Test 14 — Sell the Heat, Not the Electrons
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
README.md
# Test 14 — Sell the Heat, Not the Electrons ## Verdict: partly supported The directional claim holds — a process-heat fusion plant breaks even at a lower plasma gain Q than an electric plant in every parameter cell tested — but the posted magnitudes (exactly ~3×, and the Q ≈ 2–4 versus Q ≈ 8–10 bands) do not follow from the published SPARC/ARC design parameters under the stated power balance. ## Headline numbers | Quantity | Value | Source / note | |---|---|---| | Required Q, electric (η = 0.35, ARC loads) | **4.6** | ARC point: P_fus = 525 MW, M = 0.275, P_fixed = 54.4 MW, r = 0, P_aux = 38.6 MW | | Required Q, process heat (η_th = 0.95, ARC loads) | **1.2** | same cell | | Ratio Q_electric / Q_heat, ARC point | **3.8** | posted "~3×"; model bound ≥ η_th/η = 2.7 | | Ratio across all 144 cells | median **5.1**, min 3.1, max 61.9 | 100% of cells ≥ 2.7 | | Cells with Q_e ∈ 6–12 and Q_h ∈ 1.5–5 | **22%** | the posted absolute bands | | Q_electric at η = 0.33, r = 0.2 | **9.4** | the only cells reaching the posted 8–10 | | Q_heat with no fixed loads | **~0.04–0.1** | break-even is nearly automatic at η_th = 0.95 | Model check of the published ARC design point (Sorbom et al. 2015 Table 1): the balance reproduces P_e = 283 MW, P_net = 190 MW and Q_e = 3.0 exactly (283.2, 190.2, 3.04), which validates the arithmetic before it is applied to the heat case. ## What this shows and cannot show - Shows: under a transparent break-even definition (P_out = P_recirc), skipping the thermal-to-electric conversion always lowers the required Q, and published recirculating loads shrink — but cannot erase — the gap, which is bounded below by η_th/η ≈ 2.7. - Shows: the claimed absolute numbers are not reproduced. At the published ARC point the electric plant needs Q ≈ 4.6 (not 8–10) and the heat plant Q ≈ 1.2 (not 2–4). Q_electric reaches 8–10 only if one stacks high fixed loads (54.4 MW) with an additional fusion-scaled load of r ≈ 0.2 and η = 0.33; Q_heat only reaches the posted band when heat recovery is degraded to η_th ≈ 0.85. - Cannot show: whether any fusion plant works, or what "break-even" should mean commercially. The posted definition is self-sustenance (output equals recirculating power); a heat plant at η_th = 0.95 nearly satisfies it even at Q < 1, because almost all fusion power is recovered as heat. A meaningful commercial test would require the plant to deliver rated useful output, which would raise the heat-case Q above the figures computed here. ## Limitations 1. **Break-even definition.** The posted definition (P_out = P_recirc) is self-sustenance, not useful delivery. Under it, the heat case collapses toward Q ≈ 0.05 when fixed loads are omitted; a plant that merely powers itself delivers no process heat to a customer. The Q_heat figures are therefore definition-dependent. 2. **Recirculating-load decomposition.** The ARC paper reports 93 MWe of recirculating power without splitting it into fixed and fusion-scaled parts; the split used here (P_fixed = 54.4 MW, r = 0–0.2) is a parameterisation, and the absolute Q values move by factors of two across the plausible range. This is the main rival explanation for the posted 8–10 figure: it implicitly assumes substantially heavier plant loads than ARC's published values. 3. **Single-machine, single-concept basis.** The parameter ranges come from two MIT high-field tokamak designs (SPARC, ARC). Low-field or inertial designs with different recirculating fractions and blanket multipliers would give different absolute Q values, though the ratio bound (≥ η_th/η) is general to any machine with the same efficiencies. 4. **Heat use efficiency.** η_th = 0.95 assumes the process can accept low-grade heat with 5% losses; real industrial process heat at 500–1000 °C carries exergy losses that the sensitivity sweep (η_th = 0.85) only partially captures. This is a model check, not a claim that any fusion plant works. ## Structure - `hypothesis.md` — claim, model and pre-specified criteria (written before analysis) - `run.py` — deterministic sweep; regenerates `results.json`, `data/*.csv`, `figures/*.png` - `results.json` — per-sub-claim verdicts and decisive numbers - `SOURCE.md` — papers, values and citations
hypothesis.md
# Test 14 — Sell the Heat, Not the Electrons (fusion process heat)
## Posted claim (Frontier Ideas, fusion-process-heat), verbatim
"Heat-only fusion breaks even at a gain factor at least ~3× lower than electricity, because the thermal-to-electric conversion loss is skipped."
## Posted prediction
The required fusion gain Q for a process-heat plant is roughly (1/η) lower than for an electric plant (η ≈ 0.33–0.4), and a heat-only plant can therefore break even at Q ≈ 2–4 where an electric plant needs Q ≈ 8–10.
## Posted refutation
Tritium breeding or other system loads force similar Q in both.
## Source links
- Creely et al. 2020, "Overview of the SPARC tokamak", J. Plasma Phys. 86:865860502, doi:10.1017/S0022377820001257.
- Sorbom et al. 2015, "ARC: A compact, high-field, fusion nuclear science facility and demonstration power plant with demountable magnets", Fusion Eng. Des. 100:378–405, doi:10.1016/j.fusengdes.2015.07.008.
- Parameters fetched from the open literature during execution; every value used is cited with source in `results.json` and `SOURCE.md`.
## Model specification (fixed before analysis)
This is a **model check only**: it tests whether the claimed numbers follow from published design parameters under a stated power balance. It is not a claim that any fusion plant works.
Definitions and balance:
- Q = P_fus / P_aux (plasma gain; P_fus fusion power, P_aux injected auxiliary heating power).
- P_th = P_fus·(1 + M) + P_aux, with M the blanket **energy** multiplication of the fusion power (not the neutron multiplier). The ARC design point implies M ≈ 0.275: Table 1 of Sorbom et al. 2015 gives P_fus = 525 MW and total thermal power P_tot = 708 MW, so 708 = 525·(1 + M) + 38.6 → M ≈ 0.275. Sweep M ∈ {0.05, 0.15, 0.275, 0.5}.
- P_out = η_use · P_th (useful output), where η_use = 0.35 for the electric case (η ∈ [0.33, 0.40] swept, matching the posted range and ARC's 0.40) and η_use ∈ [0.85, 0.95, 1.0] for direct process heat (design specifies η_th = 0.95 as the headline heat case).
- Recirculating power: P_recirc = P_aux + P_fixed + r·P_fus, where P_fixed covers cryo/magnets/pumps and r·P_fus covers loads that scale with fusion power (coolant pumping, tritium plant). Published design points set the ranges: ARC recirculates 283 − 190 = 93 MWe, of which 38.6 MW is heating, so P_fixed ≈ 54.4 MW and r = 54.4/525 ≈ 0.104; sweep P_fixed ∈ {0, 30, 54.4} MW, r ∈ {0, 0.05, 0.104, 0.20}, P_aux ∈ {12.7, 25, 38.6} MW (12.7 = 140/11, the SPARC Q = 11 point; 25 = SPARC's installed ICRH; 38.6 = ARC).
- Break-even is defined exactly as posted: P_out = P_recirc, i.e. the plant just powers itself. Solving for the required plasma gain gives
Q_req = (P_fixed + (1 − η_use)·P_aux) / (P_aux·(η_use·(1 + M) − r))
for each (η_use, M, r, P_fixed, P_aux) cell. Cells where the denominator ≤ 0 are recorded as "no finite Q closes the balance" (loads grow faster than usable output).
## Pre-specified criteria for this test (written before analysis)
Three sub-claims, each verdict separately, plus an overall verdict.
1. **Directional claim** (heat-only needs lower Q than electric): hold on the ratio ρ = Q_req(electric, η = 0.35) / Q_req(heat, η_th = 0.95) at matched (M, r, P_fixed, P_aux).
- supported if ρ ≥ 2.7 in ≥ 80% of parameter cells;
- partly supported if ρ > 1 in ≥ 80% of cells but the ≥ 2.7 condition fails;
- not supported if breeding/aux loads erase the difference (ρ ≤ 1 in ≥ 20% of cells or median ρ ≤ 1).
2. **Magnitude claim** ("at least ~3×", i.e. ρ ≈ 1/η ≈ 2.9): supported if the median ρ across cells lies in [2.7, 3.6]; partly supported if median ρ > 1 but outside that band (the direction holds, the 3× figure does not); not supported otherwise.
3. **Absolute break-even claim** (Q_heat ≈ 2–4 vs Q_electric ≈ 8–10): supported if, across the published parameter ranges, Q_req(electric) lands in 6–12 (claim 8–10 ± 25%) and Q_req(heat, η_th = 0.95) lands in 1.5–5 (claim 2–4 ± 25%) in ≥ 50% of cells; partly supported if the electric figure lands near the claimed band but the heat figure does not (or vice versa); not supported if neither band is reproduced with published parameters.
4. **Overall verdict**: supported only if all three sub-claims are supported; partly supported if the direction is correct but magnitude or absolutes fail; not supported as stated if the claimed numbers do not arise from the published parameters under any defensible parameter setting; not testable only if sources cannot be obtained.
Sensitivity: repeat with η = 0.33 and 0.40 (electric) and η_th = 0.85, 1.0 (heat). All numbers deterministic; no randomness is involved.