Physics-Stellarator

Computational plasma dynamics in Perl, with a full model and 3‑D visualisation of the Wendelstein 7‑X stellarator.

The distribution provides two modules:

| Module | Role | |--------|------| | Physics::CPD | Pure‑Perl Computational Plasma Dynamics engine — fundamental magnetised‑plasma parameters from density, temperature, magnetic field and ion species. | | Physics::CPD::Stellarator | Extends Physics::CPD with stellarator geometry and physics, using Wendelstein 7‑X (W7‑X, IPP Greifswald) as the default configuration, plus plotting and 3‑D design diagrams. |

Features

Physics::CPD — plasma physics engine (no heavy dependencies)

• Characteristic frequencies: electron/ion plasma and cyclotron frequencies.
• Characteristic lengths/speeds: Debye length, electron/ion Larmor radii, thermal, Alfvén and ion‑sound speeds.
• Energetics: kinetic and magnetic pressure, plasma β.
• Collisional transport (NRL Plasma Formulary): Coulomb logarithm, collision frequency, mean free path, Spitzer resistivity.
• Multi‑species ions (H, D, T, He, He3, C, O, …); temperatures in eV.

Physics::CPD::Stellarator — Wendelstein 7‑X model

• Device parameters: major/minor radius, 5 field periods, coil counts, rotational transform ι, design β limit, pulse length, ECRH gyrotron.
• Derived physics: aspect ratio, plasma volume/surface, ISS04 confinement‑time scaling, stored energy, the stellarator Sudo density limit, β/density‑limit fractions, the Lawson triple product, and the ECRH resonant field.
• 3‑D geometry: the last‑closed flux surface as a VMEC‑style Fourier series R(u,v), Z(u,v), the helical magnetic axis, nested flux surfaces and modular field coils — fully parameterised so you can model other stellarators by supplying your own boundary coefficients.
• Plotting via PDL::Graphics::Gnuplot (headless‑safe PNG output): 3‑D design diagram, poloidal cross sections, radial profiles, confinement scans.

Installation

perl Makefile.PL
make
make test
make install

Requirements:

• Runtime (core physics): Moo.
• Plotting / 3‑D (optional): PDL, PDL::Graphics::Gnuplot and a gnuplot binary. These are loaded on demand — the physics API works without them.

Quick start

Plasma parameters

use Physics::CPD;

my $plasma = Physics::CPD->new(
    electron_density     => 1e20,   # m^-3
    electron_temperature => 5000,   # eV
    ion_temperature      => 3000,   # eV
    magnetic_field       => 3.0,    # T
    ion_species          => 'D',
);

print $plasma->report;
printf "beta = %.2f %%\n", 100 * $plasma->plasma_beta;

Wendelstein 7‑X

use Physics::CPD::Stellarator;

my $w7x = Physics::CPD::Stellarator->new(
    electron_density     => 8e19,
    electron_temperature => 4000,
    ion_temperature      => 2500,
    magnetic_field       => 2.5,
    heating_power        => 10,     # MW
);

print $w7x->device_report;

printf "ISS04 tau_E = %.3f s\n",  $w7x->confinement_time_iss04;
printf "stored W    = %.1f MJ\n", $w7x->stored_energy_MJ;

# Visualisations (PNG files)
$w7x->plot_3d( output => 'w7x_3d.png' );              # 3-D design diagram
$w7x->plot_cross_sections( output => 'w7x_cross.png');# flux-surface sections
$w7x->plot_profiles( output => 'w7x_profiles.png' );  # radial profiles
$w7x->plot_confinement_scan( output => 'w7x_conf.png',
                             parameter => 'heating_power', from => 1, to => 20 );

The 3‑D diagram shows the twisted, bean‑shaped plasma boundary (the five field periods), the helical magnetic axis and the tilted modular coils.

Examples

Runnable scripts in examples/:

• plasma_parameters.pl — Physics::CPD standalone.
• w7x_simulation.pl — W7‑X report and a density scan (τ_E, triple product, β).
• plot_3d_design.pl — writes all four PNG visualisations (perl examples/plot_3d_design.pl [output_dir]).

Wendelstein 7‑X reference parameters (defaults)

| Quantity | Value | |----------|-------| | Major radius R0 | 5.5 m | | Minor radius a | 0.53 m | | Aspect ratio | ≈ 10.4 | | Field periods | 5 | | Magnetic field | up to 3 T (2.5 T typical) | | Plasma volume | ≈ 30 m³ | | Non‑planar / planar coils | 50 / 20 | | Rotational transform ι | ≈ 0.8 – 1.2 | | ECRH | 140 GHz, 2nd‑harmonic X‑mode → 2.5 T | | Design β limit | ≈ 5 % |

Physics references

• Klinger et al., “Overview of first Wendelstein 7‑X high‑performance operation”, Nucl. Fusion 59 (2019) 112004.
• Yamada et al., ISS04 confinement scaling, Nucl. Fusion 45 (2005) 1684.
• Sudo et al., stellarator density limit, Nucl. Fusion 30 (1990) 11.
• Huba, NRL Plasma Formulary (collisional parameters).

License

Released under the GNU General Public License v3.0 — see the LICENSE file for the full text.