Simulations of guiding of low-energy ions through a single nanocapillary in insulating materials

Abstract

Simulations of guiding of low-energy ions through a single nanocapillary in insulating polymers are reported. The nanocapillary has a diameter of 100 nm and a length of 10 µm. Different from previous work, in our simulations a hyperbolic function is used to describe the decay of the charges deposited on the capillary surface. The present simulations reproduce the self-organized charge-up process occurring in the capillary. It is shown that lower-energy ions undergo more oscillations to get guiding equilibrium than those of higher-energy ions, resulting in a longer charging time, which is in good agreement with previous experimental results. Moreover, the experimentally observed mass independence of ion guiding is proved in our simulations. In particular, it is found that the maximum of the repulsive field within the capillary is independent of the ion energy as well as the tilt angle. To counterbalance the increasing of the transversal energy caused by increasing the tilt angle or incident energy, the effective length of the repulsive field is expanded in a self-organizing manner.

Simulations of Ion-Guiding Through Insulating Nanocapillaries of Varying Diameter: Interpretation of Experimental Results

“…Hence, the lowest drift mobility of 0.001 nm 2 /V•s will also be tested in simulations for the capillaries with diameters of 200 and 400 nm. It should be noted that the mobilities used here and previously in [43,45] are rather small in comparison with the values given in the literature [56][57][58], which suggests further studies. Figure 9 presents results for 400 nm capillaries again using the three mobility values from Table 3.…”

“…In pioneering simulations [39][40][41] a diffusion model was used wherein the deposited charges perform a random walk along the surface and inside the bulk of the capillary. As diffusion is a relatively weak process [42], a different concept was adopted in capillary guiding simulations [43][44][45] involving a non-linear (exponential) charge drift approach, which is based on the model of Frenkel [46]. Moreover, ion-guiding was treated rather accurately by means of solving the continuity equations for the conducted charges [47,48].…”

Simulations of transmission of 1 MeV protons through an insulating macrocapillary

“…More importantly, in this work the transmission of 1 MeV protons caused by the atomic scatterings with atoms in the capillary bulk is taken into account as well as by the guiding due to charge-patch deflections. The trajectories of protons entering the capillary were calculated by solving Newton's equation of motion, as used often previously [13,14,22,23,32]. If a proton hits the capillary wall it would be scattered due to collisions with the capillary atoms, which would lead to an energy loss and to a change in direction.…”

“…The key of the model is the charge patch formed by ions deposited at the capillary surface, which is governed by the dynamical equilibrium between the charge deposition and the discharge via the material conductivity. The simulations [13,14] reveal that the extension of the charge patch along the capillary axis is of great importance in successful guiding.…”

“…For keV ions with nano-or macro-capillaries, a so-called guiding effect was observed that ions can pass through the capillaries tilted by a relatively large angle, keeping their initial energy and charge state [1,2] (and references therein). This guiding effect has been interpreted by the self-organized charge-up model, which was continuously improved by various experimental results [3][4][5][6][7][8][9] and theoretical calculations [10][11][12][13][14][15]. The key of the model is the charge patch formed by ions deposited at the capillary surface, which is governed by the dynamical equilibrium between the charge deposition and the discharge via the material conductivity.…”