  When an ion beam is injected into a tapered insulating capillary, the induced
self-organized radial Coulomb potential in the capillary is able to focus the
beam like an electrostatic lens. However, because of the continued accumulation
of charge in the capillary, an equilibrium is rarely attained and the injected
beam is eventually "Coulomb" blocked by the capillary's potential. We propose
an original add-on to the capillary setup, which can be tested experimentally
and which is expected to hinder the Coulomb blocking. We investigate
numerically the benefits and limits of the modified capillary setup. We show in
how far the intensity and emittance of the injected beam control the
transmission rate through conically tapered capillaries. Our results indicate
that the add-on succeeds to stabilize the asymptotic transmission rate for a
larger range of beam intensities and emittances, while reaching a near optimal
transmitted fraction up to 90%
