Principle of an Electromagnetic Lens

A magnetic lens consists of a coil of copper wires inside the iron pole pieces. A current through the coils creates a magnetic field (symbolized by red lines) in the bore of the pole pieces. The rotationally symmetric magnetic field is inhomogeneous in such a way that it is weak in the center of the gap and becomes stronger close to the bore. Electrons close to the center are less strongly deflected than those passing the lens far from the axis. The overall effect is that a beam of parallel electrons is focused into a spot (so-called cross-over).

In a magnetic field, an electron experiences the Lorentz force F:

F = -e (E + v x B)
|F| = evBsin(v,B)

E: strength of electric field
B: strength of magnetic field
e/v: charge/velocity of electrons

The focusing effect of a magnetic lens therefore increases with the magnetic field B, which can be controlled via the current flowing through the coils. As it follows from the vector product, the resulting force F is perpendicular to v and to B. This leads to a helical trajectory of the electrons and to the magnetic rotation (image is rotated in respect of the object).

Comparison to light optics