the potassium case

eye-dim, silicon-bright — the K frame pair

K radiance render, deep red — what the cell sees at 767 nm [MODEL — render, guided-cavity K radiance]

K honest dim, nearly invisible — what the eye sees [MODEL — photometric honest dim; 767 sits at the eye's edge]

same photons, two judgments: near-dark to the eye, full-power to the silicon. That is the whole potassium thesis in two frames.

1 · spectral match — why 767 wins

Na D and K doublet over Si EQE with thermalization waste annotated — Na D (589) and K doublet (766.5/769.9) over the Si EQE curve [ESTIMATE, C60 family] and B(λ, 2400/2800 K). Thermalization waste shaded: 0.98 eV/ph (Na) vs 0.50 eV/ph (K). regen: uv run --python 3.12 --with numpy --with matplotlib python flasmon/fig_k_spectral.py

2 · the drive — potassium hugs zero

mu required for equal radiance vs T, Na and K — μ_γ required for equal radiance (row-18 inversion): at 2400 K, Na needs +0.52, K needs +0.03; **at 2800 K, K is super-Planckian at μ = 0 by +0.24 eV**. The pinch that was marginal for sodium evaporates for potassium. regen: uv run --python 3.12 --with numpy --with matplotlib python flasmon/fig_k_drive.py

3 · the water ladder — when the channel pumps

water ladder regime map: excess and threshold boost vs high-v lifetime — oxy-hydrogen's product is H₂O born vibrationally excited; the manifold is the inversion. Regime map from flasmon/water_ladder.py: the alkali channel pumps whenever the high-v states live longer than ~10⁻¹⁵ cm³/s-class — the Sugden-evidence window. [nascent E_v ESTIMATE 1.7 eV; coupling ESTIMATE, Sugden-era lineage] regen: uv run --python 3.12 --with numpy --with matplotlib python flasmon/fig_k_ladder.py

4 · the mirror trade — two ledgers, two crossovers

mirror marginal value vs suns, cell-side and full-device — a trade, not a presumed win: the C60 rear metallization already returns 50–80% of sub-gap photons [ESTIMATE, coupon owed]. With η_mono credited, the K cell-side stays in tax territory through 12 suns (−30 W/m² at 7, −15 at 12); the device ledger earns from ~1–3 suns, +19% at 7 → +35% at 12. Sub-gap content of a 2800 K cavity: **70%** [computed — quadrature fixed 2026-07-21; the 39% previously shown here carried a grid-spacing factor]. regen: uv run --python 3.12 --with numpy --with matplotlib python flasmon/fig_k_mirror.py

5 · the twin-tube stack

twin-tube radial stack with KCl wicking window — gas core → inner quartz → condensation annulus → outer quartz → vacuum → heat-mirror facet → C60. With the mirror credited: T_core = 2530, T_inner = 1152, T_outer = 942 K. The KCl wicking window (1044–1214 K) lands exactly on the inner tube surface — the film lives there, pure salt, no eutectic, no molten bath [DESIGN]. regen: uv run --python 3.12 --with numpy --with matplotlib python flasmon/fig_k_twin.py

6 · the device from outside — escape spectra and fields

escaping spectrum vs mu, self-reversed D line evolving — what a spectrometer outside the device sees as the drive rises: the escaping spectrum at μ_γ = 0 / +0.25 / +0.40 / +0.60 eV — κ-ladder escape rows × generalized-Planck source. Self-reversal deepens before the wings lift: the degree of self-reversal is a secondary gauge of the radiatively pumped potential [MODEL]. regen: uv run --python 3.12 --with numpy --with matplotlib python flasmon/fig_p_escape.py

T(r,z) and emission density field maps — the solved fields: T(r,z) with core/annulus/wall structure and the emission-density companion — same style as the twin-tube stack, here as maps [MODEL — static-merge machinery]. regen: uv run --python 3.12 --with numpy --with matplotlib python flasmon/fig_p_fields.py

the headline, in one table

	Na D (589 nm)	K D (767 nm)
photon energy	2.105 eV	1.616 eV
waste vs Si gap (1.12)	0.98 eV/ph	0.50 eV/ph
η_mono @ 7 kW/m², 60 °C [derived: EQE 0.99 [T NREL/SPWR 2013] × diode theory; FF 0.80 MODEL]	0.255	0.335
μ needed for equal radiance	—	−0.489 eV
at 2400 K	+0.52	+0.03
at 2800 K	+0.25	−0.24 (free)
Planck brightness ratio	1.0	×2.0–2.8
ionization exp(−IP/kT) @2800	5.6×10⁻¹⁰	1.5×10⁻⁸ (27×)

the sodium flasmon was the proof; the potassium flasmon is the product — half the photon waste, a pinch that evaporates, a cell that was already made for it.

the ledger

drive equal-radiance drive: μ_K = μ_Na − 0.489 eV. At 2800 K the K line is super-Planckian at μ = 0 by +0.24 eV of headroom; the chemistry pinch relaxes from yield ≈ 1 (Na at 2400) to ≈ 0.1–0.15 (K). [reconstructed | ESTIMATE cycle ~2× faster] coupling oxy-hydrogen removes CO₂ — the only true drain (thermalizes, never re-excites). The alkali-H₂O channel is a coupling whose direction the reservoir sets: it pumps when the ladder is driven, quenches only when cold [frame: water_ladder.py]. cascade Na(3p) → K(4p) E–E transfer (exothermic 0.489 eV): Na = antenna, K = emitter. Transfer efficiency 3% @10% K, 15% @50%, 24% @90% [ESTIMATE k_EE = 10⁻¹⁰]; the ladder threshold at 1.616 eV is ~7× more populated than at 2.105 eV. system point vacuum jacket (radiation-only wall), KCl loop (mp 1044 K — easier than NaCl), strong recuperation (η = 0.9). Model steady state: T_core ≈ 2530 K, T_annulus ≈ 2090 K, T_wall ≈ 1210 K, P_line ≈ 550 W at 2.1 kW fuel. suns on cell r2 matrices, 0.847 electrical capture: 7 suns needs 7,470 W radiated → 2.2 kW_e (ΔT_cell = 40 K, η_mono = 0.352); 10 suns needs 10,680 W radiated → 2.8 kW_e (ΔT_cell = 60 K, η_mono = 0.314) [derived: EQE 0.99 [T NREL/SPWR 2013] × diode theory, −1.75 mV/K; FF 0.80 MODEL pending bench I-V]. Achievable at the anticipated regimes: device side is a 30–70 kW-fuel class at β ≈ 0.3 [β: MODEL design class — not measured; see ROW18-INHERITANCE-AUDIT]; cell side holds with liquid-class cooling in the ΔT = 20–60 K band — each 10 K of cell temperature costs ~0.9% absolute, so the fin design is priced, not decorative.

costs and open questions

K(4p) cross sections ~1.5× Na(3p) [ESTIMATE] — σ_H is the single biggest unknown in the K quench budget.
K chemistry is less characterized than Na's — the KOH/KH cycle is structurally analogous but its rates carry [ESTIMATE] throughout.
ion loss channel: 27× ionization cuts both ways — K⁺ drift to walls is a real sink at design densities.
KCl corrosivity ≈ NaCl; materials program inherits unchanged.
the overshoot coupling ([K]/[KOH] ∝ s) mirrors sodium's breathing [MODEL].
FF 0.80 is [MODEL] — one bench I-V sweep under the Na source closes FF, Voc1, and high-injection at once; it is the top recommended measurement.
current density is 1.5× the naive broadband estimate: 67 A/full-cell at 7 kW/m² 767 nm — split-3 (22 A/strip) is the baseline at the design point; split-5 holds 21 kW/m² at 40 A/strip; resistive loss fraction ∝ X/n².
C60 Gen3 packaging: tin-barrier metallization + chloride sealing at the salt-loop interface [T-sheet]; −0.29%/K n-type derate folded into every η_mono above.

what was run — regenerate everything

figure / artifact	script	command	output
k-spectral.svg/.png	flasmon/fig_k_spectral.py	uv run --python 3.12 --with numpy --with matplotlib python fig_k_spectral.py	✓ deployed
k-drive.svg/.png	flasmon/fig_k_drive.py	uv run --python 3.12 --with numpy --with matplotlib python fig_k_drive.py	✓ deployed
k-ladder.svg/.png	flasmon/fig_k_ladder.py	uv run --python 3.12 --with numpy --with matplotlib python fig_k_ladder.py	✓ deployed
k-mirror.svg/.png	flasmon/fig_k_mirror.py	uv run --python 3.12 --with numpy --with matplotlib python fig_k_mirror.py	✓ deployed
k-twin.svg/.png	flasmon/fig_k_twin.py	uv run --python 3.12 --with numpy --with matplotlib python fig_k_twin.py	✓ deployed
p-escape.svg/.png	flasmon/fig_p_escape.py	uv run --python 3.12 --with numpy --with matplotlib python fig_p_escape.py	✓ deployed
p-fields.svg/.png	flasmon/fig_p_fields.py	uv run --python 3.12 --with numpy --with matplotlib python fig_p_fields.py	✓ deployed
K frame pair	night render fork (vf-tracer)	sites/flasmon.com/assets/night/ring-end-on-v12-K-*.png	✓ on disk
drive + pinch numbers	flasmon/potassium.py, catalytic.py	uv run --python 3.12 --with numpy python potassium.py	✓ ran
water-ladder regime map	flasmon/water_ladder.py	uv run --python 3.12 --with numpy python water_ladder.py	✓ ran
mirror trade study	flasmon/mirror_trade.py	uv run --python 3.12 --with numpy python mirror_trade.py	✓ ran
system model (K config)	flasmon/system_model.py	uv run --python 3.12 --with numpy --with matplotlib python system_model.py 0.9	✓ ran
gates	flasmon/Makefile	make -C flasmon gates	4/4 PASS