ABSTRACT

In order to trace the path of a particle through a lens, we have to integrate the equation of motion and it is convenient and simple to work in terms of the Picht equation. We need to know the function T (z) to find the focal properties and we shall see later that we also need to know the axial derivative, T ′(z), if we wish to obtain information on the aberrations. The first stage in the calculation is the determination of the axial potential, from which, with its derivative, we construct T (z). We shall consider ways of generating the potential distribution for lenses with more than two electrodes later, but in the first instance we concentrate our attention on lenses having only two electrodes. If the electrode potentials are V1 and V2, we can express the axial potential in one of the forms

V (z) = 12 (V1 + V2)+ 12 (V2 − V1)+(z) = V1 + (V2 − V1),(z)

where +(z) and ,(z) are functions which range between∓1 and between 0 and 1 respectively as z→∓∞.