Page "Electron beam welding" Paragraph 27

The focusing effect of a rotationally symmetrical magnetic field on the trajectory of electrons is the result of complicated influence of magnetic field on a moving electron.

This effect is a force proportional to the induction B of the field and electron velocity v. The vector product of the radial component of induction Br and axial component of velocity va is a force perpendicular to those vectors, making the electron to move around the axis.

Additional effect of this motion in the same magnetic field is another force F oriented radially to the axis, which is responsible for the focusing effect of the magnetic lens.

The resulting trajectory of electrons in magnetic lens is a curve similar to a helix.

In this context it should be mentioned that variations of focal length ( exciting current ) shall course a slight rotation of the beam cross-section.