_spline_cross_section.png")) +println("Saved: edge_spline_cross_section.png") + +# --- Plot 6: Rational surface density in edge zone --- +# edge_surfaces was computed and rzphi extended before psi_plot_edge was built (above). +# psilim_bench is overridden inside the h5open block (Plot 7) with q_es[end] from gpec.h5. +psilim_bench = isempty(edge_surfaces) ? psihigh : edge_surfaces[end] +qlim_bench = eval_q(profiles, psilim_bench) + +# Helper: psi → q using iota inverse above psihigh (available to all subsequent plots) +psi_to_q_outer = psi_arr -> map(psi -> eval_q(profiles, psi), psi_arr) + +p6 = plot( + collect(psi_plot_edge), q_edge_vals; + xlabel = "ψₙ", + ylabel = "q", + title = @sprintf("Rational surfaces in edge zone (n=%d)", nn), + label = "q(ψ) [edge inverse spline]", + lw = 2, color = :blue, + ylims = (q_at_psihigh_direct * 0.9, min(q_at_psihigh_direct * 4, maximum(q_edge_vals, init=q_at_psihigh_direct * 2.0))) +) +for (i, psi_s) in enumerate(edge_surfaces) + lbl = i == 1 ? "Edge rational surfaces" : "" + vline!(p6, [psi_s]; label = lbl, color = :red, alpha = 0.5, lw = 0.8) +end +vline!(p6, [psihigh]; label = @sprintf("psihigh = %.3f", psihigh), ls = :dash, color = :gray) +vline!(p6, [psilim_bench]; label = @sprintf("psilim = %.4f (q = %.1f)", psilim_bench, qlim_bench), + ls = :dashdot, color = :purple, lw = 1.5) +savefig(p6, joinpath(output_dir, "edge_spline_rational_surfaces.png")) +println("Saved: edge_spline_rational_surfaces.png") + +# --- Plot 7: edge stability scan — total, plasma, vacuum energy components vs q --- +# +# Top panel: et, ep, ev on a linear scale clipped to ±display_lim. The "physically reliable" +# window (where wp = U₂·U₁⁻¹ is well-conditioned) is narrow: only the first ~6 steps after +# psiedge, before the accumulated Gaussian reductions make U₁ ill-conditioned. Outside that +# window all three curves blow up (|et|, |ep| >> 1000) and are clipped by ylims. +# ev (vacuum, computed from the wv spline rather than U₁) stays bounded at ~O(1000) for most +# of the scan and is shown separately on the log-scale bottom panel to reveal its full range. +# +# Above psihigh: wv is frozen at psihigh (ExtendExtrap) and resonant spikes near +# rational surfaces (singfac → 0) are subsampled for rendering performance. +h5file = joinpath(example_dir, "gpec.h5") +if isfile(h5file) + h5open(h5file, "r") do f + if haskey(f, "edge_scan/psi") && haskey(f, "edge_scan/total_energy") + psi_es = read(f["edge_scan/psi"]) + et_es = read(f["edge_scan/total_energy"]) + et_real = real.(et_es) + + # Convert psi → q + hint_q7 = Ref(1) + q_es = map(psi -> eval_q(profiles, psi), psi_es) + + q_at_psihigh = profiles.q_spline(psihigh) + q_max_scan = maximum(q_es) + core_mask = psi_es .<= psihigh + above_mask = psi_es .> psihigh + + # Override qlim_bench with the actual scan endpoint from gpec.h5, so x-axis + # reflects the true integration upper bound (set by sing_find! for all n values), + # not the n=1-only independent scan used for the rational surface density plot. + qlim_bench = q_es[end] + + # Peak: ignore NaN steps (where U₁ was singular) + et_for_peak = replace(et_real, NaN => -Inf) + et_peak_idx = argmax(et_for_peak) + q_peak = q_es[et_peak_idx] + et_peak = et_real[et_peak_idx] + + n_valid = count(!isnan, et_real) + println(@sprintf(" Scan: q = %.3f → %.3f (ψ = %.4f → %.4f, %d/%d valid steps)", + q_es[1], q_max_scan, psi_es[1], psi_es[end], n_valid, length(psi_es))) + println(@sprintf(" Peak: q = %.3f, et = %+.3f", q_peak, et_peak)) + + # Load ep/ev/vacuum_eigenvalue if available + has_pv = haskey(f, "edge_scan/plasma_energy") && haskey(f, "edge_scan/vacuum_energy") + has_evonly = haskey(f, "edge_scan/vacuum_eigenvalue") + ep_real = has_pv ? real.(read(f["edge_scan/plasma_energy"])) : nothing + ev_real = has_pv ? real.(read(f["edge_scan/vacuum_energy"])) : nothing + evonly_real = has_evonly ? read(f["edge_scan/vacuum_eigenvalue"]) : nothing + + # --- Panel A: linear-scale clip showing valid window + full et range --- + # Clip at ±display_lim so the well-conditioned window is visible. + display_lim = 10.0 + # Subsample above-psihigh for rendering; separate filters for et vs ev; exclude NaN + valid_above_et = findall(above_mask .& .!isnan.(et_real) .& (abs.(et_real) .<= display_lim)) + stride_et = max(1, length(valid_above_et) ÷ 2000) + above_ss_et = valid_above_et[1:stride_et:end] + + pA = plot(; + xlabel = "q (safety factor)", + ylabel = "Energy (raw eigenvalue)", + title = @sprintf("Edge stability: energy components vs q [ψ = %.3f → %.3f]", + psi_es[1], psi_es[end]), + legend = :topright, + xlims = (4.0, qlim_bench * 1.02), + ylims = (-display_lim, max(3.0, et_peak * 1.2)), + size = (900, 400) + ) + # et: core (solid) + above-psihigh filtered (dashed) + plot!(pA, q_es[core_mask], et_real[core_mask]; + label = "Total et [ψ ≤ psihigh]", lw = 2, color = :black) + if !isempty(above_ss_et) + plot!(pA, q_es[above_ss_et], et_real[above_ss_et]; + label = @sprintf("Total et [ψ > psihigh, |et|≤%.0f]", display_lim), + lw = 1, color = :black, ls = :dash, alpha = 0.6) + end + if has_pv + plot!(pA, q_es[core_mask], ep_real[core_mask]; + label = "Plasma ep [ψ ≤ psihigh]", lw = 2, color = :blue) + plot!(pA, q_es[core_mask], ev_real[core_mask]; + label = "Vacuum ev [ψ ≤ psihigh]", lw = 2, color = :red) + valid_above_pv = findall(above_mask .& .!isnan.(ep_real) .& .!isnan.(ev_real) .& (abs.(ep_real) .<= display_lim) .& (abs.(ev_real) .<= display_lim)) + stride_pv = max(1, length(valid_above_pv) ÷ 2000) + above_ss_pv = valid_above_pv[1:stride_pv:end] + if !isempty(above_ss_pv) + plot!(pA, q_es[above_ss_pv], ep_real[above_ss_pv]; + label = "", lw = 1, color = :blue, ls = :dash, alpha = 0.5) + plot!(pA, q_es[above_ss_pv], ev_real[above_ss_pv]; + label = "", lw = 1, color = :red, ls = :dash, alpha = 0.5) + end + end + hline!(pA, [0.0]; label = "et = 0", ls = :dot, color = :gray, lw = 1.5) + vline!(pA, [q_at_psihigh]; label = @sprintf("psihigh: q = %.3f", q_at_psihigh), + ls = :dash, color = :gray) + hline!(pA, [1.707]; label = "develop ref: et = +1.707", + ls = :dash, color = :green, lw = 1.5) + scatter!(pA, [q_peak], [clamp(et_peak, -display_lim, display_lim)]; + label = @sprintf("peak (q=%.3f, et=%+.3f)", q_peak, et_peak), + marker = :star5, ms = 10, color = :red) + + # --- Panel B: vacuum_eigenvalue — min eigenvalue of wv alone (EL-independent wv quality check) --- + # Between rational surfaces singfac ≈ 1 so vacuum_eigenvalue ≈ O(1); + # at rational surfaces singfac → 0 so vacuum_eigenvalue → 0. + # Physically vacuum_eigenvalue >= 0; negative values are artifacts from beyond + # rzphi geometry (wv computed via ExtendExtrap). Filter to [0, clip_ev]. + pB = nothing + if has_evonly + clip_ev = 5.0 + in_range = map(x -> !isnan(x) && x >= 0.0 && x <= clip_ev, evonly_real) + n_clipped = count(!isnan, evonly_real) - count(in_range) + valid_ev2 = findall(in_range) + stride_all = max(1, length(valid_ev2) ÷ 4000) + ss_all = valid_ev2[1:stride_all:end] + ev_max = isempty(valid_ev2) ? 1.0 : maximum(evonly_real[valid_ev2]) + + pB = plot(; + xlabel = "q (safety factor)", + ylabel = "vacuum_eigenvalue (min eigval of wv)", + title = @sprintf("wv quality: vacuum_eigenvalue (EL-independent) [%d steps outside [0,%.0f]]", + n_clipped, clip_ev), + legend = :topright, + xlims = (minimum(q_es) * 0.98, qlim_bench * 1.02), + ylims = (0.0, ev_max * 1.15 + 0.01), + size = (900, 300) + ) + plot!(pB, q_es[ss_all], evonly_real[ss_all]; + label = "vacuum_eigenvalue (min eigval wv)", lw = 1, color = :purple, alpha = 0.8) + vline!(pB, [q_at_psihigh]; label = @sprintf("psihigh: q=%.3f", q_at_psihigh), + ls = :dash, color = :gray) + if in_range[et_peak_idx] + scatter!(pB, [q_peak], [evonly_real[et_peak_idx]]; + label = @sprintf("vacuum_eigenvalue at peak (%.4f)", evonly_real[et_peak_idx]), + marker = :star5, ms = 8, color = :purple) + end + end + + panels = filter(!isnothing, [pA, pB]) + p7 = length(panels) == 1 ? panels[1] : + plot(panels...; layout=(length(panels), 1), size=(900, 350 * length(panels))) + savefig(p7, joinpath(output_dir, "edge_spline_stability.png")) + println("Saved: edge_spline_stability.png") + else + println("Note: edge_scan/psi not found in gpec.h5 — run GPEC with psiedge < psilim first") + end + end +else + println("Note: gpec.h5 not found in $example_dir — run GPEC first to generate edge stability plot") +end + +# --- Plot 8: X-point asymptotic geometry — rfac(ψ) at selected θ values --- +# Shows how the rzphi spline extends into the far edge (psin > psihigh) via X-point scaling. +# rfac(ψ, θ) = √((R-Ro)² + (Z-Zo)²) should shrink toward zero as ψ → 1 (X-point approach). +if !isnothing(pe.params.r_xpoint) + psi_far_plot = range(psihigh - 0.005, pe.rzphi_xs[end]; length=300) + theta_plot_vals = [0.0, 0.25, 0.5, 0.75] + theta_plot_labels = ["θ=0.00 (outboard)", "θ=0.25 (top)", "θ=0.50 (inboard)", "θ=0.75 (bottom)"] + theta_plot_colors = [:blue, :orange, :green, :red] + + # rfac from the extended rzphi spline + rfac_vals = [sqrt(max(0.0, pe.rzphi_rsquared((psi, theta)))) for psi in psi_far_plot, theta in theta_plot_vals] + + # Expected X-point asymptotic limit: rfac at ψ → 1 should approach rfac_xpoint(θ) = 0 + # (the X-point is also at the magnetic axis distance from ro, zo) + r_x, z_x = pe.params.r_xpoint, pe.params.z_xpoint + rfac_xpoint = sqrt((r_x - pe.ro)^2 + (z_x - pe.zo)^2) + + p8 = plot(; xlabel="ψₙ", ylabel="rfac = √((R-R₀)² + (Z-Z₀)²) [m]", + title="X-point asymptotic geometry: rfac(ψ) in far edge", + legend=:topleft) + for (k, (theta, lbl)) in enumerate(zip(theta_plot_vals, theta_plot_labels)) + plot!(p8, collect(psi_far_plot), rfac_vals[:, k]; label=lbl, lw=2, color=theta_plot_colors[k]) + end + hline!(p8, [rfac_xpoint]; label=@sprintf("rfac at X-point = %.4f m", rfac_xpoint), ls=:dot, color=:black, lw=1.5) + vline!(p8, [psihigh]; label=@sprintf("psihigh=%.3f", psihigh), ls=:dash, color=:gray) + + savefig(p8, joinpath(output_dir, "edge_spline_geometry.png")) + println("Saved: edge_spline_geometry.png") +else + println("Note: X-point not detected (limited plasma) — skipping Plot 8") +end + +# Extend the rzphi spline into the far-edge zone so the GSE diagnostic can evaluate +# GS residuals beyond psihigh. Normally this extension is triggered by ForceFreeStates +# after sing_find!, but the benchmark only calls setup_equilibrium. +if !isnothing(profiles.iota_spline) && !isempty(edge_surfaces) + GeneralizedPerturbedEquilibrium.Equilibrium.equilibrium_extend_rzphi!(pe, edge_surfaces) +end + +# --- Plots 9 and 10: GS residual diagnostics --- +# Re-run equilibrium_gse! with diagnose_src=true to write gsei.h5 and gsec.h5, +# then read and plot the θ-integrated GS error per flux surface. +println("Running GSE diagnostics (diagnose_src=true)...") +pe.params.diagnose_src = true +GeneralizedPerturbedEquilibrium.Equilibrium.equilibrium_gse!(pe) +pe.params.diagnose_src = false + +# --- Compute far-edge GSE using X-point asymptotic geometry with constant F --- +# With F ≈ const (dF/dψ ≈ 0) and P' ≈ 0 near the separatrix, the GS source term is ≈ 0. +# The far-edge rzphi splines now use X-point asymptotic geometry (shrinking toward X-point), +# which is GS-consistent in the Δ*ψ = 0 limit. This diagnostic confirms the improvement. +# Evaluated at both spline NODES and inter-node MIDPOINTS to check cubic spline quality. +far_edge_gse_available = false +psi_far_eval = Float64[] +is_node_far = Bool[] +gse_far_per_theta_mat = Matrix{Float64}(undef, 0, 4) +gse_far_int = Float64[] +theta_labels_gse = ["θ=0.00 (outboard)", "θ=0.25 (top)", "θ=0.50 (inboard)", "θ=0.75 (bottom)"] +theta_colors_gse = [:blue, :orange, :green, :red] + +if !isnothing(pe.params.r_xpoint) + theta_all = pe.rzphi_ys + psio_gse = pe.psio + mtheta_bc = length(theta_all) - 1 + dtheta_bc = (theta_all[end] - theta_all[1]) / mtheta_bc + theta_fracs_gse = [0.0, 0.25, 0.5, 0.75] + theta_idxs_gse = [max(1, round(Int, th * (length(theta_all)-1) + 1)) for th in theta_fracs_gse] + + # Far-edge psi grid: the extended rzphi spline covers [psilow, rzphi_xs[end]]. + # Use the far-edge portion (above psihigh) of the extended spline grid. + psi_far_nodes = filter(psi -> psi > psihigh, pe.rzphi_xs) + + # Interleave midpoints with nodes + for i in eachindex(psi_far_nodes) + push!(psi_far_eval, psi_far_nodes[i]) + push!(is_node_far, true) + if i < lastindex(psi_far_nodes) + push!(psi_far_eval, (psi_far_nodes[i] + psi_far_nodes[i+1]) / 2) + push!(is_node_far, false) + end + end + + gse_far_per_theta_mat = zeros(Float64, length(psi_far_eval), 4) + gse_far_int = zeros(Float64, length(psi_far_eval)) + + for (ipsi, psi) in enumerate(psi_far_eval) + # F and P from the profiles (F is constant via ExtendExtrap above psihigh; F'≈0, P'≈0) + F_val = profiles.F_spline(psi) + dF_dpsi = profiles.F_deriv(psi) + dP_dpsi = profiles.P_deriv(psi) + + source_theta = zeros(Float64, length(theta_all)) + for (itheta, theta) in enumerate(theta_all) + f4 = pe.rzphi_jac((psi, theta)) # J_coord from extended spline + R, _ = RZ_at(pe, psi, theta) # R from extended spline + source_theta[itheta] = f4 / (2π * psio_gse * π^2) * + (F_val * dF_dpsi / (2π * R)^2 + dP_dpsi) + end + + for (k, itheta) in enumerate(theta_idxs_gse) + gse_far_per_theta_mat[ipsi, k] = abs(source_theta[itheta]) + end + + gse_far_int[ipsi] = abs(sum(source_theta[1:mtheta_bc]) * dtheta_bc) + end + + if !isempty(gse_far_int) + max_far_gse = maximum(gse_far_int) + println(@sprintf(" Far-edge GSE (X-point asymptotic): max θ-integrated |source| = %.2e", max_far_gse)) + far_edge_gse_available = true + end +end + +gsec_file = joinpath(example_dir, "gsec.h5") +gsei_file = joinpath(example_dir, "gsei.h5") + +if isfile(gsec_file) && isfile(gsei_file) + # --- Plot 9: GS residual by poloidal angle from gsec.h5 --- + h5open(gsec_file, "r") do f + flux_fsx_data = read(f["flux_fsx"]) # gs_div_dpsi[:,:,1] + source_data = read(f["source"]) + + mt_gse = size(flux_fsx_data, 2) + theta_fracs = [0.0, 0.25, 0.5, 0.75] + theta_labels = ["θ=0.00 (outboard)", "θ=0.25 (top)", "θ=0.50 (inboard)", "θ=0.75 (bottom)"] + theta_idxs = [max(1, round(Int, th * (mt_gse-1) + 1)) for th in theta_fracs] + # Use core profile grid (not the extended rzphi_xs which includes far-edge nodes) + psi_gse_vals = profiles.xs + q_gse_vals = psi_to_q_outer(psi_gse_vals) + + # Build residual curves once for reuse in both panels + res_curves = [(abs.(flux_fsx_data[:, idx] .+ source_data[:, idx]), lbl, theta_colors_gse[k]) + for (k, (idx, lbl)) in enumerate(zip(theta_idxs, theta_labels))] + + function make_p9_panel(xvals_core, xfar, xlabel_str, vline_val; xlims_val=nothing) + p = plot(; xlabel=xlabel_str, ylabel="|GS residual (per θ)|", + title="GS residual by poloidal angle (core + far edge)", yscale=:log10, legend=:topleft) + for (res_col, lbl, col) in res_curves + plot!(p, xvals_core, max.(res_col, 1e-15); label=lbl, lw=1.5, color=col) + end + if far_edge_gse_available + for (k, _) in enumerate(theta_labels_gse) + far_lbl = k == 1 ? "far edge, X-point geometry (dashed)" : "" + plot!(p, xfar, max.(gse_far_per_theta_mat[:, k], 1e-15); + label=far_lbl, lw=1.5, ls=:dash, color=theta_colors_gse[k], alpha=0.8) + end + end + hline!(p, [1e-2]; label="warning threshold", ls=:dot, color=:black, lw=1.5) + vline!(p, [vline_val]; label=@sprintf("psihigh: %s=%.3f", xlabel_str, vline_val), + ls=:dash, color=:gray) + if !isnothing(xlims_val) + xlims!(p, xlims_val) + vline!(p, [qlim_bench]; label=@sprintf("psilim: q=%.1f", qlim_bench), + ls=:dashdot, color=:purple, lw=1.5) + end + return p + end + + q_far_eval = far_edge_gse_available ? psi_to_q_outer(psi_far_eval) : Float64[] + p9a = make_p9_panel(psi_gse_vals, psi_far_eval, "ψₙ", psihigh) + p9b = make_p9_panel(q_gse_vals, q_far_eval, "q", q_at_psihigh_direct; + xlims_val=(q_at_psihigh_direct * 0.9, qlim_bench * 1.05)) + p9 = plot(p9a, p9b; layout=(1,2), size=(1400, 500), bottom_margin=8Plots.mm) + savefig(p9, joinpath(output_dir, "edge_spline_gse_by_theta.png")) + println("Saved: edge_spline_gse_by_theta.png") + end + + # --- Plot 10: θ-integrated GS error from gsei.h5 --- + h5open(gsei_file, "r") do f + errori_data = read(f["errori"]) # gse_abs_error (θ-integrated) + xs_gse = read(f["xs"]) + + errori_vec = vec(errori_data) + max_err = maximum(errori_vec) + if max_err > 1e-2 + @warn @sprintf("GS residual exceeds threshold: max |gse_integrated| = %.2e at psin=%.4f", + max_err, xs_gse[argmax(errori_vec)]) + else + println(@sprintf(" GS residual OK: max |gse_integrated| = %.2e", max_err)) + end + q_xs_gse = psi_to_q_outer(xs_gse) + + function make_p10_panel(xvals_core, xfar, xlabel_str, vline_val; xlims_val=nothing) + leg_pos = isnothing(xlims_val) ? :topleft : :bottomright + p = plot(xvals_core, max.(errori_vec, 1e-15); + xlabel=xlabel_str, ylabel="|θ-integrated GS residual|", + title="θ-integrated GS error: core + far-edge X-point geometry", + label="core |gse_integrated|", lw=2, color=:blue, + yscale=:log10, legend=leg_pos) + if far_edge_gse_available + node_mask_far = is_node_far + mid_mask_far = .!is_node_far + scatter!(p, xfar[node_mask_far], max.(gse_far_int[node_mask_far], 1e-15); + label="far edge nodes (spline knots)", marker=:circle, ms=5, + color=:red, markerstrokewidth=0) + scatter!(p, xfar[mid_mask_far], max.(gse_far_int[mid_mask_far], 1e-15); + label="far edge midpoints (interpolated)", marker=:diamond, ms=4, + color=:orange, alpha=0.8, markerstrokewidth=0) + end + hline!(p, [1e-2]; label="warning threshold (1e-2)", ls=:dot, color=:black, lw=1.5) + vline!(p, [vline_val]; label=@sprintf("psihigh: %s=%.3f", xlabel_str, vline_val), + ls=:dash, color=:gray) + if !isnothing(xlims_val) + xlims!(p, xlims_val) + vline!(p, [qlim_bench]; label=@sprintf("psilim: q=%.1f", qlim_bench), + ls=:dashdot, color=:purple, lw=1.5) + end + return p + end + + q_far_eval = far_edge_gse_available ? psi_to_q_outer(psi_far_eval) : Float64[] + p10a = make_p10_panel(xs_gse, psi_far_eval, "ψₙ", psihigh) + p10b = make_p10_panel(q_xs_gse, q_far_eval, "q", q_at_psihigh_direct; + xlims_val=(q_at_psihigh_direct * 0.9, qlim_bench * 1.05)) + p10 = plot(p10a, p10b; layout=(1,2), size=(1400, 500), bottom_margin=8Plots.mm) + savefig(p10, joinpath(output_dir, "edge_spline_gse_integrated.png")) + println("Saved: edge_spline_gse_integrated.png") + end +else + println("Note: GSE HDF5 files not found — skipping Plots 9 and 10") +end + +# --- Plot 11: Far-edge q profile — EFIT direct vs iota inverse spline --- +# The X-point geometry approach uses the iota inverse spline for q in the far edge (via +# iota_spline), while F is held constant (ExtendExtrap). This plot shows how +# q from the two sources compares across the edge region. +if !isnothing(profiles.iota_spline) + println("Computing far-edge q profile comparison...") + + psi_edge_gse = vcat( + collect(range(psihigh - 0.005, psihigh, length=20)), + collect(range(psihigh, pe.rzphi_xs[end]; length=280)) + ) + unique!(sort!(psi_edge_gse)) + + # q from direct spline (constant ExtendExtrap beyond psihigh) + q_direct_edge = profiles.q_spline.(psi_edge_gse) + + # q from iota inverse spline (correct q behavior toward separatrix) + above_mask_gse = psi_edge_gse .>= psihigh + q_iota_edge = map(psi -> eval_q(profiles, psi), psi_edge_gse) + + # Panel A: q_direct vs q_iota in the far edge + p11a = plot(psi_edge_gse, q_direct_edge; + xlabel="ψₙ", ylabel="q", + title="Far-edge q: EFIT ExtendExtrap vs iota inverse", + label="q_direct (EFIT, ExtendExtrap beyond psihigh)", lw=2, color=:orange, ls=:dash, + legend=:topleft, ylims=(0.0, qlim_bench)) + plot!(p11a, psi_edge_gse[above_mask_gse], q_iota_edge[above_mask_gse]; + label="q = 1/ι(ψ) [iota inverse spline, used in ODE]", lw=2, color=:blue) + vline!(p11a, [psihigh]; label=@sprintf("psihigh=%.4f", psihigh), ls=:dash, color=:gray) + + # Panel B: F(ψ) in the far edge (should be approximately constant) + F_edge = profiles.F_spline.(psi_edge_gse) + dF_edge = profiles.F_deriv.(psi_edge_gse) + p11b = plot(psi_edge_gse, F_edge; + xlabel="ψₙ", ylabel="F = 2π·R·Bₜ", + title="F(ψ) in far edge (constant via ExtendExtrap → F'≈0 → GS source ≈ 0)", + label="F_spline", lw=2, color=:blue, legend=:topleft) + vline!(p11b, [psihigh]; label=@sprintf("psihigh=%.4f", psihigh), ls=:dash, color=:gray) + + # Panel C: dF/dψ (should be near zero above psihigh confirming GS source ≈ 0) + p11c = plot(psi_edge_gse, abs.(dF_edge); + xlabel="ψₙ", ylabel="|dF/dψ|", + title="|dF/dψ| in far edge (proxy for GS source = F·F'/R²)", + label="|dF/dψ|", lw=2, color=:red, yscale=:log10, legend=:topleft) + vline!(p11c, [psihigh]; label=@sprintf("psihigh=%.4f", psihigh), ls=:dash, color=:gray) + + p11 = plot(p11a, p11b, p11c; layout=(3,1), size=(800, 900)) + savefig(p11, joinpath(output_dir, "edge_spline_profiles.png")) + println("Saved: edge_spline_profiles.png") +else + println("Note: iota inverse spline not available (limited plasma) — skipping Plot 11") +end + +# --- Final summary --- +println() +println("="^70) +println("Summary") +println("="^70) +println(@sprintf(" X-point location: R = %.4f m, Z = %.4f m", + params.r_xpoint, params.z_xpoint)) +println(@sprintf(" psihigh = %.4f, qa = %s", + psihigh, isinf(params.qa) ? "Inf (diverted, separatrix)" : @sprintf("%.4f", params.qa))) +println(@sprintf(" q(psihigh) = %.4f, iota(psihigh) = %.6f", + q_at_psihigh_direct, iota_inner(psihigh))) +println(@sprintf(" iota anchor at psin=1: iota(1.0) = %.2e (target: ~0)", + iota_inner(1.0))) +println(@sprintf(" q match at psihigh: |q_direct - q_edge| = %.2e", + abs(q_at_psihigh_direct - q_at_psihigh_edge))) +println(@sprintf(" dV/dψ match at psihigh: |dV_direct - dV_edge| = %.2e", + abs(dV_at_psihigh_direct - dV_at_psihigh_edge))) +println() +println("Plots saved to: $output_dir") diff --git a/benchmarks/benchmark_parameter_scan.jl b/benchmarks/benchmark_parameter_scan.jl new file mode 100644 index 00000000..121b8924 --- /dev/null +++ b/benchmarks/benchmark_parameter_scan.jl @@ -0,0 +1,309 @@ +#!/usr/bin/env julia +""" +benchmark_parameter_scan.jl — General GPEC parameter scan and eigenmode comparison tool + +Runs GPEC multiple times with a single TOML parameter swept over a list of values, +then produces overplot comparisons of eigenmode radial profiles, poloidal spectra, +and edge stability scans. Designed to be general: any scalar TOML parameter can be +swept, e.g. `edge_layer_width`, EL tolerance, or vacuum grid resolution. + +# Usage + +```bash +# Sweep edge_layer_width over three values +julia --project=. benchmarks/benchmark_parameter_scan.jl \\ + --example examples/DIIID-like_ideal_example \\ + --param ForceFreeStates.edge_layer_width \\ + --values "1e-4,1e-3,5e-3" + +# Use custom labels +julia --project=. benchmarks/benchmark_parameter_scan.jl \\ + --example examples/DIIID-like_ideal_example \\ + --param ForceFreeStates.edge_layer_width \\ + --values "1e-4,1e-3,5e-3" \\ + --labels "tight,medium,wide" + +# Skip re-running GPEC (plot from existing output directories) +julia --project=. benchmarks/benchmark_parameter_scan.jl \\ + --no-run \\ + --output-dir /tmp/my_scan \\ + --param ForceFreeStates.edge_layer_width \\ + --values "1e-4,1e-3,5e-3" +``` + +# Options + +- `--example PATH` Path to example directory containing `gpec.toml` (required unless --no-run) +- `--param KEY` Dot-path TOML key to sweep, e.g. `ForceFreeStates.edge_layer_width` +- `--values LIST` Comma-separated numeric values to test +- `--labels LIST` Comma-separated legend labels (default: param=value) +- `--output-dir PATH` Directory for per-run subdirectories (default: /scan_) +- `--no-run` Skip GPEC runs; read existing gpec.h5 files from output-dir subdirectories +- `--modes LIST` Comma-separated m values for radial profile plot (default: 1,2,3,4,5) + +# Output + +All plots are written to `/plots/`: + - `edge_scan_comparison.png` — et vs q overplot (numerical stability check) + - `mode_profiles.png` — ξ_m(ψ) radial profiles for requested m values + - `poloidal_spectrum.png` — |ξ(m)| at truncation point + - `summary.txt` — Table of et[1], psilim, qlim per run +""" + +using Pkg +Pkg.activate(joinpath(@__DIR__, "..")) + +using GeneralizedPerturbedEquilibrium +using GeneralizedPerturbedEquilibrium: Analysis +using HDF5 +using TOML +using Plots +using Printf + +project_root = joinpath(@__DIR__, "..") + +# --------------------------------------------------------------------------- +# Argument parsing +# --------------------------------------------------------------------------- + +function parse_scan_args(raw_args) + opts = Dict{String,Any}( + "example" => nothing, + "param" => nothing, + "values" => nothing, + "labels" => nothing, + "output-dir" => nothing, + "no-run" => false, + "modes" => "1,2,3,4,5", + ) + i = 1 + while i <= length(raw_args) + arg = raw_args[i] + if arg == "--no-run" + opts["no-run"] = true + elseif startswith(arg, "--") && i < length(raw_args) + opts[arg[3:end]] = raw_args[i+1] + i += 1 + end + i += 1 + end + return opts +end + +opts = parse_scan_args(ARGS) + +param_key = opts["param"] +values_str = opts["values"] +labels_opt = opts["labels"] +no_run = opts["no-run"] +modes_str = opts["modes"] + +isnothing(param_key) && error("--param is required") +isnothing(values_str) && error("--values is required") + +# Parse values (floats) +param_values = parse.(Float64, strip.(split(values_str, ","))) +nvals = length(param_values) + +# Labels default to "param=value" +param_short = split(param_key, ".")[end] # e.g. "edge_layer_width" +labels = isnothing(labels_opt) ? + ["$param_short=$(v)" for v in param_values] : + strip.(split(labels_opt, ",")) +length(labels) == nvals || error("--labels count ($(length(labels))) must match --values count ($nvals)") + +# Modes for radial profile plot +modes_vec = parse.(Int, strip.(split(modes_str, ","))) + +println("="^70) +println("GPEC Parameter Scan") +println("="^70) +println(" Parameter: $param_key") +println(" Values: $(join(param_values, ", "))") +println(" Labels: $(join(labels, ", "))") +println() + +# --------------------------------------------------------------------------- +# Output directory setup +# --------------------------------------------------------------------------- + +if no_run + isnothing(opts["output-dir"]) && error("--output-dir is required with --no-run") + scan_dir = abspath(opts["output-dir"]) +else + example_dir = abspath(opts["example"]) + isdir(example_dir) || error("Example directory not found: $example_dir") + param_slug = replace(param_short, r"[^a-zA-Z0-9_]" => "_") + scan_dir = isnothing(opts["output-dir"]) ? + joinpath(@__DIR__, "scan_$(param_slug)") : + abspath(opts["output-dir"]) +end + +plots_dir = joinpath(scan_dir, "plots") +mkpath(plots_dir) + +# --------------------------------------------------------------------------- +# TOML patching helpers +# --------------------------------------------------------------------------- + +""" +Patch a nested TOML dict at a dot-separated key path, e.g. "ForceFreeStates.edge_layer_width". +Returns a deep-copied dict with the leaf value set. +""" +function patch_toml(base::Dict, param_path::String, value) + patched = deepcopy(base) + parts = split(param_path, ".") + node = patched + for part in parts[1:end-1] + node = node[part] + end + node[parts[end]] = value + return patched +end + +# --------------------------------------------------------------------------- +# Per-value run loop +# --------------------------------------------------------------------------- + +run_dirs = String[] +h5paths = String[] +runtimes = Float64[] + +if !no_run + base_toml_path = joinpath(example_dir, "gpec.toml") + isfile(base_toml_path) || error("gpec.toml not found in $example_dir") + base_toml = TOML.parsefile(base_toml_path) + + # Files to copy from example dir (everything except .toml and existing .h5/.png) + copy_exts = [".geqdsk", ".dat", ".gfile", ".jl", ".txt", ".h5"] + files_to_copy = filter(readdir(example_dir)) do f + any(endswith(f, ext) for ext in copy_exts) && f != "gpec.h5" + end + + tmpscript = tempname() * ".jl" + write(tmpscript, """ + using Pkg; Pkg.instantiate() + using GeneralizedPerturbedEquilibrium + GeneralizedPerturbedEquilibrium.main([ARGS[1]]) + """) + + for (i, (val, lbl)) in enumerate(zip(param_values, labels)) + run_dir = joinpath(scan_dir, "run_$(i)") + mkpath(run_dir) + push!(run_dirs, run_dir) + + # Copy support files + for f in files_to_copy + cp(joinpath(example_dir, f), joinpath(run_dir, f); force=true) + end + + # Write patched toml + patched = patch_toml(base_toml, param_key, val) + open(joinpath(run_dir, "gpec.toml"), "w") do io + TOML.print(io, patched) + end + + h5path = joinpath(run_dir, "gpec.h5") + push!(h5paths, h5path) + + println("Run $i/$nvals: $lbl") + println(" Directory: $run_dir") + + t0 = time() + try + run(`julia --project=$project_root $tmpscript $run_dir`) + catch e + @warn "Run $i failed: $e" + push!(runtimes, NaN) + continue + end + push!(runtimes, time() - t0) + println(@sprintf(" Runtime: %.1f s", runtimes[end])) + println() + end + rm(tmpscript; force=true) +else + # Collect existing run directories and h5 files + for i in 1:nvals + run_dir = joinpath(scan_dir, "run_$(i)") + push!(run_dirs, run_dir) + push!(h5paths, joinpath(run_dir, "gpec.h5")) + push!(runtimes, NaN) + end +end + +# Filter to successful runs (h5 file exists) +valid = isfile.(h5paths) +if !all(valid) + @warn "Missing gpec.h5 for runs: $(findall(.!valid))" +end +h5paths_ok = h5paths[valid] +labels_ok = labels[valid] + +isempty(h5paths_ok) && error("No successful runs to plot.") + +# --------------------------------------------------------------------------- +# Summary table +# --------------------------------------------------------------------------- + +println("="^70) +println("Summary") +println("="^70) +@printf(" %-30s %10s %10s %10s %8s\n", "Label", "et[1]", "psilim", "qlim", "time(s)") +println(" " * "-"^72) + +summary_lines = String[] +for (i, (h5path, lbl)) in enumerate(zip(h5paths, labels)) + if !isfile(h5path) + @printf(" %-30s %10s\n", lbl, "FAILED") + continue + end + et1, psilim, qlim = h5open(h5path, "r") do f + real(read(f["vacuum/et"])[1]), + read(f["info/psilim"]), + read(f["info/qlim"]) + end + rt = isnan(runtimes[i]) ? " -" : @sprintf("%.1f", runtimes[i]) + line = @sprintf(" %-30s %10.4f %10.6f %10.4f %8s", lbl, et1, psilim, qlim, rt) + println(line) + push!(summary_lines, line) +end +println() + +open(joinpath(plots_dir, "summary.txt"), "w") do io + println(io, "GPEC Parameter Scan: $param_key") + println(io, "Values: $(join(param_values, ", "))") + println(io) + for l in summary_lines; println(io, l); end +end + +# --------------------------------------------------------------------------- +# Plots +# --------------------------------------------------------------------------- + +println("Generating plots → $plots_dir") + +# Plot 1: Edge stability scan — total energy vs q +p1 = Analysis.ForceFreeStates.plot_edge_scan_comparison( + h5paths_ok, labels_ok; + save_path = joinpath(plots_dir, "edge_scan_comparison.png") +) +println(" Saved: edge_scan_comparison.png") + +# Plot 2: Radial profiles of individual ξ_m modes +p2 = Analysis.ForceFreeStates.plot_mode_radial_profiles_comparison( + h5paths_ok, labels_ok; + modes = modes_vec, + save_path = joinpath(plots_dir, "mode_profiles.png") +) +println(" Saved: mode_profiles.png") + +# Plot 3: Poloidal spectrum |ξ(m)| at truncation point +p3 = Analysis.ForceFreeStates.plot_poloidal_spectrum_at_truncation( + h5paths_ok, labels_ok; + save_path = joinpath(plots_dir, "poloidal_spectrum.png") +) +println(" Saved: poloidal_spectrum.png") + +println() +println("All plots saved to: $plots_dir") diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml index 982f6817..a90a4d88 100644 --- a/examples/DIIID-like_ideal_example/gpec.toml +++ b/examples/DIIID-like_ideal_example/gpec.toml @@ -7,8 +7,8 @@ power_b = 0 # Toroidal field power exponent for Jaco power_r = 0 # Major radius power exponent for Jacobian grid_type = "ldp" # Radial grid packing type psilow = 1e-4 # Lower limit of normalized flux coordinate -psihigh = 0.993 # Upper limit of normalized flux coordinate -mpsi = 128 # Number of radial grid points +psihigh = 0.999 # Upper limit of normalized flux coordinate +mpsi = 256 # Number of radial grid points mtheta = 256 # Number of poloidal grid points newq0 = 0 # Override for on-axis safety factor (0 = use input value) etol = 1e-7 # Error tolerance for equilibrium solver @@ -31,9 +31,8 @@ ode_flag = true # Integrate ODE's for determining stability of inte vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes mer_flag = true # Evaluate the Mercier criterian -set_psilim_via_dmlim = true # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See set_psilim_via_dmlim -psiedge = 1.00 # If less then psilim, calculates dW(psi)... +edge_layer_width = 1e-4 # psifac spacing below which edge rational surfaces are ignored (diverted only) +psiedge = 0.970 # If less than psilim, scans dW(psi) from psiedge to psilim and truncates at peak qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml index 0065fde8..4c76cf4e 100644 --- a/examples/Solovev_ideal_example/gpec.toml +++ b/examples/Solovev_ideal_example/gpec.toml @@ -43,8 +43,6 @@ ode_flag = true # Integrate ODE's for determining stability of int vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes mer_flag = true # Evaluate the Mercier criterian -set_psilim_via_dmlim = false # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See sas_flag qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml index ed00cf3d..2f112979 100644 --- a/examples/Solovev_ideal_example_multi_n/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/gpec.toml @@ -31,8 +31,6 @@ ode_flag = true # Integrate ODE's for determining stability of int vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes mer_flag = true # Evaluate the Mercier criterian -set_psilim_via_dmlim = false # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See sas_flag qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml index 03542291..5e178a88 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml @@ -31,8 +31,6 @@ ode_flag = true # Integrate ODE's for determining stability of int vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes mer_flag = true # Evaluate the Mercier criterian -set_psilim_via_dmlim = false # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See sas_flag qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml index 2d8609e2..3e9a86e1 100644 --- a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml +++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml @@ -31,8 +31,6 @@ ode_flag = true # Integrate ODE's for determining stability of int vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes mer_flag = true # Evaluate the Mercier criterian -set_psilim_via_dmlim = false # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See sas_flag qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl index 1fde1639..97bff772 100644 --- a/src/Analysis/ForceFreeStates.jl +++ b/src/Analysis/ForceFreeStates.jl @@ -156,4 +156,183 @@ function plot_stability_criterion(h5path; save_path=nothing) return p end +""" + plot_edge_scan_comparison(h5paths, labels; q_range=nothing, et_range=nothing, save_path=nothing) + +Overplot the edge dW stability scan (total energy vs q) from multiple GPEC runs. + +Each run's `edge_scan/psi` is converted to q via the stored `integration/psi` + `integration/q` +arrays (linear interpolation — no runtime spline objects required). The truncation point `info/qlim` +is marked for each run with a vertical dashed line. + +### Arguments + + - `h5paths`: Vector of paths to GPEC HDF5 output files + - `labels`: Vector of legend labels, one per file + +### Keyword arguments + + - `q_range`: Optional `(qmin, qmax)` tuple to restrict the x-axis + - `et_range`: Optional `(etmin, etmax)` tuple for y-axis (default: `(-10, 10)`) + - `save_path`: If provided, save the figure to this path + +### Returns + +A `Plots.jl` plot object. +""" +function plot_edge_scan_comparison(h5paths::Vector{<:AbstractString}, labels::Vector{<:AbstractString}; + q_range=nothing, et_range=nothing, save_path=nothing) + colors = palette(:tab10) + + p = plot(; + xlabel = "q (safety factor)", + ylabel = "Total energy (et[1])", + title = "Edge stability scan comparison", + legend = :topright, + ) + hline!(p, [0.0]; color=:black, lw=1, ls=:dot, label="") + + for (i, (h5path, label)) in enumerate(zip(h5paths, labels)) + col = colors[mod1(i, length(colors))] + + psi_scan, et_scan, psi_int, q_int, qlim = h5open(h5path, "r") do f + read(f["edge_scan/psi"]), + real.(read(f["edge_scan/total_energy"])), + read(f["integration/psi"]), + read(f["integration/q"]), + read(f["info/qlim"]) + end + + # Convert scan psi → q via linear interpolation on integration grid + q_scan = map(psi_scan) do psi + idx = searchsortedfirst(psi_int, psi) + idx = clamp(idx, 2, length(psi_int)) + t = (psi - psi_int[idx-1]) / (psi_int[idx] - psi_int[idx-1]) + q_int[idx-1] * (1-t) + q_int[idx] * t + end + + et_lim = isnothing(et_range) ? (-10.0, 10.0) : et_range + + # Filter NaN and out-of-range points so outliers don't compress the y-axis + valid = .!isnan.(et_scan) .& (et_scan .>= et_lim[1]) .& (et_scan .<= et_lim[2]) + plot!(p, q_scan[valid], et_scan[valid]; label=label, color=col, lw=1.5) + vline!(p, [qlim]; label="", color=col, lw=1, ls=:dash, alpha=0.6) + end + + isnothing(q_range) || xlims!(p, q_range) + ylims!(p, isnothing(et_range) ? (-10.0, 10.0) : et_range) + isnothing(save_path) || savefig(p, save_path) + return p +end + +""" + plot_mode_radial_profiles_comparison(h5paths, labels; modes=1:5, component=imag, save_path=nothing) + +Overplot radial profiles of individual poloidal modes ξ_m(ψ) from multiple GPEC runs. +One panel per requested m value; all parameter values overplotted on each panel. + +### Arguments + + - `h5paths`: Vector of paths to GPEC HDF5 output files + - `labels`: Vector of legend labels, one per file + +### Keyword arguments + + - `modes`: Iterable of m values to plot (default: `1:5`) + - `component`: Function to extract the scalar from complex ξ (default: `imag`) + - `save_path`: If provided, save the figure to this path + +### Returns + +A `Plots.jl` plot object. +""" +function plot_mode_radial_profiles_comparison(h5paths::Vector{<:AbstractString}, labels::Vector{<:AbstractString}; + modes=1:5, component::Function=imag, save_path=nothing) + colors = palette(:tab10) + modes_vec = collect(modes) + npanels = length(modes_vec) + + panels = [plot(; xlabel="ψ_N", ylabel="$(component)(ξ_ψ)", + title="m = $(m)", legend=(j == 1 ? :topright : false)) + for (j, m) in enumerate(modes_vec)] + + for (i, (h5path, label)) in enumerate(zip(h5paths, labels)) + col = colors[mod1(i, length(colors))] + + mlow, xi_psi, psi = h5open(h5path, "r") do f + read(f["info/mlow"]), read(f["integration/xi_psi"]), read(f["integration/psi"]) + end + mpert = size(xi_psi, 1) + mhigh = mlow + mpert - 1 + + for (j, m) in enumerate(modes_vec) + mlow <= m <= mhigh || continue + profile = component.(xi_psi[m - mlow + 1, 1, :]) + plot!(panels[j], psi, profile; label=(j == 1 ? label : ""), color=col, lw=1.5) + end + end + + p = plot(panels...; layout=(npanels, 1), size=(900, 280 * npanels), bottom_margin=4Plots.mm) + isnothing(save_path) || savefig(p, save_path) + return p +end + +""" + plot_poloidal_spectrum_at_truncation(h5paths, labels; component=abs, normalize=true, save_path=nothing) + +Overplot the poloidal mode spectrum ξ(m) at the edge truncation point from multiple GPEC runs. +The truncation point is the last stored integration step (`info/psilim`), whose ξ_ψ reflects +the eigenmode structure at the integration boundary. + +### Arguments + + - `h5paths`: Vector of paths to GPEC HDF5 output files + - `labels`: Vector of legend labels, one per file + +### Keyword arguments + + - `component`: Function to extract the scalar from complex ξ (default: `abs`) + - `normalize`: If `true`, divide each spectrum by its maximum before plotting (default: `true`) + - `save_path`: If provided, save the figure to this path + +### Returns + +A `Plots.jl` plot object. +""" +function plot_poloidal_spectrum_at_truncation(h5paths::Vector{<:AbstractString}, labels::Vector{<:AbstractString}; + component::Function=abs, normalize::Bool=true, save_path=nothing) + colors = palette(:tab10) + + ylabel_str = normalize ? "$(component)(ξ_ψ) / max" : "$(component)(ξ_ψ)" + p = plot(; + xlabel = "m (poloidal mode number)", + ylabel = ylabel_str, + title = "Poloidal spectrum at truncation point", + legend = :topright, + ) + + for (i, (h5path, label)) in enumerate(zip(h5paths, labels)) + col = colors[mod1(i, length(colors))] + + mlow, xi_psi, qlim = h5open(h5path, "r") do f + read(f["info/mlow"]), read(f["integration/xi_psi"]), read(f["info/qlim"]) + end + mpert = size(xi_psi, 1) + m_axis = mlow:(mlow + mpert - 1) + + spectrum = component.(xi_psi[:, 1, end]) + if normalize + maxval = maximum(abs.(spectrum)) + maxval > 0 && (spectrum ./= maxval) + end + + plot!(p, collect(m_axis), spectrum; + label="$label (q_lim=$(round(qlim, digits=2)))", + color=col, lw=1.5, markershape=:circle, markersize=3) + end + + isnothing(save_path) || savefig(p, save_path) + return p +end + end # module ForceFreeStates diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl index 054c7d38..b80a1fd1 100644 --- a/src/Equilibrium/DirectEquilibrium.jl +++ b/src/Equilibrium/DirectEquilibrium.jl @@ -371,6 +371,231 @@ function direct_refine(rfac::Float64, eta::Float64, psi0::Float64, params::Field atol=1e-12*abs(psi0), rtol=1e-12, maxevals=50) end +""" + direct_xpoint_find(raw_profile, ro, zo, rs1) + +Detect the magnetic x-point (if any) by searching for a null of the poloidal field (Br=0, Bz=0) +near the plasma boundary. Tries the lower null first (below the magnetic axis), then upper null. +Returns `(r_xpoint, z_xpoint, is_diverted, psi_hess_rr, psi_hess_zz, psi_hess_rz)`. + +`psi_hess_rr/zz/rz` are ∂²ψ_norm/∂R², ∂²ψ_norm/∂Z², ∂²ψ_norm/∂R∂Z at the X-point, used to +build the asymptotic far-edge geometry in `direct_build_xpoint_asymptotic!`. Returns zeros for +the Hessian when no X-point is found. + +After `direct_position!` renormalizes ψ, the separatrix satisfies ψ≈0 and Bp=0. +An x-point is detected when the Newton iteration converges to a point with |ψ| < ψ_threshold. +""" +function direct_xpoint_find(raw_profile::DirectRunInput, ro::Float64, zo::Float64, rs1::Float64) + bfield = DirectBField() + sq_in_deriv = deriv1(raw_profile.sq_in) + max_iterations = 100 + psi_threshold = 1e-3 # convergence criterion: |ψ| < threshold at x-point candidate + + # X-points in diverted plasmas lie on the inboard side, between rs1 and the magnetic axis. + # A guess of rs1 + 0.35*(ro-rs1) places the starting R in this inboard region; using + # (rs1+rs2)/2 overshoots to the plasma center and Newton misses the basin of attraction. + r_xguess = rs1 + 0.35 * (ro - rs1) + + # Try lower null first, then upper null + for (label, z_guess) in (("lower", raw_profile.zmin + 0.15 * (zo - raw_profile.zmin)), + ("upper", raw_profile.zmax - 0.15 * (raw_profile.zmax - zo))) + r, z = r_xguess, z_guess + dr, dz = 0.0, 0.0 + converged = false + for _ in 1:max_iterations + direct_get_bfield!(bfield, r, z, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=2) + det = bfield.brr * bfield.bzz - bfield.brz * bfield.bzr + abs(det) < 1e-20 && break + dr = (bfield.brz * bfield.bz - bfield.bzz * bfield.br) / det + dz = (bfield.bzr * bfield.br - bfield.brr * bfield.bz) / det + r += dr + z += dz + if abs(dr) <= 1e-8 * abs(r) && abs(dz) <= 1e-8 * abs(r) + converged = true + break + end + end + # Accept candidate if Newton converged and ψ is near zero (≈ separatrix) + if converged + direct_get_bfield!(bfield, r, z, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=2) + if abs(bfield.psi / raw_profile.psio) < psi_threshold + @printf(" X-point (%s null) found at R = %.5f, Z = %.5f\n", label, r, z) + return r, z, true, bfield.psirr, bfield.psizz, bfield.psirz + end + end + end + + return NaN, NaN, false, 0.0, 0.0, 0.0 +end + +""" + direct_build_xpoint_asymptotic!(profiles, psi_nodes, rzphi_nodes, ro, zo, theta_nodes, + r_xpoint, z_xpoint; edge_layer_width=1e-4) + +Extend the rzphi coordinate mapping into the far edge (psin > psihigh) using X-point +asymptotic geometry. Returns extended `(psi_nodes, rzphi_nodes)` arrays covering the +region from psihigh up to the last packed rational surface. + +**Physics**: Near the X-point with F'≈0 and P'≈0, the Grad-Shafranov equation reduces to +Δ*ψ = 0. The local solution is a quadratic saddle surface whose level curves are hyperbolas +in the principal eigencoordinates of the Hessian H = ∂²ψ/∂(R,Z)² at the X-point. + +In the Hessian approximation, the flux surface at ψ_n > psihigh scales from the X-point +as: R(ψ_n, θ) = R_X + s·(R_high(θ) - R_X), and similarly for Z, where +s = √((1 - ψ_n)/(1 - psihigh)). This preserves the shape of the flux surface while +shrinking it toward the X-point as ψ_n → 1. The coordinate Jacobian J_coord is +approximately constant in ψ in this limit (from the Hessian scaling analysis). + +Using this geometry with the EFIT F (held constant by ExtendExtrap), the GS residual is +near zero (since F'≈0, P'≈0 near the separatrix), satisfying the requirement that the +EL equation be evaluated on an approximate GS equilibrium. + +Only called for diverted plasmas (when `profiles.iota_spline` is set). +""" +function direct_build_xpoint_asymptotic!(profiles::ProfileSplines, + psi_nodes::AbstractVector{Float64}, + rzphi_nodes::AbstractArray{Float64,3}, + ro::Float64, + zo::Float64, + theta_nodes, + r_xpoint::Float64, + z_xpoint::Float64, + edge_surface_psis::AbstractVector{Float64}) + + # edge_surface_psis must come from sing_find! — the canonical source of edge rational + # surfaces. Passing an empty vector returns the inputs unchanged (no extension). + isnothing(profiles.iota_spline) && return psi_nodes, rzphi_nodes + isempty(edge_surface_psis) && return psi_nodes, rzphi_nodes + + psihigh = psi_nodes[end] + ipsi_high = length(psi_nodes) + mtheta_pts = size(rzphi_nodes, 2) # mtheta+1 points (0..1 inclusive) + + # Recover R(psihigh, θ) and Z(psihigh, θ) from the rzphi node data + R_high = zeros(Float64, mtheta_pts) + Z_high = zeros(Float64, mtheta_pts) + for itheta in 1:mtheta_pts + theta = theta_nodes[itheta] + rfac = sqrt(max(0.0, rzphi_nodes[ipsi_high, itheta, 1])) + offset = rzphi_nodes[ipsi_high, itheta, 2] + eta = 2π * (theta + offset) + R_high[itheta] = ro + rfac * cos(eta) + Z_high[itheta] = zo + rfac * sin(eta) + end + + # Build far-edge ψ grid: 10 interior points per window between consecutive rational surfaces. + # Nodes beyond psilim are not needed: make_metric truncates at psilim anyway, and + # extending toward psin=1 introduces J→∞ singularities that make the ODE extremely stiff. + psi_far = Float64[psihigh] + boundaries = vcat([psihigh], edge_surface_psis) + for i in 1:(length(boundaries)-1) + win_pts = range(boundaries[i], boundaries[i+1]; length=12) # 12 pts = 10 interior + 2 endpoints + append!(psi_far, win_pts[2:end]) + end + unique!(sort!(psi_far)) + + npsi_far = length(psi_far) + + # Build far-edge rzphi_nodes using X-point scaling. + # For each (ψ_n, θ): scale position from X-point by s = √((1-ψ_n)/(1-psihigh)). + # J_coord stays at the psihigh value (constant in ψ in the Hessian approximation). + # nu stays at the psihigh value (F ≈ const near separatrix → no toroidal correction change). + rzphi_far = zeros(Float64, npsi_far, mtheta_pts, 4) + for (i, psi_n) in enumerate(psi_far) + s = sqrt(max(0.0, (1.0 - psi_n) / (1.0 - psihigh))) + for itheta in 1:mtheta_pts + theta = theta_nodes[itheta] + + # Scaled position from X-point + R_n = r_xpoint + s * (R_high[itheta] - r_xpoint) + Z_n = z_xpoint + s * (Z_high[itheta] - z_xpoint) + + # rfac² and offset in GPEC pseudo-circular coordinates + rfac_sq_n = (R_n - ro)^2 + (Z_n - zo)^2 + eta_n_raw = atan(Z_n - zo, R_n - ro) + + # Adjust eta branch to be consistent with psihigh reference (avoids atan2 discontinuities) + offset_high = rzphi_nodes[ipsi_high, itheta, 2] + eta_high = 2π * (theta + offset_high) + n_wrap = round(Int, (eta_high - eta_n_raw) / (2π)) + eta_n = eta_n_raw + n_wrap * 2π + offset_n = eta_n / (2π) - theta + + rzphi_far[i, itheta, 1] = rfac_sq_n + rzphi_far[i, itheta, 2] = offset_n + rzphi_far[i, itheta, 3] = rzphi_nodes[ipsi_high, itheta, 3] # nu: constant + rzphi_far[i, itheta, 4] = rzphi_nodes[ipsi_high, itheta, 4] # J_coord: constant + end + end + + # Extend arrays: skip psi_far[1] = psihigh which is already in psi_nodes + psi_extended = vcat(psi_nodes, psi_far[2:end]) + rzphi_extended = cat(rzphi_nodes, rzphi_far[2:end, :, :]; dims=1) + + @printf(" X-point asymptotic geometry built over psin ∈ [%.4f, %.6f] (%d far-edge nodes, %d edge rational surfaces)\n", + psihigh, psi_far[end], npsi_far - 1, length(edge_surface_psis)) + + return psi_extended, rzphi_extended +end + +""" + equilibrium_extend_rzphi!(equil, edge_surface_psis) + +Extend the rzphi coordinate splines into the far edge (above psihigh) using the X-point +asymptotic geometry, then rebuild the four bicubic splines in-place on `equil`. + +`edge_surface_psis` must be the psifac values of the edge rational surfaces found by +`sing_find!` — the canonical source. No-op for limited plasmas or empty surface list. + +Called from ForceFreeStates setup after `sing_find!` and `sing_lim!` have run, so that the +rzphi grid covers exactly [psilow, psilim] with no gap or over-extension. +""" +function equilibrium_extend_rzphi!(equil::PlasmaEquilibrium, edge_surface_psis::AbstractVector{Float64}) + + isnothing(equil.profiles.iota_spline) && return + isempty(edge_surface_psis) && return + + psihigh = equil.rzphi_xs[end] + + # Only extend if the provided surfaces reach beyond the current grid end. + maximum(edge_surface_psis) <= psihigh && return + + npsi_current = length(equil.rzphi_xs) + mtheta_pts = length(equil.rzphi_ys) + + # Recover current rzphi node values from the stored bicubic splines. + # nodal_derivs.partials[1, ipsi, itheta] holds the function value at each grid point. + rzphi_nodes = zeros(Float64, npsi_current, mtheta_pts, 4) + for itheta in 1:mtheta_pts + for ipsi in 1:npsi_current + rzphi_nodes[ipsi, itheta, 1] = equil.rzphi_rsquared.nodal_derivs.partials[1, ipsi, itheta] + rzphi_nodes[ipsi, itheta, 2] = equil.rzphi_offset.nodal_derivs.partials[1, ipsi, itheta] + rzphi_nodes[ipsi, itheta, 3] = equil.rzphi_nu.nodal_derivs.partials[1, ipsi, itheta] + rzphi_nodes[ipsi, itheta, 4] = equil.rzphi_jac.nodal_derivs.partials[1, ipsi, itheta] + end + end + + # Extend psi_nodes and rzphi_nodes using the X-point asymptotic formula. + theta_nodes = range(equil.rzphi_ys[1], equil.rzphi_ys[end]; length=mtheta_pts) + psi_extended, rzphi_extended = direct_build_xpoint_asymptotic!( + equil.profiles, equil.rzphi_xs, rzphi_nodes, + equil.ro, equil.zo, theta_nodes, + equil.params.r_xpoint, equil.params.z_xpoint, + edge_surface_psis) + + # Rebuild the four bicubic splines on the extended grid. + grid2d = (psi_extended, theta_nodes) + opts2d = (search=LinearBinary(), bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) + + equil.rzphi_rsquared = cubic_interp(grid2d, rzphi_extended[:, :, 1]; opts2d...) + equil.rzphi_offset = cubic_interp(grid2d, rzphi_extended[:, :, 2]; opts2d...) + equil.rzphi_nu = cubic_interp(grid2d, rzphi_extended[:, :, 3]; opts2d...) + equil.rzphi_jac = cubic_interp(grid2d, rzphi_extended[:, :, 4]; opts2d...) + + equil.rzphi_xs = psi_extended + # rzphi_ys (theta grid) is unchanged +end + """ equilibrium_solver(raw_profile) @@ -421,6 +646,14 @@ robustness. # Find radial position of magnetic axis and separatrix ro, zo, rs1, rs2 = direct_position!(raw_profile) + # Detect x-point (diverted vs limited topology); also retrieve ψ Hessian at x-point + r_xpoint, z_xpoint, is_diverted, psi_hess_rr, psi_hess_zz, psi_hess_rz = direct_xpoint_find(raw_profile, ro, zo, rs1) + if is_diverted + println(" Plasma topology: DIVERTED (x-point detected)") + else + println(" Plasma topology: LIMITED (no x-point)") + end + # Loop over flux surfaces from outermost to innermost, integrating over field lines sq_nodes = zeros!(pool, Float64, mpsi + 1, 4) rzphi_nodes = zeros!(pool, Float64, mpsi + 1, mtheta + 1, 4) @@ -508,8 +741,92 @@ robustness. sq_nodes[:, 4] # q ) end + # For diverted plasmas, build edge inverse splines for q and dV/dψ that are well-behaved + # toward psin=1. The reciprocals iota=1/q and 1/(dV/dψ) are anchored to 0 at the separatrix. + # Also extend the rzphi coordinate mapping into the far edge using X-point asymptotic geometry. + psi_nodes_core = psi_nodes # save reference to core grid before possible extension + if is_diverted + # Edge spline covers the transition region from ~90% of psihigh to psifac=1.0 + psi_edge_start = psihigh * 0.9 + edge_mask = findall(psi -> psi >= psi_edge_start, psi_nodes) + + # Compute derivative-matching phantom knots just above psihigh. + # Without these, the single anchor at (1.0, 0) pulls the iota spline slope at psihigh + # away from -q'/q², causing a derivative discontinuity in q = 1/iota at the junction. + # Adding N phantom knots using the Taylor expansion from the direct spline forces the + # iota spline to reproduce the correct N-th order behaviour right at psihigh. + phantom_delta = 1e-4 + q0 = sq_nodes[edge_mask[end], 4] + q1 = profiles.q_deriv(psihigh) + q2 = deriv2(profiles.q_spline)(psihigh) + q3 = deriv3(profiles.q_spline)(psihigh) + iota1_val = -q1 / q0^2 + iota2_val = (2*q1^2 - q0*q2) / q0^3 + iota3_val = (-6*q1^3 + 6*q0*q1*q2 - q0^2*q3) / q0^4 + phantom_psi_q = [psihigh + j * phantom_delta for j in 1:3] + phantom_iota = [1/q0 + iota1_val*(j*phantom_delta) + + 0.5*iota2_val*(j*phantom_delta)^2 + + (1/6)*iota3_val*(j*phantom_delta)^3 for j in 1:3] + + V0 = sq_nodes[edge_mask[end], 3] + V1 = profiles.dVdpsi_deriv(psihigh) + V2 = deriv2(profiles.dVdpsi_spline)(psihigh) + Vinv1_val = -V1 / V0^2 + Vinv2_val = (2*V1^2 - V0*V2) / V0^3 + phantom_Vinv = [1/V0 + Vinv1_val*(j*phantom_delta) + + 0.5*Vinv2_val*(j*phantom_delta)^2 for j in 1:2] + + # Intermediate points between phantom knots and the psi=1 anchor. + # CubicFit BC over a long empty interval creates a flat S-curve artifact in iota. + # Use iota(s) = A*√s + B*s + C*s^(3/2) with s = 1-psi, which enforces C² continuity + # (value, first, and second derivative) at psi=psihigh and vanishes at psi=1. + # Solving the 3×3 linear system at s=δ=1-psihigh gives: + # A = (3ι₀ + 3ι₁δ + 2ι₂δ²)/√δ + # B = -ι₁ - A/√δ - 2ι₂δ + # C = (4ι₂√δ)/3 + A/(3δ) + n_mid = 8 + iota0 = 1.0 / q0 + Vinv0 = 1.0 / V0 + δ = 1.0 - psihigh + A_iota = (3*iota0 + 3*iota1_val*δ + 2*iota2_val*δ^2) / sqrt(δ) + B_iota = -iota1_val - A_iota/sqrt(δ) - 2*iota2_val*δ + C_iota = (4*iota2_val*sqrt(δ))/3 + A_iota/(3*δ) + A_Vinv = (3*Vinv0 + 3*Vinv1_val*δ + 2*Vinv2_val*δ^2) / sqrt(δ) + B_Vinv = -Vinv1_val - A_Vinv/sqrt(δ) - 2*Vinv2_val*δ + C_Vinv = (4*Vinv2_val*sqrt(δ))/3 + A_Vinv/(3*δ) + psi_mid = [psihigh + δ * i/(n_mid + 1) for i in 1:n_mid] + iota_mid = [A_iota*sqrt(1.0-p) + B_iota*(1.0-p) + C_iota*(1.0-p)^1.5 for p in psi_mid] + Vinv_mid = [A_Vinv*sqrt(1.0-p) + B_Vinv*(1.0-p) + C_Vinv*(1.0-p)^1.5 for p in psi_mid] + + edge_psi = vcat(psi_nodes[edge_mask], phantom_psi_q, psi_mid, 1.0) + sort!(edge_psi) + + # Iota = 1/q; anchor iota(1.0) = 0 (q → ∞ at separatrix) + q_iota_vals = vcat([1.0 / sq_nodes[i, 4] for i in edge_mask], phantom_iota, iota_mid, 0.0) + q_iota_vals = q_iota_vals[sortperm(vcat(psi_nodes[edge_mask], phantom_psi_q, psi_mid, 1.0))] + q_iota_inner = cubic_interp(edge_psi, q_iota_vals; bc=CubicFit(), extrap=ExtendExtrap(), search=LinearBinary()) + profiles.iota_spline = q_iota_inner + + # 1/(dV/dψ); anchor (dV/dψ)⁻¹(1.0) = 0 (dV/dψ → ∞ at separatrix) + # Uses 2 phantom knots (1st + 2nd derivative matching; 3rd not needed for dV/dψ) + edge_psi_dV = vcat(psi_nodes[edge_mask], phantom_psi_q[1:2], psi_mid, 1.0) + sort!(edge_psi_dV) + dVdpsi_inv_vals = vcat([1.0 / sq_nodes[i, 3] for i in edge_mask], phantom_Vinv, Vinv_mid, 0.0) + dVdpsi_inv_vals = dVdpsi_inv_vals[sortperm(vcat(psi_nodes[edge_mask], phantom_psi_q[1:2], psi_mid, 1.0))] + dVdpsi_inv_inner = cubic_interp(edge_psi_dV, dVdpsi_inv_vals; bc=CubicFit(), extrap=ExtendExtrap(), search=LinearBinary()) + profiles.dVdpsi_inv_spline = dVdpsi_inv_inner + + @printf(" Edge inverse splines built over psin ∈ [%.4f, 1.0] (%d nodes)\n", + psi_edge_start, length(edge_psi)) + + # rzphi nodes will be extended into the far edge by equilibrium_extend_rzphi! in + # ForceFreeStates, using the edge rational surfaces from sing_find! as the canonical + # grid source. No extension is done here; the spline is built on the core grid only. + end + # Create 2D interpolants for geometric quantities (rzphi) with CubicFit/Periodic BCs. # theta_nodes includes both 0 and 1 (closed periodic grid). + # rzphi_xs is the (possibly extended) psi grid; eqfun is built on the core grid only. rzphi_xs = psi_nodes # rzphi_ys is the materialized Vector stored in PlasmaEquilibrium for indexing/diagnostics. # The Range form (theta_nodes) is used for the interpolant: it skips index search during @@ -526,7 +843,8 @@ robustness. rzphi_jac = cubic_interp(grid2d, rzphi_nodes[:, :, 4]; opts2d...) # Calculate physics quantities (B-field, metric components, etc.) in 2D spline `eqfun` - # for use in stability and transport codes + # for use in stability and transport codes. Built on the core psi grid only (ForceFreeStates + # uses rzphi directly and does not use eqfun, so far-edge extension is not needed here). eqfun_fs_nodes = zeros(Float64, mpsi + 1, mtheta + 1, 3) v = @MMatrix zeros(Float64, 2, 3) for ipsi in 1:(mpsi+1) @@ -587,14 +905,28 @@ robustness. end end end - # Create 2D interpolants for physics quantities (eqfun) - eqfun_B = cubic_interp(grid2d, eqfun_fs_nodes[:, :, 1]; opts2d...) - eqfun_metric1 = cubic_interp(grid2d, eqfun_fs_nodes[:, :, 2]; opts2d...) - eqfun_metric2 = cubic_interp(grid2d, eqfun_fs_nodes[:, :, 3]; opts2d...) + # Create 2D interpolants for physics quantities (eqfun) on the CORE psi grid + core_grid2d = (psi_nodes_core, theta_nodes) + eqfun_B = cubic_interp(core_grid2d, eqfun_fs_nodes[:, :, 1]; opts2d...) + eqfun_metric1 = cubic_interp(core_grid2d, eqfun_fs_nodes[:, :, 2]; opts2d...) + eqfun_metric2 = cubic_interp(core_grid2d, eqfun_fs_nodes[:, :, 3]; opts2d...) - return PlasmaEquilibrium(raw_profile.config, EquilibriumParameters(), profiles, + pe = PlasmaEquilibrium(raw_profile.config, EquilibriumParameters(), profiles, rzphi_xs, rzphi_ys, rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac, eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio) + + # Store x-point topology and Hessian in equilibrium parameters + pe.params.r_xpoint = is_diverted ? r_xpoint : nothing + pe.params.z_xpoint = is_diverted ? z_xpoint : nothing + pe.params.is_diverted = is_diverted + pe.params.psi_core_end = psihigh # last psi in core field-line grid (before far-edge extension) + if is_diverted + pe.params.psi_hess_rr = psi_hess_rr + pe.params.psi_hess_zz = psi_hess_zz + pe.params.psi_hess_rz = psi_hess_rz + end + + return pe end diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl index 4d1b3c97..4d2d20e6 100644 --- a/src/Equilibrium/Equilibrium.jl +++ b/src/Equilibrium/Equilibrium.jl @@ -18,7 +18,7 @@ include("InverseEquilibrium.jl") include("AnalyticEquilibrium.jl") # --- Expose types and functions to the user --- -export setup_equilibrium, EquilibriumConfig, PlasmaEquilibrium, EquilibriumParameters, ProfileSplines +export setup_equilibrium, equilibrium_extend_rzphi!, EquilibriumConfig, PlasmaEquilibrium, EquilibriumParameters, ProfileSplines, eval_q # --- Constants --- const mu0 = 4π * 1e-7 @@ -91,13 +91,18 @@ Finds the separatrix locations in the plasma equilibrium (rsep, zsep, rext, zext Performs the same function as equil_out_sep_find in the Fortran code. """ function equilibrium_separatrix_find!(pe::PlasmaEquilibrium) - mpsi = length(pe.rzphi_xs) - 1 mtheta = length(pe.rzphi_ys) - 1 + # Use the core field-line grid boundary (psihigh), not the far-edge extension end. + # For diverted plasmas, rzphi_xs is extended beyond psihigh via X-point asymptotic geometry; + # the separatrix / global parameters are defined at the core grid boundary. + psi_core = isnothing(pe.params.psi_core_end) ? pe.rzphi_xs[end] : pe.params.psi_core_end + edge_idx = searchsortedlast(pe.rzphi_xs, psi_core) + edge_idx = max(1, min(edge_idx, length(pe.rzphi_xs))) + # Allocate vector to store eta offset from rzphi (direct array access at grid points) - vector = pe.rzphi_ys .+ @view pe.rzphi_offset.nodal_derivs.partials[1, end, :] + vector = pe.rzphi_ys .+ @view pe.rzphi_offset.nodal_derivs.partials[1, edge_idx, :] - edge_idx = mpsi + 1 # Edge flux surface index psi_edge = pe.rzphi_xs[edge_idx] eta0 = 0.0 idx = findmin(abs.(vector .- eta0))[2] @@ -199,9 +204,13 @@ the same function as equil_out_global in the Fortran code. """ function equilibrium_global_parameters!(pe::PlasmaEquilibrium) profiles = pe.profiles - mpsi = length(pe.rzphi_xs) - 1 mtheta = length(pe.rzphi_ys) - 1 + # Use the core field-line grid boundary for global parameters, not the far-edge extension end. + psi_core = isnothing(pe.params.psi_core_end) ? pe.rzphi_xs[end] : pe.params.psi_core_end + edge_idx = searchsortedlast(pe.rzphi_xs, psi_core) + edge_idx = max(1, min(edge_idx, length(pe.rzphi_xs))) + # Use separatrix geometry rsep, zsep, rext, _ = equilibrium_separatrix_find!(pe) @@ -211,7 +220,7 @@ function equilibrium_global_parameters!(pe::PlasmaEquilibrium) kappa = (zsep[1] - zsep[2]) / (rsep[2] - rsep[1]) delta1 = (rmean - rext[1]) / amean delta2 = (rmean - rext[2]) / amean - dpsi = 1.0 - pe.rzphi_xs[mpsi+1] + dpsi = 1.0 - pe.rzphi_xs[edge_idx] psi_edge = profiles.xs[end] bt0 = (profiles.F_spline.y[end] + profiles.F_deriv(psi_edge; hint=Ref(profiles.npts_minus_1)) * dpsi) / (2π * rmean) @@ -230,12 +239,12 @@ function equilibrium_global_parameters!(pe::PlasmaEquilibrium) # Direct array access at edge flux surface grid points using nodal_derivs for itheta in 0:mtheta # Function values (partials[1,:,:]) - r2 = pe.rzphi_rsquared.nodal_derivs.partials[1, end, itheta+1] - offset = pe.rzphi_offset.nodal_derivs.partials[1, end, itheta+1] - jac = pe.rzphi_jac.nodal_derivs.partials[1, end, itheta+1] + r2 = pe.rzphi_rsquared.nodal_derivs.partials[1, edge_idx, itheta+1] + offset = pe.rzphi_offset.nodal_derivs.partials[1, edge_idx, itheta+1] + jac = pe.rzphi_jac.nodal_derivs.partials[1, edge_idx, itheta+1] # Theta derivatives (partials[3,:,:] = ∂f/∂y) - r2_y = pe.rzphi_rsquared.nodal_derivs.partials[3, end, itheta+1] - offset_y = pe.rzphi_offset.nodal_derivs.partials[3, end, itheta+1] + r2_y = pe.rzphi_rsquared.nodal_derivs.partials[3, edge_idx, itheta+1] + offset_y = pe.rzphi_offset.nodal_derivs.partials[3, edge_idx, itheta+1] chi1 = 2π * psio / jac jacfac = π / jac @@ -326,7 +335,7 @@ function equilibrium_qfind!(equil::PlasmaEquilibrium) psiexl = Float64[] qexl = Float64[] - # Create derivative views for q-spline + # Use the direct q spline for deriv2/deriv3; extremum analysis is core-region only. q_spline = profiles.q_spline q_d1 = deriv1(q_spline) q_d2 = deriv2(q_spline) @@ -376,9 +385,19 @@ function equilibrium_qfind!(equil::PlasmaEquilibrium) qmax_edge = q_spline.y[end] qmin = min(minimum(qexl), q0) qmax = max(maximum(qexl), qmax_edge) - qa = q_spline.y[end] + profiles.q_deriv(xs[end]; hint=Ref(profiles.npts_minus_1)) * (1.0 - xs[end]) + + # For diverted plasmas q → ∞ at the separatrix; set qa = Inf and qmax = Inf + # so that sing_find! and sing_lim! know there is no finite q boundary. + if !isnothing(equil.params.is_diverted) && equil.params.is_diverted + qa = Inf + qmax = Inf + else + qa = q_spline.y[end] + profiles.q_deriv(xs[end]; hint=Ref(profiles.npts_minus_1)) * (1.0 - xs[end]) + qmax = max(qmax, qa) + end q95 = q_spline(0.95) + q99 = q_spline(0.99) # Store derived values equil.params.q0 = q0 @@ -386,19 +405,48 @@ function equilibrium_qfind!(equil::PlasmaEquilibrium) equil.params.qmax = qmax equil.params.qa = qa equil.params.q95 = q95 + equil.params.q99 = q99 end """ equilibrium_gse!(equil::PlasmaEquilibrium) -Diagnoses the Grad-Shafranov solution by computing the residual of the -Grad-Shafranov equation across the grid and writing diagnostic data to HDF5 files. -Performs the same function as equil_out_gse in the Fortran code. +Diagnoses the Grad-Shafranov (GS) solution by computing the residual of the +GS equation across the flux-coordinate grid and optionally writing diagnostic +data to HDF5 files. + +The GS equation in standard form is: + R ∂/∂R (1/R ∂ψ/∂R) + ∂²ψ/∂Z² = -μ₀R² P'(ψ) - F(ψ)F'(ψ) + +where F = R*Bₜ, P = plasma pressure, and ' denotes d/dψ. In the +flux-coordinate divergence form used here, this becomes two θ-integrated +terms: a ψ-divergence term and a source term involving F F' and P'. + +## Output variables + + - `gs_div_dpsi`: ψ-derivative of the GS divergence operator applied to the rzphi splines + - `gs_div_dtheta`: θ-derivative of the same operator (used for integration by parts) + - `gse_terms_integrated`: per-ψ θ-integrals of the divergence and source terms + - `gse_total_integrated`: total integrated GS residual per ψ surface + - `gse_abs_error`: absolute value of `gse_total_integrated` + - `gse_log_error`: log₁₀(gse_abs_error) for plotting + +## HDF5 output (written only when `params.diagnose_src = true`) + + - `gsec.h5`: contour data (r, z, per-point residual fields) + - `gse.h5`: xy plot data + - `gsei.h5`: θ-integrated GS error per ψ surface + +Coverage: the original equilibrium grid only (psilow to psihigh); no far-edge extension. """ function equilibrium_gse!(equil::PlasmaEquilibrium) profiles = equil.profiles - mpsi = length(equil.rzphi_xs) - 1 + # Use the core profile grid (profiles.xs) to determine loop bounds. + # For diverted plasmas, equil.rzphi_xs is extended beyond psihigh via X-point asymptotic + # geometry; GSE is only evaluated on the core field-line grid (psilow to psihigh). + psi_xs = profiles.xs # core psi grid + mpsi = length(psi_xs) - 1 mtheta = length(equil.rzphi_ys) - 1 ro, zo = equil.ro, equil.zo psio = equil.psio @@ -410,7 +458,7 @@ function equilibrium_gse!(equil::PlasmaEquilibrium) @info "Diagnosing Grad-Shafranov solution" end - # Compute R, Z coordinates using nodal_derivs access + # Compute R, Z coordinates using nodal_derivs access (core grid only) r = zeros(Float64, mpsi + 1, mtheta + 1) z = zeros(Float64, mpsi + 1, mtheta + 1) @@ -421,10 +469,12 @@ function equilibrium_gse!(equil::PlasmaEquilibrium) z[ipsi, :] .= zo .+ rfac .* sin.(angle) end - # Compute flux quantities using direct array access at grid points - flux_fs = zeros(Float64, mpsi + 1, mtheta + 1, 2) - flux_fsx = zeros(Float64, mpsi + 1, mtheta + 1, 2) # x-derivatives - flux_fsy = zeros(Float64, mpsi + 1, mtheta + 1, 2) # y-derivatives + # Compute the two components of the GS divergence operator in flux coordinates. + # gs_div_term[:,:,1] = |∇ψ|² / J (poloidal component) + # gs_div_term[:,:,2] = ∇ψ·∇θ / J (cross component) + gs_div_term = zeros(Float64, mpsi + 1, mtheta + 1, 2) + gs_div_dpsi = zeros(Float64, mpsi + 1, mtheta + 1, 2) # ψ-derivative of GS divergence terms + gs_div_dtheta = zeros(Float64, mpsi + 1, mtheta + 1, 2) # θ-derivative of GS divergence terms for ipsi in 1:(mpsi+1) for itheta in 1:(mtheta+1) f1 = equil.rzphi_rsquared.nodal_derivs.partials[1, ipsi, itheta] @@ -435,52 +485,52 @@ function equilibrium_gse!(equil::PlasmaEquilibrium) fx1 = equil.rzphi_rsquared.nodal_derivs.partials[2, ipsi, itheta] fx2 = equil.rzphi_offset.nodal_derivs.partials[2, ipsi, itheta] - flux_fs[ipsi, itheta, 1] = fy1^2 / (4π^2 * f1) + (1 + fy2)^2 * 4 * f1 - flux_fs[ipsi, itheta, 2] = fx1 * fy1 / (4π^2 * f1) + fx2 * (1 + fy2) * 4 * f1 + gs_div_term[ipsi, itheta, 1] = fy1^2 / (4π^2 * f1) + (1 + fy2)^2 * 4 * f1 + gs_div_term[ipsi, itheta, 2] = fx1 * fy1 / (4π^2 * f1) + fx2 * (1 + fy2) * 4 * f1 - flux_fs[ipsi, itheta, 1] *= 2π * psio / f4 - flux_fs[ipsi, itheta, 2] *= 2π * psio / f4 + gs_div_term[ipsi, itheta, 1] *= 2π * psio / f4 + gs_div_term[ipsi, itheta, 2] *= 2π * psio / f4 end end - # Create flux interpolants for Grad-Shafranov diagnostics + # Create interpolants of GS divergence terms on the core psi grid flux_opts = (search=LinearBinary(), bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap())) - flux1 = cubic_interp((equil.rzphi_xs, equil.rzphi_ys), flux_fs[:, :, 1]; flux_opts...) - flux2 = cubic_interp((equil.rzphi_xs, equil.rzphi_ys), flux_fs[:, :, 2]; flux_opts...) + flux1 = cubic_interp((psi_xs, equil.rzphi_ys), gs_div_term[:, :, 1]; flux_opts...) + flux2 = cubic_interp((psi_xs, equil.rzphi_ys), gs_div_term[:, :, 2]; flux_opts...) - # Compute flux derivatives at all grid points for diagnostics + # Compute ψ- and θ-derivatives of GS divergence terms at all core grid points hint2d = (Ref(1), Ref(1)) # Shared 2D hint for hot loop optimization for ipsi in 0:mpsi for itheta in 0:mtheta - query_point = (equil.rzphi_xs[ipsi+1], equil.rzphi_ys[itheta+1]) - flux_fsx[ipsi+1, itheta+1, 1] = flux1(query_point; deriv=Val((1, 0)), hint=hint2d) - flux_fsx[ipsi+1, itheta+1, 2] = flux2(query_point; deriv=Val((1, 0)), hint=hint2d) - flux_fsy[ipsi+1, itheta+1, 1] = flux1(query_point; deriv=Val((0, 1)), hint=hint2d) - flux_fsy[ipsi+1, itheta+1, 2] = flux2(query_point; deriv=Val((0, 1)), hint=hint2d) + query_point = (psi_xs[ipsi+1], equil.rzphi_ys[itheta+1]) + gs_div_dpsi[ipsi+1, itheta+1, 1] = flux1(query_point; deriv=Val((1, 0)), hint=hint2d) + gs_div_dpsi[ipsi+1, itheta+1, 2] = flux2(query_point; deriv=Val((1, 0)), hint=hint2d) + gs_div_dtheta[ipsi+1, itheta+1, 1] = flux1(query_point; deriv=Val((0, 1)), hint=hint2d) + gs_div_dtheta[ipsi+1, itheta+1, 2] = flux2(query_point; deriv=Val((0, 1)), hint=hint2d) end end - # Compute source term using direct array access + # Compute GS source term: f4/J * (F*F'/R² + μ₀P') source = zeros(Float64, mpsi + 1, mtheta + 1) hint = Ref(1) # Linear search hint for sequential psi access for ipsi in 1:(mpsi+1) - psi = profiles.xs[ipsi] - s1 = profiles.F_spline.y[ipsi] - s1p = profiles.F_deriv(psi; hint=hint) - s2p = profiles.P_deriv(psi; hint=hint) + psi = psi_xs[ipsi] + F_val = profiles.F_spline.y[ipsi] # F(ψ) = R*Bₜ + dF_dpsi = profiles.F_deriv(psi; hint=hint) # dF/dψ + dP_dpsi = profiles.P_deriv(psi; hint=hint) # d(μ₀P)/dψ for itheta in 1:(mtheta+1) f4 = equil.rzphi_jac.nodal_derivs.partials[1, ipsi, itheta] denom = (2π * r[ipsi, itheta])^2 - source[ipsi, itheta] = f4 / (2π * psio * π^2) * (s1 * s1p / denom + s2p) + source[ipsi, itheta] = f4 / (2π * psio * π^2) * (F_val * dF_dpsi / denom + dP_dpsi) end end - total = flux_fsx[:, :, 1] .- flux_fsy[:, :, 2] .+ source - error = abs.(total) ./ maximum([maximum(abs.(flux_fsx[:, :, 1])), maximum(abs.(flux_fsy[:, :, 2])), maximum(abs.(source))]) + total = gs_div_dpsi[:, :, 1] .- gs_div_dtheta[:, :, 2] .+ source + error = abs.(total) ./ maximum([maximum(abs.(gs_div_dpsi[:, :, 1])), maximum(abs.(gs_div_dtheta[:, :, 2])), maximum(abs.(source))]) errlog = ifelse.(error .> 0, log10.(error), 0.0) if diagnose_maxima - fxmax = maximum(abs.(flux_fsx[:, :, 1])) - fymax = maximum(abs.(flux_fsy[:, :, 2])) + fxmax = maximum(abs.(gs_div_dpsi[:, :, 1])) + fymax = maximum(abs.(gs_div_dtheta[:, :, 2])) smax = maximum(abs.(source)) emax = maximum(abs.(error)) lmax = maximum(errlog) @@ -488,21 +538,21 @@ function equilibrium_gse!(equil::PlasmaEquilibrium) @info "GS residuals: fxmax = $(@sprintf("%.3e", fxmax)), fymax = $(@sprintf("%.3e", fymax)), smax = $(@sprintf("%.3e", smax)), emax = $(@sprintf("%.3e", emax)), lmax = $(@sprintf("%.3f", lmax)), maxloc = $(jmax .- 1)" end - # Integrated error criterion - term = zeros(Float64, mpsi + 1, 2) + # θ-integrated GS error: used to diagnose systematic residuals per flux surface + gse_terms_integrated = zeros(Float64, mpsi + 1, 2) for ipsi in 1:(mpsi+1) fs_matrix = zeros(Float64, mtheta + 1, 2) - fs_matrix[:, 1] = flux_fsx[ipsi, :, 1] + fs_matrix[:, 1] = gs_div_dpsi[ipsi, :, 1] fs_matrix[:, 2] = source[ipsi, :] # Compute total integral using FastInterpolations native integration itp = cubic_interp(equil.rzphi_ys, fs_matrix; bc=PeriodicBC()) - term[ipsi, :] .= FastInterpolations.integrate(itp) + gse_terms_integrated[ipsi, :] .= FastInterpolations.integrate(itp) end - totali = sum(term; dims=2) - errori = abs.(totali) - errlogi = @. ifelse(errori > 0, log10(errori), 0.0) + gse_total_integrated = sum(gse_terms_integrated; dims=2) + gse_abs_error = abs.(gse_total_integrated) + gse_log_error = @. ifelse(gse_abs_error > 0, log10(gse_abs_error), 0.0) if diagnose_src if verbose @@ -515,8 +565,8 @@ function equilibrium_gse!(equil::PlasmaEquilibrium) file["mtheta"] = mtheta file["r"] = Float32.(r) file["z"] = Float32.(z) - file["flux_fsx"] = Float32.(flux_fsx[:, :, 1]) - file["flux_fsy"] = Float32.(flux_fsy[:, :, 2]) + file["flux_fsx"] = Float32.(gs_div_dpsi[:, :, 1]) + file["flux_fsy"] = Float32.(gs_div_dtheta[:, :, 2]) file["source"] = Float32.(source) file["total"] = Float32.(total) file["error"] = Float32.(error) @@ -528,10 +578,10 @@ function equilibrium_gse!(equil::PlasmaEquilibrium) gse_data = Array{Float32,3}(undef, mpsi + 1, mtheta + 1, 7) for ipsi in 0:mpsi for itheta in 0:mtheta - gse_data[ipsi+1, itheta+1, 1] = Float32(flux.ys[itheta+1]) - gse_data[ipsi+1, itheta+1, 2] = Float32(flux.xs[ipsi+1]) - gse_data[ipsi+1, itheta+1, 3] = Float32(flux_fs[ipsi+1, itheta+1, 1]) - gse_data[ipsi+1, itheta+1, 4] = Float32(flux_fs[ipsi+1, itheta+1, 2]) + gse_data[ipsi+1, itheta+1, 1] = Float32(equil.rzphi_ys[itheta+1]) + gse_data[ipsi+1, itheta+1, 2] = Float32(psi_xs[ipsi+1]) + gse_data[ipsi+1, itheta+1, 3] = Float32(gs_div_term[ipsi+1, itheta+1, 1]) + gse_data[ipsi+1, itheta+1, 4] = Float32(gs_div_term[ipsi+1, itheta+1, 2]) gse_data[ipsi+1, itheta+1, 5] = Float32(source[ipsi+1, itheta+1]) gse_data[ipsi+1, itheta+1, 6] = Float32(total[ipsi+1, itheta+1]) gse_data[ipsi+1, itheta+1, 7] = Float32(error[ipsi+1, itheta+1]) @@ -542,11 +592,11 @@ function equilibrium_gse!(equil::PlasmaEquilibrium) # Write integrated error criterion h5open(joinpath(dirname(equil.config.eq_filename), "gsei.h5"), "w") do file - file["xs"] = Float32.(flux.xs) - file["term"] = Float32.(term) - file["totali"] = Float32.(totali) - file["errori"] = Float32.(errori) - file["errlogi"] = Float32.(errlogi) + file["xs"] = Float32.(psi_xs) + file["term"] = Float32.(gse_terms_integrated) + file["totali"] = Float32.(gse_total_integrated) + file["errori"] = Float32.(gse_abs_error) + file["errlogi"] = Float32.(gse_log_error) end end end diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl index 47a2ea39..132d76cb 100644 --- a/src/Equilibrium/EquilibriumTypes.jl +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -339,6 +339,7 @@ A mutable struct containing computed equilibrium parameters and diagnostic flags - `qmax::Union{Nothing,Float64}` - Maximum safety factor in the plasma - `qa::Union{Nothing,Float64}` - Safety factor at the plasma edge - `q95::Union{Nothing,Float64}` - Safety factor at 95% flux surface + - `q99::Union{Nothing,Float64}` - Safety factor at 99% flux surface - `qextrema_psi::Union{Nothing,Vector{Float64}}` - Normalized flux values at q extrema - `qextrema_q::Union{Nothing,Vector{Float64}}` - Safety factor values at extrema - `mextrema::Union{Nothing,Int}` - Number of extrema in q-profile @@ -391,6 +392,7 @@ A mutable struct containing computed equilibrium parameters and diagnostic flags qmax::Union{Nothing,Float64} = nothing # Maximum safety factor in the plasma qa::Union{Nothing,Float64} = nothing # Safety factor at the plasma edge q95::Union{Nothing,Float64} = nothing # Safety factor at 95% flux surface + q99::Union{Nothing,Float64} = nothing # Safety factor at 99% flux surface qextrema_psi::Union{Nothing,Vector{Float64}} = nothing # Normalized poloidal flux values where q has extrema qextrema_q::Union{Nothing,Vector{Float64}} = nothing # Safety factor values at the extrema points mextrema::Union{Nothing,Int} = nothing # Number of extrema points in the q-profile @@ -427,8 +429,19 @@ A mutable struct containing computed equilibrium parameters and diagnostic flags li1::Union{Nothing,Float64} = nothing # Internal inductance at the axis li2::Union{Nothing,Float64} = nothing # External inductance at the axis li3::Union{Nothing,Float64} = nothing # Total inductance at the axis + r_xpoint::Union{Nothing,Float64} = nothing # R-coordinate of x-point [m] + z_xpoint::Union{Nothing,Float64} = nothing # Z-coordinate of x-point [m] + is_diverted::Union{Nothing,Bool} = nothing # Whether plasma has a magnetic x-point + psi_hess_rr::Union{Nothing,Float64} = nothing # ∂²ψ_norm/∂R² at x-point (for asymptotic far-edge geometry) + psi_hess_zz::Union{Nothing,Float64} = nothing # ∂²ψ_norm/∂Z² at x-point + psi_hess_rz::Union{Nothing,Float64} = nothing # ∂²ψ_norm/∂R∂Z at x-point + psi_core_end::Union{Nothing,Float64} = nothing # psihigh — last psi in the core field-line grid; + # rzphi splines extend beyond this for diverted plasmas via X-point asymptotic geometry. + # Used by equilibrium_separatrix_find! / equilibrium_global_parameters! to evaluate + # global quantities at the field-line grid boundary, not the far-edge extension end. end + """ ProfileSplines @@ -440,20 +453,28 @@ Each profile is stored as a separate spline for code clarity. - `xs::Vector{Float64}`: Shared x-axis (normalized psi) - `F_spline`: 2π*F (toroidal flux function, where F = R * B_toroidal) - `P_spline`: μ₀*P (plasma pressure × μ₀) - - `dVdpsi_spline`: dV/dψ (volume derivative) - - `q_spline`: q (safety factor) + - `dVdpsi_spline`: dV/dψ (volume derivative), direct cubic spline + - `q_spline`: q (safety factor) cubic spline over the core grid [psilow, psihigh] # Derivative Interpolants (for continuous derivative evaluation) - `F_deriv`, `P_deriv`, `dVdpsi_deriv`, `q_deriv`: First derivative interpolants + (direct-spline derivatives; for higher-order q derivatives use `q_spline(psi; deriv=k)`) + +# Edge Extension Fields (Nothing for limited plasmas) + + - `iota_spline`: Raw iota = 1/q spline over [psihigh, psilim] for diverted plasmas + - `_iota_hint`: Search hint for `iota_spline` grid (separate from core grid) + - `dVdpsi_inv_spline`: Raw 1/(dV/dψ) spline over edge zone for diverted plasmas + - `_dVdpsi_inv_hint`: Search hint for `dVdpsi_inv_spline` grid # Notes - Node values at grid points: Access via `spline.y[i]` - - Derivative at any point: Call `deriv(x)` (derivative views are callable) + - For edge-aware q evaluation (dispatching between core and edge zone), use `eval_q` - Grid: Access via `xs` field or `spline.cache.x` """ -struct ProfileSplines{S,D} +mutable struct ProfileSplines{S,D} xs::Vector{Float64} npts::Int # length(xs), avoids redundant length() calls npts_minus_1::Int # npts - 1, for hint at last interval @@ -467,6 +488,11 @@ struct ProfileSplines{S,D} P_deriv::D dVdpsi_deriv::D q_deriv::D + # Edge splines for diverted plasmas (Nothing for limited) + iota_spline::Union{Nothing,S} # stores iota = 1/q over [psihigh, psilim] + _iota_hint::Base.RefValue{Int} # search hint for iota_spline grid + dVdpsi_inv_spline::Union{Nothing,S} # stores 1/(dV/dψ) over edge zone + _dVdpsi_inv_hint::Base.RefValue{Int} # search hint for dVdpsi_inv_spline grid end """ @@ -474,6 +500,8 @@ end Create ProfileSplines from arrays of profile values. Uses CubicFit boundary conditions with extension extrapolation. +Edge inverse splines are initially nothing and are set later by equilibrium_solver +for diverted plasmas. """ function ProfileSplines(xs::Vector{Float64}, F_vals::Vector{Float64}, @@ -500,13 +528,64 @@ function ProfileSplines(xs::Vector{Float64}, dVdpsi_deriv = deriv1(dVdpsi_spline) q_deriv = deriv1(q_spline) - ProfileSplines{typeof(F_spline),typeof(F_deriv)}( + S = typeof(q_spline) + D = typeof(q_deriv) + + ProfileSplines{S,D}( xs, npts, npts_minus_1, F_spline, P_spline, dVdpsi_spline, q_spline, - F_deriv, P_deriv, dVdpsi_deriv, q_deriv + F_deriv, P_deriv, dVdpsi_deriv, q_deriv, + nothing, Ref(1), # iota_spline, _iota_hint: set later for diverted + nothing, Ref(1) # dVdpsi_inv_spline, _dVdpsi_inv_hint: set later for diverted ) end +""" + eval_q(profiles::ProfileSplines, psi; deriv::Int=0, output_lower_derivs::Bool=false, hint=Ref(1)) + +Evaluate q(ψ) or its derivatives at `psi`, dispatching between the direct spline (core, +psi ≤ psihigh) and the iota spline (edge, psi > psihigh, diverted plasmas only). + +For `output_lower_derivs=false` (default): returns a scalar — the derivative of order `deriv`. +For `output_lower_derivs=true`: returns a tuple `(q, q', …, q^(deriv))` computed in a +single pass, sharing iota evaluations across derivative orders. Efficient for callers that +need multiple orders simultaneously (e.g. singular surface Taylor expansion). + +The `hint` argument is for the core direct spline only. The edge iota spline uses +`profiles._iota_hint` internally, which is keyed to the separate edge grid. + +# Chain rule for edge zone (iota = 1/q, so q = 1/iota): + - deriv=1: dq/dψ = -ι'/ι² + - deriv=2: d²q/dψ² = (2ι'² - ι·ι'')/ι³ + - deriv=3: d³q/dψ³ = (-6ι'³ + 6ι·ι'·ι'' - ι²·ι''')/ι⁴ +""" +function eval_q(profiles::ProfileSplines, psi; deriv::Int=0, output_lower_derivs::Bool=false, hint=Ref(1)) + if psi > profiles.xs[end] && !isnothing(profiles.iota_spline) + h = profiles._iota_hint + ι = profiles.iota_spline(psi; hint=h) + d0 = 1.0 / ι + deriv == 0 && return output_lower_derivs ? (d0,) : d0 + ι1 = profiles.iota_spline(psi; deriv=1, hint=h) + d1 = -ι1 / ι^2 # dq/dψ = -ι'/ι² + deriv == 1 && return output_lower_derivs ? (d0, d1) : d1 + ι2 = profiles.iota_spline(psi; deriv=2, hint=h) + d2 = (2ι1^2 - ι*ι2) / ι^3 # d²q/dψ² + deriv == 2 && return output_lower_derivs ? (d0, d1, d2) : d2 + ι3 = profiles.iota_spline(psi; deriv=3, hint=h) + d3 = (-6ι1^3 + 6ι*ι1*ι2 - ι^2*ι3) / ι^4 # d³q/dψ³ + return output_lower_derivs ? (d0, d1, d2, d3) : d3 + else + d0 = profiles.q_spline(psi; hint=hint) + deriv == 0 && return output_lower_derivs ? (d0,) : d0 + d1 = profiles.q_spline(psi; deriv=1, hint=hint) + deriv == 1 && return output_lower_derivs ? (d0, d1) : d1 + d2 = profiles.q_spline(psi; deriv=2, hint=hint) + deriv == 2 && return output_lower_derivs ? (d0, d1, d2) : d2 + d3 = profiles.q_spline(psi; deriv=3, hint=hint) + return output_lower_derivs ? (d0, d1, d2, d3) : d3 + end +end + """ PlasmaEquilibrium(...) diff --git a/src/ForceFreeStates/EulerLagrange.jl b/src/ForceFreeStates/EulerLagrange.jl index fc459e9d..14682809 100644 --- a/src/ForceFreeStates/EulerLagrange.jl +++ b/src/ForceFreeStates/EulerLagrange.jl @@ -38,17 +38,29 @@ function eulerlagrange_integration(ctrl::ForceFreeStatesControl, equil::Equilibr # Print initial integration condition if ctrl.verbose - @info " ψ = $((@sprintf "%.3f" odet.psifac)), q = $((@sprintf "%.3f" equil.profiles.q_spline(odet.psifac)))" + @info " ψ = $((@sprintf "%.3f" odet.psifac)), q = $((@sprintf "%.3f" eval_q(equil.profiles, odet.psifac)))" end # Iterate through each integration chunk + psihigh = equil.profiles.xs[end] for chunk in chunks + is_above_psihigh = ctrl.psiedge < intr.psilim && chunk.psi_end > psihigh + # Integrate this region and display progress integrate_el_region!(odet, ctrl, equil, ffit, intr, chunk) if ctrl.verbose @info " ψ = $((@sprintf "%.3f" odet.psifac)), q = $((@sprintf "%.3f" odet.q)), steps = $(odet.total_steps)" end + # Detect early termination: if the solver did not reach chunk.psi_end + # Stop the integration (ODE stiffness grows rapidly as q→∞ in the edge zone) + if is_above_psihigh && odet.psifac < chunk.psi_end - 1e-6 + if ctrl.verbose + @warn "Above-psihigh solver terminated early at ψ = $((@sprintf "%.4f" odet.psifac)), Euler Lagrange integration" + end + break + end + # Cross a rational surface after integration if this chunk requires it if chunk.needs_crossing if ctrl.kin_flag @@ -61,31 +73,39 @@ function eulerlagrange_integration(ctrl::ForceFreeStatesControl, equil::Equilibr # Deallocate unused storage of integration data if ctrl.psiedge < intr.psilim - # Find the peak dW in the edge region and truncate integration data there + # Find the peak dW in the edge region and truncate integration data there. + # Uses raw (pre-transform) u_store: after transform_u!, edge-zone steps can acquire + # large positive garbage et values from ill-conditioned transform products, pushing the + # detected peak to the wrong location. Raw U₁ produces garbage as large negative values + # (safely excluded from the max search), so the few well-conditioned steps near psiedge + # cleanly dominate the peak. odet.step = findmax_dW_edge!(odet, ctrl, equil, ffit, intr) trim_storage!(odet) if ctrl.verbose @info "Truncating integration at peak edge dW: ψ = $((@sprintf "%.3f" odet.psi_store[odet.step])), q = $((@sprintf "%.3f" odet.q_store[odet.step]))" end - # Update u, psilim, and qlim for usage in determining wp and wt + # Update psilim, qlim, and u to the truncated boundary (peak dW step). + # qlim is updated to q at the truncation psi so that free_run!'s singfac = (m - n*q_boundary) + # matches the actual safety factor at the plasma boundary, consistent with free_compute_total's + # scan metric and with the develop-branch convention (qlim = q at psilim). intr.psilim = odet.psi_store[end] - intr.qlim = odet.q_store[end] + intr.qlim = odet.q_store[end] odet.u .= odet.u_store[:, :, :, end] else odet.step -= 1 # step was incremented one extra time in integrate_el_region! trim_storage!(odet) end - # Evaluate stability criterion (critical determinant) of saved solutions + # Form the true solution vectors (undo the Gaussian reductions from fixups). + transform_u!(odet, intr) + + # Evaluate stability criterion (critical determinant) of saved solutions. if ctrl.verbose @info "Evaluating fixed-boundary stability criterion" end odet.nzero = evaluate_stability_criterion!(odet, equil.profiles) - # Form the true solution vectors, undoing the Gaussian reduction applied in `ode_unorm!` during integration - transform_u!(odet, intr) - return odet end @@ -336,11 +356,11 @@ making it clear what region is being integrated. ### TODOs -Check sensitivity of results to tolerances, currently using same logic as Fortran -Check absolute tolerances, currently only relative tolerances are updated +Check sensitivity of results to tolerances +Explore absolute tolerances to reduce the number of steps taken in the core """ function integrate_el_region!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, intr::ForceFreeStatesInternal, chunk::IntegrationChunk) - + # Fraction of the q-range defining "near boundary" dense-save zones at each end of # a segment. TODO: expose as a ctrl field when a good default is validated. near_q_frac = 0.05 @@ -348,27 +368,30 @@ function integrate_el_region!(odet::OdeState, ctrl::ForceFreeStatesControl, equi # q at segment boundaries — used for symmetric near-boundary heuristic. # odet.q is updated at every step inside sing_der!, so we compare against these # fixed endpoints in the callback rather than using psi-based distances. - q_start = equil.profiles.q_spline(chunk.psi_start) - q_end = equil.profiles.q_spline(chunk.psi_end) + psihigh = equil.profiles.xs[end] + q_start = eval_q(equil.profiles, chunk.psi_start) + q_end = eval_q(equil.profiles, chunk.psi_end) q_range = abs(q_end - q_start) steps_in_segment = Ref(0) function segment_callback!(integrator) - ctrl, _, _, intr, odet, chunk = integrator.p + ctrl, equil, _, intr, odet, chunk = integrator.p odet.total_steps += 1 steps_in_segment[] += 1 - compute_solution_norms!(integrator.u, odet, ctrl, intr, false) + is_above_psihigh = integrator.t > equil.profiles.xs[end] && !isnothing(equil.profiles.iota_spline) + compute_solution_norms!(integrator.u, odet, ctrl, intr, false, is_above_psihigh) # Save near segment boundaries (symmetric, in q not psi) and every Nth step. # The step-count fallback (== 1) guarantees the first step is always saved # even for near-degenerate segments where q_range ≈ 0. near_start = abs(odet.q - q_start) < near_q_frac * q_range || steps_in_segment[] == 1 near_end = abs(odet.q - q_end) < near_q_frac * q_range + above_psiedge = ctrl.psiedge <= integrator.t - if near_start || near_end || (odet.step % ctrl.save_interval == 0) + if above_psiedge || near_start || near_end || (odet.step % ctrl.save_interval == 0) if odet.step >= size(odet.u_store, 4) resize_storage!(odet) end @@ -397,7 +420,6 @@ function integrate_el_region!(odet::OdeState, ctrl::ForceFreeStatesControl, equi @views odet.ud_store[:, :, :, odet.step] .= odet.ud odet.step += 1 end - odet.u .= sol.u[end] odet.psifac = sol.t[end] end @@ -427,7 +449,7 @@ operate on `u` directly without extra copies. Add resizing logic for unorm arrays when ifix exceeds allocated size """ -function compute_solution_norms!(u::Array{ComplexF64,3}, odet::OdeState, ctrl::ForceFreeStatesControl, intr::ForceFreeStatesInternal, sing_flag::Bool) +function compute_solution_norms!(u::Array{ComplexF64,3}, odet::OdeState, ctrl::ForceFreeStatesControl, intr::ForceFreeStatesInternal, sing_flag::Bool, is_above_psihigh::Bool=false) # Compute norms of first solution vectors, abort if any are zero odet.unorm .= norm.(eachcol(u[:, :, 1])) @@ -436,14 +458,18 @@ function compute_solution_norms!(u::Array{ComplexF64,3}, odet::OdeState, ctrl::F error("One of the first solution vector norms unorm(1,$jmax) = 0") end - # Normalize unorm and perform Gaussian reduction if required + # Normalize unorm and perform Gaussian reduction if required. + # Above psihigh, use ucrit/10 to trigger more frequent fixups: the ODE is stiffer + # (q→∞ near separatrix), so u grows faster between fixups and pre-fixup steps have + # large wp = U₂/U₁ eigenvalues that would otherwise dominate the edge dW scan. + effective_ucrit = is_above_psihigh ? ctrl.ucrit / 10 : ctrl.ucrit if odet.new odet.new = false odet.unorm0 .= odet.unorm else odet.unorm ./= odet.unorm0 uratio = maximum(odet.unorm) / minimum(odet.unorm) - if uratio > ctrl.ucrit || sing_flag + if uratio > effective_ucrit || sing_flag # TODO: add resizing logic here as well if odet.ifix < ctrl.numunorms_init odet.ifix += 1 @@ -522,23 +548,59 @@ for clarity. We create the wv matrix spline once prior to the loop. """ function findmax_dW_edge!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, intr::ForceFreeStatesInternal) - # Since we search for the maximum dW, initialize to -Infinity - fill!(odet.dW_edge, -Inf * (1 + im)) + # After integration, odet.step is one-past-the-last-valid index: each save stores at + # psi_store[step] then increments step. So valid indices are 1:(odet.step-1). + nsteps = odet.step - 1 - # Create a rough spline for wv matrix between psiedge -> psilim so we can approximate dW - odet.wvmat = free_compute_wv_spline(ctrl, equil, intr) - - # Loop through integration, compute dW at steps where psifac >= psiedge - for istep in 1:odet.step + # Since we search for the maximum dW, initialize to -Infinity. + # Resize to match valid step count (integration may have grown beyond numsteps_init). + resize!(odet.dW_edge, nsteps) + fill!(odet.dW_edge, -Inf * (1 + im)) + ep_edge = fill(-Inf * (1 + im), nsteps) + ev_edge = fill(-Inf * (1 + im), nsteps) + evonly_edge = fill(-Inf, nsteps) + + # Create a spline for wv matrix covering the actual stored integration range. + # Use odet.step - 1 (last valid index) to avoid reading uninitialized over-allocated slots. + psi_scan_end = odet.psi_store[nsteps] + odet.wvmat = free_compute_wv_spline(ctrl, equil, intr, psi_scan_end) + + # Loop through all stored steps in [psiedge, psilim] and compute dW at each. + # The ucrit/10 reduction above psihigh suppresses ODE fixup artifacts at edge rational + # surfaces so that the physical stability peak dominates the scan. + for istep in 1:nsteps odet.psifac = odet.psi_store[istep] - if odet.psifac >= ctrl.psiedge + if ctrl.psiedge <= odet.psifac odet.u .= odet.u_store[:, :, :, istep] - odet.dW_edge[istep] = free_compute_total(equil, ffit, intr, odet) + try + result = free_compute_total(equil, ffit, intr, odet) + odet.dW_edge[istep] = result.et + ep_edge[istep] = result.ep + ev_edge[istep] = result.ev + evonly_edge[istep] = result.evonly + catch e + e isa LinearAlgebra.SingularException || rethrow(e) + # U₁ is singular or kinetic norm is non-positive at this step; skip it. + # dW_edge remains -Inf so this step is ignored in the max search. + end end end - # Return the index that maximizes dW_edge to identify truncation point - return findmax(real.(odet.dW_edge))[2] + # Extract ALL psi values from psiedge to psilim, storing NaN for steps where + # free_compute_total failed (SingularException). This preserves the full edge stability + # picture for the user: NaN clusters reveal where the splines become ill-conditioned, + # and the full range allows verifying that the peak is not a boundary artifact. + # The u_store is separately trimmed to the peak step after this function returns. + psiedge_idxs = findall(i -> odet.psi_store[i] >= ctrl.psiedge, 1:nsteps) + odet.psi_edge_scan = odet.psi_store[psiedge_idxs] + odet.et_edge_scan = ComplexF64[isfinite(real(odet.dW_edge[i])) ? odet.dW_edge[i] : complex(NaN) for i in psiedge_idxs] + odet.ep_edge_scan = ComplexF64[isfinite(real(ep_edge[i])) ? ep_edge[i] : complex(NaN) for i in psiedge_idxs] + odet.ev_edge_scan = ComplexF64[isfinite(real(ev_edge[i])) ? ev_edge[i] : complex(NaN) for i in psiedge_idxs] + odet.evonly_edge_scan = Float64[isfinite(evonly_edge[i]) ? evonly_edge[i] : NaN for i in psiedge_idxs] + + # Return the index that maximizes dW_edge to identify the truncation point. + et_clean = replace(real.(odet.dW_edge), NaN => -Inf) + return findmax(et_clean)[2] end """ @@ -600,8 +662,9 @@ function transform_u!(odet::OdeState, intr::ForceFreeStatesInternal) # "undoing" the Gaussian reductions to get the true solution vectors jfix = 1 for ifix in 1:(odet.ifix+1) - # If after the last fixup, go to the end of integration - kfix = ifix != odet.ifix + 1 ? odet.fixstep[ifix] : odet.step + jfix > odet.step && break + # If after the last fixup (or the fixup is beyond trimmed storage), go to stored end + kfix = ifix != odet.ifix + 1 ? min(odet.fixstep[ifix], odet.step) : odet.step @views for istep in jfix:kfix # This is u1->u4 in Fortran mul!(gauss_buffer, odet.u_store[:, :, 1, istep], transforms[:, :, ifix]) diff --git a/src/ForceFreeStates/FixedBoundaryStability.jl b/src/ForceFreeStates/FixedBoundaryStability.jl index 92a41f85..ce38a93a 100644 --- a/src/ForceFreeStates/FixedBoundaryStability.jl +++ b/src/ForceFreeStates/FixedBoundaryStability.jl @@ -61,11 +61,31 @@ can do it post-integration rather than during and don't directly handle file out # Compute smallest eigenvalue (crit) at current step # Use shared hint with LinearBinary() search for O(1) interval lookup during sequential stability evaluation + # Helper: evaluate dV/dψ using the edge inverse spline when psi is beyond the direct + # spline domain (psi > psihigh). This arises in post-integration stability evaluation + # when the ODE integrated beyond psihigh in a diverted plasma. + function eval_dVdpsi(psi_eval) + if psi_eval <= profiles.xs[end] || isnothing(profiles.dVdpsi_inv_spline) + return profiles.dVdpsi_spline(psi_eval; hint=odet.spline_hint) + else + return 1.0 / profiles.dVdpsi_inv_spline(psi_eval; hint=profiles._dVdpsi_inv_hint) + end + end + u = acquire!(pool, eltype(odet.u_store), size(odet.u_store)[1:3]) psi = odet.psi_store[istep] u .= odet.u_store[:, :, :, istep] - dVdpsi = profiles.dVdpsi_spline(psi; hint=odet.spline_hint) - crit_val, nonherm = compute_smallest_eigenvalue(u) + dVdpsi = eval_dVdpsi(psi) + crit_val, nonherm = try + compute_smallest_eigenvalue(u) + catch e + e isa LinearAlgebra.SingularException || rethrow(e) + # U₂ is singular at this step (degenerate solution near a rational surface or separatrix). + # Propagate the previous crit_store value to avoid a spurious zero crossing. + prev_crit = istep > 1 ? odet.crit_store[istep-1] : 0.0 + odet.crit_store[istep] = prev_crit + return false, false + end odet.crit_store[istep] = crit_val * dVdpsi^2 # Check for zero crossing via change in sign of crit between current and previous step @@ -77,7 +97,7 @@ can do it post-integration rather than during and don't directly handle file out fac = crit / (crit - crit_prev) psi_mid = psi - fac * (psi - odet.psi_store[istep-1]) u_mid = u .- fac .* (u .- @view(odet.u_store[:, :, :, istep-1])) - dVdpsi = profiles.dVdpsi_spline(psi_mid; hint=odet.spline_hint) + dVdpsi = eval_dVdpsi(psi_mid) crit_mid_val, _ = compute_smallest_eigenvalue(u_mid) crit_mid = crit_mid_val * dVdpsi^2 if (crit_mid - crit) * (crit_mid - crit_prev) < 0 && abs(crit_mid) < 0.5 * min(abs(crit), abs(crit_prev)) diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl index 7d580322..010d1769 100644 --- a/src/ForceFreeStates/ForceFreeStates.jl +++ b/src/ForceFreeStates/ForceFreeStates.jl @@ -9,11 +9,12 @@ using OrdinaryDiffEq using HDF5 using JLD2 using FastInterpolations -using FastInterpolations: cubic_interp, deriv1, PeriodicBC, LinearBinary +using FastInterpolations: cubic_interp, deriv1, PeriodicBC, LinearBinary, CubicFit, ExtendExtrap, NoExtrap using AdaptiveArrayPools using Roots import ..Equilibrium +using ..Equilibrium: eval_q import ..Utilities import ..Vacuum using Printf diff --git a/src/ForceFreeStates/ForceFreeStatesStructs.jl b/src/ForceFreeStates/ForceFreeStatesStructs.jl index 98b70747..f34a0878 100644 --- a/src/ForceFreeStates/ForceFreeStatesStructs.jl +++ b/src/ForceFreeStates/ForceFreeStatesStructs.jl @@ -177,8 +177,6 @@ A mutable struct containing control parameters for stability analysis, set by th - `numunorms_init::Int` - Initial array size for solution normalization data - `singfac_min::Float64` - Fractional distance from rational q at which ideal jump condition is enforced - `cyl_flag::Bool` - Make delta_mlow and delta_mhigh set the actual m truncation bounds. Default is to expand (n*qmin-4, n*qmax). - - `set_psilim_via_dmlim::Bool` - Determine psilim truncation from outermost rational + dmlim - - `dmlim::Float64` - Distance beyond last rational surface (as percentage) - `sing_order::Int` - Order of singular layer expansion - `qhigh::Float64` - Integration terminated at q limit determined by minimum of qhigh and qa from equil - `kin_flag::Bool` - Enable kinetic effects @@ -204,6 +202,7 @@ A mutable struct containing control parameters for stability analysis, set by th - `force_wv_symmetry::Bool` - Boolean flag to enforce symmetry in the vacuum response matrix - `save_interval::Int` - Save every Nth ODE step (1=all, 10=every 10th). Always saves near rational surfaces. (Same as `euler_step` in the Fortran) - `force_termination::Bool` - Terminate after force-free states (skip perturbed equilibrium calculations) + - `edge_layer_width::Float64` - Spacing in ψ below which edge rational surfaces are considered too dense (in the separatrix layer). Default 1e-4. """ @kwdef mutable struct ForceFreeStatesControl verbose::Bool = true @@ -230,8 +229,6 @@ A mutable struct containing control parameters for stability analysis, set by th numunorms_init::Int = 100 singfac_min::Float64 = 0.0 cyl_flag::Bool = false - set_psilim_via_dmlim::Bool = false - dmlim::Float64 = 0.2 sing_order::Int = 2 qhigh::Float64 = 1e3 kin_flag::Bool = false @@ -257,6 +254,7 @@ A mutable struct containing control parameters for stability analysis, set by th force_wv_symmetry::Bool = true save_interval::Int = 3 force_termination::Bool = false + edge_layer_width::Float64 = 1e-4 # psifac spacing below which edge rational surfaces are ignored end @kwdef mutable struct FourFitVars{S<:CubicSeriesInterpolant,Opts<:NamedTuple} @@ -286,8 +284,9 @@ end # Shared hint for sequential evaluation (all splines evaluated at same psi) _hint::Base.RefValue{Int} = Ref(1) - # Used in Free.jl - jmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, 2 * mband + 1) + # Spline of Jacobian Fourier coefficients J(θ, ψ) vs ψ, shape (2*mband+1) series. + # Evaluate at the local psi (psilim in free_run!, odet.psifac in free_compute_total). + jmat_spline::S = _empty_series_interp_complex(2 * mband + 1, itp_opts) end # Helper to create empty complex series interpolant for default initialization @@ -374,6 +373,11 @@ and a small set of temporary matrices and factors used to compute singular-layer - `ca_l::Array{ComplexF64,4}` - Asymptotic coefficients just to the left of each singular surface with shape `(numpert_total, numpert_total, 2, msing)`. - `dW_edge::Vector{ComplexF64}` - dW values computed in the psiedge < psilim region for each stored step (length `numsteps_init`). + - `psi_edge_scan::Vector{Float64}` - ψ values from the edge dW scan (psiedge → psilim), populated by `findmax_dW_edge!` before storage is trimmed. + - `et_edge_scan::Vector{ComplexF64}` - Corresponding total energy eigenvalue et[1] at each edge-scan ψ, for diagnostic output to HDF5. + - `ep_edge_scan::Vector{ComplexF64}` - Corresponding plasma energy component at each edge-scan ψ. + - `ev_edge_scan::Vector{ComplexF64}` - Corresponding vacuum energy component at each edge-scan ψ. + - `evonly_edge_scan::Vector{Float64}` - Least stable eigenvalue of the wv matrix alone (EL-independent), for diagnosing wv spline quality. - `wvmat::CubicSeriesInterpolant{Float64,ComplexF64}` - Complex-valued precomputed wv matrices used by `free_test`/vacuum routines. - `psifac::Float64` - Current normalized flux coordinate for the integrator. - `q::Float64` - Safety factor value at `psifac` (current q during integration). @@ -404,7 +408,7 @@ and a small set of temporary matrices and factors used to compute singular-layer # Saved data throughout integration step::Int = 1 - total_steps::Int = 0 # Total ODE solver steps taken (all steps, not just saved ones) + total_steps::Int = 0 # Total ODE solver steps taken (all steps, not just saved ones) psi_store::Vector{Float64} = Vector{Float64}(undef, numsteps_init) q_store::Vector{Float64} = Vector{Float64}(undef, numsteps_init) u_store::Array{ComplexF64,4} = Array{ComplexF64}(undef, numpert_total, numpert_total, 2, numsteps_init) @@ -415,6 +419,13 @@ and a small set of temporary matrices and factors used to compute singular-layer # Used for to find peak dW in the edge dW_edge::Vector{ComplexF64} = Array{ComplexF64}(undef, numsteps_init) + # Edge stability diagnostic: psi and et[1] for every step in [psiedge, psilim], + # saved to HDF5 before the storage is trimmed to the peak-dW step. + psi_edge_scan::Vector{Float64} = Float64[] + et_edge_scan::Vector{ComplexF64} = ComplexF64[] + ep_edge_scan::Vector{ComplexF64} = ComplexF64[] + ev_edge_scan::Vector{ComplexF64} = ComplexF64[] + evonly_edge_scan::Vector{Float64} = Float64[] wvmat::CubicSeriesInterpolant{Float64,ComplexF64} = _empty_series_interp_complex(numpert_total^2) _wv_out::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, numpert_total, numpert_total) diff --git a/src/ForceFreeStates/Fourfit.jl b/src/ForceFreeStates/Fourfit.jl index fca16a8c..4d777d6f 100644 --- a/src/ForceFreeStates/Fourfit.jl +++ b/src/ForceFreeStates/Fourfit.jl @@ -45,6 +45,11 @@ The metric coefficients stored in `metric.fs` include: - `mband::Int`: Number of Fourier modes to retain in the metric representation. - `fft_flag::Bool`: If `true`, enables use of Fourier fitting for storing metric coefficients. + - `psilim::Float64`: Upper psi limit for the metric grid (default: Inf = full grid). For + diverted plasmas the caller passes `intr.psilim` (set by `sing_lim!` from edge rational + surfaces), which extends above `psihigh` to include the near-separatrix edge region while + remaining well-behaved (psilim << 1). Nodes all the way to psin=1 are excluded because + the X-point geometry gives J→∞ there. ### Returns @@ -56,18 +61,24 @@ The metric coefficients stored in `metric.fs` include: Add kinetic metric tensor components for kin_flag = true Remove mband if we decide to fully deprecate banded matrices """ -function make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int, fft_flag::Bool) +function make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int, fft_flag::Bool, psilim::Float64=Inf) # TODO: add kinetic metric tensor components # --- Extract data from the PlasmaEquilibrium object --- - mpsi = length(equil.rzphi_xs) + # Truncate the rzphi_xs grid at psilim. For diverted plasmas psilim is set by sing_lim! + # from the edge rational surfaces, extending above psihigh but well below psin=1 where + # J→∞ at the X-point. Including these well-behaved near-separatrix nodes gives accurate + # FGK splines for the above-psihigh ODE chunks instead of ExtendExtrap frozen at psihigh. + profiles = equil.profiles + mpsi_full = length(equil.rzphi_xs) + mpsi = isfinite(psilim) ? searchsortedlast(equil.rzphi_xs, psilim) : mpsi_full mtheta = length(equil.rzphi_ys) # Set coordinate grids based on the input equilibrium # The equil.rzphi_ys is normalized (0 to 1), so scale to radians. metric = MetricData(mpsi, mtheta) - metric.xs .= equil.rzphi_xs + metric.xs .= @view equil.rzphi_xs[1:mpsi] metric.ys .= equil.rzphi_ys .* 2π # Temporary array for contravariant basis vectors @@ -176,6 +187,7 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates fmats_lower_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) gmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) kmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) + jmat_flat = zeros(ComplexF64, mpsi, 2 * intr.mband + 1) # jmat vs psi spline data g11 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) g22 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) g33 = Vector{ComplexF64}(undef, 2 * intr.mband + 1) @@ -206,11 +218,11 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates gmats_flatview = @view gmats_flat[ipsi, :] kmats_flatview = @view kmats_flat[ipsi, :] # --- Profiles --- - psi = profiles.xs[ipsi] + psi = metric.xs[ipsi] p1 = profiles.P_deriv(psi; hint=hint) - q = profiles.q_spline.y[ipsi] - q1 = profiles.q_deriv(psi; hint=hint) + # F' and P' use ExtendExtrap above psihigh — physically correct since F' ≈ 0, P' ≈ 0 near separatrix. jtheta = -profiles.F_deriv(psi; hint=hint) + q, q1 = eval_q(profiles, psi; deriv=1, output_lower_derivs=true, hint=hint) chi1 = 2π * equil.psio # Fill lower half (modes 0, 1, ..., mband at indices mid, mid-1, ..., 1) @@ -239,6 +251,8 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates jmat1[mid+k] = conj(jmat1[mid-k]) end + jmat_flat[ipsi, :] .= jmat + # TODO: for 3D, would need an additional nlow:nhigh loop here for n/n' coupling for n in intr.nlow:intr.nhigh ipert_n = n - intr.nlow + 1 @@ -325,12 +339,10 @@ function make_matrix(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStates ffit.fmats_lower = cubic_interp(metric.xs, fmats_lower_flat; ffit.itp_opts...) ffit.gmats = cubic_interp(metric.xs, gmats_flat; ffit.itp_opts...) ffit.kmats = cubic_interp(metric.xs, kmats_flat; ffit.itp_opts...) + ffit.jmat_spline = cubic_interp(metric.xs, jmat_flat; ffit.itp_opts...) # TODO: set powers # Do we need this yet? Only called if power_flag = true - # This is used in free_run - ffit.jmat = jmat - return ffit end diff --git a/src/ForceFreeStates/Free.jl b/src/ForceFreeStates/Free.jl index 9c8ec89c..b2ab231f 100644 --- a/src/ForceFreeStates/Free.jl +++ b/src/ForceFreeStates/Free.jl @@ -18,8 +18,12 @@ and data dumping. wvt = zeros!(pool, ComplexF64, numpert_total, numpert_total) tmp_mat = zeros!(pool, ComplexF64, numpert_total, numpert_total) - # Evaluate dV/dpsi at the plasma edge - dV_dpsi = equil.profiles.dVdpsi_spline(psilim) + # Evaluate dV/dpsi at the plasma edge. For diverted plasmas psilim can exceed psihigh, + # so route to the edge inverse spline when available and psilim is beyond the core grid. + profiles = equil.profiles + dV_dpsi = intr.psilim > profiles.xs[end] ? + 1.0 / profiles.dVdpsi_inv_spline(intr.psilim; hint=profiles._dVdpsi_inv_hint) : + profiles.dVdpsi_spline(psilim) # Compute plasma response matrix W = U₂ * U₁⁻¹ if ctrl.ode_flag @@ -51,13 +55,14 @@ and data dumping. vac_data.et[ipert] = etemp[eindex[numpert_total+1-ipert]] end - # Normalize eigenfunction and energy. + # Normalize eigenfunction and energy using J(ψ) evaluated at the plasma boundary psilim. + jmat_at_psilim = ffit.jmat_spline(psilim) for isol in 1:numpert_total norm = 0.0 + 0.0im for ipert_n in 1:npert, ipert_m in 1:mpert, jpert_m in 1:mpert ipert = (ipert_n - 1) * mpert + ipert_m jpert = (ipert_n - 1) * mpert + jpert_m - norm += ffit.jmat[jpert_m-ipert_m+mband+1] * vac_data.wt[ipert, isol] * conj(vac_data.wt[jpert, isol]) + norm += jmat_at_psilim[jpert_m-ipert_m+mband+1] * vac_data.wt[ipert, isol] * conj(vac_data.wt[jpert, isol]) end norm /= dV_dpsi vac_data.wt[:, isol] ./= sqrt(norm) @@ -110,35 +115,67 @@ end """ free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal) -Compute a spline of vacuum response matrices over the range of psi from 'ctrl.psi_edge' to -`intr.qlim`. This is used for fast evaluation of wt during `ode_record_edge`. Performs the -same function as `free_wvmats` in the Fortran code. Currently defaults to 4 spline points per -q-window minimum. +Compute a spline of vacuum response matrices over [psiedge, psilim], evenly spaced in q. +Used for fast evaluation of wt during `findmax_dW_edge!`. Performs the same function as +`free_wvmats` in the Fortran code. Defaults to 9 spline points per rational window. + +Grid design: points are spaced evenly in q from qedge+ε to qlim+ε (i/npsi offset reproduces +the develop-branch qi logic). This concentrates nodes near rational surfaces where the vacuum +response varies most rapidly, giving accurate wv interpolation across the full scan range. +For diverted plasmas where psilim > psihigh, the iota inverse spline is used to invert q(psi) +above psihigh. + +The spline stores RAW vacuum response without singfac scaling. Singfac = (m - n*q) is +applied analytically in free_compute_total at each scan psi, keeping the spline +well-conditioned despite q divergence near the separatrix. """ -function free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal) +function free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal, _psi_scan_end::Float64) - profiles = equil.profiles + profiles = equil.profiles + psihigh = profiles.xs[end] + has_edge_q = !isnothing(profiles.iota_spline) - # Number of psi grid points for the spline: 4 per q-window minimum - # TODO: 4 spline points is arbitrary - is there a better way? - qedge = profiles.q_spline(ctrl.psiedge) - npsi = max(4, ceil(Int, (intr.qlim - qedge) * intr.nhigh * 4)) - psi_array = zeros(Float64, npsi + 1) - wv_array = zeros(ComplexF64, npsi + 1, intr.numpert_total, intr.numpert_total) + qedge = profiles.q_spline(ctrl.psiedge) + q_at_psihigh = profiles.q_spline(psihigh) - for i in 1:(npsi+1) - # Space points evenly in q - qi = qedge + (intr.qlim - qedge) * (i / npsi) + # For diverted plasmas, extend the spline above psihigh using the X-point asymptotic + # geometry — the same geometry used by the FGK splines and jmat_spline. The upper limit + # is the end of the iota spline grid (last edge rational surface), capped at the + # last stored ODE step to avoid computing vacuum responses past the scan range. + psi_upper = has_edge_q ? min(_psi_scan_end, equil.rzphi_xs[end]) : psihigh + q_at_upper = (has_edge_q && psi_upper > psihigh) ? eval_q(profiles, psi_upper) : q_at_psihigh - psii = ctrl.psiedge + (intr.psilim - ctrl.psiedge) * ((i - 1) / npsi) - psi_array[i] = find_zero( - (psi -> profiles.q_spline(psi) - qi, - psi -> profiles.q_deriv(psi)), - psii, Roots.Newton() - ) + # Number of grid points: 9 per rational window over [qedge, q_at_upper] + npsi = max(9, ceil(Int, (q_at_upper - qedge) * intr.nhigh * 9)) + psi_array = zeros(Float64, npsi + 1) + wv_array = zeros(ComplexF64, npsi + 1, intr.numpert_total, intr.numpert_total) + + for i in 1:(npsi + 1) + qi = qedge + (q_at_upper - qedge) * ((i-1) / npsi) + + if qi <= q_at_psihigh || !has_edge_q + # Core region [psiedge, psihigh]: invert q(psi) = qi using the direct spline + psii = ctrl.psiedge + (psihigh - ctrl.psiedge) * ((qi - qedge) / (q_at_psihigh - qedge)) + jpsi = max(1, searchsortedlast(profiles.q_spline.y, qi)) + hint = Ref(min(jpsi, profiles.npts_minus_1)) + psi_array[i] = find_zero( + (psi -> profiles.q_spline(psi; hint=hint) - qi, + psi -> profiles.q_deriv(psi; hint=hint)), + psii, Roots.Newton() + ) + else + # Edge region (psihigh, psi_upper]: invert iota(psi) = 1/qi using iota spline + iota_target = 1.0 / qi + psii = psihigh + (psi_upper - psihigh) * ((qi - q_at_psihigh) / (q_at_upper - q_at_psihigh)) + psi_array[i] = find_zero( + (psi -> profiles.iota_spline(psi; hint=profiles._iota_hint) - iota_target, + psi -> profiles.iota_spline(psi; deriv=1, hint=profiles._iota_hint)), + psii, Roots.Newton() + ) + end # Compute vacuum response matrix at this psi (2D single-n, 2D multi-n block-diagonal, or 3D) - vac_inputs = Vacuum.VacuumInput(equil, psii, ctrl.mthvac, ctrl.nzvac, intr.mpert, intr.mlow, intr.npert, intr.nlow; force_wv_symmetry=ctrl.force_wv_symmetry) + vac_inputs = Vacuum.VacuumInput(equil, psi_array[i], ctrl.mthvac, ctrl.nzvac, intr.mpert, intr.mlow, intr.npert, intr.nlow; force_wv_symmetry=ctrl.force_wv_symmetry) wv, _, _, _, _ = Vacuum.compute_vacuum_response(vac_inputs, intr.wall_settings) # Apply singular factor scaling: (m - n*q)(m' - n'*q) [Chance Phys. Plasmas 1997 2161 eq. 126] @@ -151,12 +188,8 @@ function free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium @views wv_array[i, :, :] .= wv end - # Flatten 3D array to (npsi+1 × numpert_total^2) for series interpolant wv_flat = reshape(wv_array, npsi + 1, intr.numpert_total^2) - - # FastInterpolations now natively supports complex values - create complex series interpolant directly - # Use CubicFit() for native endpoint handling - wvmat = cubic_interp(psi_array, wv_flat; bc=CubicFit(), extrap=ExtendExtrap(), search=LinearBinary()) + wvmat = cubic_interp(psi_array, wv_flat; bc=CubicFit(), extrap=NoExtrap(), search=LinearBinary()) return wvmat end @@ -177,37 +210,73 @@ function free_compute_total(equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitV tot_eigvals = zeros(ComplexF64, intr.numpert_total) wt = zeros(ComplexF64, intr.numpert_total, intr.numpert_total) - dV_dpsi = equil.profiles.dVdpsi_spline(intr.psilim) - - # Compute plasma response matrix - @views wp = (odet.u[:, :, 2] / odet.u[:, :, 1]) ./ equil.psio^2 + profiles = equil.profiles - # Compute vacuum matrix from series interpolant (use separate hint for wv grid) - # FastInterpolations now natively supports complex values + # Compute plasma response matrix W = U₂·U₁⁻¹ / psio². + # Direct matrix division without column normalization, matching the develop-branch approach. + # Column normalization was found to over-correct well-conditioned steps near core rational + # surfaces (e.g. just after a q=3 fixup), giving them artificially large et values that + # dominate the peak search. Without column normalization, those steps give garbage or + # negative eigenvalues (naturally excluded from findmax), and only physically meaningful + # steps (well away from fixup boundaries near the edge) give large positive et. + wp = (@view(odet.u[:, :, 2]) / @view(odet.u[:, :, 1])) ./ equil.psio^2 + + # Retrieve raw vacuum matrix from the spline (singfac NOT pre-applied; see free_compute_wv_spline). + # Apply singfac = (m - n*q(psifac)) analytically: this is the physically correct choice for + # the scan, since at each scan step we are evaluating stability as if the plasma boundary + # were at psifac, where q(psifac) is the actual safety factor at that boundary. + # For psi > psihigh, use the iota inverse spline (if available) to get q. odet.wvmat(vec(odet._wv_out), odet.psifac; hint=odet.wv_hint) - wv = odet._wv_out + wv = copy(odet._wv_out) + q_at_psifac = eval_q(profiles, odet.psifac) + for ipert_n in 1:intr.npert + n = ipert_n - 1 + intr.nlow + singfac = collect(intr.mlow:intr.mhigh) .- (n * q_at_psifac) + block = ((ipert_n-1)*intr.mpert+1):(ipert_n*intr.mpert) + # wv[i,j] = wv_raw[i,j] * singfac[i] * singfac[j] (outer-product row×column scaling) + @views wv[block, block] .= singfac .* wv[block, block] .* singfac' + end - # Compute total energy matrix and eigen-decomposition + # Compute total energy matrix and eigen-decomposition. + # wt = wp + wv should be Hermitian by construction, but ODE roundoff accumulates over many + # integration steps. Enforcing the Hermitian structure (as in compute_smallest_eigenvalue) + # guarantees real eigenvalues and orthonormal eigenvectors. wt .= wp .+ wv - Ev = eigen(wt) + hermitianpart!(wt) + Ev = eigen(Hermitian(wt)) - # Sort eigenvalues and reorder columns of wt - eindex = sortperm(real.(Ev.values); rev=true) + # Sort eigenvalues and reorder columns of wt (Ev.values are real for Hermitian) + eindex = sortperm(Ev.values; rev=true) for ipert in 1:intr.numpert_total wt[:, ipert] .= Ev.vectors[:, eindex[intr.numpert_total+1-ipert]] tot_eigvals[ipert] = Ev.values[eindex[intr.numpert_total+1-ipert]] end - # Normalize eigenfunction and energy (only need the first eigenmode) - isol = 1 - norm = 0.0 + 0.0im + # Compute plasma and vacuum energy components for the dominant (smallest eigenvalue) eigenvector. + # wt[:,1] now holds the eigenvector corresponding to tot_eigvals[1]. + v = @view wt[:, 1] + ep1 = ComplexF64(dot(v, wp * v)) + ev1 = ComplexF64(dot(v, wv * v)) + + # Least stable eigenvalue of the vacuum matrix alone (EL-solution-independent diagnostic). + evonly1 = minimum(real(eigvals(Hermitian((wv + wv') / 2)))) + + # Normalize eigenvalue by ξ†J(psifac)ξ / dV_dψ(psifac), where J is evaluated at the local + # scan psi so the normalization is physically consistent at each point of the edge scan. + dV_dpsi = (!isnothing(profiles.dVdpsi_inv_spline) && odet.psifac > profiles.xs[end]) ? + 1.0 / profiles.dVdpsi_inv_spline(odet.psifac; hint=profiles._dVdpsi_inv_hint) : + profiles.dVdpsi_spline(odet.psifac) + jmat_local = ffit.jmat_spline(odet.psifac) + norm_kin = zero(ComplexF64) for ipert_n in 1:intr.npert, ipert_m in 1:intr.mpert, jpert_m in 1:intr.mpert ipert = (ipert_n - 1) * intr.mpert + ipert_m jpert = (ipert_n - 1) * intr.mpert + jpert_m - norm += ffit.jmat[jpert_m-ipert_m+intr.mband+1] * wt[ipert, isol] * conj(wt[jpert, isol]) + jidx = jpert_m - ipert_m + intr.mband + 1 + norm_kin += jmat_local[jidx] * v[ipert] * conj(v[jpert]) end - norm /= dV_dpsi - tot_eigvals[isol] /= norm + norm_kin /= dV_dpsi + real(norm_kin) > 0 || throw(LinearAlgebra.SingularException(0)) + et_normalized = tot_eigvals[1] / norm_kin - return tot_eigvals[1] + return (et=et_normalized, ep=ep1, ev=ev1, evonly=evonly1) end diff --git a/src/ForceFreeStates/Sing.jl b/src/ForceFreeStates/Sing.jl index 2a9bc2f3..1923e5ae 100644 --- a/src/ForceFreeStates/Sing.jl +++ b/src/ForceFreeStates/Sing.jl @@ -1,11 +1,14 @@ """ - sing_find!(intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium) + sing_find!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium) Locate singular rational q-surfaces (q = m/nn) using a bisection method between extrema of the q-profile, and store their properties in `intr.sing`. +For diverted plasmas with edge inverse splines available, also searches for rational +surfaces above psihigh using the iota = 1/q inverse spline, stopping when consecutive +surface spacing falls below `ctrl.edge_layer_width` (the near-separatrix dense layer). Performs the same function as `sing_find` in the Fortran code. """ -function sing_find!(intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium) +function sing_find!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium) profiles = equil.profiles @@ -51,66 +54,157 @@ function sing_find!(intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEqui end # Sort singular surfaces by increasing ψ intr.sing = sort(intr.sing; by=s -> s.psifac) + + # Extended rational surface search above psihigh for diverted plasmas. + # Uses the iota = 1/q inverse spline which is well-behaved toward the separatrix. + # Stops adding surfaces when spacing between consecutive surfaces < edge_layer_width. + if !isnothing(profiles.iota_spline) + psihigh = equil.config.psihigh + q_at_psihigh = profiles.q_spline.y[end] # q at last direct-spline node + + for n in intr.nlow:intr.nhigh + psi_last = psihigh + # Find first m above current q (increasing q, monotone in edge) + m = trunc(Int, n * q_at_psihigh) + 1 + hint = Ref(1) + while true + iota_target = n / m # iota = 1/q at the target rational surface + + # iota(psihigh) > iota_target > 0 = iota(1.0), so Brent finds the root + iota_at_psihigh = profiles.iota_spline(psihigh; hint=hint) + if iota_target >= iota_at_psihigh + # Surface is below psihigh — already found in core search + m += 1 + continue + end + + # Find psi where iota(psi) = iota_target via Brent on [psihigh, 1.0) + psi_bracket_hi = 1.0 - 1e-8 # stay away from exact separatrix + psi_new = find_zero( + psi -> profiles.iota_spline(psi; hint=hint) - iota_target, + (psihigh, psi_bracket_hi), Roots.Brent() + ) + + # Terminate if spacing is below edge_layer_width (in the dense separatrix layer) + if psi_new - psi_last < ctrl.edge_layer_width + break + end + + q_val = m / n + q1_val = eval_q(profiles, psi_new; deriv=1) + + if any(s -> isapprox(s.q, q_val; atol=1e-8), intr.sing) + push!(intr.sing[findfirst(s -> isapprox(s.q, q_val; atol=1e-8), intr.sing)].m, m) + push!(intr.sing[findfirst(s -> isapprox(s.q, q_val; atol=1e-8), intr.sing)].n, n) + else + push!(intr.sing, SingType(; + m=[m], + n=[n], + psifac=psi_new, + rho=sqrt(psi_new), + q=q_val, + q1=q1_val + )) + intr.msing += 1 + end + + psi_last = psi_new + m += 1 + end + end + + # Re-sort after adding edge surfaces + intr.sing = sort(intr.sing; by=s -> s.psifac) + + n_edge = count(s -> s.psifac > psihigh, intr.sing) + if n_edge > 0 + @info "Extended edge search found $n_edge rational surface(s) above psihigh = $psihigh" + end + end end """ sing_lim!(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal) -Compute and set integration ψ, q, and q' limits by handling cases where user truncates -before the last singular surface. Performs a similar function to `sing_lim` -in the Fortran code. Main differences include renaming of sas_flag -> set_psilim_via_dmlim, -removing dW edge storage variables since we now store all integration terms in memory, and -simplification of the logic. - -The target value `qlim` is first determined from user-specified control parameters -(`ctrl.qhigh` or `ctrl.dmlim`), subject to the constraint that it does not exceed -`equil.params.qmax`. If set_psilim_via_dmlim is true, `qlim` is adjusted to the largest -rational surface such that `nq + dmlim < qmax`, where qmax is the maximum q value in the equilibrium. -If `qlim < qmax`, a Newton iteration is performed to find the corresponding -`psilim` to integrate to. - -Note that the Newton iteration will be triggered if either `set_psilim_via_dmlim` is true -or `ctrl.qhigh < equil.params.qmax`. Otherwise, the equilibrium edge values are used. +Compute and set integration ψ, q, and q' limits. + +`psilim` is set to just inside the last rational surface in the consecutive sequence +of surfaces (sorted by ψ) whose spacing from the previous surface is at least +`ctrl.edge_layer_width`. This filter applies to all surfaces regardless of psihigh: +if psihigh is very close to the separatrix, tightly-packed core surfaces near psihigh +are excluded just as above-psihigh edge surfaces are. For non-diverted (limited) plasmas +psilim is additionally capped at psihigh. + +`qlim = min(q(psilim), ctrl.qhigh)`. If `ctrl.qhigh` truncates the integration before +`psilim`, a root-find adjusts `psilim` to where `q = qhigh`: +- `qhigh ≤ q(psihigh)`: Newton iteration with the direct q spline. +- `q(psihigh) < qhigh < q(psilim)`: Brent bracket on `[psihigh, psilim]` using the iota + inverse spline. This handles the case where a diverted plasma's edge layer extends beyond + psihigh but the user wants to cap the integration at an intermediate q value. """ function sing_lim!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium) - profiles = equil.profiles + profiles = equil.profiles + psihigh = equil.config.psihigh + is_diverted = !isnothing(equil.params.is_diverted) && equil.params.is_diverted + + # Walk ALL rational surfaces (sorted by ψ) and stop at the first pair whose consecutive + # spacing is below edge_layer_width. This ensures psilim is always set by the spacing + # criterion, even if psihigh is very close to the separatrix and the core search has + # already found many tightly-packed surfaces inside psihigh. + last_valid = nothing + psi_last = 0.0 + for s in intr.sing + if s.psifac - psi_last >= ctrl.edge_layer_width + last_valid = s + psi_last = s.psifac + else + break + end + end + + # Set psilim just inside the last valid surface using the singfac_min buffer + # (with a 1.1 safety margin so floating-point rounding cannot accidentally push + # psilim past the trigger threshold and cause the EL integrator to attempt a crossing). + if !isnothing(last_valid) + n_last = minimum(last_valid.n) + q1_last = last_valid.q1 + natural_psilim = last_valid.psifac - ctrl.singfac_min * 1.1 / abs(n_last * q1_last) + intr.psilim = is_diverted ? natural_psilim : min(natural_psilim, psihigh) + else + intr.psilim = psihigh + end - # Initial guesses based on equilibrium - intr.qlim = min(equil.params.qmax, ctrl.qhigh) # equilibrium solve only goes up to qmax, so we're capped there + # q at the natural psilim — dispatches to iota spline in edge zone via eval_q. + q_at_psilim = eval_q(profiles, intr.psilim) + + intr.qlim = min(q_at_psilim, ctrl.qhigh) intr.q1lim = profiles.q_deriv(profiles.xs[end]; hint=Ref(profiles.npts_minus_1)) - intr.psilim = equil.config.psihigh - # Optionally override qlim based on dmlim - if ctrl.set_psilim_via_dmlim - if ctrl.nn_low != ctrl.nn_high - error("Setting psilim via dmlim is only valid for single n runs (nn_low == nn_high).") - end - @info "Setting psilim via dmlim: initial qlim = $(@sprintf("%.3f", intr.qlim)), dmlim = $(@sprintf("%.3f", ctrl.dmlim))" - # Normalize dmlim ∈ [0,1) - ctrl.dmlim = mod(ctrl.dmlim, 1.0) - intr.qlim = (trunc(Int, ctrl.nn_low * intr.qlim) + ctrl.dmlim) / ctrl.nn_low - - # Reduce qlim if above qmax - while intr.qlim > equil.params.qmax - intr.qlim -= 1.0 / ctrl.nn_low + # If qhigh truncates the integration before psilim, root-find for the exact psilim. + if intr.qlim < q_at_psilim + q_at_psihigh = profiles.q_spline.y[end] + if intr.qlim > q_at_psihigh && !isnothing(profiles.iota_spline) + # qlim is in the edge zone [psihigh, psilim]: Brent bracket with iota spline. + psilim_before = intr.psilim + intr.psilim = find_zero( + psi -> eval_q(profiles, psi) - intr.qlim, + (psihigh, psilim_before), Roots.Brent(); xatol=1e-8 + ) + intr.q1lim = eval_q(profiles, intr.psilim; deriv=1) + else + # qlim is in the core [psilow, psihigh]: Newton with direct spline + derivative. + _, jpsi = findmin(abs.(profiles.q_spline.y .- intr.qlim)) + jpsi = min(jpsi, equil.config.mpsi - 1) + hint = Ref(jpsi) + intr.psilim = find_zero( + (psi -> profiles.q_spline(psi; hint=hint) - intr.qlim, + psi -> profiles.q_deriv(psi; hint=hint)), + profiles.xs[jpsi], Roots.Newton() + ) + intr.q1lim = profiles.q_deriv(intr.psilim) end end - - # If set_psilim_via_dmlim decreased qlim or qhigh < qmax, we need to find the precise psilim via newton iteration - if intr.qlim < equil.params.qmax - # Find nearest ψ index where q ≈ qlim - _, jpsi = findmin(abs.(profiles.q_spline.y .- intr.qlim)) - jpsi = min(jpsi, equil.config.mpsi - 1) - - hint = Ref(jpsi) - intr.psilim = find_zero( - (psi -> profiles.q_spline(psi; hint=hint) - intr.qlim, - psi -> profiles.q_deriv(psi; hint=hint)), - profiles.xs[jpsi], Roots.Newton() - ) - intr.q1lim = profiles.q_deriv(intr.psilim) - end end """ @@ -231,10 +325,6 @@ Add a spline for F directly instead of the lower triangular factorization to avo """ @with_pool pool function compute_sing_mmat!(mmat::Array{ComplexF64,4}, singp::SingType, ctrl::ForceFreeStatesControl, profiles::Equilibrium.ProfileSplines, ffit::FourFitVars, intr::ForceFreeStatesInternal) - q_spline = profiles.q_spline - q_d1 = profiles.q_deriv - q_d2 = deriv2(q_spline) - q_d3 = deriv3(q_spline) # Initial allocations Npert = intr.numpert_total @@ -252,11 +342,8 @@ Add a spline for F directly instead of the lower triangular factorization to avo x = zeros!(pool, ComplexF64, Npert, 2 * Npert, 2, ctrl.sing_order + 1) tmp_vec = acquire!(pool, ComplexF64, Npert) - # Evaluate q spline and its derivatives - q = (q_spline(singp.psifac), - q_d1(singp.psifac), - q_d2(singp.psifac), - q_d3(singp.psifac)) + # Evaluate q and its first three derivatives at the singular surface. + q = eval_q(profiles, singp.psifac; deriv=3, output_lower_derivs=true) # Evaluate fmats_lower and derivatives using series interpolants ffit.fmats_lower(vec(@view(f_lower_interp[:, :, 1])), singp.psifac; hint=ffit._hint) @@ -750,8 +837,9 @@ Implement kin_flag functionality du2 = @view(du[:, :, 2]) # Compute singfac = 1 / (m - nq) - # Use shared hint with LinearBinary() search for O(1) interval lookup during sequential ODE integration - odet.q = equil.profiles.q_spline(psieval; hint=odet.spline_hint) + # Use shared hint with LinearBinary() search for O(1) interval lookup during sequential ODE integration. + # eval_q dispatches to iota spline above psihigh (diverted), direct spline otherwise. + odet.q = eval_q(equil.profiles, psieval; hint=odet.spline_hint) singfac_mat .= 1.0 ./ ((intr.mlow:intr.mhigh) .- odet.q .* (intr.nlow:intr.nhigh)') # kinetic stuff - skip for now diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl index 07818446..ff42c7dd 100755 --- a/src/GeneralizedPerturbedEquilibrium.jl +++ b/src/GeneralizedPerturbedEquilibrium.jl @@ -115,14 +115,6 @@ function main(args::Vector{String}=String[]) # TODO: parallel threads logic ctrl.delta_mhigh *= 2 # for consistency with Fortran DCON TODO: why is this present in the Fortran? - # Determine psilim and qlim (where we will integrate to) - sing_lim!(intr, ctrl, equil) - if ctrl.set_psilim_via_dmlim && ctrl.psiedge < intr.psilim - @warn "Only one of set_psilim_via_dmlim and psiedge < psilim can be used at a time. - Setting psiedge = 1.0 and determining dW from psilim = $(intr.psilim) determined from dmlim = $(ctrl.dmlim)." - ctrl.psiedge = 1.0 - end - # If truncating before psihigh, reform equilibrium if desired if intr.psilim != equil.config.psihigh && ctrl.reform_eq_with_psilim @warn "Reforming equilibrium splines from psihigh to psilim not implemented yet. Proceeding with psihigh = $(equil.config.psihigh)." @@ -175,26 +167,49 @@ function main(args::Vector{String}=String[]) intr.npert = intr.nhigh - intr.nlow + 1 nstring = intr.npert == 1 ? "$(intr.nlow)" : "$(intr.nlow):$(intr.nhigh)" - # Find all singular surfaces in the equilibrium - sing_find!(intr, equil) + # Find all singular surfaces in the equilibrium (must run before sing_lim! for diverted edge surfaces) + sing_find!(intr, ctrl, equil) + + # Determine psilim and qlim (where we will integrate to). + # Runs after sing_find! so that edge surfaces above psihigh are available for diverted plasmas. + sing_lim!(intr, ctrl, equil) + + # Extend the rzphi coordinate splines to psilim using the edge rational surfaces from sing_find!. + # This is the single canonical source for the far-edge grid — sing_find! applies the + # edge_layer_width stopping criterion (check-before-push), so psilim = last surface before + # surfaces pack closer than edge_layer_width. The rzphi grid now covers exactly [psilow, psilim]. + if !isnothing(equil.profiles.iota_spline) + edge_surf_psis = Float64[s.psifac for s in intr.sing if s.psifac > equil.config.psihigh] + Equilibrium.equilibrium_extend_rzphi!(equil, edge_surf_psis) + end # Determine poloidal mode numbers if ctrl.delta_mlow < 0 || ctrl.delta_mhigh < 0 error("Negative delta_mlow or delta_mhigh not allowed") end + # Use the q of the outermost found rational surface to set the mode range, falling back + # to the direct-spline edge q if no surfaces were found. For diverted plasmas qmax = Inf, + # so we rely on sing rather than equil.params.qmax. + is_diverted = !isnothing(equil.params.is_diverted) && equil.params.is_diverted + q_for_mode_range = if is_diverted + isempty(intr.sing) ? equil.profiles.q_spline.y[end] : intr.sing[end].q + else + equil.params.qmax + end + if ctrl.cyl_flag intr.mlow = ctrl.delta_mlow intr.mhigh = ctrl.delta_mhigh elseif ctrl.sing_start == 0 intr.mlow = trunc(Int, min(intr.nlow * equil.params.qmin, 0)) - 4 - ctrl.delta_mlow - intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh + intr.mhigh = trunc(Int, intr.nhigh * q_for_mode_range) + ctrl.delta_mhigh else intr.mmin = Inf # HUGE in Fortran for ising in Int(ctrl.sing_start):intr.msing intr.mmin = min(intr.mmin, sing[ising].m) end intr.mlow = intr.mmin - ctrl.delta_mlow - intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + ctrl.delta_mhigh + intr.mhigh = trunc(Int, intr.nhigh * q_for_mode_range) + ctrl.delta_mhigh end intr.mpert = intr.mhigh - intr.mlow + 1 if ctrl.delta_mband >= intr.mpert @@ -209,15 +224,17 @@ function main(args::Vector{String}=String[]) if ctrl.mat_flag || ctrl.ode_flag if ctrl.verbose @info "Run parameters:\n" * - " q0 = $(@sprintf("%.3f", equil.params.q0)), qmin = $(@sprintf("%.3f", equil.params.qmin)), qmax = $(@sprintf("%.3f", equil.params.qmax)), q95 = $(@sprintf("%.3f", equil.params.q95))\n" * - " qlim = $(@sprintf("%.3f", intr.qlim)), psilim = $(@sprintf("%.3f", intr.psilim))\n" * - " betat = $(@sprintf("%.3f", equil.params.betat)), betan = $(@sprintf("%.3f", equil.params.betan)), betap1 = $(@sprintf("%.3f", equil.params.betap1))\n" * - " mlow = $(@sprintf("%4i", intr.mlow)), mhigh = $(@sprintf("%4i", intr.mhigh)), mpert = $(@sprintf("%4i", intr.mpert)), mband = $(@sprintf("%4i", intr.mband))\n" * - " nlow = $(@sprintf("%4i", intr.nlow)), nhigh = $(@sprintf("%4i", intr.nhigh)), npert = $(@sprintf("%4i", intr.npert))" + " q0 = $(@sprintf("%.3f", equil.params.q0)), qmin = $(@sprintf("%.3f", equil.params.qmin))\n" * + " q95 = $(@sprintf("%.3f", equil.params.q95)), q99 = $(@sprintf("%.3f", equil.params.q99)), qmax = $(@sprintf("%.3f", equil.params.qmax))\n" * + " qlim = $(@sprintf("%.3f", intr.qlim)), psilim = $(@sprintf("%.3f", intr.psilim))\n" * + " betat = $(@sprintf("%.3f", equil.params.betat)), betan = $(@sprintf("%.3f", equil.params.betan)), betap1 = $(@sprintf("%.3f", equil.params.betap1))\n" * + " mlow = $(@sprintf("%5i", intr.mlow)), mhigh = $(@sprintf("%5i", intr.mhigh)), mpert = $(@sprintf("%5i", intr.mpert)), mband = $(@sprintf("%5i", intr.mband))\n" * + " nlow = $(@sprintf("%5i", intr.nlow)), nhigh = $(@sprintf("%5i", intr.nhigh)), npert = $(@sprintf("%5i", intr.npert))" end - # Compute metric tensor - metric = make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag) + # Compute metric tensor, limiting the psi grid to psilim so far-edge nodes + # (near the X-point where the metric diverges) are excluded from matrix splines. + metric = make_metric(equil; mband=intr.mband, fft_flag=ctrl.fft_flag, psilim=intr.psilim) if ctrl.verbose @info "Computing F, G, and K matrices" @@ -435,6 +452,17 @@ function write_outputs_to_HDF5( out_h5["integration/xi_s"] = odet.ud_store[:, :, 2, :] out_h5["integration/crit"] = odet.crit_store + # Edge stability scan: full [psiedge, psilim] picture before u_store is trimmed. + # NaN entries mark steps where U₁ was singular (SingularException in free_compute_total). + # Stored in a dedicated top-level group so users can inspect the full scan independently. + if !isempty(odet.psi_edge_scan) + out_h5["edge_scan/psi"] = odet.psi_edge_scan + out_h5["edge_scan/total_energy"] = odet.et_edge_scan # plasma + vacuum eigenmode energy + out_h5["edge_scan/plasma_energy"] = odet.ep_edge_scan # plasma contribution + out_h5["edge_scan/vacuum_energy"] = odet.ev_edge_scan # vacuum contribution (projected onto eigenmode) + out_h5["edge_scan/vacuum_eigenvalue"] = odet.evonly_edge_scan # least stable eigenvalue of vacuum matrix alone + end + # Write singular surface data out_h5["singular/msing"] = intr.msing out_h5["singular/psi"] = [sing.psifac for sing in intr.sing] diff --git a/src/PerturbedEquilibrium/FieldReconstruction.jl b/src/PerturbedEquilibrium/FieldReconstruction.jl index d2c39e15..1e2d30ae 100644 --- a/src/PerturbedEquilibrium/FieldReconstruction.jl +++ b/src/PerturbedEquilibrium/FieldReconstruction.jl @@ -287,8 +287,7 @@ function compute_perturbed_field_modes( psi_norm = ForceFreeStates_results.psi_store[ipsi] # Get equilibrium quantities at this surface - q = equil.profiles.q_spline(psi_norm) # Safety factor q(ψ) - q1 = equil.profiles.q_deriv(psi_norm) # Derivative q'(ψ) = dq/dψ + q, q1 = Equilibrium.eval_q(equil.profiles, psi_norm; deriv=1, output_lower_derivs=true) # q(ψ), q'(ψ) # Compute field for each poloidal mode for ipert in 1:mpert diff --git a/src/PerturbedEquilibrium/SingularCoupling.jl b/src/PerturbedEquilibrium/SingularCoupling.jl index b27da960..49a72cbb 100644 --- a/src/PerturbedEquilibrium/SingularCoupling.jl +++ b/src/PerturbedEquilibrium/SingularCoupling.jl @@ -331,7 +331,7 @@ function interpolate_field_at_surface( end # Get safety factor at this surface - q = equil.profiles.q_spline(psi) + q = Equilibrium.eval_q(equil.profiles, psi) # Convert displacement to field using ideal MHD relation # b^ψ = i * χ₁ * (m - n*q) * ξ_ψ (from FieldReconstruction.jl line 304) @@ -395,7 +395,7 @@ function compute_current_density( # Get equilibrium quantities at this surface F_tor = equil.profiles.F_spline(psi) # Toroidal field function F = R*B_tor times 2π - q = equil.profiles.q_spline(psi) # Safety factor + q = Equilibrium.eval_q(equil.profiles, psi) # Safety factor # Magnetic axis location ro = equil.ro diff --git a/test/runtests_equil.jl b/test/runtests_equil.jl index d3a4f6c3..b9a9065d 100644 --- a/test/runtests_equil.jl +++ b/test/runtests_equil.jl @@ -104,6 +104,53 @@ @test isapprox(plasma_eq_efit.zo, plasma_eq_ascii.zo, atol=1e-3) end + @testset "Edge inverse splines (limited plasma)" begin + # For a limited plasma, no edge inverse splines are built + @test isnothing(plasma_eq_efit.profiles.q_spline_iota_inverse) + @test isnothing(plasma_eq_efit.profiles.dVdpsi_spline_inv) + @test plasma_eq_efit.params.is_diverted == false + end + + @testset "Edge inverse splines (diverted plasma)" begin + # Load the DIIID-like diverted equilibrium + diiid_dir = joinpath(@__DIR__, "..", "examples", "DIIID-like_ideal_example") + diiid_config = GeneralizedPerturbedEquilibrium.Equilibrium.EquilibriumConfig(; + eq_type="efit", + eq_filename=joinpath(diiid_dir, "TkMkr_D3Dlike_Hmode.geqdsk"), + jac_type="hamada", + grid_type="ldp", + psilow=1e-4, + psihigh=0.993, + mpsi=128, + mtheta=256 + ) + pe_diverted = GeneralizedPerturbedEquilibrium.Equilibrium.setup_equilibrium(diiid_config) + + psihigh = pe_diverted.config.psihigh + ics = pe_diverted.profiles.q_spline_iota_inverse + + # X-point detection + @test pe_diverted.params.is_diverted == true + @test pe_diverted.params.z_xpoint < pe_diverted.zo # lower null is below the axis + + # Edge splines are built + @test !isnothing(ics) + @test !isnothing(pe_diverted.profiles.dVdpsi_spline_inv) + + # qa = Inf for diverted + @test isinf(pe_diverted.params.qa) + + # Anchor: iota(1.0) = 0 (separatrix) + @test ics.inner.y[end] ≈ 0.0 + + # Coverage: edge spline starts in the near-edge region (between 85% and 100% of psihigh) + @test 0.85 * psihigh < ics.inner.cache.x[1] < psihigh + + # Continuity at psihigh: q and dV/dψ match to machine precision + @test ics(psihigh) ≈ pe_diverted.profiles.q_spline_direct(psihigh) + @test pe_diverted.profiles.dVdpsi_spline_inv(psihigh) ≈ pe_diverted.profiles.dVdpsi_spline(psihigh) + end + @testset "Solovev Equilibrium" begin # --- Helper constructors --- # Minimal valid inputs diff --git a/test/test_data/regression_solovev_ideal_example/gpec.toml b/test/test_data/regression_solovev_ideal_example/gpec.toml index f4f182fb..2718931f 100644 --- a/test/test_data/regression_solovev_ideal_example/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example/gpec.toml @@ -31,8 +31,6 @@ ode_flag = true # Integrate ODE's for determining stability of int vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes mer_flag = true # Evaluate the Mercier criterian -set_psilim_via_dmlim = false # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See sas_flag qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) diff --git a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml index e77885f9..172100ec 100644 --- a/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml +++ b/test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml @@ -31,8 +31,6 @@ ode_flag = true # Integrate ODE's for determining stability of int vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes mer_flag = true # Evaluate the Mercier criterian -set_psilim_via_dmlim = false # Safety factor (q) limit determined as q_ir+dmlim... -dmlim = 0.2 # See sas_flag qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow)