Pumps & Conductance — Mean Free Path

Three Flow Regimes

Gas behaves completely differently depending on pressure. At high pressure, molecules collide constantly and flow like a fluid. At UHV, each molecule bounces independently from wall to wall, never meeting another. The Knudsen number (mean free path / tube diameter) tells you which regime you are in.

PRESSURE

1 mbar

Mean Free Path

66 µm

Knudsen Number (d=10cm)

6.6 × 10⁻⁴

Regime

Viscous

VISCOUS FLOW

Molecules interact constantly and push each other along. The flow behaves like water in a pipe. This is the domain of roughing pumps (scroll, roots). Conductance depends on pressure and viscosity.

Mean Free Path Explorer

Interactive simulation with gas species, temperature control, monolayer calculator, race mode, and more.
→ Open the full Mean Free Path Explorer

The Pump Zoo

Each pump technology has strengths and blind spots. Knowing what each pump cannot do is just as important as knowing what it can.

Turbo-Molecular

High-speed rotating blades impart momentum to molecules. Works only in molecular flow. Needs a backing pump (scroll or diaphragm). Compression ratio drops for light gases.

Pumps: all gases (N₂, H₂O, CO, CO₂, HC, Ar)

Weak: H₂ and He (low compression ratio ~10³ vs ~10⁹ for N₂)

Ion Pump (Gamma / VacIon)

Ionizes gas and buries ions in titanium cathode. Current = pressure measurement. No vibrations, no oil. Must start below ~10⁻⁵ Torr. Lifetime limited by cathode erosion.

Pumps: N₂, CO, CO₂, H₂O, H₂ (excellent)

Weak: Ar, He (noble gas instability), CH₄

NEG (CapaciTorr / St707)

Non-Evaporable Getter: ZrVFe alloy absorbs H₂ into the bulk, and getters CO, CO₂, N₂, H₂O on the surface. Must be activated at ~450°C. Finite capacity for CO/CO₂ (surface saturation).

Pumps: H₂ (huge capacity), CO, CO₂, N₂, H₂O

Does NOT pump: Ar, He, CH₄, heavy HC

Scroll / Dry Pump

Oil-free roughing pump. Two interleaved scrolls compress gas mechanically. No backstreaming risk. Used as backing for turbos or standalone for rough vacuum.

Pumps: all gases (rough vacuum)

Limit: ~10⁻² mbar ultimate. Not for HV/UHV alone.

Cryopump

Condenses gas on surfaces at ~10–20 K. Pumps everything including noble gases. Must be regenerated periodically (warm up, pump out accumulated gas). Risk of pressure burst if cryo fails.

Pumps: ALL gases (including Ar, He at ~4 K)

Risk: requires regeneration, catastrophic burst on failure

Why Pressure Stalls

Four fundamentally different reasons why the pressure stops going down. The fix depends entirely on which one it is.

Conductance Limited

The tube between pump and chamber is too narrow. The pump spins at full speed but molecules cannot reach it fast enough. Wider, shorter tubes fix this.

Pump Speed Limited

The pump is too small for the volume and outgassing rate. A bigger pump or adding a NEG will help.

Outgassing Limited

The chamber walls produce more gas than the pump removes. Baking is the solution. This is the normal regime during bake-outs.

Real Leak

A hole to atmosphere. P_min = Q_leak / S_eff. No amount of pumping or baking will help. Find and fix the leak.

Conductance calculator: adjust tube dimensions to see how geometry limits your effective pumping.

TUBE DIAMETER 4 cm

TUBE LENGTH 50 cm

Conductance (N₂, 295 K)

-- L/s

With S_pump = 300 L/s

-- L/s effective

Pump utilization

--%

Effective Pumping Speed

The pump speed on the datasheet is not what the chamber sees. The connecting tube acts as a resistor. The key equation:

1/S_eff = 1/S_pump + 1/C_tube

If C_tube « S_pump, the tube is the bottleneck and the pump is wasted. Drag the slider to see the effect.

C_TUBE 50 L/s

S_pump

300 L/s

+

C_tube

50 L/s

→

S_eff

43 L/s

14% of pump speed

Equations & Parameters

Knudsen number:
Kn = λ / d
λ = k_BT / (√2 · π · d_mol² · P)
d_mol ≈ 3.7×10⁻¹⁰ m for N₂. Kn > 1 → molecular, Kn < 0.01 → viscous.

Molecular conductance — long tube:
C = 12.1 · D³ / L · √(T / M) [L/s]
D = diameter (cm), L = length (cm), T (K), M (g/mol). Valid for L/D > 10.

Molecular conductance — orifice:
C = 11.6 · A · √(T / M) [L/s]
A = aperture area (cm²). This is the maximum conductance for a given opening.

Effective speed & ultimate pressure:
1/S_eff = 1/S_p + 1/C
P_ult = Q_total / S_eff
Q_total = sum of all gas loads (outgassing + leaks) in Torr·L/s.

Pump type	S (N₂) L/s	S (H₂) L/s	S (Ar) L/s	S (CH₄) L/s	Ultimate (Torr)
Turbo 300 L/s	300	250	280	290	~10⁻¹⁰
Turbo 70 L/s	70	55	65	68	~10⁻¹⁰
Ion pump 60 L/s (diode)	60	50	2	6	~10⁻¹¹
Ion pump 60 L/s (StarCell)	60	50	30	10	~10⁻¹¹
NEG (CapaciTorr D400)	200	400	0	0	~10⁻¹² (H₂)
NEG (St707 strip, 1m)	300	1500	0	0	~10⁻¹² (H₂)
Cryo (1500 L/s)	1500	2500	1200	1500	~10⁻¹⁰
Scroll (dry)	~5 m³/h (displacement pump)				~10⁻² mbar

Ion pump current ↔ pressure:
I = K · P · S
K ≈ 0.1 A/(Torr·L/s) for N₂. At 10⁻⁹ Torr with a 60 L/s pump: I ≈ 6 nA.

NEG alloy	H₂ capacity (Torr·L/g)	CO capacity (Torr·L/g)	CO₂ capacity (Torr·L/g)	Activation T
St707 (ZrVFe)	1500	5	3	450°C / 45 min
St101 (ZrAl)	600	10	8	750°C / 45 min
ZAO (TiZrV thin film)	0.1 (per cm²)	0.001	0.0005	180°C / 24 h

References

[1] J.F. O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed., Wiley, 2003 — Ch. 3: Gas Flow, Ch. 4: Pumps.
[2] K. Jousten (ed.), Handbook of Vacuum Technology, 2nd ed., Wiley-VCH, 2016 — Ch. 4: Gas Flow, Ch. 5: Vacuum Pumps.
[3] SAES Getters, "CapaciTorr and St707 Technical Data Sheets."
[4] Agilent (Varian), "Ion Pump Technical Manual," Publication 699908399.
[5] Pfeiffer Vacuum, "Turbopump Selection Guide," 2022.