Turbomolecular pump
[1][2] These pumps work on the principle that gas molecules can be given momentum in a desired direction by repeated collision with a moving solid surface.
A blade needs to be thick and stable enough for high pressure operation and as thin as possible and slightly bent for maximum compression.
For high compression ratios the throat between adjacent rotor blades (as shown in the image) is pointing as much as possible in the forward direction.
The geometric progression tells us that infinite stages could ideally fit into a finite axial length.
The finite length in this case is the full height of the housing as the bearings, the motor, and controller and some of the coolers can be installed inside on the axis.
Turbomolecular pumps must operate at very high speeds, and the heat buildup due to friction imposes design limitations.
Because the magnetic bearings and the temperature cycles allow for only a limited clearance between rotor and stator, the blades at the high pressure stages are somewhat degenerated into a single helical foil each.
The transition from vacuum to nitrogen and from a running to a still turbopump has to be synchronized precisely to avoid mechanical stress to the pump and overpressure at the exhaust.
Minimally, this degree must be stabilized electronically (or by a diamagnetic material, which is too unstable to be used in a precision pump bearing).
Another way (ignoring losses in magnetic cores at high frequencies) is to construct this bearing as an axis with a sphere at each end.
Hall effect sensors can be used to sense the rotational position and the other degrees of freedom can be measured capacitively.
From a practical construction standpoint, a feasible gap between the blade sets is on the order of 1 mm, so a turbopump will stall (no net pumping) if exhausted directly to the atmosphere.
The backing pressure is rarely below 10−3 mbar (mean free path ≈ 70 mm) because the flow resistance of the vacuum pipe between the turbopump and the roughing pump becomes significant.
