Crate plasmoid 

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, the thermal tunnelling exponent of heavy ions, 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
nuclear	AME2020 mass excesses, Q-values that refuse unbalanced reactions (with β⁺, electron capture and β⁻), atomic rest energies, specific energy capped at c², production power and the atoms an energy can make, NIST’s natural isotopic compositions, the stable fission partners of a nucleus, and the contamination test of an element mix	AME2020; NIST isotopic compositions; Priem et al. 2008
aneutronic	Q-values (pinned to nuclear’s AME2020 table), 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.
• Nuclear accounting: AME2020’s printed atomic masses to 10⁻⁸ u; Bosch & Hale’s D–D branches, oxygen burning (Woosley, Heger & Weaver) and every aneutronic Q constant; the talk’s reactions, unbalanced ones refused; ¹⁸⁴W’s only stable Ca + Xe split; NIST’s compositions summing to 1; Priem et al.’s steel fingerprint.
• 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).

Modules

aneutronic

Aneutronic fuels and their power balance: Q-values, the neutrons D–³He still makes, and why p–¹¹B fights bremsstrahlung and synchrotron radiation.

collisions

Collisions in a plasma: Spitzer’s resistivity, which the pinch and reconnection calculators share.

conversion

Electricity without a steam cycle: direct conversion of charged fusion products, inductive recovery in pulsed machines, and the plant arithmetic that decides whether any of it nets power.

discharge

Gas discharges and the thin gas around them: when a gas gap breaks down, how far a molecule flies between collisions, when a wire goes into corona, what a glow does to a body in it, and how the gas drags on a body moving or turning through it at any pressure. Together they decide whether a high-voltage rig “in vacuum” is free of ions, and how long a suspended body keeps swinging.

fusion

Getting nuclei through the Coulomb barrier: tunnelling and Gamow peaks, reaction rates, ignition, electron screening, muon catalysis and gravitational confinement in stars, with the checks that test claims of low-energy fusion.

nuclear

Nuclear accounting: the masses of nuclides, the energy a reaction releases or costs, which isotopes occur in nature, and the bookkeeping that turns a claimed rate of transmutation into the power and radiation it would need.

pinch

Z-pinches and the dense plasma focus: Bennett equilibrium, the Pease–Braginskii current, Lee model scalings, and the pinch’s gravitational twin, the self-gravitating filament.

relaxation

Plasmoids: how magnetised plasma organises itself. Taylor relaxation, spheromaks, field-reversed configurations, magnetic reconnection, and the energy a free plasmoid can hold.

tokamak

The engineering scalings a tokamak design is checked against: the edge safety factor (and the Kruskal–Shafranov kink limit behind it), the Greenwald density limit, the Troyon beta limit, and the IPB98(y,2) energy-confinement law.