|
| 1 | +# Architecture |
| 2 | + |
| 3 | +## Computational Workflow |
| 4 | + |
| 5 | +GPEC follows a three-stage analysis pipeline: |
| 6 | + |
| 7 | +1. **Equilibrium** → Solve Grad-Shafranov equation, compute flux surfaces, safety factor q-profile |
| 8 | +2. **Stability Analysis** → Solve ideal MHD eigenvalue problem (DCON-style), identify singular surfaces |
| 9 | +3. **Perturbed Equilibrium** → Compute plasma response to external fields, analyze singular coupling and island formation |
| 10 | + |
| 11 | +This workflow is reflected in the modular structure and data flow. |
| 12 | + |
| 13 | +## Module Structure |
| 14 | + |
| 15 | +GPEC consists of **seven main modules** organized in `src/`: |
| 16 | + |
| 17 | +### Foundation Modules |
| 18 | + |
| 19 | +1. **Splines** (`src/Splines/`) - Numerical interpolation library |
| 20 | + - `CubicSpline.jl` - 1D cubic spline interpolation |
| 21 | + - `BicubicSpline.jl` - 2D bicubic spline interpolation |
| 22 | + - `FourierSpline.jl` - Fourier-based spline interpolation |
| 23 | + - Status: Mature, pure Julia implementation |
| 24 | + |
| 25 | +2. **Utilities** (`src/Utilities/`) - Shared computational tools |
| 26 | + - `FourierTransforms.jl` - Efficient Fourier transform utilities with pre-computed basis functions |
| 27 | + - Provides type-stable functor pattern for repeated transforms |
| 28 | + - Used by Vacuum and PerturbedEquilibrium modules |
| 29 | + |
| 30 | +### Core Physics Modules |
| 31 | + |
| 32 | +3. **Equilibrium** (`src/Equilibrium/`) - MHD equilibrium solvers |
| 33 | + - Main entry point: `setup_equilibrium(path)` or `setup_equilibrium(config)` |
| 34 | + - Supports multiple equilibrium types: |
| 35 | + - `efit` - EFIT g-file format |
| 36 | + - `chease`, `chease2` - CHEASE equilibrium code formats |
| 37 | + - `lar` - Large Aspect Ratio analytical model |
| 38 | + - `sol` - Solovev analytical equilibrium |
| 39 | + - Key files: |
| 40 | + - `EquilibriumTypes.jl` - Core data structures |
| 41 | + - `ReadEquilibrium.jl` - Parsing equilibrium files |
| 42 | + - `DirectEquilibrium.jl` - Direct Grad-Shafranov solver |
| 43 | + - `InverseEquilibrium.jl` - Inverse equilibrium solver |
| 44 | + - `AnalyticEquilibrium.jl` - Analytical solutions |
| 45 | + - Status: Stable and feature-complete |
| 46 | + |
| 47 | +4. **Vacuum** (`src/Vacuum/`) - Vacuum field calculations and Green's functions |
| 48 | + - Computes vacuum response matrices for ideal MHD analysis |
| 49 | + - Calculates both **interior** (grri) and **exterior** (grre) Green's functions |
| 50 | + - Main functions: |
| 51 | + - `compute_vacuum_response()` - Pure Julia implementation |
| 52 | + - Key files: |
| 53 | + - `VacuumStructs.jl` - Data structures |
| 54 | + - `VacuumInternals.jl` - Core algorithms |
| 55 | + - `VacuumFromEquilibrium.jl` - Integration with equilibrium data |
| 56 | + - Status: **Pure Julia implementation complete and available** |
| 57 | + |
| 58 | +5. **ForceFreeStates** (`src/ForceFreeStates/`) - Ideal MHD stability analysis (DCON-style) |
| 59 | + - Solves ideal MHD eigenvalue problem with force-free boundary conditions |
| 60 | + - Identifies singular surfaces where ξ·∇ψ = 0 |
| 61 | + - Key files: |
| 62 | + - `ForceFreeStatesStructs.jl` - Core data structures |
| 63 | + - `Ode.jl` - ODE solver for Euler-Lagrange equations |
| 64 | + - `Sing.jl` - Singular point handling and layer analysis |
| 65 | + - `Fourfit.jl` - Fourier fitting routines |
| 66 | + - `FixedBoundaryStability.jl` - Fixed boundary analysis |
| 67 | + - `Free.jl` - Free boundary stability |
| 68 | + - `Ballooning.jl` - Local stability scan: Mercier D_I, resistive interchange D_R, and high-n ballooning Δ' (s–α). Replaces the former standalone `Mercier.jl`. |
| 69 | + - Status: Stable, core DCON functionality implemented |
| 70 | + |
| 71 | +### Perturbed Equilibrium Modules |
| 72 | + |
| 73 | +6. **ForcingTerms** (`src/ForcingTerms/`) - External field specification |
| 74 | + - Handles external magnetic field perturbations (coils, RMP, etc.) |
| 75 | + - Supports ASCII and HDF5 forcing data formats |
| 76 | + - `ForcingMode` data structure specifies amplitude and phase for each (m,n) component |
| 77 | + - Status: Complete and functional |
| 78 | + |
| 79 | +7. **PerturbedEquilibrium** (`src/PerturbedEquilibrium/`) - **GPEC-style plasma response** |
| 80 | + - Computes plasma response to external forcing |
| 81 | + - Calculates singular coupling metrics at rational surfaces |
| 82 | + - Key files: |
| 83 | + - `PerturbedEquilibrium.jl` - Main entry point |
| 84 | + - `PerturbedEquilibriumStructs.jl` - Data structures |
| 85 | + - `ResponseMatrices.jl` - Permeability matrix calculation |
| 86 | + - `FieldReconstruction.jl` - Mode-space field reconstruction |
| 87 | + - `Response.jl` - Plasma response computation |
| 88 | + - `SingularCoupling.jl` - **Singular surface analysis** including: |
| 89 | + - Delta prime (Δ') tearing stability parameter |
| 90 | + - Resonant flux and currents at rational surfaces |
| 91 | + - Island half-widths and Chirikov parameters |
| 92 | + - Green's functions at interior flux surfaces |
| 93 | + - Surface inductance for singular surfaces |
| 94 | + - `Utils.jl` - Helper functions |
| 95 | + - Status: Core plasma response and singular coupling calculations implemented; active area of development |
| 96 | + |
| 97 | +## Configuration |
| 98 | + |
| 99 | +**Unified Configuration File**: `gpec.toml` |
| 100 | + |
| 101 | +All GPEC modules are configured via a single TOML file with the following sections: |
| 102 | + |
| 103 | +- `[Equilibrium]` - Equilibrium solver settings |
| 104 | +- `[Wall]` - Wall geometry and vacuum region |
| 105 | +- `[ForceFreeStates]` - Stability analysis parameters |
| 106 | +- `[PerturbedEquilibrium]` - Perturbed equilibrium settings |
| 107 | +- `[ForcingTerms]` - External field specification |
| 108 | + |
| 109 | +Key parameters: |
| 110 | +- `force_termination` - Set to `true` to exit after equilibrium/stability (skip perturbed equilibrium) |
| 111 | +- `output_file` - Output filename (default: `gpec.h5`) |
| 112 | + |
| 113 | +Example configuration files are provided in: |
| 114 | +- `examples/Solovev_ideal_example/gpec.toml` |
| 115 | +- `examples/DIIID-like_ideal_example/gpec.toml` |
| 116 | + |
| 117 | +**Note**: Legacy configuration files (`equil.toml`, `vac.in`) are deprecated. |
| 118 | + |
| 119 | +## Data Flow |
| 120 | + |
| 121 | +The complete GPEC analysis pipeline: |
| 122 | + |
| 123 | +1. **Equilibrium Setup**: |
| 124 | + - `setup_equilibrium(config)` reads configuration from `gpec.toml` |
| 125 | + - Parses equilibrium data (EFIT, CHEASE, or analytical) |
| 126 | + - Runs Grad-Shafranov solver (direct or inverse) |
| 127 | + - Computes global parameters: q-profile, pressure, current density, β |
| 128 | + - Creates bicubic splines for (ψ, θ, φ) → (R, Z, Φ) mapping |
| 129 | + - Outputs: `PlasmaEquilibrium` object |
| 130 | + |
| 131 | +2. **Vacuum Response**: |
| 132 | + - Initialize plasma and wall surfaces from equilibrium |
| 133 | + - Compute vacuum response matrices (wv, grri, grre) |
| 134 | + - Calculate both interior and exterior Green's functions |
| 135 | + - Pure Julia implementation |
| 136 | + |
| 137 | +3. **Stability Analysis** (ForceFreeStates): |
| 138 | + - Solve ideal MHD Euler-Lagrange equations via ODE integration |
| 139 | + - Identify singular surfaces where q = m/n |
| 140 | + - Compute Δ' at each singular surface |
| 141 | + - Calculate potential and kinetic energies |
| 142 | + - Check Mercier and ballooning stability criteria |
| 143 | + - Outputs: Eigenmode structure ξ(ψ,θ) |
| 144 | + |
| 145 | +4. **Perturbed Equilibrium** (GPEC-style): |
| 146 | + - Load external forcing data (coil fields, RMP configuration) |
| 147 | + - Compute plasma response using permeability matrices |
| 148 | + - Reconstruct mode-space fields (ξ_modes, b_modes) |
| 149 | + - Calculate singular coupling metrics at rational surfaces: |
| 150 | + - Δ' (tearing stability parameter) |
| 151 | + - Island half-widths |
| 152 | + - Chirikov overlap parameter |
| 153 | + - Resonant flux and currents |
| 154 | + - Outputs: `PerturbedEquilibriumState` with response fields and diagnostics |
| 155 | + |
| 156 | +5. **Output**: |
| 157 | + - All results saved to single HDF5 file (default: `gpec.h5`) |
| 158 | + - HDF5 groups: `input/`, `info/`, `equil/`, `splines/`, `locstab/`, `integration/`, `singular/`, `vacuum/`, and perturbed equilibrium data |
| 159 | + |
| 160 | +## Key Data Structures |
| 161 | + |
| 162 | +### Equilibrium |
| 163 | +- `PlasmaEquilibrium` - Main equilibrium container with bicubic splines (rzphi), 1D profiles (sq), and global parameters |
| 164 | +- `EquilibriumConfig` - Configuration loaded from TOML files |
| 165 | + |
| 166 | +### Vacuum |
| 167 | +- `VacuumInput` - Input parameters for vacuum calculations |
| 168 | +- `WallShapeSettings` - Wall geometry configuration |
| 169 | + |
| 170 | +### Stability |
| 171 | +- `SingType` - Singular surface data including: |
| 172 | + - Rational surface location (ψ, q = m/n) |
| 173 | + - Δ' (tearing stability parameter) |
| 174 | + - Eigenmode structure at singular surface |
| 175 | + - Green's functions (grri, grre) at interior singular surfaces |
| 176 | + - Surface inductance |
| 177 | + |
| 178 | +### Perturbed Equilibrium |
| 179 | +- `PerturbedEquilibriumControl` - User-facing TOML configuration parameters |
| 180 | +- `PerturbedEquilibriumInternal` - Internal state with mode arrays |
| 181 | +- `PerturbedEquilibriumState` - Results including: |
| 182 | + - Response fields (ξ_modes, b_modes) in mode space |
| 183 | + - Singular coupling matrices [msing × numpert_total] |
| 184 | + - Island diagnostics (half-widths, Chirikov parameters) |
| 185 | +- `ForcingMode` - External forcing specification (m, n, amplitude, phase) |
| 186 | + |
| 187 | +## Module Dependencies |
| 188 | + |
| 189 | +``` |
| 190 | +GeneralizedPerturbedEquilibrium |
| 191 | +├── Splines (foundation) |
| 192 | +├── Utilities (shared tools) |
| 193 | +│ └── FourierTransforms |
| 194 | +├── Equilibrium (uses Splines) |
| 195 | +├── Vacuum (uses Splines, Equilibrium, Utilities) |
| 196 | +├── ForcingTerms (data I/O) |
| 197 | +├── ForceFreeStates (uses Equilibrium, Vacuum, Splines) |
| 198 | +└── PerturbedEquilibrium (uses ForceFreeStates, Vacuum, ForcingTerms, Utilities) |
| 199 | +``` |
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