Presets
Playback
Insulation
Vacuum quality, superinsulation layers and the surface emissivity set the radiation and gas loads.
Supports, load and cold head
Mechanical supports bring heat in by conduction; the cold head can only take away so much at each temperature.
Layers
Model checks
The science
Three ways heat leaks in
Radiation between concentric surfaces of emissivity eps: P = sigma A (T_h^4 - T_c^4) / (2/eps - 1). Putting N floating, low-emissivity layers (multilayer insulation, MLI) between them divides the load by N + 1. Residual gas: at low pressure molecules fly straight from warm to cold wall (free-molecular regime), so the heat flux is proportional to pressure, h = a (gamma + 1) / (gamma - 1) p sqrt(R / (8 pi M T)); near 1 Pa it saturates at ordinary gas conduction. Solid supports: Fourier conduction with a temperature-dependent conductivity, P = (A / L) integral k(T) dT; with k = k0 T / 300 this is k0 A (T_h^2 - T_c^2) / (2 L 300).
Cold head
A two-stage cryocooler cannot cool arbitrarily: it has a capacity curve for each stage (tens of watts near 45 K for stage 1, about one watt at 4.2 K for stage 2). Steady temperatures are where capacity equals the heat load, which the page finds by bisection (the intersection in the second graph). The cool-down curve integrates C(T) dT/dt = load - capacity with an implicit step, using a table of copper specific heat (it drops by a factor of a thousand between 300 K and 4 K, which is why the last stretch cools fast).
Honest simplifications
The capacity curves, areas and the 1.6 height-to-diameter ratio are illustrative, not data of a product. Stage 2 is thermally linked to the sample stage only; gas is treated as air; contact resistances, the cold-finger conduction and cooler vibration are ignored. The 3D page shows the same chamber as a qualitative cutaway; this page is the quantitative companion. The animation runs at 0.25 hours per second.
What to try
- Set MLI layers to 0 and watch the radiation load on stage 1 jump.
- Pick Poor vacuum: gas conduction now competes with radiation and the stage stops reaching 4 K.
- Pick Big thermal mass: the same steady state, but a much slower cool-down curve.
- Raise the sample heat load until stage 2 can no longer stay below 5 K.