pyna-chaos 0.8.5

Python library for dynamical systems and magnetic confinement fusion analysis

pyna -- Python DYNAmics

pyna (Python DYNAmics) is a research library for dynamical systems and magnetic confinement fusion (MCF) plasma physics. It covers the full workflow from analytic equilibria and field-line tracing to topological island analysis, manifold visualization, and non-resonant torus deformation theory.

Author: Wenyin Wei · PyPI: pyna-chaos · Julia companion: Juna.jl

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✨ Highlights

Feature	Details
🔀 Field-line tracing	RK4 integrator, parallel CPU, optional CUDA (118× speedup)
🌀 Poincaré sections & island chains	Multi-section crossing accumulation, island-chain extraction, X/O-point analysis
🗺️ Manifold visualization	Publication-quality stable/unstable manifold plots for tokamaks
🧲 Toroidal geometry	Coordinates, coils, diagnostics, and field-line tooling
📐 Magnetic coordinates	PEST, Boozer, Hamada, Equal-arc transformations
📡 Torus deformation	Non-resonant BNF-derived analytic spectral theory (Wei 2025)
⚡ C++ acceleration	Optional cyna backend for performance-critical ops

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📦 Installation

# Stable release (PyPI)
pip install pyna-chaos

# Development version
git clone https://github.com/WenyinWei/pyna.git
cd pyna
pip install -e ".[dev]"

# With GPU support (CUDA 12)
pip install "pyna-chaos[cuda]"

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🚀 Quick Start

Field-line tracing

from pyna.toroidal.equilibrium import EquilibriumSolovev as SolovevEquilibrium
from pyna.flt import FieldLineTracer

eq = SolovevEquilibrium.iter_like()
tracer = FieldLineTracer(eq.Bfield)
trajectory = tracer.trace(R0=2.0, Z0=0.0, phi_end=200 * 2 * 3.14159)

Poincaré crossings and island chains

import numpy as np
from pyna.flt import FieldLineTracer
from pyna.topo.poincare import PoincareAccumulator, poincare_from_fieldlines
from pyna.topo.section import ToroidalSection

# Canonical section type for topology APIs.
section = ToroidalSection(0.0)
acc = PoincareAccumulator([section])

# or trace directly from field lines
start_pts = np.array([
    [1.8, 0.0, 0.0],
    [2.0, 0.0, 0.0],
    [2.2, 0.0, 0.0],
])
acc = poincare_from_fieldlines(
    field_func=field_func,
    start_pts=start_pts,
    sections=[section],
    t_max=500 * 2 * np.pi,
    backend=tracer,
)
crossings = acc.crossing_array(0)

EAST tokamak manifold visualization

from pyna.toroidal.visual.tokamak_manifold import (
    plot_equilibrium_cross_section,
    plot_poincare_orbits,
    plot_manifold_bundle,
)
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(5, 7))
plot_equilibrium_cross_section(ax, eq)
plot_poincare_orbits(ax, orbits, cmap_by='psi_norm')
plot_manifold_bundle(ax, stable_manifold, unstable_manifold)
plt.savefig("east_manifold.png", dpi=300)

Torus deformation calculation

import numpy as np
from pyna import toroidal

# The package root now exposes the preferred toroidal namespace directly.
non_resonant_deformation_spectrum = toroidal.non_resonant_deformation_spectrum
poincare_section_deformation = toroidal.poincare_section_deformation
mean_radial_displacement = toroidal.mean_radial_displacement
split_radial_perturbation_spectrum = toroidal.split_radial_perturbation_spectrum

# Define perturbation spectrum (m, n, δBr, δBθ, δBφ in T·m)
m = np.array([1, 2, 3])
n = np.array([1, 1, 1])
dBr = np.array([1e-4+0j, 5e-5+0j, 2e-5+0j])
dBth = np.zeros(3, dtype=complex)
dBph = np.zeros(3, dtype=complex)

split = split_radial_perturbation_spectrum(m, n, dBr, iota=0.35)
spec = split.nonresonant_deformation(
    iota=0.35, Bphi=4.5, Btheta=0.3,
    dBth_mn=dBth, dBph_mn=dBph,
)
mean_dr = mean_radial_displacement(delta_iota=1e-4, iota_prime=-0.1)
print(f"Mean radial displacement: {mean_dr:.4f} m")

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📂 Module Overview

Core dynamical systems

Module	Description
pyna.system	Abstract dynamical system hierarchy (DynamicalSystem, VectorField*D)
pyna.flt	Field-line tracer: RK4, parallel CPU, CUDA/OpenCL backends
pyna.topo.toroidal_island	Rational surface location, theoretical island half-width
pyna.topo.poincare	Multi-section crossing accumulation and section helpers
pyna.topo.manifold	Stable/unstable manifold computation
pyna.topo.toroidal_cycle	Periodic orbit (X/O cycle) detection and analysis
pyna.coord	Flux coordinate transformations
pyna.draw	High-level plotting utilities
pyna.gc	Guiding-centre orbit integration
pyna.interact	Interactive widgets (Jupyter)
pyna.utils	Miscellaneous helpers

Toroidal plasma physics (pyna.toroidal)

pyna.toroidal is the toroidal-geometry namespace for coordinates, coils, diagnostics, control helpers, and visualisation.

Submodule	Description
toroidal.equilibrium	Toroidal equilibrium helpers still present in-repo pending extraction
toroidal.coords	PEST, Boozer, Hamada, Equal-arc magnetic coordinate systems
toroidal.coils	Coil geometry, Biot-Savart, RMP coil-set models
toroidal.control	Topology control: gap response, q-profile response
toroidal.diagnostics	Plasma diagnostic observables
toroidal.visual	Publication-quality tokamak figures (tokamak_manifold)
toroidal.torus_deformation	Non-resonant torus deformation (BNF spectral theory, Wei 2025)

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🔬 Theory

Non-resonant torus deformation

Under an external perturbation δB, each invariant torus (flux surface) deforms analytically. The displacement field δr = (δr, δθ, δφ) is computed in Fourier space via the formula (Theorem 2 of Wei 2025):

(δr)_mn = (δBr)_mn / [i · (mι + n) · Bφ]

For axisymmetric (n = 0) poloidal-field coil perturbations the mean radial shift reduces to:

⟨δr⟩ = −δι / ι'

where δι is the first-order rotational-transform variation. Resonant B^r Fourier components (mι+n=0) are separated for island-width analysis, while non-resonant components drive smooth flux-surface deformation. These results are implemented in pyna.toroidal.torus_deformation.

Poincaré maps & manifolds

A Poincaré section φ = φ₀ turns the continuous field-line flow into an area-preserving 2-D map. Near an X-point the stable (W^s) and unstable (W^u) manifolds intersect transversally, generating the heteroclinic tangle responsible for chaotic transport. pyna.topo provides algorithms to compute, visualize, and measure these structures.

Grad-Shafranov equilibrium

Toroidal MHD equilibrium satisfies ΔψGS = −μ₀R²dp/dψ − F dF/dψ. pyna.toroidal.equilibrium exposes Solov'ev analytic solutions and a numerical GS solver with free-boundary capability.

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📚 Documentation

Full documentation (API reference, tutorials, theory notes) is hosted at: https://wenyinwei.github.io/pyna/

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🤝 Contributing

Contributions are welcome! Please open an issue or pull request on GitHub.

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📄 License

GPL-3.0-or-later © 2024-2026 Wenyin Wei