An electrostatic field that attracts ions toward a common centre—i.e., a radial field—will also exert a focusing action on a divergent beam of ions as shown in Figure 3. The radial force on the ions due to the electrostatic field will be Ez, the product of the field E and the ionic charge z, and is equal to the centripetal force mv²r, of mass m moving with velocity v about a radius r. Thus, one may write the equation

The radius of the arc traversed by the ions will be proportional to their kinetic energy, and an electric sector will thus produce an energy spectrum of the ions passing through it. Alternatively, if narrow collimating slits are placed at either end of the sector, a monoenergetic beam of ions can be selected.

Combined electric and magnetic field analysis

Use of an electric wedge or sector to obtain a monoenergetic beam of ions, which is then separated for mass analysis by a magnetic sector, is another possible technique. General equations for combined electric and magnetic sectors have been developed; they show that a suitable combination of fields will give direction focusing for an ion beam of given mass-to-charge ratio, even though the beam may be heterogeneous in energy. The term double focusing is used for those combinations in which the angular and velocity aberrations effectively cancel.

Two of the best examples of double-focusing mass spectroscopes, both of which have been used in a variety of commercial instruments, were built by Mattauch and Richard Herzog in West Germany and by the American physicist Alfred O. Nier and his collaborators. The Mattauch-Herzog geometry is shown in Figure 4. Ions of all masses focus along a line that coincides with the second magnetic field boundary. Many versions of this design have been used when high resolution (up to 10⁵) is desired for accurate mass and abundance measurements and general analytical work. It can give good spectra, even for a spread of 5 percent in energy of the ion beam, and can be used with virtually any ion source. The resolved ion beams can be recorded electrically or with a photographic plate.

Nier’s design is illustrated in Figure 5. In this instrument, Nier was able to achieve high sensitivity as well as high resolution. Using an electron-bombardment ion source, a resolving power of 2 × 10⁵ has been attained in a commercial instrument. The design has yielded mass measurements of the highest precision for a very large number of the isotopes, and it has also been the most popular design for high-resolution work in organic chemistry.

z-axis focusing

The form of focusing in the analyzers described above has assumed that the forces acting upon an ion lie entirely in the same plane, generally referred to as the x-y plane, with the y axis defining the direction of the beam. This is adequate for most applications in magnetic sector machines where the beam is ribbon-shaped and where slight deviations in velocity in the z direction, which is perpendicular to the principal plane, cause negligible beam loss. At the entrance and exit of a trajectory passing through a field produced by a magnet, the field is not parallel but rather is bowed out. As a consequence, an ion encounters a small, but not negligible, field component parallel to the x-y plane, which generates a correspondingly small force in the z direction. Magnets have been constructed that take advantage of such forces to focus the beam in the z direction. It is possible to make the x focus and z focus coincident. Focusing in the z direction is often accomplished electrostatically by a suitably arranged pair of electrodes in the ion source.

Time of flight

The simplest form of mass analysis that does not use magnetic fields depends on the differing speeds of ions with the same energy but different masses. The ion source is generally of the electron-impact type and has one or more electrodes modulated so as to extract ions for a time that is brief compared with the time it takes them to reach the detector. The ion velocities, as given above by v = Square root of√2zV/m, and the distance between source and detector allow the mass to be calculated directly. In practice, the response of the detector is displayed on a cathode-ray oscillograph and recorded by a computer. This method has two advantages: it is fast and, if desired, can display the entire mass spectrum. Its deficiencies are poor resolution, poor accuracy of signal, and poor efficiency, due to the short period during which ions are extracted from the source.