Optimum transport in charged particle analysers

The optimum transport of charged particle beams in a device with some required constraints may be achieved by using the Lagrange multiplier technique. Applications to energy analysers and mass spectrometers are given to show that the maximum transport can be obtained by making a compromise between the semiangular aperture and the resolution slit width. An analyser having a higher order of residual spherical aberration gives larger transport at high resolution and thus is a more sensitive device. Matching the emittance of a source to the acceptance of a device is necessary for the entire optical path.