Focusing properties of a bounded cylindrical field

Numerical solution of motion equations has been used in the non-relativistic limit in order to determine the focussing properties of the cylindrical field between concentric cylinders of radii R₁, R₂ with two boundaries along the Z-axis, for charged particles entering the field parallel to the symmetry axis. The field is a solution of the Laplace equation ²U(R, Z)=0, with the boundary conditions as follows: U(R₁, Z)=U(R, 0)=U(R, L)=0, U(R₂, Z)=V. It was shown that this field can be used for the energy analysis with second order focussing.