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A hollow D-shaped electrode that shields a circulating ion from the accelerating electric field during one half-turn. Two opposed cyclotron dees provide two shielded regions separated by a gap; their electric potential difference alternates. The vacuum reduces collisions with residual gas. An ion source supplies particles near the center, and an extraction system directs an outer orbit toward a particle detector or target. Useful electric current depends on retaining particles near the median plane and delivering them to the outlet, as well as on increasing their kinetic energy.

An electrostatic accelerator gives a charged particle kinetic energy by taking it through a sustained electric potential difference. Its ion source, accelerating tube and target form a particularly direct chain: prepare a charge, let an electric field do work, and measure what arrives or what the target emits. A vacuum reduces collisions with gas before the beam reaches its target. The Cockcroft-Walton generator supplies the potential by accumulating electric charge on capacitors.

An ion source produces ions for a beam or another experiment. Ionization changes the charge state of an atom or molecule; an applied electric field can then extract charged particles into a transport region. The resulting particle beam depends on the ionization mechanism, extraction geometry and the distribution of initial positions and velocities.

One arrangement uses an electron beam to ionize a gas and an electrode voltage to extract the products. Surface ionization is another mechanism: suitable atoms can leave a hot surface as ions, as in the surface ionization detector. Producing an ion and identifying its species are separate operations, so a source may need downstream mass spectrometry or other selection when several charged species are present.

A mass spectrometer is an instrument that produces or receives ions, separates them according to mass-to-charge ratio, and records their signals. Its major functions are supplied by an ion source, a mass analyzer and a mass spectrometer detector. The result is a mass spectrum; interpreting a peak also requires knowing which ionic chemical species produced it.

The 1955 instrument described by W. C. Wiley and I. H. McLaren provides a concrete apparatus example. An ion source and accelerating fields launch ions into an evacuated drift region toward a collector. Arrival times separate mass-to-charge ratios; the paper analyses how initial positions and velocities broaden the recorded peaks, and uses a two-field ion-gun geometry to improve focusing.^[ref] This is one analyzer design, not a definition requiring every mass spectrometer to measure flight time.

For an ideal time-of-flight mass spectrometer, neglect initial speed and acceleration duration. Across an electric potential difference $U$, an ion of positive electric charge $q$ gains $qU=m{v}^2/2$. A field-free drift of length $L$ then givesIf one peak arrives at $40\mu \mathrm{s}$ and another at $44\mu \mathrm{s}$, identical acceleration and drift conditions imply a mass-to-charge ratio ratio $(44/40{)}^2=1.21$. It is a mass ratio only if the charge states are also equal. Peak position, width and intensity answer different questions: ionic identity, resolving ability and response-weighted abundance.

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]

A time-of-flight mass spectrometer is a mass spectrometer whose analyzer infers mass-to-charge ratio from ion arrival times. A simple arrangement uses an ion source, pulsed acceleration, a drift region under vacuum and a mass spectrometer detector. The 1955 Wiley–McLaren instrument connected such an apparatus to calculations of how initial position and velocity spread affect resolution.^[ref]

In an ideal drift, $t_{\mathrm{drift}}=L\sqrt{m/(2qU)}$ for flight length $L$, positive charge $q$ and accelerating electric potential difference $U$. Recorded arrival time can also include a time-of-flight timing offset $t_0$. A useful ideal instrument calibration model iswhere $x$ is the numerical mass-to-charge coordinate in a declared unit and $k$ absorbs the instrument geometry and unit conversion.

For original invented standards, let $x=25$ arrive at $12\mu \mathrm{s}$ and $x=100$ at $22\mu \mathrm{s}$. Since the square roots are 5 and 10, $k=2\mu \mathrm{s}$ and $t_0=2\mu \mathrm{s}$. An unknown arriving at $17\mu \mathrm{s}$ then has $x=((17-2)/2{)}^2=56.25$. Ignoring the offset and scaling from the first standard alone would instead give $25(17/12{)}^2\approx 50.17$. A timing offset becomes a mass-assignment error when omitted from the model.

Real peaks have finite widths. Space focusing and time-lag focusing address specified sources of that spread; neither is simply a longer wait before detection. Calibration standards, acquisition timing and focusing conditions therefore belong in the interpretation of a measured spectrum.