Tutorials and Examples

The public notebooks are grouped by workflow. The documentation build copies notebooks/ into the Sphinx source tree, so paths below mirror the repository layout.

Recommended Learning Path

Start with Quick Start, then work through the generic geometry workflow, stochastic models, and then toroidal monodromy/RMP examples:

1. Mini Cases

2. SDE Monte Carlo Distributions

3. RMP Stellarator Resonance Analysis

4. Tutorial: Monodromy Matrix and Orbit Shift on an Analytic X-type Saddle Cycle

5. Island Jacobian Analysis: Periodic Orbits and Monodromy Matrices

6. RMP Island Width Validation – Solov’ev Analytic Equilibrium

General Dynamical Systems

• SDE Monte Carlo Distributions

The generic geometry workflow and analytic stellarator fixed-point workflow are now folded into the RMP resonance tutorial instead of being published as standalone text-only notebooks. That tutorial shows the same promotion chain: sampled crossings -> fixed-point geometry -> X/O classification -> manifold and coordinate-grid overlays.

Stochastic Differential Equations

The SDE tutorial is pre-executed locally because distribution estimation often uses tens or hundreds of thousands of Monte Carlo paths. GitHub Pages renders the saved outputs instead of spending CI time on the heavy sampling cells.

Magnetic Coordinates and Equilibria

• Magnetic Coordinate Systems in Tokamak Equilibria

RMPs, Islands and Poincare Analysis

Start with the resonance analysis notebook when studying magnetic topology. It now covers divergence-free RMP templates, the important m=1 branch, cyna fixed-point validation, multi-component contravariant B^r magnetic-spectrum atlases, modular q/m/n resonance maps with optional Poincare and island overlays, mixed RMP/nRMP spectra, total nRMP response from all non-resonant modes, field-line speed modulation, and perturbation-order checks.

• RMP Stellarator Resonance Analysis
• RMP Island Width Validation – Solov’ev Analytic Equilibrium
• Island Jacobian Analysis: Periodic Orbits and Monodromy Matrices

RMP_resonance_exec.ipynb is kept in the repository as an execution/cache variant of the resonance analysis workflow, but the public documentation links to the explanatory version above.

Monodromy and Manifolds

• Tutorial: Möbius Saddle Cycle — Period-Doubling and Negative Eigenvalues
• Tutorial: Monodromy Matrix and Orbit Shift on an Analytic X-type Saddle Cycle

Classical and General Dynamical Systems

The repository also includes lightweight notebooks under notebooks/examples: Lorenz_attractor.ipynb, resonance_1_1_map.ipynb, Mobiusian_saddle_cycle.ipynb, Xcycle_construction.ipynb and FPT_DX_to_DP_sympy.ipynb. They are kept as source examples rather than executed documentation pages because several are scratch-style notebooks without section titles.

Static Tutorial Figures

Several longer workflows are represented in the repository as static figures and generated outputs under notebooks/tutorials. They cover q-profile diagnostics, PEST/Boozer/Hamada/equal-arc coordinates, island suppression scans, phase control, Poincare manifolds and Solov’ev single-null examples.