A simple diagnostic for electron beams.

This sketch shows an elongated electron beam sweeping past a detector wire array. The current vs time depends on the shape and inclination of the electron beam. The problem is to find a convenient way to describe the beam so that the transport system can be tuned.

This can be fit with simple combinations of Error Functions:

Having a fitting function with a small number of parameters is a great aid in characterizing the beam's properties. This makes a consistent and iterative approach to an idealized condition much easier than merely having, for example, FWHM and amplitude as available measures.