Part 4a: Modeling Stellaris

Supports the main post. The viewer is the page; these notes are context for its frames. Part 3, the full harness, explains goals and rounds.

We started with a model that could price the Stellaris design but mostly just repeated the paper's numbers back to us. Over about a month, we ran 28 goals against it to turn the model into something that actually computes the plant from its design: from 55 calculations, 6 checks and 14 parts to 199, 67 and 76.

Model evolution viewer

Step through the goals with the slider or arrows. Select a part to open it, then select a calculation to see its inputs and equations. Frame links in the themes return here. Expand gives the graph the whole window.

Six themes in the model’s evolution

Looking back over those goals, they generally fall within six themes.

1. Replacing typed-in numbers with physics

The starting model was mostly fixed numbers from the paper and from 1costingFE: key system attributes (like field strength) were not modeled as a function of design parameters (like coil current). A typical goal took one of those attributes and modeled it from its design parameters, anchored so that it still reproduces the paper at the design point.

  • The magnetic field is modeled from the coil count, coil current and major radius (frame 3, record: work/orchestration/goals/magnet-closure/trail.md).
  • The heating required to sustain the plasma is modeled from field, density and temperature through the ISS04 confinement scaling (frame 4, record: work/orchestration/goals/operating-point-closure/trail.md).
  • Pumping power is modeled from the coolant flow and pressure loss, cycle efficiency from the power cycle, and availability from the maintenance calendar (frame 10, record: work/orchestration/goals/plant-closure/trail.md).
  • Tritium breeding is modeled from blanket thickness, using five OpenMC neutron-transport runs (frame 21, answer: work/orchestration/goals/computed-tritium-breeding/answer.md). Net electricity is modeled from the salt heat and temperature through a steam cycle (frame 27, answer: work/orchestration/goals/current-model-comparison-readiness/answer.md).

2. Making the model push back

Modeling an attribute is not enough. The model also has to say when a design choice is not feasible. So we run studies: sweep the design parameters, see what LCOE is sensitive to, and find where the engineering limits are. If a sweep shows that a parameter can change cost without ever hitting a limit, then the model is missing a physical constraint. Modeling that constraint becomes the next goal.

  • The recirculating-power limit barely fired, at 32 of 948 swept points, because pumping power was 1 MW, a 1costingFE default 130 to 195 times too low. At the sourced 195 MW it fires at 184 points, and the design point's cost rose 21 percent (frame 2, record: work/orchestration/goals/p-pump-fence/trail.md).
  • Raising the magnetic field added cost but improved nothing, because field reached no plasma calculation, so the cheapest point always sat at the lowest field the beta limit allowed. With confinement scaling, field now buys sustainment (frame 4, study: exploration/stellarator_e2e/studies/20260823-magnet-technology-ab/record.md).
  • More coil current was free. We sized the winding pack from the current, so more current meant a bigger, more stressed coil and a larger cold mass (frame 5, record: work/orchestration/goals/priced-levers/trail.md). Frame 28 made the pack a supplied design choice, so more current now raises its stress and current density instead of its size.
  • Operating points kept passing even when plasma self-heating exceeded the modeled losses, because the model checked that the installed heating was enough but not whether there was already too much heat to balance. We added a power-balance check under the model's assumptions. It marks 1,113 of the 1,839 passing sampled points as failing, leaving 726, and the failing points stay in the results. The check does not rule out ignition: a point that needs exactly zero heating passes. Evaluating the failing points properly would need burn-control mechanisms the model does not represent (frame 8, record: work/orchestration/goals/burn-control/trail.md).
  • A fatter plasma cost nothing at the magnet. We made the coil bore set the peak field and casing mass, and the fattest plasmas at the paper's radius failed the conductor limit (frame 9, record: work/orchestration/goals/minor-radius/trail.md). Frame 28 made casing mass a supplied input, but the bore still sets the peak field.
  • Nothing checked that the winding pack fits its casing or that the conductor has current margin. We added both. The reference design fails both under the assumed casing walls, insulation and tape performance: 370 mm of pack in 250 mm of casing, and 29.65 kA of critical current against 50 kA operating (frames 16 and 17, fit: work/orchestration/goals/winding-pack-casing-fit/answer.md, current: work/orchestration/goals/absolute-conductor-current-margin/answer.md).

3. Making cost follow the design

Modeling the physics does not fix the costing: an account can still be a lump sum that ignores the design. We wanted each account to follow the equipment, priced by quantity, with installation and, for equipment that wears out, spares and replacements. These goals also sized that equipment from the calculated demand (like heat exchangers from heat load). Frame 28 made the equipment a supplied choice, checked against that demand. The cooling goal is the largest LCOE move in the run.

  • Cooling: replacing a single $205M allowance with priced circulators, pumps, piping and heat exchangers raised the estimate to $8.2B, and LCOE from 150 to 311 $/MWh, on the 18-circuit study case. About $7.4B of that is primary piping and heat exchangers, priced from assumed dimensions and nuclear-grade stainless fabrication (frame 22, answer: work/orchestration/goals/installed-cooling-equipment-costs/answer.md). We had modeled an all-helium blanket, while a reviewer pointed to a helium/water split in Stellaris, so the figure shows what drives cost in the configuration we chose, not what Stellaris's cooling should cost.
  • Buildings sized from the equipment they hold and the maintenance they support (frame 23, answer: work/orchestration/goals/layout-based-facilities/answer.md). Fuel processing cost scales with throughput (frame 25, answer: work/orchestration/goals/throughput-based-fuel-processing-costs/answer.md).
  • The winding pack's single cost multiplier was replaced by material inventory, tape procurement and winding operations, and a later goal priced the tape by its purchased length (frames 13 and 15, claim: work/orchestration/goals/magnet-design-transfer/transfer-claim.md, answer: work/orchestration/goals/tape-procurement-consistency/answer.md).
  • Then we graded the estimate's maturity and where the cost concentrates: a Class 5 conceptual estimate, with cooling, magnets and facilities at 73 percent of direct cost (frame 26, answer: work/orchestration/goals/cost-estimate-maturity-and-uncertainty/answer.md).

4. Following the engineering design pattern

Inputs are choices an engineer would make (like coil current or exchanger area), and the model calculates the consequences of those choices in causal order. The model must not size equipment to meet a demand, because then it has decided which parameters are free instead of the engineer. We broke this rule without noticing, and the ARIES reveal caught it.

  • Restructured 14 flat parts into 23 nested physical parts with ports, so a subsystem can be swapped for a trade study. Every output stayed identical (frame 12, record: work/orchestration/goals/structural-decomposition/trail.md).
  • Several calculations sized magnet inventory, facilities, fuel processing and cooling equipment from demand. Those became inputs, with 33 capacity checks that fail when the supplied equipment is too small (frame 28, answer: work/orchestration/goals/preserve-model-design-choices/answer.md).

5. Reconciling against Stellaris

Once an attribute is modeled, its value can differ from the paper. We trace each difference to its cause rather than tuning it away, since the cause might be our model, our reading of the paper, or the paper itself.

  • Stored energy was 9 percent above the paper, because the helium ash had been given the fuel's flat profile. With the paper's profile rule, required heating dropped from 90.6 to 49.1 MW against 50 installed, and the last 2.7 percent of the gap is the paper's own (frame 7, record: work/orchestration/goals/stored-energy-basis/trail.md). Part 3 walks this goal.
  • The wall-load check compared a flat-wall average to the paper's peak limit. Now it computes the peak, which the design failed narrowly, 4.088 against 4.05 MW/m², until the ash fix (frame 6, record: work/orchestration/goals/wall-and-heating/trail.md).
  • Checked whether our reference is one coherent published design point. It is not, and each remaining difference was classified by cause (comments only, so no frame; answer: work/orchestration/goals/stellaris-reference-reconciliation/answer.md).

6. Fixing defects

All of this adds code, and code has bugs, so some goals were repairs.

  • An audit found 20 findings: heating demand confused with installed capacity, a duplicated major radius, finance formulas that divided by zero at equal interest and inflation rates, missing range checks (frame 11, record: work/orchestration/goals/fusion-audit-remediation/trail.md).
  • A conductor cost multiplier applied twice (frame 15, answer: work/orchestration/goals/tape-procurement-consistency/answer.md).

Model limits

The models are still limited to the ranges they were built for. For example, the conductor performance model, which gives the current the superconducting tape can carry at a given field, is only valid for peak fields between 20 and 32 T, and the tritium breeding calculation was built from neutron-transport runs at the Stellaris radius, so it only covers blanket thicknesses of 0.6 to 1.0 m at that radius (frame 29, answer: work/orchestration/goals/model-evaluation-domain-readiness/answer.md). Expanding the design space the model can handle is more work to be done. We look at this question further in Part 4b.

In the recordFrame records

Counts come from each committed snapshot. Results below are the viewer’s agent condensations of the cited records; they have not been owner-reviewed. Each result describes the model as that frame left it; frame 28 later made magnet, facility, fuel-processing and cooling sizes supplied inputs. The six themes above use the checked write-up text.

FrameCalculations / checks / partsRecorded result and source
1. Starting point: the migrated model55 / 6 / 14The model as the first goals found it: 55 calcs and 6 checks, every calc scoped to the plant root. It follows the migration to the current snapshot format and work item WI-030, which added a computed volume-averaged beta and a conductor peak-field limit. The first two goals, cryo-volume-basis and p-pump-basis, examined this version. p-pump-basis found the 1 MW pumping power indefensible and routed the fix to WI-033; the regenerated model first appears in the next frame.
commits 89f78130 and ba5c9945; work/orchestration/goals/cryo-volume-basis/; work/orchestration/goals/p-pump-basis/; .project/completed/CHANGELOG.md (Goal Harness Item 5)
2. Rerunning the model with pumping power corrected to 195 MW55 / 6 / 14The goal regenerated the model package so it carried the pumping power already corrected from 1 MW to 195 MW, then ran a study on it. The recirculating-power check now fails at 184 swept points instead of 32. LCOE at the baseline design rose from 275.264 to 333.067 $/MWh (+21.0%), with all six checks still passing there.
work/orchestration/goals/p-pump-fence/trail.md § Round 1 result — 2026-08-29 (Last semantic outcome); § Goal close — 2026-08-29
3. Deriving the magnets from their own design60 / 7 / 14The magnet's field, a structural limit and its cost now come from the coil design instead of cited constants. The on-axis field is computed from coil current and geometry, a winding-pack stress check pushes back on coil sizing, and magnet cost is split into separately sized accounts. Baseline LCOE fell from 333.067 to 304.482 $/MWh.
work/orchestration/goals/magnet-closure/trail.md § Round 1 result — 2026-08-30; § T-004 return — 2026-08-30; § Goal close — 2026-09-01
4. Checking the plasma operating point against the machine61 / 8 / 14The plasma operating point is now checked against the machine instead of typed in. A confinement relation (ISS04) links field and heating to density and temperature, and a new sustained-heating check pushes back. The study found no feasible point at the printed 50 MW of installed heating; feasibility returns at about 91 MW.
work/orchestration/goals/operating-point-closure/trail.md § Goal close — 2026-09-02; § Round 2 result — 2026-09-01 (L-005)
5. Making the escape levers carry real costs65 / 9 / 14The winding pack is now sized from coil current, the cold volume is computed, and a conductor strain check was added; the design point did not move. The study still found no feasible point at the printed 50 MW. There the neutron wall load alone blocks 27 of 240 points, the conductor limit 6. The goal closed by redirect.
work/orchestration/goals/priced-levers/trail.md § Round 1 result — 2026-09-03; § Goal close — 2026-09-03; work/orchestration/goals/priced-levers/goal.md § Amendment 2026-09-03
6. Making the wall-load and heating checks honest68 / 9 / 14Heating became a real chain from wall-plug power to plasma-coupled power, and the wall-load check now compares a computed peak with the paper's printed peak. The machine as designed then slightly fails the wall limit (4.088 against 4.05) and baseline LCOE rose from 307.087 to 313.513 $/MWh. A working point at the printed heating needs a fatter plasma.
work/orchestration/goals/wall-and-heating/trail.md § Goal close — 2026-09-05; § Round 2 result — 2026-09-04; commit cb355321 message (LCOE figures)
7. Why the stored energy ran 9% high68 / 9 / 14The model's stored energy sat 9% above the paper's printed value because the helium ash was given the fuel's flat profile; the printed value is not a target. Computing the ash profile from the paper's own rule dropped the required heating from 90.6 to 49.1 MW against a 50 MW limit. Both failing baseline checks now pass, with nothing tuned.
work/orchestration/goals/stored-energy-basis/trail.md § Goal close — 2026-09-06; § T-001 return — 2026-09-05 (round 2)
8. Checking that the plasma power balance closes68 / 10 / 14The sustainment check became two-sided: the heating a point needs must be zero or positive, and no more than what is installed. No number changed; at all 7,712 re-run points the new check failed exactly those whose self-heating exceeded their modeled losses, and a point needing zero heating passes. The cheapest feasible machine stayed at 202 $/MWh, and the machine as designed needs 49 of its 50 MW.
work/orchestration/goals/burn-control/trail.md § Goal close — 2026-09-07
9. Making a fatter plasma cost something70 / 10 / 14The magnet chain now computes conductor peak field, stored magnetic energy and casing mass from the coil bore, anchored so the design point reproduces exactly. A fatter plasma is caught by the conductor limit only where the bore is large relative to the major radius. The cheapest machine is unchanged at 202 $/MWh, because there the bore is nearly free.
work/orchestration/goals/minor-radius/trail.md § Goal close — 2026-09-08
10. Compute the plant's pumping power, cycle efficiency and availability from the design76 / 14 / 14The goal replaced three fixed plant multipliers (pumping power, cycle efficiency, availability) with calculations from the design and added fuel, divertor-heat and vacuum flow calculations. The baseline LCOE fell from 322.32 to 224.61 $/MWh, and the new divertor heat check fails at the design point. A fresh grader later found 17 of 23 rubric cells at target.
work/orchestration/goals/plant-closure/trail.md (T-004, T-005, T-006 returns; Round 5 result; Owner packet acceptance 2026-09-12); work/analysis/20260912-plant-closure-consolidated-grade.md
11. Fix the defects found by the fusion model audit77 / 18 / 14The goal repaired defects from a 20-finding model audit. Heating now uses operating demand separately from installed capacity, the plant owns one major radius, finance formulas handle zero and equal rates, and magnet, cryogenic, winding and primary-loop inputs are range-checked. Six findings have bounded corrections, nine are partial and five remain open, so the goal is unanswered.
work/orchestration/goals/fusion-audit-remediation/trail.md (Round 4, 5, 7-11 results; T-051 return and Round 12 result, 2026-09-13); work/orchestration/mfe-financial-rate-limits.md
12. Restructure the model into nested physical parts without changing its numbers77 / 18 / 23The goal reorganized the stellarator model into nested physical parts with declared ports and connections, leaving every calculation definition untouched. At the baseline all 158 output channels and 18 verdicts matched the previous package, and LCOE stayed at 224.27. A wider two-package comparison matched on all 769 points reached before the owner stopped it.
work/orchestration/goals/structural-decomposition/trail.md (Amendment 2026-09-13 after T-004, lines 108-118)
13. Price the winding pack and conductor so magnet results can move off the reference design80 / 18 / 23The goal split winding-pack cost into explicit material inventory, tape procurement and winding operations, then added a priced conductor field-capability setting. A 108-case study found magnet sizing, limits and component costs respond consistently, but the evidence does not qualify an engineering design range. The reference LCOE became 142.507 $/MWh, a replacement estimate, not demonstrated savings.
work/orchestration/goals/magnet-design-transfer/transfer-claim.md; work/orchestration/goals/magnet-design-transfer/trail.md (Round 2 result; Goal close 2026-09-14)
14. Make winding length, cooling load and support structure follow the coil the model builds86 / 18 / 23The goal made winding length follow the coil bore, added lead, radiation and support heat loads to refrigeration at two temperature stages, and priced a total support-mass fit. Design-point LCOE rose from 142.51 to 146.31 $/MWh and refrigeration power from 0.864 to 2.138 MW. The cheapest sampled feasible machine stayed at R = 12.7 m, a = 1.7 m.
work/orchestration/goals/magnet-coil-realism/answer.md
15. Price conductor tape by its physical length86 / 18 / 23Tape procurement now prices the same composite-tape length the model builds, and the field-envelope multiplier is applied once. At the reference point tape cost falls from $804.00 million to $731.57 million, and LCOE from $146.31 to $144.74/MWh. Only three of 64 study cases satisfy all eighteen constraints, and all three use an extrapolated 30 T envelope.
work/orchestration/goals/tape-procurement-consistency/answer.md
16. Check that the winding pack fits inside its casing87 / 19 / 23The model gained a fit check that compares the winding pack plus insulation and clearance against an independently set casing interior. The reference fails: it needs 370 mm radially and has 250 mm. Across 116 study cases, passes drop from 45 to twelve, and all three earlier nominal-geometry passes are rejected.
work/orchestration/goals/winding-pack-casing-fit/answer.md
17. Estimate conductor critical current and operating margin88 / 20 / 23The model now estimates the reference conductor's critical current from its tape inventory and checks operating current against an allowed fraction of 0.80. The reference fails: 29.65 kA critical current against 50.00 kA operating current, a margin of −26.28 kA. In the 295-case study, all thirteen combined passes depend on an assumed orientation factor of 3.
work/orchestration/goals/absolute-conductor-current-margin/answer.md
18. Account for what the magnet manufacturing charges cover89 / 20 / 23The goal mapped what each magnet procurement and manufacturing charge covers and found no demonstrated duplicate charge. It added a conditional inter-pancake insulation stock cost of $421,131.97 and made the steel support rate one explicit $18/kg all-in assumption. LCOE moves from $144.738301 to $144.747431/MWh, and the remaining process costs stay unpriced and visible.
work/orchestration/goals/magnet-manufacturing-cost-completeness/answer.md; work/orchestration/goals/magnet-manufacturing-cost-completeness/account-ledger.md
19. Size the magnet tape inventory from the required current90 / 20 / 23The model gained an optional mode that sizes tape inventory from the actual field and the allowed operating fraction; legacy mode stays the default. In 324 default cases the current check always passes and 154 also fit their casing, but none passes the other eighteen constraints. This is a bounded negative answer, not proof of global infeasibility.
work/orchestration/goals/joint-magnet-sizing-feasibility/answer.md
20. Trace divertor heat from plasma exhaust to peak load90 / 20 / 23The model now reports where plasma heating power goes: radiated, deposited on the divertor target, or uncaptured, plus the area implied by the source heat profile. The peak-load formula, the 10 MW/m² limit and every existing constraint are unchanged. The reference peak stays 10.517842 MW/m², and none of 27 study cases passes all 20 constraints.
work/orchestration/goals/divertor-peak-heat-load/answer.md
21. Calculate tritium breeding from the blanket92 / 20 / 23The model now calculates the tritium breeding ratio from blanket thickness using neutron-transport results, replacing the manually assigned 1.074, and fails designs that breed too little. The current 0.80 m blanket fails: its numerical lower estimate of 1.18615 is below the 1.190 fuel requirement. The 0.825–1.00 m samples pass breeding but violate the peak-field limit.
work/orchestration/goals/computed-tritium-breeding/answer.md
22. Installed cooling equipment costs97 / 20 / 30The model now sizes and separately prices helium circulators, salt pumps, piping and helium-to-salt heat exchangers, with installation, spares, coolant inventories and scheduled replacements. For the selected 18-circuit design, the old $205 million cooling allowance became an $8.2 billion equipment estimate, and electricity cost rose from $150 to $311/MWh. Independent review passed it at the target depth.
work/orchestration/goals/installed-cooling-equipment-costs/answer.md
23. Buildings sized from equipment and maintenance needs133 / 25 / 57The model now derives 25 separately costed buildings and transfer links from equipment dimensions, component movement space and dated maintenance inventories, including shielded maintenance wings and remote-handling routes. At the 14-circuit reference, plant capital rose $199 million and electricity cost went from $270.8 to $273.5/MWh. Independent review passed it at the target depth.
work/orchestration/goals/layout-based-facilities/answer.md
24. Fuel inventory, startup stock and processing throughput134 / 25 / 64The model now calculates tritium held in the fuel system, startup supply and processing throughput from explicit assumptions. At the reference point it holds 4.418 kg of tritium, needs 4.400 kg of initial external supply and processes 7.743 kg of tritium per operating day. Fuel-processing costs and electricity cost are unchanged. Independent review passed it at the target depth.
work/orchestration/goals/fuel-inventory-and-startup/answer.md
25. Fuel-processing cost that follows throughput135 / 25 / 64Fuel-processing capital now follows the calculated running exhaust flow through a sourced scaling relationship, replacing the old allowance once. At the reference point the account fell from $120.7 million to $22.8 million, and electricity cost from $273.455 to $271.584/MWh. These are matched model results, not procurement savings. Independent review passed it at the target depth.
work/orchestration/goals/throughput-based-fuel-processing-costs/answer.md
26. Cost-estimate maturity and uncertainty135 / 25 / 64The goal assessed the estimate as a provisional Class 5 conceptual estimate and mapped 23 direct cost accounts; cooling, magnets and facilities hold 73% of direct cost. It added one shared stainless fabrication-price input to the model. Across 36 source alternatives, capital spans $15.9–19.3 billion and electricity cost $245–290/MWh. This is a partial envelope, not a confidence interval.
work/orchestration/goals/cost-estimate-maturity-and-uncertainty/answer.md
27. Getting the current model ready for comparison138 / 28 / 76A water-state steam cycle now connects salt heat to electricity, replacing a conversion fit that bypassed the 465°C salt supply. At the raw baseline, net electricity fell from 1,009 to 850 MW and electricity cost rose from $271.6 to $318.7/MWh. The owner adopted the independently reproduced package as r3. Four engineering failures remain visible.
work/orchestration/goals/current-model-comparison-readiness/answer.md; work/orchestration/goals/current-model-comparison-readiness/approval-packet.md
28. Keeping supplied design choices through evaluation199 / 67 / 76The model now evaluates and costs supplied designs without silently selecting different hardware. Round 1 preserved supplied magnet, facility, fuel-processor and cooling choices. Round 2 made equipment prices follow the chosen purchase and added 33 capacity checks, for 67 in total. Independent review passed both rounds. The baseline still fails six engineering checks.
work/orchestration/goals/preserve-model-design-choices/answer.md
29. How far the repaired model can be evaluated199 / 67 / 76Broad readiness is not established: the intended size range exceeds the current breeding-geometry and conductor support. The model now refuses invalid compressor suction conditions explicitly and gives useful conductor-domain messages. It does not expand the supported design space. File-read verification and a synthetic comparison adapter were completed within their documented limits.
work/orchestration/goals/model-evaluation-domain-readiness/answer.md