Particle accelerators also use electric and magnetic fields to guide the particles being accelerated, but in many cases these fields are not static but dynamic frequently the current density in the particle beam is very high. These are not the only devices that depend on charged-particle optics, however. Subsequently, several commercial ventures were launched, and French, British, Dutch, Japanese, Swiss, American, Czechoslovakian, and Russian electron microscopes appeared on the market as well as the German instruments. Comparable work on the development of an electrostatic instrument was being done by the AEG Company. The latter was a direct descendant of the prototypes built by Max Knoll, Ernst Ruska, and Bodo von Borries from 1932 onwards. The fundamental equations and formulas of the subject were derived during the 1930s, with Walter Glaser and Otto Scherzer contributing many original ideas, and by the end of the decade the German Siemens Company had put the first commercial electron microscope with magnetic lenses on the market. The first approximate formula for the focal length was given by Busch in 1926вЂ“1927. The first experiments on electron diffraction were made in the 1920s, shortly after Louis de Broglie associated the notion of wavelength with particles, and in the same decade Hans Busch showed that the effect of a rotationally symmetric magnetic field acting on a beam of electrons traveling close to the symmetry axis could be described in optical terms. The mention of wavelength reminds us that their behavior is also governed by SchrГ¶dinger's equation, and the resulting description of the propagation of particle beams is needed to discuss the resolution of electron-optical instruments, notably electron microscopes, and indeed any physical effect involving charged particles in which the wavelength is not negligible.Д¬harged-particle optics is still a young subject. In these remarks, we have been regarding charged particles as classical particles, obeying Newton's laws. The other important field configuration is the analog of the glass prism here the axis is no longer straight but a plane curve, typically a circle, and such fields separate particles of different energy or wavelength just as glass prisms redistribute white light into a spectrum. If the fields are not rotationally symmetric but possess planes of symmetry or antisymmetry that intersect along the optic axis, they have an analog in toric lenses, for example the glass lenses in spectacles that correct astigmatism. Focusing can be described by cardinal elements, and the associated defects resemble the geometric and chromatic aberrations of the lenses used in light microscopes, telescopes, and other optical instruments.

If the fields are rotationally symmetric about an axis, for example, their effects are closely analogous to those of round glass lenses on light rays. It is then possible to describe the deviations of the particle motion by the fields in the familiar language of optics. There are many devices in which charged particles travel in a restricted zone in the neighborhood of a curve, or axis, which is frequently a straight line, and in the vast majority of these devices, the electric or magnetic fields exhibit some very simple symmetry. Hawkes, in Encyclopedia of Physical Science and Technology (Third Edition), 2003 I IntroductionД¬harged particles in motion are deflected by electric and magnetic fields, and their behavior is described either by the Lorentz equation, which is Newton's equation of motion modified to include any relativistic effects, or by SchrГ¶dinger's equation when spin is negligible.

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