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Differential pumping maintains different gas pressures in connected regions by restricting the connecting gas flow and pumping each region separately. A small aperture or narrow tube limits the vacuum conductance between stages.

In the molecular flow regime, a connection with conductance $C$ carries throughput $Q=C(p_1-p_2)$. A downstream stage pumped at effective speed $S$ has $S{p}_2=C(p_1-p_2)$ in steady state, giving $p_2/p_1=C/(S+C)$. This lets a source operate at a higher pressure while an adjacent particle beam travels in a better vacuum.^[ref]

A gas load is the rate at which gas enters or is released into a vacuum system, expressed as pressure-volume per time at a stated temperature. Contributions include leaks, outgassing and intentional gas injection.

For a chamber at fixed volume $V$ and temperature, $V\dot{p}=Q-Sp$ balances a constant load against pumping. The steady pressure is $p=Q/S$. Reducing the load can therefore improve the pressure as effectively as increasing the pumping speed.^[ref]

In molecular flow, the gas mean free path is large compared with the channel or vessel dimensions, so molecules encounter walls more frequently than one another. The Knudsen number $\mathrm{Kn}=\lambda /L$ characterizes this regime.

For a small aperture of area $A$ between equilibrium gas reservoirs, the vacuum conductance is $C=A\overline{v}/4$, where $\overline{v}$ is the mean molecular speed. At fixed temperature this scales as the inverse square root of molecular mass. Continuum viscous-flow formulas need not apply.^[ref]

Outgassing is gas release from materials or their surfaces into the surrounding space. In a vacuum chamber it contributes to the gas load, even when the seals have no leak. Adsorbed water and dissolved gases can have very different release times.

The relation $p\approx Q/S$ shows why surface preparation and material choice matter: increasing pumping speed addresses removal, while reducing outgassing addresses the source. A pressure-rise measurement with pumping isolated estimates total release only after accounting for leaks and temperature changes.^[ref]

Paolo Chiggiato authored teaching material on vacuum technology for ion sources and accelerators. The treatment connects gas sources, molecular transport, conductance and pumping with the pressure profile actually achieved in an apparatus.^[ref]

The pumping speed at a specified inlet is the gas throughput divided by the inlet pressure: $S=Q/p$. Its units are volume per time, commonly litres per second. A pump's speed depends on gas species and operating conditions.

Connecting a pump of speed $S_p$ through a line of vacuum conductance $C$ gives $1/S_{\mathrm{eff}}=1/S_p+1/C$ in the linear flow regime. Thus a large pump cannot compensate for an arbitrarily restrictive connection.^[ref]

A laboratory vacuum is a region with substantially reduced gas pressure, rather than an experimentally perfect absence of matter. Lowering the number density increases the mean free path, allowing a molecular beam to travel with fewer collisions. In molecular flow, the mean free path exceeds the apparatus dimensions, so wall encounters dominate.

A vacuum pump competes with leaks and outgassing. For an isothermal vessel of volume $V$, constant gas load $Q$ in pressure-volume per unit time, and effective pumping speed $S$, gas balance givesThis ideal model predicts a pump-down time constant $V/S$ and a limiting pressure $Q/S$. A restricted connecting pipe reduces the effective pumping speed; a larger pump alone need not fix it. Measuring the pressure transient tests the model, while deviations can reveal changing outgassing or pumping speed.^[ref]

Vacuum conductance relates gas throughput to a pressure difference across a connection: $Q=C(p_1-p_2)$. For throughput in $\mathrm{Pa}{\mathrm{m}}^3{\mathrm{s}}^{-1}$, conductance $C$ has units ${\mathrm{m}}^3{\mathrm{s}}^{-1}$, the same units as pumping speed.

For a pump of speed $S$ connected through a line of conductance $C$, a simple steady balance gives $1/S_{\mathrm{eff}}=1/S+1/C$. Thus a $100\mathrm{L}{\mathrm{s}}^{-1}$ pump behind a $10\mathrm{L}{\mathrm{s}}^{-1}$ connection supplies only about $9.1\mathrm{L}{\mathrm{s}}^{-1}$ at the chamber. Conductance depends on geometry, gas and flow regime; the pressure-independent molecular-flow value should not be used indiscriminately in viscous flow.^[ref]

A vacuum pump lowers gas pressure by removing gas from a vessel or trapping it so that it no longer contributes to the free gas population. Mechanical displacement, momentum transfer and capture are distinct operating mechanisms.

Its relevant performance includes pumping speed, attainable pressure and gas dependence. The pressure achieved in an apparatus also depends on connecting vacuum conductance, leaks and outgassing; the pump's advertised limit is therefore not a complete system specification.^[ref]

Vacuum technology creates, measures and maintains gas pressures below the surroundings for experiments and manufacturing. Pumps remove gas while leaks, permeation and outgassing replenish it. Clean surfaces and appropriate materials can therefore matter as much as nominal pump capacity.

In a simple steady model, a gas throughput $Q$ balanced by effective pumping speed $S_{\mathrm{eff}}$ gives $p=Q/S_{\mathrm{eff}}$. Connecting pipes reduce that speed through their vacuum conductance. The model assumes a specified gas, flow regime and suitable pressure-gauge interpretation; a pressure reading is not automatically a composition-independent measurement of every residual species.^[ref]