Einzel lens

It consists of three or more sets of cylindrical or rectangular apertures or tubes in series along an axis.

The electrostatic potential in the lens is symmetric, so the ions will regain their initial energy on exiting the lens, although the velocity of the outer particles will be altered such that they converge on to the axis.

The equation for the change in radial velocity for a particle as it passes between any pair of cylinders in the lens is:

with z axis passing through the middle of the lens, and r being the direction normal to z.

If the lens is constructed with cylindrical electrodes, the field is symmetrical around z.

Solving the equation above twice to find the change in radial velocity for each pair of plates can be used to calculate the focal length of the lens.

The einzel lens principle in a simplified form was also used as a focusing mechanism in display and television cathode ray tubes,[3][4] and has the advantage of providing a good sharply focused spot throughout the useful life of the tube's electron gun, with minimal or no readjustment needed (many monochrome TVs did not have or need focus controls), although in high-resolution monochrome displays and all colour CRT displays a (technician-adjustable) focus potentiometer control is provided.

Implementation of an einzel lens showing the ion path. Six plates are parallel to the ion flight path with the middle plate at a particular potential.
A perspective view of an einzel lens.
Path of ions as they travel through an einzel lens. The ion mass is 200 k Da accelerated to 40 kV, the middle plate potential is at 200 V, and the plate size is 1 m (note that these values are atypical for illustrative purposes).