lens action in the magnetic field

When an electron passes through the magnetic field produced by the polepiece of a lens in the vertical direction (from above to below), the electron traveling at an off-axis position firstly undergoes Lamor rotation due to the horizontal components of the magnetic field. Then, the electron receives a converging force toward the optical axis due to a Lorentz force between the rotational velocity component of the electron and the vertical component of the magnetic field of the lens. The magnetic-field components, which yield the converging force proportional to  (angle between the electron beam and the optical axis), are used as the lens action. The strength of the lens action is controlled by the electric current applied to the coils producing the electro-magnetic-field.

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