Electron optics

Electron optics is a mathematical framework for the calculation of particle paths along given electrostatic or magnetostatic fields. The term optics is used because a charged particle beam can be manipulated using magnetic or electrostatic lenses in a similar fashion to the manipulation of a light beam with optical lenses.

Electron optics calculations are, besides other uses, needed for electron microscopes and are also crucial for the design of modern particle accelerators. In paraxial approximation, the calculations can be done using ray transfer matrix analysis.

Electrons are charged particles (point charges with rest mass). The electron also has an associated spin of + 1/2. While in motion an electron possesses kinetic energy, regardless of any imposed charge field—this could be achieved by accelerating electrons via a voltage differential into a screened "field-free" region, which initially imparts the energy required to accelerate the electron. Given sufficient voltage, the electron can be accelerated sufficiently fast to exhibit measurable relativistic effects, and the velocity must be accounted for relativistically. According to the wave particle duality, electrons can also be considered as wave propagations and therefore have associated wave properties such as wavelength, phase and amplitude.

With respect to electron optics, the nature of the electron as a charged particle causes electrons to interact with imposed electron fields, and their spin causes magnetic field interactions as well. These interactions form the fundamentals of electron optical theory.

...
Wikipedia