Ion-beam focusing by self-organized axis-symmetric potentials in insulating capillaries

In a combined theoretical and experimental study, we give evidence that the self-organized electric potential in tapered glass capillaries has the strength to focus a low-energy ion beam. Similar to Einzel lenses, the on-axis injected beam is focused by an axis-symmetric potential, generated by the charge accumulated in the insulating capillary. We argue that for capillaries with large aspect ratio, the mechanism responsible for the focusing in our experiment is different from the one shown in earlier experiments. We found that the potential inside the capillary had to reach about 70% of the extraction potential of the ion source in order to be strong enough to focus the beam through the capillary. With increasing injected current intensities, the transmitted current density is shown to increase up to a factor 10 with respect to the injected one. An original experimental setup is used to monitor the accumulated total charge in the capillary linking the latter to the transmitted fraction of the beam. This way, we can clearly identify the different stages of the transmission in real time, and in particular the Coulomb blocking, and explain why it occurred inevitable in this setup. The experimental data are corroborated by our simulations, which allow a valuable and comprehensive insight into the dynamics of the self-organized Coulomb potential. The latter controls the focusing effect and explains many features such as why the transmitted fraction increases with the injected intensity.