This article demonstrates the einzel lens simulation distributed with SIMION.
The purpose of an einzel lens is to focus ions. Focusing is achieved with an electrical field whose potential energy surface resembles a saddle. Within certain bounds, a single einzel lens can focus both positive and negative ions flying through it.
Shown below in 3D and XY views, the einzel lens consists of three concentric ring electrodes: two outer rings typically held at ground potential and center rings held at a dissimilar voltage (positive or negative with respect to the outer electrodes). In this example, the center electrode is at +110V, and the outer electrodes are at ground. A group of positive ions are flown into the lens at initial parallel trajectories, subsequently bending toward a focal point.
The focusing effect is demonstrated in the following potential energy map. Note how the potential valley near the exit causes ions to "roll" inward--to use a physical analogy.
If we fast adjust (i.e. scale) the potential on the middle electrode to a higher value (+150V), the focus point comes closer to the lens. By taking advantage of superposition, scaling of the potential on an electrode is quick and does not require the field be recomputed from scratch (via the Laplace equation and other methods).
In fact, we can make the middle electrode negative (-210V) and still achieve a focusing effect.
Below we demonstrate one of SIMION's charge repulsion estimation methods. By enabling beam repulsion with a beam current of 1.0E-7 A, the ions tend to repel each other and avoid focusing.