Physics models & simulation
Equilibria, transport, neutronics, heating and the reduced-order physics the twin and controller rely on. 542 pages
The breeder's 14 MeV neutron flux is a schedulable service for irradiation, testing, and isotope production, arbitrated against tritium breeding.
One-dimensional transport codes evolve plasma density, temperature, and current profiles along the minor radius using flux-surface-averaged conservation laws.
Since live A/B on a single machine is unsafe, Kronos compares models by counterfactual replay on the twin and by matched shadow evaluation, not by splitting live traffic.
Using learned models to speed up, replace steps in, or guide expensive plasma and reactor simulations.
Turning neutron flux into activation inventories and displacement damage for the breeder blanket and burner structure over their lives.
Adiabatic demagnetization cools by aligning and then slowly randomizing magnetic moments, reaching microkelvin temperatures below the range of dilution refrigerators.
The roadmap — formal assurance, physics-fidelity twins, stronger algorithms, and fleet-scale trust. We publish the gaps, not just the wins: each is real, sequenced to a milestone,
The transverse magnetic-tension wave of MHD, and the eigenmodes it forms in a nonuniform confined plasma.
Transverse waves that travel along magnetic field lines as if they were tensioned strings.
AlphaZero replaces MCTS rollouts with a learned network and trains purely by self-play from the rules alone.
The tandem mirror confines ions with an electrostatic potential set by charge neutrality; the Pastukhov relation ties confinement time to that potential.
Biased electrodes and plug heating shape the electrostatic potential that plugs the tandem mirror; the interface senses and drives that potential.
Tandem-mirror confinement lives or dies on the end-plug ambipolar potential; the safety envelope bounds it against a rapid confinement-loss transient.
Computing the electrostatic barriers that plug the burner's magnetic mirror, the control problem at the heart of tandem-mirror confinement.
Amplitude amplification turns a rare 'good' outcome from probability p into one found in about 1/sqrt(p) tries - the quadratic Monte-Carlo speedup most relevant to Kronos's neutron
Quantum amplitude estimation offers a quadratic speedup for Monte Carlo integrals like neutron transport, useful only far past today's hardware.
A twin flags anomalies as persistent, unexplained gaps between what it predicts and what the sensors report.
An interface is a contract between parts of a system; honoring it lets pieces built by different people, at different times, work together.
Arithmetic intensity is the ratio of arithmetic operations performed to bytes moved from memory, and it decides whether a kernel is memory- or compute-bound.
Beam-tracing codes extend ray tracing to finite-width Gaussian beams, capturing diffraction and focusing that a zero-width ray cannot represent.
Keeping the plasma pressure below the stability ceiling set by pressure-driven magnetohydrodynamic modes.
Thermal-hydraulics codes model heat removal and coolant flow in the blanket, turning neutron heating into temperatures and stresses.
The plasma drives part of its own current; closing that self-consistency loop between pressure, current, and equilibrium is a fixed-point problem the twin must solve.
The closed set of collisional fluid transport coefficients for a magnetized two-fluid plasma.
The telemetry that constrains the breeder's magnetic equilibrium — magnetics, profiles, shape — is the fabric's most safety-relevant feature set.
The operational indicators that define a good breeder run — shot quality, shape fidelity, magnet health, and tritium-cycle context — with no economics.
Failure modes of the Hyperion superconducting magnet set at 16.84 T peak field, and the detection and protection each demands.
A breeder campaign chains shots and tracks tritium and helium-3 production accounting as durable, auditable state across the run.
The blanket surrounding a D-T plasma captures neutrons to breed tritium and carry away heat, and its coolant and purge flows are actively controlled.
Regulating fusion power in a burning plasma, where self-heating couples temperature and reaction rate in a potentially unstable loop.
The operator surface for the D-3He tandem mirror: end-plug density, the ambipolar potential well, and direct energy conversion of a 5.44%-neutron-fraction output.
Aegis is the burner packaged for fixed defense installations, the same tandem-mirror generator in a site-hardened enclosure.
The central cell is the long middle region where the deuterium-helium-3 plasma burns, held between the two end plugs.
Direct energy conversion decelerates escaping ions against biased collector grids; the interface reads per-grid currents and sets grid potentials.
The burner fuses deuterium with helium-3, a reaction that releases its energy mostly as charged particles.
The burner uses radio-frequency and neutral-beam heating to reach the high temperatures deuterium-helium-3 fusion demands.
The plug throats are the intense high-field regions at each end that reflect plasma back into the central cell.
The operational indicators for the tandem mirror — plug density, potential-well depth, DEC grid stability — shown against design references, without economics.
The mirror coils shape the axial field, gentle in the central cell and intense at the plugs, to confine the plasma.
Deuterium-helium-3 fuel keeps neutrons to 5.44 percent of the fusion power, easing shielding compared with deuterium-tritium.
Confinement in the burner combines magnetic mirroring with electrostatic plugging along a single straight axis.
A tandem mirror confines plasma between high-field end plugs; controlling the plug potentials is the heart of running the burner.
A tandem mirror confines plasma between strong end plugs, so controlling the high-field plug coils is central to the burner's operation.
The burner twin tracks the plug and throat fields, plasma confinement, and direct energy conversion of a deuterium-helium-3 tandem mirror.
The burner is a deuterium-helium-3 tandem-mirror generator, a long linear machine with high-field plugs at each end.
Every gram of regulated isotope and every activated component is tracked as byproduct material from creation to disposition, closing to the operational mass balance.
Each twin is tuned so its predictions match its specific machine, correcting the gap between an idealized model and real hardware.
How individual shots accumulate into a campaign, and how duty cycle sets the ceiling on breeder availability and tritium output.
Every factual claim in a copilot answer links to a retrieved source or a twin run; unsourced assertions are flagged as defects.
Open-field-line configurations like magnetic mirrors need codes that model end losses, ambipolar potentials, and direct energy conversion rather than closed flux surfaces.
Power supplies convert grid power into the precisely regulated currents the magnet coils need, and their fast inner loops underpin all magnetic control.
The dimensionless ratio that places a plasma in the banana, plateau, or Pfirsch-Schluter transport regime.
A twin keeps a running ledger of the accumulated damage in each critical component, based on its real operating history.
Designing a fusion device is a stack of hard computational problems, from plasma simulation to combinatorial optimization of the machine.
Fusion research leans on HPC to model plasma turbulence, stability, and neutron transport across scales no single method or machine spans alone.
Using automated image analysis to inspect components and surfaces for defects more consistently than manual review.
Forecasting sudden losses of plasma confinement early enough to mitigate them before they stress the machine.
The fuel cycle ties breeding, extraction, storage, and injection into one loop that must balance continuously; computing keeps it balanced.
Planning production, decay, storage, and delivery of isotopes whose inventory changes on its own over time.
Solving the coupled electromagnetic, mechanical, thermal, and superconductor physics that decide whether a magnet can be built.
Tracking which materials become radioactive under neutron exposure, how much, and how it decays, over the life of a plant.
A fusion machine's 14 MeV neutrons are a research tool; computing plans irradiations, predicts results, and interprets them for users.
Simulating how 14 MeV neutrons travel, breed tritium, deposit heat, and damage materials so blankets and shields can be sized.
Combining failure probabilities and consequences across many scenarios into an integrated, quantified picture of risk.
Tracking every gram of tritium through breeding, extraction, storage, and burn so the fuel cycle closes on paper before it must close in hardware.
Every quantity the twin reports carries a confidence score, and control behavior is tied to that score so the machine is driven cautiously when the twin is unsure.
The Lagrangian and its dual underlie MPC, reconstruction, and scenario design; they turn constrained problems into solvable stationarity conditions.
Assembling a copilot's working context from the live twin state vector, retrieval, and task framing under a strict token and latency budget.
Allocating a finite context budget across system framing, twin state, and retrieved evidence so the most decision-relevant tokens are always present.
Counterflow heat exchangers precool the incoming helium-3 against the outgoing dilute stream, and their design sets the base temperature of a dilution refrigerator.
How control differs for an open-ended mirror machine, where confinement rests on end-plug fields and potentials rather than a closed current.
The burner generator is a tandem mirror, not a tokamak, so its control centers on plug fields, axial confinement, and direct conversion.
A live 3D rendering of the machine with L3 twin state painted onto real geometry — flux surfaces, thermal fields, and neutron flux where an operator expects to find them.
The cooling power at the mixing chamber depends on helium-3 circulation rate and temperature, following an approximately quadratic law that sets what loads a fridge can absorb.
Cooling loops carry heat from magnets, heating systems, and plasma-facing components to a heat sink, regulated to hold every component in its window.
Orchestration reconciles L3 twin predictions and L5 copilot proposals into a single bounded action, resolving disagreement conservatively.
The window through which L5 copilots explain, recommend, and answer — always advisory, always with citations and confidence, never issuing commands on their own.
The 2-D plasma pressure distribution, reconstructed in flux coordinates from Thomson scattering, interferometry, and magnetics, is the fabric's richest engineered feature.
A counterfactual explanation states the smallest change to an input that would flip the model decision.
How Kronos links neutronics, thermomechanics, and MHD so the interactions between them are captured, not assumed away.
The Power, Neutronics, Thermomechanics, and MHD modules are solved as a weakly coupled multi-physics system each twin step.
A single surface to supervise more than one machine at once — breeder and burner side by side, and multiple units of a kind — without diluting per-machine depth.
Superconducting magnets run near a few kelvin, so a helium refrigeration plant must hold temperature and flow steady against a swinging heat load.
Superconducting and many spin qubits operate near 10 millikelvin, reached by a dilution refrigerator that exploits helium isotope mixing.
Section planes remove half the machine so the layered build from plasma to cryostat is visible in a single glance.
Empirical relationships fit across devices that predict confinement and performance from engineering parameters.
Regression across many devices yields empirical scaling laws that predict energy-confinement time from engineering parameters, guiding new-device design.
Dead-time compensation restores control performance to processes with transport delay by predicting or accounting for the delayed response.
Grid-tie modulation matches direct-conversion output to grid demand and rides through faults; it is the burner's electrical-export interface.
Networks infer plasma position, shape, and current from arrays of magnetic sensors, and detect and correct faulty probe signals in real time.
Deterministic transport codes discretize the Boltzmann transport equation on grids in space, angle, and energy, complementing Monte-Carlo methods.
Deuterium is the common fuel for both machines; its supply interface is a metering-and-purity loop feeding the fueling actuators.
Deuterium fuels both machines; L7 tracks its inventory, purity, and consumption rate against burn plans so fuel never becomes the limiting constraint.
A digital twin is a live, data-fed model of a physical system that mirrors its state and predicts its behavior.
A twin is a layered federation: sensing and ingestion, a physics or surrogate core, an assimilation loop, and a decision and interface layer.
A digital twin is a living model kept in step with a physical system through a continuous flow of measured data.
A digital twin is a living, physics-faithful software model that stays synchronized with the real machine; Kronos runs coupled twins of its breeder and burners to design, build, an
A twin is assembled from ingestion, modeling, assimilation, orchestration, storage, and interface layers, each with distinct requirements.
Fast, data-informed models of a device that mirror its behavior for study, control design, and what-if analysis.
The general concept of a live, validated simulation paired with a physical system, and what makes one trustworthy.
A digital twin is a running simulation kept synchronized with the real machine, used to see inside it, test decisions, and predict what happens next.
Twin refinement is the periodic re-grounding of the digital twin's surrogates against measured pulse data so its predictions stay faithful to the real machine.
The relation between frequency and wavevector that classifies every linear wave and instability in a plasma.
Estimating in real time whether a plasma is approaching a sudden loss of confinement, early enough for the stack to act.
Classifiers that estimate, from live diagnostics, whether a tokamak plasma is approaching a sudden loss of confinement.
The divertor and expander handle the exhaust heat and particles of both machines; their telemetry guards the components that meet the plasma edge.
L1 manages the breeder divertor and burner end expander so exhaust heat and particles land on surfaces engineered to take them.
The divertor (breeder) and the burner's expander both handle exhaust flux; their interfaces control detachment and strike-point loading.
Detachment cools and dilutes the plasma before it reaches the divertor target, spreading heat over gas and radiation instead of concentrating it on a surface.
Regulating the plasma edge so the heat reaching the divertor is radiated away before it can damage the target.
Keeping the power landing on divertor targets within material limits combines strike-point sweeping, flux spreading, and detachment.
Infrared cameras give a 2-D surface-temperature field on the divertor and first wall; the interface turns raw frames into calibrated heat-flux maps.
The universal instabilities driven by density and temperature gradients that dominate cross-field transport.
The universal instability driven by density and temperature gradients, the seed of most plasma turbulence.
Reconstruction codes fit a Grad-Shafranov equilibrium to magnetic and kinetic measurements, giving the best-estimate flux map of a real discharge.
ECE radiometry measures the electron temperature profile and its fluctuations from the plasma's own cyclotron emission, fast and spatially resolved.
Electron cyclotron systems deposit power at the electron gyro-frequency using high-power millimeter-wave beams from gyrotrons, aimed by steerable mirrors.
ECRH modeling combines ray-tracing and Fokker-Planck physics to predict the highly localized heating and current drive from electron-cyclotron waves.
Empirical power-law fits that predict confinement time from machine size, field, current, and heating.
Reasoning over the breeder's tritium and helium-3 balance and the burner's D-3He supply, grounded in the twin's fuel-cycle module.
Turning condition, history, and neutron-fluence exposure into inspection and intervention plans, with remote-handling constraints made explicit.
Reasoning over REBCO strain, temperature margin, and quench precursors for the breeder's 16.84 T magnets and the burner's 26.49 T plug coils.
Running many perturbed twin copies forward produces a distribution of futures, quantifying forecast uncertainty rather than a single guess.
Equilibrium coils supply the vertical field that balances the plasma's outward force and set the plasma current profile through the central solenoid.
Shape-control codes link real-time equilibrium estimates to coil commands, holding the plasma boundary and X-point at their targets throughout a discharge.
Equilibrium reconstruction solves for the magnetic configuration that balances plasma pressure against magnetic forces and fits the diagnostics.
Real-time reconstruction fits a Grad-Shafranov solution to magnetic and kinetic diagnostics, an ill-posed inverse problem regularized and accelerated for the control loop.
Reconstruction codes fit a Grad-Shafranov equilibrium to experimental magnetic and internal measurements, inferring the plasma state that best explains the data.
Learning fast approximations to the Grad-Shafranov solution that maps magnetic measurements to plasma shape and current.
Mapping converts a two-dimensional equilibrium into the flux-surface geometry and metric coefficients that one-dimensional transport solvers require.
Small unavoidable asymmetries in the field can lock plasma modes and trigger disruptions, so correction coils cancel these error fields.
Tiny asymmetries in the magnetic field can lock modes and disrupt the plasma; correction coils cancel them under feedback.
Curated end-to-end scenarios with known-good answers that test a copilot's full reasoning loop against grounded truth for both machines.
Exascale systems perform on the order of a billion billion operations per second, a milestone that reshaped how large simulations are written.
Extended MHD codes add two-fluid, gyroviscous, and Hall terms to the ideal picture, capturing physics between single-fluid MHD and full kinetics.
L7 speaks the standards the outside world already uses for grid dispatch, isotope custody, and regulatory reporting, so the plant integrates without bespoke adapters.
Fast-ion diagnostics track the energetic ions that carry fusion and heating power, essential for the burner's D-3He physics and the breeder's heating.
Validated, normalized channels are combined into physics-meaningful features — instantaneous Q, core pressure map, magnet strain deltas — that the AI layer consumes.
Feature selection keeps the informative inputs and drops the rest, reducing overfitting, cost, and complexity.
How Kronos turns the continuous equations of equilibrium, MHD, and thermomechanics into large sparse systems a computer can solve.
L7 forecasts how much firm power each unit can guarantee over the horizon by fusing twin health estimates, maintenance plans, and fuel availability.
Tracking erosion, deposition, and thermal fatigue of the plasma-facing components that set how long a campaign can run.
The plasma-facing thermal loop watches surface heat flux and can trigger fast fueling or power cuts before a first-wall component overheats.
When the plasma shape is prescribed, fixed-boundary solvers compute the interior equilibrium accurately and efficiently for stability and transport studies.
Kronos runs two populations: a foundry of breeders that make fuel and materials, and a fleet of burners that make power; L7 coordinates them as one system.
When many similar machines run, their twins share learned patterns and priors while each keeps its own state and history.
Flux loops integrate the magnetic flux threading a closed path, giving the fabric the slow, absolute magnetics that anchor equilibrium reconstruction.
A shock-capturing technique that blends a high-order flux with a diffusive low-order flux to prevent new extrema from forming.
Flux-surface and field-aligned coordinates align the computational grid with magnetic surfaces, matching the strong anisotropy of magnetized transport.
Gyrokinetic simulations trade domain size for cost: flux-tube runs are local and cheap, global runs capture large-scale structure at far higher expense.
The breeder's plasma boundary is not fixed; Kronos's free-boundary PINN co-solves the plasma equilibrium and the external coil currents that hold its shape.
Free-boundary solvers compute the plasma shape and position self-consistently with external coil currents rather than prescribing the boundary.
Free-boundary codes solve the plasma equilibrium together with the external coil fields, letting the plasma shape and boundary emerge from the solution.
In a real tokamak the plasma boundary is unknown a priori; it is set by external coil currents, turning equilibrium into a coupled interior-exterior free-boundary problem.
L1 coordinates real-time fuel delivery against isotope inventory, keeping the breeder's D-T mix and the burner's D-3He mix on target as fueling actuators fire.
Real-time isotope accounting tracks tritium, deuterium, and helium-3 through the fuel cycle so the fabric can balance breeding against burn.
Fueling control times and places fuel delivery, using gas and pellets to build and hold density where the plasma needs it.
A fusion program that breeds and manages tritium produces helium-3 as a decay product, offering a source of the isotope decoupled from legacy stockpiles.
The velocity-averaged product of cross section and speed that sets how fast a fuel mixture fuses.
Gas puffing feeds fuel to the plasma edge through fast valves, giving quick but shallow density control that anchors the fueling system.
Piezo servo valves give the fast, shallow end of the fueling authority spectrum; their interface is a millisecond flow-command loop with hard interlocks.
Generative models propose candidate operating scenarios that meet performance and stability targets, widening the search beyond hand-tuned recipes.
Proposing candidate operating scenarios with learned models, then screening them with physics.
Global gyrokinetic codes simulate turbulence across a macroscopic plasma volume, retaining profile variation and long-wavelength transport that flux-tube codes omit.
How L0-trained models feed the KRONOS-CTRL twin so its Power, Neutronics, Thermomechanics, and MHD modules run a 50 to 100 ms predictive shadow.
A parallel farm computing breeder magnetohydrostatic equilibria that anchor the negative-triangularity shape and seed the twin PINN.
The plant's physics couples magnet, plasma, blanket, and conversion train; a GNN over that coupling graph learns cross-subsystem dynamics the twin needs.
The vacuum field of every PF coil is a Green's function of the Grad-Shafranov operator; superposing them turns shape control into a linear-algebra problem.
The favorable turbulence scaling in which diffusivity shrinks with the normalized gyroradius.
The two fundamental frequencies of a plasma: gyration about field lines and collective electrostatic oscillation.
Gyrokinetic solvers evolve a reduced kinetic equation that averages over fast gyration, cutting phase-space dimension while retaining turbulence physics.
Gyrokinetic codes simulate the microturbulence that dominates cross-field transport by solving a reduced kinetic equation on the gyro-averaged distribution.
First-principles turbulence solves that supply the transport coefficients no reduced model can reliably predict for either machine.
An extension of MHD that retains the Hall term, decoupling ion and electron motion at small scales.
Every physical interface is declared as a typed contract so the control stack targets a stable abstraction, not a specific vendor part.
Before either machine energizes, L1 is validated against the digital twin in hardware-in-the-loop tests that exercise every loop and failsafe deterministically.
The divertor absorbs the plasma's exhaust heat; keeping that heat load survivable is one of the hardest problems in a fusion plant.
The total auxiliary heating power is the main lever on plasma temperature and stored energy, and it is modulated in real time to hit control targets.
Because helium is a finite resource, laboratories capture and re-liquefy boil-off gas, closing the loop on both helium-4 and precious helium-3.
The phase diagram of liquid helium-3 and helium-4 mixtures shows the tricritical point and the phase-separation curve that make dilution refrigeration possible.
Liquid helium-3 is a textbook Fermi liquid: its atoms are fermions whose collective behavior is described by quasiparticles with an enhanced effective mass.
Helium-3 is itself a candidate fusion fuel, most practically burned with deuterium, offering reactions that release much of their energy in charged particles.
A simple helium-3 evaporation cryostat reaches a few hundred millikelvin, while a dilution refrigerator uses the isotope mixture to go an order of magnitude colder.
Nearly all terrestrial helium-3 is a decay product of tritium, formed as tritium undergoes beta decay with a 12.3-year half-life.
Helium-3 is a breeder byproduct and the burner's fuel; its handling interface spans separation, inventory, and the 400x supply gate.
Helium-3 is a premier neutron-capture gas: it absorbs slow neutrons with high efficiency and produces an easily detected charged-particle signal.
Hyperpolarized helium-3 gas lets magnetic resonance imaging visualize the air spaces of the lungs, which are otherwise invisible to conventional MRI.
Breeder helium-3 (~1.97 kg/yr) is both a saleable isotope and the burner's fuel; L7 arbitrates between external offtake and internal fleet demand.
Recovering usable helium-3 requires separating it from helium-4 and other gases, exploiting the isotopes' small mass difference by physical means.
The Hyperion model is a compact deuterium-tritium spherical tokamak whose layered shells breed tritium around the plasma.
The breeding blanket wraps the plasma to capture fusion neutrons, breed tritium in lithium, and carry away the fusion heat.
The cryostat is the outer vacuum enclosure that keeps the superconducting magnets cold by isolating them from ambient heat.
Non-inductive current drive sustains the 9.66 MA plasma current after the central solenoid's inductive flux runs out.
The divertor is the exhaust component that channels heat and helium ash out of the plasma while protecting the chamber walls.
The first wall is the plasma-facing surface that takes the heat and particle flux and shields the breeding blanket behind it.
Fueling systems replace burned deuterium and tritium, with frozen pellets fired deep into the plasma to reach the core.
External heating raises the plasma to fusion temperatures and, with current drive, sustains it beyond the inductive phase.
The support structure carries the enormous magnetic forces on the coils, holding the field geometry rigid under load.
The neutron shield sits behind the blanket to protect the vacuum vessel, the superconducting coils, and the structure from radiation.
Hyperion runs a D-shaped plasma with negative triangularity of -0.30, a shaping choice drawn honestly in the model.
The poloidal-field coils shape and position the plasma, setting its elongation, its negative triangularity, and its vertical stability.
The toroidal-field coils produce the field that circles the torus, confining the plasma at 8 T on axis and 16.84 T peak.
The tritium plant interface extracts bred tritium from the blanket, processes it, and returns clean fuel to the machine.
The vacuum vessel is the sealed chamber that holds the plasma in high vacuum and forms the primary confinement boundary.
Ports are the vessel penetrations that admit heating, fueling, diagnostics, and maintenance access to the plasma.
The ice-piston injector forms and launches solid D-T pellets for deep fueling of the breeder; its interface carries preload, extrude, and launch commands.
The cryogenic ICE-PISTON preload cycle sets the magnets' mechanical baseline; its telemetry defines the reference every strain feature is measured against.
Ideal magnetohydrodynamic stability codes test whether a plasma equilibrium is stable to large-scale distortions by evaluating a potential-energy functional.
The two pressure ceilings set by external kink stability, with and without a perfectly conducting boundary.
Injecting a small amount of a radiating impurity spreads exhaust power over the plasma volume and edge, protecting the divertor and first wall.
Impurity transport codes follow non-fuel ions through their charge states, predicting radiation, dilution, and accumulation in the plasma core.
Infrared cameras turn the glow of hot surfaces into real-time temperature maps that reveal heat-flux patterns and hot spots on the wall.
Recognizing which MHD mode or plasma event is present from diagnostic signatures.
A live estimate of fusion gain fuses neutron flux, input-power, and profile telemetry into the ratio the whole program is judged on.
Overflow happens when an arithmetic result exceeds the range a fixed-width integer can hold.
Integrated frameworks orchestrate many physics codes into one self-consistent whole-device simulation, passing data between equilibrium, transport, heating, and edge modules.
Ownership of a physical interface is assigned by its worst-case timing requirement, not by which team is smartest about the physics.
Interferometer chords give fast line-integrated density; polarimetry adds internal field information; the interface unfolds chords into profiles.
An isosurface is the set of points where a scalar field equals a chosen value; marching cubes extracts it as a triangle mesh.
Accountancy is the slowest, most auditable physical interface: a reconciled mass balance for tritium, helium-3, and deuterium across both machines.
A continuous mass balance tracks every gram of tritium and helium-3 from creation through burn, decay, retention, and shipment, with no unexplained gaps.
A fusion neutron source produces valuable isotopes; scheduling irradiation and processing to meet demand is a computational planning problem.
Kapitza resistance is the thermal barrier at a solid-liquid helium interface that dominates heat transfer at millikelvin temperatures and forces the use of huge sintered surfaces.
The MHD Stability module holds the plasma shape, equilibrium, and stability margins that anchor the whole twin.
The Neutronics module tracks neutron flux and spectrum, tritium breeding balance, and the residual D-D output for both machines.
KRONOS-CTRL is the coupled digital twin that holds a live physics state of each machine and projects it forward as a predictive shadow.
The Thermomechanics module maps thermal loads and strain across the vessel, magnets, and divertor, turning physics into structural-health state.
The same L3 framework instantiates differently for a spherical tokamak and a tandem mirror; here is what changes and what stays the same.
For Hyperion, the central L3 task is holding a valid, stable Grad-Shafranov equilibrium at 9.66 MA in a compact spherical geometry.
The burner extracts electricity directly from its end-loss plasma; L3 governs the multi-modal DEC train and its coupling back to confinement.
For the tandem-mirror burner, confinement stands or falls on end-plug density, and L3's central task is to hold it against a fast collapse mode.
GNNs, PINNs, anomaly ensembles, MPC, and the KRONOS-CTRL digital twin with its predictive shadow.
Layer 5 turns the digital twin, physics models, and data fabric into three advisory copilots — Plasma, Engineering, and Operations — that reason but never actuate directly.
Layer 7 is built and validated now against the digital twin and simulated counterparties; it carries live external traffic only as real units commission from FOAK ~2030.
The size and rate of a charged particle's spiral around a magnetic field line, the basic scales of magnetization.
Sub-millisecond feedback that stabilizes the fastest-growing plasma instabilities, chiefly vertical position and resistive-wall modes.
The layer that schedules references through a discharge - ramp-up, flat-top, ramp-down - and adapts the plan as conditions evolve.
A forward-running simulation of the plasma that forecasts where the current trajectory leads, so the stack can act before limits are reached.
Each layer exposes an explicit, testable interface to its neighbors — the contracts that make the stack certifiable one layer at a time.
Twins span a ladder from status mirrors to full predictive physics; the right rung depends on the question being asked.
Ideal MHD stability codes test whether an equilibrium is stable to small perfectly conducting perturbations by solving an eigenvalue problem.
Lithium in the breeder blanket converts 14 MeV neutrons into tritium; L7 links lithium supply, the TBR design lever, and tritium output as one balance.
The breeding blanket is a sensed-and-controlled subsystem: coolant, purge, and temperature interfaces set the effective tritium breeding ratio.
Local (flux-tube) gyrokinetic codes simulate microturbulence in a small volume along one field line, delivering transport fluxes at modest cost.
Tuning sets a loop's responsiveness; gain scheduling changes the tuning as the plasma moves through very different operating conditions.
Learned models find the coil-current set that produces a desired plasma shape and position, both offline for design and in real time for control.
Surrogates predict how impurities move and accumulate in the plasma, informing radiation control and avoidance of performance-limiting buildup.
Surrogates and optimizers explore coil geometries and current sets that produce a target magnetic field while respecting stress and superconductor limits.
Surrogates estimate magnetohydrodynamic stability boundaries fast enough for scenario design and real-time avoidance of unstable operating points.
Surrogates approximate neutral-beam deposition and current drive, giving fast estimates of heating and driven current for scenario design and control.
Learned models accelerate gyrokinetic turbulence simulation by replacing costly subcomponents or emulating full flux outputs.
Neural models predict the height and width of the edge transport barrier, a key driver of overall confinement in high-confinement plasmas.
Reduced transport surrogates learn the mapping from plasma profiles to transport coefficients, enabling whole-discharge simulation at interactive speed.
Surrogates approximate radio-frequency wave heating and current drive, replacing slow wave-propagation solvers in scenario and control loops.
A focused surrogate predicts the tritium breeding ratio from blanket design parameters, accelerating the search for a self-sufficient fuel cycle.
Surrogate models approximate expensive neutron-transport simulations, giving fast estimates of tritium breeding, heating, and shielding for design scans.
Neural closures replace unresolved turbulent fluxes in reduced plasma models, capturing effects that would otherwise require expensive kinetic simulation.
Plasma transport is expensive to compute yet needed everywhere; learned surrogates make it fast enough for design and control.
The change in REBCO magnet strain against the ICE-PISTON preload baseline is a first-class feature guarding the highest-field components of both machines.
A magnet twin tracks current, temperature margin, mechanical load, and quench risk in the superconducting coils that confine the plasma.
Flux loops, magnetic probes, and Rogowski coils supply the measurements that equilibrium reconstruction codes fit, and their modeling is part of the code chain.
Following field lines through a magnetic configuration reveals confinement structure, flux surfaces, and where confinement breaks down.
The nested toroidal surfaces traced by field lines, on which pressure and temperature are constant.
The invariants and loss-cone conditions that govern how a converging magnetic field traps charged particles.
The radial variation of the field-line pitch, a primary stabilizing ingredient for pressure-driven and current-driven instabilities.
Flux loops and Mirnov coils are the fastest, most trusted sensors on the breeder; their interface feeds real-time equilibrium and stability control.
The three fundamental linear wave modes of a magnetized conducting fluid: shear Alfven, fast, and slow magnetosonic.
The compressional fast and slow MHD waves in which magnetic and thermal pressure jointly provide restoring force.
Finding all palindromic substrings, and the longest palindrome, in linear time by reusing mirror symmetry.
Layer by layer, how the eight-layer architecture instantiates on the D-T spherical tokamak — from FPGA coil control to neutronics retraining.
Layer by layer, how the same architecture instantiates on the D-3He tandem-mirror generator — from plug control to direct energy conversion.
The mitigation actuators must open, deliver, and take effect on a schedule tight enough to radiate the plasma's energy before it lands on the wall.
Predicting how structural and plasma-facing materials change under neutron irradiation, heat, and stress over a plant's life.
D-T fusion produces 14 MeV neutrons that damage materials in ways ordinary reactors do not; qualifying materials couples irradiation data with computation.
The math behind each layer — PINNs, Grad-Shafranov, MPC, GNNs, state estimation — anchored to Kronos's use.
The four field equations that, coupled to charged-particle motion, govern all electromagnetic behavior of a plasma.
MCNP-class codes are established general-purpose Monte-Carlo transport tools, long used as reference standards for neutronics, shielding, and dosimetry.
The static balance grad p = J x B that every confined plasma must satisfy at each instant.
The magnetohydrodynamic solves that establish stability limits for both machines and generate training data for the twin's MHD module.
Millikelvin cooling keeps quantum processors thousandths of a degree above absolute zero - and its scaling strain on helium-3 is part of Kronos's isotope thesis.
Fast magnetic pickup coils resolve MHD fluctuations and mode structure, the fabric's earliest window on instability and disruption.
Magnetic diagnostics form the densest subgraph in Kronos's constellation, and the GNN uses their geometry to reconstruct MHD mode structure.
Open-field-line configurations such as magnetic mirrors need dedicated codes for confinement, end losses, and stability that differ from tokamak tools.
Mirror descent generalizes gradient descent by measuring distance with a problem-adapted geometry instead of the Euclidean norm.
Open-field mirrors are prone to flute/interchange instability; stability requires a magnetic well (minimum-B), and the burner's ability to build one is a live physics gate.
How the ratio of peak to minimum field defines which particles are trapped and which escape a magnetic mirror.
The 17 T throat field sets the mirror ratio that confines the burner plasma; the supervisor guards both the field and the coil producing it.
Monte Carlo integrates the high-dimensional problems fusion poses - neutron transport and uncertainty propagation - and variance reduction makes it affordable.
How random sampling underpins neutron transport and uncertainty studies, and where learning accelerates it.
Monte Carlo transport simulates radiation by following random particle histories and averaging their contributions to estimate transport quantities.
Monte-Carlo neutron transport follows individual particle histories through complex geometry to compute flux, heating, activation, and tritium breeding.
Holding the negative-triangularity ELM-free shape of Hyperion is an MPC problem over poloidal-field coil currents and the free-boundary equilibrium.
Wide equilibrium and stability campaigns mapping the breeder's delta -0.30 ELM-free shape and its operating margins.
Collisional transport enhanced by toroidal geometry and trapped-particle orbits, the irreducible floor beneath turbulent losses.
Collisional transport enhanced by toroidal geometry and trapped-particle orbits, the irreducible confinement floor.
Neutral-beam codes model how injected fast neutrals ionize, deposit, and slow down in the plasma, delivering heating, current, fueling, and rotation.
Neutral beams heat and drive current in the plasma by shooting energetic neutral atoms through the confining field, and their power is finely controlled.
Neutral transport codes track un-ionized atoms and molecules through the plasma, supplying the fueling, recycling, and charge-exchange sources the plasma models need.
Neutral-beam heating is a primary actuator on both machines; L1 modulates delivered beam power deterministically for heating, current drive, and fast protection.
The neutral-beam interface delivers heating, current drive, and fueling with a fast-notch protection path that can blank the beam within microseconds.
Kinetic neutral codes track atoms and molecules recycling from surfaces, a physics essential to fueling, radiation, and divertor detachment.
Helium-3 counters are the gold standard for detecting neutrons - a second major draw on the same scarce isotope, reinforcing why Kronos's fusion-sourced helium-3 matters.
Neutron flux, spectra, and cameras measure fusion rate and 14 MeV yield; the interface feeds the fusion-power estimate and the breeding budget.
Spatially resolved neutron fluence tracks where 14 MeV neutrons deposit, feeding tritium-breeding accounting and materials-life monitoring in the breeder.
Calibrated neutron monitors give the fabric a direct measure of fusion rate — 14 MeV for the breeder, a low 5.44% fraction for the burner.
Neutron transport codes track fusion neutrons through the blanket and structure to predict heating, breeding, and shielding.
Neutron transport computes where neutrons go and what they do, the foundation for breeding, shielding, and materials damage predictions.
Live displacement damage, helium production, and activation inventory.
Tracing 14 MeV neutrons through Hyperion's blanket to quantify tritium breeding, heating, and activation across the TBR lever set.
Quantifying the D-3He reaction's 5.44 percent neutron fraction so the burner's shielding and direct-conversion train are designed honestly.
A neutronics twin tracks the fusion neutron field and its effects: heating, breeding, activation, and material damage throughout the machine.
Nonlinear MHD codes evolve large-amplitude instabilities in time, following islands, sawteeth, ELMs, and disruptions past the linear regime.
The ratio of the ion gyroradius to the plasma size, the key parameter for scaling turbulent transport across devices.
Off-normal detection watches for the early signs of a failing discharge and switches from performance to recovery or safe termination.
The same eight-layer stack runs the breeder tokamak and the burner tandem mirror; only the physics the top layers reason about changes.
OpenMC is an open-source Monte-Carlo particle transport code widely used for fusion neutronics, with a scriptable interface and modern geometry support.
A plain sequence from a fully cold machine to first plasma, and every point where the stack can hold, abort, or safe the plant.
Generating and sequencing the commissioning procedures that take the breeder from construction start (Q2 2027) toward FOAK first tritium (~2030).
Assembling an approved scenario into an ordered, precondition-checked runbook where each side-effecting step routes through L4 and human confirmation.
A scenario is the full time trajectory of a discharge; optimizing it means shaping the whole path, not just a steady operating point.
Orange blocks are the physics itself — plasma, magnets, divertor, and the direct-energy-conversion train — the hardware the whole stack exists to serve.
The osmotic pressure of helium-3 dissolved in superfluid helium-4 drives the circulation of a dilution refrigerator and sets its internal flows.
Overfitting memorizes training noise and fails on new data; underfitting is too simple to capture real structure.
L7 is where the plant meets the wider world: exporting firm power and scarce isotopes, importing feedstock and parts, as a node in two coupled economies.
The coupled current- and pressure-driven instability that limits the edge transport barrier and triggers ELMs.
Pellet codes model how frozen fuel pellets ablate as they enter the plasma, predicting where fuel is deposited and how the density profile responds.
Frozen fuel pellets fired deep into the plasma deliver particles to the core where gas puffing cannot reach, giving efficient core fueling.
Performance tuning applies targeted changes, guided by measurement, to move a code closer to the hardware's limits without changing its results.
The poloidal-field and central-solenoid supplies are the breeder's shape and position actuators, driven by MPC and clamped by the field envelope.
Poloidal-field coils are the breeder's shape actuators; L1 drives their currents to hold the negative-triangularity, delta -0.30 boundary that defines the ELM-free regime.
Real-time divertor and first-wall thermal and erosion prediction.
Every place the Kronos control stack touches metal, gas, or plasma is a typed interface with an owning layer, a latency budget, and a calibration record.
How the stack touches each subsystem — magnets & ice-piston, fuel cycle, vessel/SHM, divertor, DEC train, diagnostics.
The termination map: every layer of the stack ends at a named subsystem — magnets, feedthroughs, vessel, divertor, fuel cycle, and the DEC train.
Beyond equilibrium, Kronos uses PINNs to evaluate ideal-MHD stability so the twin knows how close the plasma is to a limit, not just where it sits.
Kronos solves the breeder's magnetohydrodynamic equilibrium with a physics-informed neural network that embeds the Grad-Shafranov operator in its loss.
The ratio of plasma pressure to magnetic pressure, the key measure of how efficiently a field confines plasma.
Drafting a breeder shot as a set of time-dependent actuator waveforms constrained to the certified safe operating envelope and checked against the twin before proposal.
For the D-3He tandem mirror, the copilot advises on end-plug density, ambipolar potential, and the direct-energy-conversion window against the 26.49 T plug line.
Advising on gas-puff and pellet fueling to hold density profiles for the breeder and central-cell/plug density for the burner, inside stability limits.
Advising on breeder plasma shape toward the delta -0.30 negative-triangularity target that underpins the ELM-free, disruption-tolerant scenario.
Bayesian and surrogate-accelerated search over the copilot's waveform parameters, using the twin as the objective and the safe envelope as a hard constraint.
Regulating the toroidal plasma current with the central solenoid and, in steady state, with non-inductive current drive.
L1 regulates the breeder plasma current toward its 9.66 MA operating value, coordinating the central solenoid and PF system deterministically.
Regulating the plasma density with gas puffing and pellet injection while respecting confinement, fueling efficiency, and stability limits.
Density control holds the plasma's particle content at a target by commanding gas and pellet fueling against real-time interferometer measurements.
The accounting of heating and loss terms that determines whether a plasma sustains its temperature.
Profiles show how temperature, density, and other quantities vary across the plasma radius, the workhorse plot of confinement physics.
Predicting radial profiles of density, temperature, and pressure faster than transport simulation allows.
Reduced linear models of how the plasma reacts to coil and actuator changes - the basis for designing magnetic control loops.
Poloidal field coils sculpt the plasma boundary and hold it in place, controlled from a real-time reconstruction of the plasma equilibrium.
Holding the plasma boundary to a target shape by regulating the currents in the poloidal field coils that surround it.
The formal state machine behind a breeder shot, its guarded transitions, and the invariants each state must hold.
State estimation fuses many noisy diagnostics into a single best estimate of the plasma state for controllers to act on.
State estimation combines a model with noisy measurements to infer the plasma's true state, including quantities no sensor reads directly.
Plasma state reconstruction infers the internal condition of a confined plasma from external diagnostics through a physics model.
The evolution equations for density, temperature, and current profiles on the slow confinement timescale.
L1 watches plasma-facing surface temperatures and acts fast to keep the breeder wall/divertor and burner collectors inside their thermal limits.
The wall and divertor tiles take intense heat while the plasma runs, so their temperatures are watched continuously to catch overloads before damage.
The burner's end-plug coils must hold 26.49 T; the actuation interface is specified honestly against a coil overstressed 3-3.9x at the design bore.
The burner's 26.49 T plug coil is overstressed 3-3.9x at the design bore - the dominant, gate-defining failure mode, stated without softening.
Sustaining the end-plug density and confining potential drives an operating regime 166-830x beyond any device, on a helium-3 supply 400x short.
The ratio of plasma pressure to the pressure of the poloidal magnetic field, a key equilibrium and stability parameter.
Predictive transport codes forecast plasma profiles for a proposed scenario by combining transport models, sources, and self-consistent equilibrium.
How a plasma reduces the internal magnetic field to make room for its own pressure.
Profiling measures where a program spends time and resources so optimization targets the true bottleneck instead of a guess.
A weak-turbulence framework in which a spectrum of small waves slowly reshapes the background distribution through velocity-space diffusion.
Quasilinear models estimate turbulent transport quickly by combining linear gyrokinetic growth rates with a saturation rule, bridging first-principles codes and transport solvers.
L1 regulates the breeder plasma's major-radius position against the design R0 of 1.2 m, keeping wall gaps and the equilibrium centered.
Managing how much of the plasma's power is radiated - useful for protecting the wall, dangerous if it runs away.
Radio-frequency systems heat plasma by launching electromagnetic waves tuned to particle resonances, and each system regulates power, frequency, and coupling.
Ray-tracing codes follow electromagnetic wave beams through the plasma along the geometric-optics path, computing where heating and current-drive power deposit.
A vertical section through Hyperion's centerline is the single most informative view, showing plasma shape and every shell.
L1 solves a fast, bounded Grad-Shafranov reconstruction each cycle to give the shape and position loops a physically consistent state estimate.
A neural RT-EFIT: reconstruct the equilibrium from magnetics inside the control loop.
Equilibrium reconstruction infers the plasma's magnetic shape and internal profiles from external measurements, fast enough to feed control.
Neural surrogates reconstruct the plasma equilibrium from magnetic measurements within the control cycle, faster than iterative reconstruction codes.
Equilibrium reconstruction infers the plasma shape, position, and internal fields from magnetic and other measurements, fast enough for control.
Fitting the plasma's magnetic equilibrium every few milliseconds so that shape, position, and profile controllers act on a consistent picture.
The equilibrium PINN doubles as a reconstructor, fusing sparse magnetic and kinetic diagnostics into a full flux map at twin cadence.
Coils are built by stacking and winding REBCO tapes into turns, then into pancakes, insulated and clamped against huge forces.
The command path to the REBCO coil supplies carries current-ramp trajectories under hard slew and field-envelope limits, revalidated at the FPGA edge.
Quench detection is the highest-authority magnet interface: a validated precursor pre-empts every other command and dumps stored energy on a fixed deadline.
Distributed strain and temperature along the winding pack feed both the quench path and the twin's slow structural-fatigue model.
Strain gauges bonded across the high-field REBCO magnets report the mechanical state of the most stressed components in either machine.
Reinforcement learning discovers policies that command heating and current-drive actuators to reach and hold target plasma states.
Learning control policies that command magnetic coils to shape and stabilize a plasma, as demonstrated in published TCV work.
Remaining useful life is the twin's forecast of how much longer a component can serve before it must be repaired or replaced.
Activated components demand robotic and teleoperated intervention; L7 coordinates remote handling against the twin so humans stay out of high-radiation zones.
How the twin's psi(R,Z) field, wall temperatures, and neutron flux are turned into a legible, confidence-aware 3D scene at display frame rate.
MHD with finite resistivity, which breaks the frozen-in law and permits reconnection and tearing modes.
Resistive MHD codes allow magnetic field lines to reconnect, capturing tearing modes and the slower, nonlinear instabilities that ideal theory cannot describe.
A perfectly conducting wall stabilizes the external kink, but a real resistive wall lets it grow slowly; feedback control of that growth is a precise linear problem.
Stabilizing slow, wall-limited magnetohydrodynamic modes with feedback coils to allow operation above the no-wall pressure limit.
Response surface methodology fits low-order polynomials to sampled data to map how outputs respond to inputs and to locate optima.
An RF source delivers full power only into a matched load, so a tuning network continuously matches the antenna's changing plasma coupling to the generator.
Deep RL has been applied, in published work, to control the magnetic shape of tokamak plasmas.
Plasma rotation stabilizes some instabilities and shears turbulence; control adjusts it through momentum input and magnetic braking.
A disruption can accelerate a beam of relativistic electrons; the mitigation path is designed to keep that beam from forming or to dissipate it benignly.
Sample average approximation replaces an intractable expectation with an average over sampled scenarios, converting a stochastic program into a solvable one.
How well a system's performance improves as resources or problem size grow.
A scalar field assigns one value per point; the main tools are color mapping, contours, isosurfaces, and volume rendering.
Scenario optimization searches for an actuator trajectory that reaches a target plasma state while respecting every operational and stability limit.
Records of bred tritium, helium-3, and neutron services are integrity-protected and access-controlled, because their trustworthiness matters to regulators and safeguards.
The digital twin drives design, training, and replay; its models and data are integrity-protected so a corrupted twin cannot poison the controllers it informs.
Shape control holds the plasma boundary on its target outline and gaps, keeping it clear of walls and on the divertor strike points.
Why plasma kinetics is one of the hardest simulation targets, and where quantum methods might, in the long term, help.
Scrape-off-layer codes model the open-field-line plasma between the separatrix and the wall, where parallel transport, recycling, and radiation set the heat load on surfaces.
Compute a tokamak plasma equilibrium by iterating the Grad-Shafranov elliptic PDE on a grid until the flux converges.
SORM improves on FORM by fitting a quadratic surface at the design point, correcting for curvature of the failure boundary.
The collisional electrical resistivity of a fully ionized plasma, falling steeply as temperature rises.
The property that a system's response stays bounded and returns to equilibrium after a disturbance.
The general problem of inferring the full plasma state from limited diagnostics, and the observers that solve it in real time.
Kronos fuses noisy multi-rate diagnostics with physics forecasts using nonlinear state estimation, so the twin holds a best estimate with quantified uncertainty.
Beta and stored-energy feedback keeps plasma pressure near its performance target while staying below the limit where pressure-driven instabilities appear.
A structural twin reconstructs the stresses in load-bearing components and integrates them into an accumulated-damage estimate over the machine's life.
The largest recurring L0 workload: billions of particle histories tracing neutron transport, breeding, and damage through both machines.
Bringing a superconducting coil to field means ramping current slowly enough that induced losses and stresses stay within safe limits.
Below the lambda point helium-4 becomes a superfluid that creeps as a thin film over any surface, a phenomenon both exploited and fought in cryogenic design.
L7 tracks what the plant consumes (deuterium, lithium, components) and what it produces (tritium, helium-3, 14 MeV neutrons) as one governed material flow.
Getting an isotope from irradiation to the end user is a timed, multi-step chain; simulating it keeps supply reliable against a decay clock.
Building fast emulators of expensive solvers so the twin can evaluate neutronics, transport, and equilibrium in real time.
Learned models that approximate expensive neutron-transport calculations for shielding, activation, and breeding studies.
A forecast that drifts from reality is worse than none; Kronos continuously corrects the twin toward live telemetry so the shadow stays anchored.
Confinement in a tandem mirror depends on maintaining the axial potential profile and mirror fields against particle and energy losses.
Modeling the burner's open-ended magnetic geometry, end-plug fields, and ambipolar potential that confine a D-3He plasma.
The burner is not a torus; its equilibrium is set by paraxial force balance and mirror confinement along an open field line, a different mathematics from Grad-Shafranov.
TD3 fixes DDPG's overestimation with twin critics, delayed policy updates, and smoothed target actions.
The resistive instability that reconnects field lines into magnetic islands at rational surfaces.
The founding kinetic transport equation, evolving a distribution function under streaming, forces, and a collision integral.
The Boris algorithm advances a charged particle in electromagnetic fields by splitting the motion into a half electric kick, a magnetic rotation, and a second kick.
The classic collisional two-fluid transport equations with explicit magnetized transport coefficients.
The breeder digital twin is the coupled model of Hyperion, Kronos's compact D-T spherical-tokamak breeder, holding its physics, engineering, and tritium accounting in one self-cons
The burner digital twin models the Aegis / MetroVolt D-3He tandem mirror, whose control problem - plug fields, ambipolar potential, and direct energy conversion - differs sharply f
A tiered mix of cloud HPC and owned bare-metal that carries every offline workload from Monte Carlo transport to twin retraining.
The conservation-of-mass equation for a plasma fluid, the first moment of the kinetic equation.
The slowly varying factor that captures the dominance of many small-angle collisions in a plasma.
The distance over which a plasma screens out electric fields, the fundamental scale of quasi-neutrality.
A continuously validated simulation model that mirrors the plasma, used for prediction, testing, and operator situational awareness.
A registry holds a live twin for every unit, tagged by machine type, generation, and configuration, forming the addressable model of the whole fleet.
A digital-twin interface binds a live or simulated model of a machine to interactive views so users can inspect, query, and reason about state.
A dilution refrigerator reaches millikelvin temperatures by pumping helium-3 across a phase boundary inside a mixture of helium-3 and helium-4.
A dilution refrigerator reaches the ~10 mK that qubits need by pumping on a helium-3/helium-4 mixture - and every one of them consumes helium-3, an isotope Kronos's fuel cycle prod
A scenario library stores proven pulse schedules and their outcomes so operators build on validated starting points rather than from scratch.
The long-wavelength limit of gyrokinetics, following guiding centers under slow drifts and collisions.
The evolution of internal energy or pressure for a plasma fluid, closing the fluid hierarchy with heat flux and sources.
An advisory agent for subsystem analysis, anomaly triage, and maintenance reasoning across magnets, vessel, fueling, and the DEC train.
Alfven's theorem: in a perfectly conducting fluid, magnetic field lines move with the plasma.
The helium-3 supply chain runs from tritium stewardship through harvesting and purification to distribution among competing scientific and security uses.
Godunov's method advances conservation laws by solving a Riemann problem at each cell interface to compute upwind-consistent fluxes.
The breeder's axisymmetric equilibrium reduces to a single nonlinear elliptic PDE for the poloidal flux, and every equilibrium tool in the stack solves or inverts it.
How the axisymmetric equilibrium equation is discretized and solved to find nested flux surfaces.
An empirical ceiling on tokamak line-averaged density set by plasma current and minor radius.
A reduced kinetic equation that averages over fast gyromotion to make turbulence simulation tractable.
The energy-transport counterpart of diffusion, governing how temperature relaxes through conductive heat flux.
Breeder byproduct helium-3 feeds both quantum-hardware cooling and future burner fuel, while burner He-3 demand dwarfs terrestrial supply.
The world's helium-3 comes almost entirely from decaying tritium - a fixed, shrinking source against rising demand, which is the market Kronos's fuel cycle can help supply.
Whether a breeder equilibrium is stable reduces to the sign of a single energy functional; its minimization defines the safe operating envelope the AI must respect.
The single-fluid, perfect-conductor model of a magnetized plasma used for equilibrium and gross stability.
A modular predictive twin — Power, Neutronics, Thermomechanics, MHD — running a 50-100 ms shadow of the machine for state estimation and control.
The condition on density and confinement time under which fusion self-heating balances plasma energy losses.
Linearizing ideal MHD about an equilibrium gives a self-adjoint force operator whose eigenvalues are growth rates; the AI learns its unstable manifold.
The force law that governs every charged particle and, aggregated, all plasma behavior.
The induction equation in the static-fluid limit, describing how magnetic field decays and penetrates by resistivity.
The conserved quantity mu that makes magnetic mirrors work and simplifies kinetic theory.
The dimensionless ratio of magnetic advection to magnetic diffusion in a conducting flow.
A map of the equation families L0 solves, from transport and MHD to transport PDEs, and the numerical methods each demands.
The equilibrium velocity distribution of a plasma species, from which reactivities and rates are computed.
The memory wall is the widening gap between how fast processors compute and how fast memory can supply data to them.
A variational test for ideal stability: if any displacement lowers the potential energy, the plasma is unstable.
A variational test for ideal stability: an equilibrium is stable if every allowed displacement raises the potential energy.
The mixing chamber is where helium-3 crosses the phase boundary from the concentrated to the dilute phase, absorbing heat and producing the coldest point in a dilution refrigerator
Newton's second law for a plasma fluid element, balancing inertia against pressure and electromagnetic forces.
The Boltzmann transport equation that both Kronos neutronics workloads solve, and why its structure dictates the compute approach.
The marginal ideal-MHD equation whose solutions test stability and yield the tearing index in the outer region.
The condensing stage cools and liquefies the incoming helium-3 stream before it enters the heat exchangers, historically done by a pumped one-kelvin pot.
Both helium isotopes are hard to keep on Earth because helium atoms are light enough to escape the atmosphere, and helium-3 is rare in the first place.
The ratio of plasma pressure to magnetic pressure, the primary measure of magnetic confinement efficiency.
An advisory agent that designs shots, optimizes scenarios, and warns on disruption or operating-point risk — grounded in the twin, never actuating on its own.
The frequency-dependent response tensor that encodes how a magnetized plasma polarizes and conducts under an oscillating field.
The natural oscillation frequency of electrons displaced from equilibrium, setting the plasma's electromagnetic response.
The plasma state observer reconstructs the full plasma state from a sparse, noisy diagnostic set in real time -- the estimator that feeds the digital twin and the control stack.
Kronos's predictive-maintenance twin tracks how components age - magnets, first wall, centrepost - so parts are serviced on evidence, not on a fixed calendar.
How a sheared radial electric field suppresses turbulence and enables transport barriers.
Ideal MHD plus finite resistivity, admitting magnetic diffusion, reconnection, and tearing instabilities.
A slow external kink that grows on the wall's resistive timescale in the gap between the no-wall and ideal-wall limits.
The nonlinear equation governing the growth and saturation of magnetic islands from tearing modes.
The thermodynamic relation giving the ionization balance of a gas in local thermal equilibrium.
The outward displacement of inner flux surfaces relative to the plasma boundary, driven by pressure and internal current.
Both Kronos machines rely on REBCO high-temperature superconductor to reach fields conventional magnets cannot deliver.
Real-time isotope balancing: how the architecture tracks and schedules tritium, helium-3, and neutron output as an operational, never economic, problem.
How the architecture controls and protects the high-field REBCO magnets and coordinates the cryogenic ice-piston preload cycle.
The still selectively evaporates helium-3 from the dilute phase, driving the osmotic circulation that keeps a dilution refrigerator running.
The resistive-MHD instability that reconnects field lines at rational surfaces, forming magnetic islands.
The ratio of tritium produced in the blanket to tritium consumed in the plasma, which must exceed one for D-T self-sufficiency.
The empirical and theoretical ceiling on normalized plasma pressure set by ideal-MHD stability.
How discrepancies between the KRONOS-CTRL twin and reality are captured, diagnosed offline, and folded back into better models.
What KRONOS-CTRL actually holds and publishes: a defined state vector with lineage that L1, MPC, and the anomaly ensemble consume.
Separate momentum and continuity equations for electrons and ions, coupled through electromagnetic fields and collisions.
The kinetic description of a collisionless plasma: a phase-space transport equation coupled to its self-consistent electric field.
A thermal-hydraulic twin tracks heat generation, transport, and removal through the coolant loops that keep the machine within limits.
A pulsed laser and spatially resolved collection give calibrated electron temperature and density profiles; the interface is timing- and calibration-critical.
The same interface, driven by the twin instead of live diagnostics, so operators rehearse both machines — including unsafe-to-create upsets — before and between real runs.
A scenario is a time-dependent path in state and actuation; direct collocation turns designing it into a large, structured nonlinear program.
Integrated analysis codes such as TRANSP combine equilibrium, transport, heating, and diagnostics into one time-dependent interpretation of a discharge.
Solving how particles, heat, and momentum move across the plasma to predict confinement and profiles for both machines.
A D-T device must recover, purify, and re-inject its fuel while accounting for every gram of tritium, all under continuous control.
A breeder twin tracks the tritium produced, bred, extracted, and consumed, closing the fuel cycle accounting in real time.
A D-T plant must breed more tritium than it burns; the breeding ratio is a computational optimization of blanket geometry and materials.
Wide, independent Monte Carlo campaigns that map breeder blanket design against the TBR lever set 1.1, 1.5, and 1.8.
Neutronics codes compute the tritium breeding ratio of a blanket, the key figure of merit for a self-sufficient deuterium-tritium fuel cycle.
Every gram of tritium in the plant is tracked through storage, processing, and the plasma so the mass balance always closes.
Tritium is bred, burned, stored, and lost continuously; accounting for every gram in real time is a safety and operations requirement.
Exportable tritium from the breeder is scheduled, assayed, and moved under full chain of custody, with self-consumption and decay accounted before anything ships.
Predicting how tritium moves through hot metal walls, a loss path and a containment concern the fuel cycle must account for.
Failure modes of breeding, extraction, and accountancy for the ~4 kg/yr tritium class and ~1.97 kg/yr helium-3 outputs.
The tritium plant interface governs breeding, extraction, isotope separation, and storage; it is a slow, accountancy-grade loop with strict containment interlocks.
Neural gyrokinetics to predict confinement — not just equilibrium.
Shared data models and interfaces let a twin's many components, and successive units, exchange information without bespoke glue.
TD3 fixes DDPG's overestimation and instability with twin critics, delayed policy updates, and target smoothing.
Kronos measures how well the twin represents each machine with concrete, per-module fidelity metrics, not a single vague score.
Verification asks whether the twin solves its equations correctly; validation asks whether those equations match reality.
A twin's insight reaches people through interfaces that must present state, uncertainty, and recommendations clearly and without misleading.
The KRONOS-CTRL twin tracks the tritium and helium-3 balance in real time so the breeder's fuel cycle stays closed and its isotope products are accounted.
A twin's predictions are only useful with honest error bars; uncertainty quantification produces and propagates those bars.
A single small leak can spoil the vacuum and, in a tritium plant, breach containment, so leak detection runs before and during operation.
An elongated negative-triangularity plasma is vertically unstable; the position loop must catch a growing displacement faster than it can run away.
Elongated and negative-triangularity plasmas are vertically unstable; the n=0 axisymmetric mode grows on the wall time and demands continuous feedback control.
The physics behind why shaped plasmas are vertically unstable and how conducting structures and feedback set the stability limit.
Elongated plasmas are vertically unstable and drift toward the wall unless a fast feedback loop actively holds them in place.
Elongated plasmas are vertically unstable and drift toward the wall unless a fast feedback loop actively holds them centered.
Distributed strain, displacement, and acoustic sensing on the vessel feed the twin's fatigue model and a slow structural-alarm path.
Rendering a simulation's internal state during a run exposes instabilities, boundary errors, and bugs that summary numbers hide.
A magnetohydrodynamic equilibrium is described by nested flux surfaces; visualizing them clarifies confinement geometry and boundary shape.
Volume rendering projects a three-dimensional scalar field directly to the screen without first extracting surfaces, revealing internal structure.
PMI codes model erosion, deposition, fuel retention, and material evolution at surfaces where the plasma meets the wall.
Wallace and Dadda trees reduce a grid of partial products to two rows in logarithmic depth, making hardware multiplication fast.
Casting Grad-Shafranov in its weak form yields the finite-element system that offline solvers use to generate the equilibrium libraries PINNs and surrogates are trained on.
High-performance computing aggregates many processors, memory, and fast networks to solve problems too large or too slow for a single machine.
An offline console where operators and engineers explore how the machine would respond to a change — driven by the twin, never touching the live plant.
Starting from the twin's current state, what-if simulation explores futures the real machine can experience only once, and safely.
A digital twin must mirror a system as fast as it evolves; surrogates compress hours-long physics into millisecond predictions that make that possible.