Physics-CPD
Generic computational plasma dynamics in Perl, with an optional stellarator fusion-reactor modelling submodule and 3‑D visualisation of the Wendelstein 7‑X stellarator.
The distribution provides two modules:
| Module | Role |
|--------|------|
| Physics::CPD | Pure‑Perl Computational Plasma Dynamics package — generic magnetised‑plasma calculations from density, temperature, magnetic field and ion species. |
| Physics::CPD::Stellarator | Fusion-reactor modelling submodule that 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 — generic plasma physics package (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 — stellarator fusion-reactor 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.
- Theoretical fusion power production (if fuelled with D‑T): Bosch‑Hale D‑T reactivity ⟨σv⟩, fusion power density and total fusion power, the neutron/alpha split, neutron wall loading and the fusion gain Q.
- 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::Gnuplotand agnuplotbinary. 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.
Theoretical fusion power
W7‑X is a research device and does not itself produce significant fusion power, but the model can estimate what a stellarator of this design would deliver if run as a deuterium–tritium reactor (a 0‑D estimate using the Bosch‑Hale reactivity):
use Physics::CPD::Stellarator;
my $reactor = Physics::CPD::Stellarator->new(
electron_density => 2.0e20, # m^-3
ion_temperature => 15000, # eV (15 keV)
magnetic_field => 2.5, # T
heating_power => 10, # MW (auxiliary)
dt_fuel_fraction => 1.0, # pure 50:50 D-T
);
print $reactor->power_report;
printf "P_fusion = %.1f MW\n", $reactor->fusion_power_MW; # ~235 MW
printf " neutrons = %.1f MW\n", $reactor->neutron_power_MW;
printf " alphas = %.1f MW\n", $reactor->alpha_power_MW;
printf "wall load = %.2f MW/m^2\n", $reactor->neutron_wall_load;
printf "gain Q = %.1f\n", $reactor->fusion_gain_Q; # P_fus / P_heat
Examples
Runnable scripts in examples/:
plasma_parameters.pl—Physics::CPDstandalone.w7x_simulation.pl— W7‑X report and a density scan (τ_E, triple product, β).power_production.pl— theoretical D‑T fusion power of the W7‑X‑class design, with ion‑temperature and density scans (P_fus, neutron wall load, Q).plot_3d_design.pl— writes all four PNG visualisations (perl examples/plot_3d_design.pl [output_dir]).
API reference
Both classes are built with Moo: every
constructor argument below is also a read/write accessor ($obj->attr to read,
$obj->attr($value) to set), and every derived quantity is a plain method that
recomputes from the current state. Temperatures are in eV; all other
quantities are SI unless a method name carries an explicit unit suffix
(_MJ, _MW, _hz, …).
Physics::CPD
Constructor attributes
| Attribute | Symbol | Unit | Default | Description |
|-----------|--------|------|---------|-------------|
| electron_density | nₑ | m⁻³ | 1e20 | electron number density |
| electron_temperature | Tₑ | eV | 1000 | electron temperature |
| ion_temperature | Tᵢ | eV | = Tₑ | ion temperature |
| magnetic_field | B | T | 1 | magnetic flux density |
| ion_species | — | — | 'H' | e, H, p, D, T, He, He3, He4, C, O |
| ion_mass | mᵢ | kg | from species | override to bypass the species table |
| ion_charge | Z | — | from species | ion charge number |
Derived quantities (methods)
| Group | Methods | Unit |
|-------|---------|------|
| Energy / density helpers | electron_temperature_joules, ion_temperature_joules, electron_temperature_kelvin, ion_temperature_kelvin, ion_density, mass_density | J, K, m⁻³, kg·m⁻³ |
| Frequencies (＋_hz variants) | electron_plasma_frequency, ion_plasma_frequency, electron_cyclotron_frequency, ion_cyclotron_frequency | rad/s (Hz) |
| Lengths & speeds | debye_length, electron_gyroradius, ion_gyroradius, electron_thermal_velocity, ion_thermal_velocity, alfven_velocity, ion_sound_speed | m, m/s |
| Pressure & energetics | plasma_pressure, magnetic_pressure, plasma_beta | Pa, Pa, – |
| Collisional transport (NRL) | coulomb_logarithm, collision_frequency, mean_free_path, spitzer_resistivity | –, s⁻¹, m, Ω·m |
| Other | plasma_parameter (N_D), as_hash, report | –, hashref, text |
as_hash returns every quantity keyed with its unit (e.g. debye_length_m);
report returns the same as a formatted, printable block.
Physics::CPD::Stellarator
Inherits everything above and overrides the default magnetic_field to 2.5 T.
Additional attributes
| Attribute | Symbol | Unit | Default | Description |
|-----------|--------|------|---------|-------------|
| config_name | — | — | 'Wendelstein 7-X …' | free-text label |
| major_radius | R₀ | m | 5.5 | major radius |
| minor_radius | a | m | 0.53 | minor radius |
| num_field_periods | Nfp | — | 5 | toroidal field periods |
| iota | ι | — | 0.96 | rotational transform |
| heating_power | P | MW | 10 | auxiliary heating power |
| num_nonplanar_coils | — | — | 50 | non-planar modular coils |
| num_planar_coils | — | — | 20 | planar coils |
| beta_limit | — | — | 0.05 | design MHD β limit |
| pulse_length | — | s | 1800 | pulse length |
| gyrotron_frequency | — | Hz | 140e9 | ECRH gyrotron frequency |
| dt_fuel_fraction | f | — | 1.0 | D-T fuel-ion fraction of nₑ (fusion methods) |
| boundary_coeffs | — | m | W7-X set | [m, n, Rbc, Zbs] Fourier rows |
| coil_radius / coil_elongation / coil_tilt | — | m / – / rad | 0.95 / 1.25 / 0.16 | 3-D coil styling |
Geometry & performance methods
| Group | Methods | Unit |
|-------|---------|------|
| Device geometry | aspect_ratio, field_period_angle, plasma_volume, plasma_surface_area, rotational_transform, safety_factor | –, rad, m³, m², –, – |
| Confinement & limits | confinement_time_iss04, stored_energy / stored_energy_MJ, sudo_density_limit, beta_fraction, density_fraction, triple_product, ecrh_resonance_field([n]) | s, J/MJ, m⁻³, –, –, keV·s·m⁻³, T |
| Radial profiles | density_profile($x[,α]), temperature_profile($x[,α]) | m⁻³, eV |
| Reporting | device_report, power_report | text |
Fusion power methods (assume a 50:50 D‑T plasma; 0‑D estimate over the plasma volume, Bosch‑Hale reactivity)
| Method | Returns | Unit |
|--------|---------|------|
| dt_reactivity([$Ti_keV]) | ⟨σv⟩ at Tᵢ (default ion_temperature) | m³/s |
| fuel_ion_density | dt_fuel_fraction × electron_density | m⁻³ |
| fusion_power_density | (n_fuel/2)² ⟨σv⟩ E_DT | W/m³ |
| fusion_power / fusion_power_MW | total fusion power | W / MW |
| neutron_power_MW | 14.07 MeV channel (to blanket) | MW |
| alpha_power_MW | 3.52 MeV channel (heats plasma) | MW |
| neutron_wall_load | neutron power / plasma surface | MW/m² |
| fusion_gain_Q | fusion_power_MW / heating_power | – |
Geometry accessors (pure Perl, return array references — no PDL required)
boundary_point($u,$v[,$scale]), surface_point_xyz($u,$v[,$scale]),
magnetic_axis([$n]), cross_section($v[,$nu,$scale]),
surface_grid([$nu,$nv,$scale]), modular_coils([$count,$npts]).
Plotting methods (require PDL + PDL::Graphics::Gnuplot; each takes an
output => filename and returns the filename written)
plot_3d, plot_cross_sections, plot_profiles, plot_confinement_scan.
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.
- Bosch & Hale, improved D‑T fusion reactivities, Nucl. Fusion 32 (1992) 611.
- Huba, NRL Plasma Formulary (collisional parameters).
License
Released under the GNU General Public License v3.0 — see the
LICENSE file for the full text.