Solar-wind protons and He-3 ions implant a few tens of nanometres into every regolith grain over the eons the surface sits exposed — real Apollo samples measure roughly 20 ppb He-3 by mass. Getting it back out means heating the grains until thermally-activated diffusion lets the trapped gas random-walk to the grain surface and escape. This 2D model numerically integrates that release directly as an ODE rather than jumping to the closed form:
dF/dt = (1 − F) / τ(T) [Arrhenius release-rate ODE]
τ(T) = τ₀ · exp(Eₐ / R·T) [grain release time constant]
with activation energy Eₐ ≈ 180 kJ/mol (representative of He-3 bound in ilmenite/glassy regolith), gas constant R = 8.314 J/(mol·K), and T in kelvin. Each animation frame advances simulated bake-time by a small Δt and steps F forward by ΔF = (1 − F)/τ(T) · Δt (explicit Euler), so the on-screen yield-vs-time curve is the actual running integral of the release rate, not a pre-computed curve. Because Eₐ/R·T sits inside an exponential, τ swings by many orders of magnitude across the practical bake range — release is negligible below roughly 500 °C and becomes fast within hours above 700 °C, the same "knee" seen in real stepped-heating extraction experiments.
- Bake temperature — sets τ(T) and therefore the integration step size ΔF each frame; grains shift from brown toward orange-hot and the escaping-gas plume thickens as T rises.
- Cycle duration — total simulated bake time; the integrator runs until t = duration.
- Batch mass — total regolith processed; extracted mass = batch mass × 20 ppb × F(t).
- Heating energy — Q = m·c·ΔT with regolith specific heat c ≈ 0.71 J/(g·K) and ΔT from a −20 °C lunar-day baseline to the bake temperature, converted to kWh. Because Q depends only on temperature while yield depends on both temperature and time, higher bake temperatures pay a fixed energy premium for a faster — but not free — yield: the energy-per-yield readout falls as duration lengthens at a given temperature, and rises again once temperature is pushed well past the point where extra heat no longer buys much more τ(T) improvement.
The animated run compresses the real duration into a fixed 12-second playback so the escaping-gas rate — proportional to dF/dt, read straight off the integrator each frame — stays visible instead of finishing instantly or taking hours.