plasmoid 0.4.1

Fusion and self-organising plasma physics, computed: Coulomb barriers and Gamow peaks, Bosch–Hale and p–¹¹B reactivities, Lawson, screening and muon catalysis; Z-pinches and the plasma focus; plasmoids, Taylor relaxation, FRCs and reconnection; aneutronic power balance and direct energy conversion; each proposal against its physical limit.
Documentation

plasmoid

Fusion and self-organising plasma physics, computed. Every function reproduces a published number, and the proposals that promise more (cold fusion, Pais's fusion device, magnetically suppressed bremsstrahlung, overunity plasmoids) are set against the limit they have to beat.

  • Getting through the Coulomb barrier: tunnelling and Gamow peaks, Bosch–Hale reaction rates, the p–¹¹B fits, the Lawson criterion, electron screening, muon catalysis, and gravity's way of doing it in stars.
  • Pinches and the plasma focus: Bennett equilibrium, the Pease–Braginskii current, Lee's plasma-focus scalings, and the pinch's gravitational twin, the self-gravitating filament.
  • Plasmoids: Taylor relaxation (∇×B = λB, what a plasma settles into by itself), spheromaks, field-reversed configurations, and reconnection, slow (Sweet–Parker) and fast (plasmoid-mediated).
  • Aneutronic power: Q-values, the neutrons D–³He still makes, and p–¹¹B's race against bremsstrahlung and synchrotron radiation.
  • Electricity without a steam cycle: multi-stage direct converters, inductive recovery in pulsed machines, and the plant arithmetic.

Install

cargo add plasmoid metrology

Example: the Coulomb barrier, and how fusion gets past it

use plasmoid::fusion::{Reaction, M_D, M_T, bosch_hale, coulomb_barrier, gamow_energy, gamow_peak, reduced_mass};

// D–T touching at 3.24 fm: a 444 keV barrier.
let barrier = coulomb_barrier(1.0, 1.0, 3.243);
// At 10 keV the reactions happen at the Gamow peak, 31 keV: tunnelling, 14× below the top.
let (peak, _) = gamow_peak(gamow_energy(1.0, 1.0, reduced_mass(M_D, M_T)), 10.0);
println!("barrier {barrier:.0} keV, Gamow peak {peak:.1} keV");
// Bosch & Hale's reaction rate there.
assert!((bosch_hale(Reaction::DT, 10.0).unwrap() / 1.1362e-22 - 1.0).abs() < 1e-3);

Example: the pinch and its gravitational twin

use metrology::{PARSEC, SOLAR_MASS};
use plasmoid::pinch::{bennett_line_density, magnetic_over_gravitational, ostriker_line_mass};

// The equation that holds a 1 MA Z-pinch together is the one that holds a molecular-cloud
// filament together, with gravity in place of magnetism (Bennett 1934, Ostriker 1964).
let cloud = ostriker_line_mass(10.0, 2.3) * PARSEC / SOLAR_MASS; // 16.6 solar masses per parsec
let pinch = bennett_line_density(1e6, 2000.0) * 3.3436e-27;     // deuterium at 2 keV, kg/m
assert!((cloud - 16.6).abs() < 0.2);
// In the pinch, magnetism beats the plasma's own gravity by 5.5×10²⁷.
assert!(magnetic_over_gravitational(1e6, pinch) > 1e27);

What is inside

Module What it computes Key sources
fusion Coulomb barrier, Sommerfeld and Gamow factors, Gamow peak, Bosch–Hale reactivities and cross sections (D–T, D–D, D–³He), p–¹¹B (Nevins–Swain, Tentori–Belloni), Lawson, screening (first-order and exact), Salpeter, muon catalysis, Lane–Emden, and the low-energy fusion checks Bosch & Hale 1992 (implementation notes); Wurzel & Hsu 2022; Tentori & Belloni 2023
pinch Bennett temperature and line density, Pease–Braginskii, Lee's peak current and yield, snowplow speed, cyclotron energy, the Ostriker filament Klír 2005; Lee 2009; Ostriker 1964 (ApJ 140, 1056)
relaxation Bessel-function model, spheromak eigenvalues, Taylor-state energy, FRC beta and s-parameter, Lundquist number, Sweet–Parker and plasmoid reconnection, the virial cap on a free plasmoid Taylor 1986; Tuszewski 1988; Loureiro et al. 2007
aneutronic Q-values, D–³He neutron fraction, relativistic bremsstrahlung, synchrotron, the p–¹¹B fusion-to-bremsstrahlung ratio Putvinski, Ryutov & Yushmanov 2019 (Nucl. Fusion 59, 076018)
collisions Spitzer's resistivity across and along the field, shared by the pinch and reconnection calculators, its coefficient checked against Braginskii's m_e/(n_e e² τ_e) NRL Plasma Formulary; Braginskii 1965
discharge Gas discharges and the thin gas around them: Paschen breakdown and its minimum with air's Townsend constants, the mean free path, Peek's corona onset, the floating potential in a glow, ion mobility, gas density and molecular speed, and slip-corrected drag on a sphere moving or turning at any Knudsen number: whether a high-voltage rig "in vacuum" is free of ions, and how long a body in it keeps swinging Raizer, Gas Discharge Physics (1991), table 4.1; Peek 1929; Hirschfelder, Curtiss & Bird 1954; Davies 1945; Lieberman & Lichtenberg
tokamak The design scalings a tokamak is checked against: edge safety factor and the kink limit, Greenwald density, Troyon beta and IPB98(y,2) confinement, with ITER and SPARC ITER Physics Basis (Nucl. Fusion 39, 1999); Creely et al. 2020 (J. Plasma Phys., SPARC)
conversion N-stage direct-collector efficiency, engineering gain of magnetic and inertial plants, pulsed inductive breakeven, laser p–¹¹B gain Moir & Barr 1973 (Nucl. Fusion 13, 35); Margarone et al. 2020

The research behind it, with every claim's status, is in the reports on the Coulomb barrier and the Schwinger limit and on Z-pinches, plasmoids and aneutronic fusion.

Applications

  • Judging a design point. tokamak checks a machine against the safety-factor, density, beta and confinement limits it must respect; examples/sparc.rs runs ITER and SPARC.
  • Reading a shot. examples/triple_products.rs places published results against the Lawson requirement at their own temperature, and examples/fusion_yields.rs turns a yield into the reactions and fuel behind it.
  • Choosing a fuel. aneutronic and conversion weigh p–¹¹B and D–³He against bremsstrahlung and set out what direct conversion returns without a steam cycle.
  • Pinches and self-organisation. pinch and relaxation give the equilibria, scalings and reconnection rates, with the gravitational twin of the Bennett relation alongside.

How it is checked

  • Bosch–Hale: all of UWFDM-1268's Table 6 (D–T, both D–D branches, D–³He at 1, 10 and 100 keV) within 0.4%; the D–T cross-section peak (5.07 b); and the Maxwellian average of the cross section against the reactivity fit.
  • p–¹¹B: the published Nevins–Swain and Tentori–Belloni tables, and their 30% and 50% gaps.
  • Lawson: Wurzel & Hsu's 2.97×10²¹ keV s m⁻³ at 14 keV and the 4.3 keV ignition temperature.
  • Pinches: Klír's 3.12 keV Bennett coefficient, the 1.4 MA Pease–Braginskii current, and Lee's Table I peak currents within 1.5%.
  • Plasmoids: Ji & Daughton's Lundquist numbers and Bhattacharjee et al.'s rates.
  • Aneutronic power: NRL's bremsstrahlung limit and Putvinski's synchrotron ratios.
  • Laser shots: Margarone's and the PALS shots' energy returns.

One of eight crates in physica: physica (all of them, plus cross-domain analogies) · metrology (constants) · geopotential (the gravity field) · gravimetry (missions and GRACE) · gravitational (waves) · gravitics (frontier gravity) · magnetics (magnetism and MHD) · plasmoid (fusion plasma).