Charge deposition, redistribution, and decay properties of insulating surfaces obtained from guiding of low-energy ions through capillaries

We present a combined experimental and theoretical study of the transmission of single charged 1-keV Ar ions through a cylindrical glass capillary of macroscopic dimensions. From quantitative measurements of the incoming and transmitted ion currents, combined with a detailed analysis, the amount of beam entering the capillary was determined. This, combined with the measured transmitted currents, was used to determine the amount of charge deposited on the inner wall of the capillary which produces the guiding electric field. We show experimental results for fully, and partially, discharged conditions of the time evolution of the guided beam intensity following a wide range of times during which the capillary was allowed to discharge in order to provide information about the insulating surface charging and discharging rates. Combining our recent theoretical model describing the charge patch dynamics with these data, it is shown that the model is consistent with the experimental transmission curve data measured after the capillary was allowed to discharge for times ranging from 5 to 1000 s or longer and for injected currents that differed by a factor of 50. In contrast, models which do not include a dynamic rearrangement of charge along the surface prior to decay were found to be inconsistent with our experimental measurements. Additional data about the time dependences of the fraction of the injected beam which is transmitted as a function of injected beam current when transmission through the capillary is inhibited due to blocking are also presented. These data have a temporal dependence consistent with our model predictions that blocking occurs when the total capillary charge, i.e., the capillary potential, reaches a certain value.

Figure 1

Scheme of the patch area.

Figure 2

Simulated transmitted fraction of a 12-pA $\mathrm{A}{\mathrm{r}}^{+}$ beam through the 5° tilted capillary tube as a function of time. The green curve stands for the simulation without secondary electrons ($N_{\mathrm{SE}}=0$). The red and black curves stand for the simulations with, respectively, one and two secondary electrons emitted per ion impact.

Figure 3

Snapshots of $\mathrm{A}{\mathrm{r}}^{+}$ trajectories (black lines), projected on the $x$ axis, through the glass capillary at 4, 11, and 74 s after the beam is injected. The injected intensity was 12 pA and the beam was tilted by 5° with respect to the capillary axis. The horizontal black lines at $x=\pm 0.29$ mm show the inner capillary surfaces. Above and below the surface lines, the red curves show the intensity (arbitrary units) of the positive charge patches at the inner surfaces. Note that for $t=74$ s the amount of charge on the lower surface at the entrance is due to surface charge relaxation along the angular direction. The blue dashed lines are the trajectories of secondary electrons emitted from the impact point. Here we used $N_{\mathrm{SE}}=2$.

Figure 4

Schematic of the apparatus showing the input aperture, the capillary and holder, the transmitted beam collection, plus the various currents that are involved.

Figure 5

The measured capillary and holder (blue squares) and transmitted (red circles) currents, $I_{\mathrm{hold}}$ and $I_{\mathrm{trans}}$, as the capillary is scanned across the beam collimating aperture for an aligned and rotated capillary (left and right figures). The black x's show a straight line projection of $I_{\mathrm{hold}}$ measured at the offset positions which are approximately the beam current. The horizontal black bars show the amount of current entering the capillary, $I_{\mathrm{inject}}$, which is determined as described in the text. For the rotated capillary, measured values as the beam is scanned in opposite directions are shown.

Figure 6

Time dependences for the various capillary currents following a 20-min discharge time. Data are for 1-keV $\mathrm{A}{\mathrm{r}}^{+}$ ions and a capillary rotation of $5^{\circ }$. The measured quantities were $I_{\mathrm{hold}}^{\mathrm{centered}}$ and $I_{\mathrm{trans}}$, (the blue and red solid curves in the online version). From these, dashed lines show calculated values for the incoming current, approximately $I_{\mathrm{hold}}^{\mathrm{centered}}+I_{\mathrm{trans}}$; the current entering the capillary, $I_{\mathrm{inject}}$; and the current deposited as the beam transits the capillary, $I_{\mathrm{dep}}$. See text for details.

Figure 7

Time dependences of ion transmission through the capillary following different times during which the capillary discharges. Left, 12-pA injected beam; center, 0.26-pA injected beam; right, 0.17-pA estimated injected beam and reversed capillary where the entrance surface is an insulator.

Figure 8

The capillary charge, determined as described in the text, as a function of discharge time. The open stars are normalized values of $I_{\mathrm{trans}}$/$I_{\mathrm{inject}}$ measured just after the beam is reinjected after specific blocking times, a method used in Ref. [1]. The solid symbols are determined using Eq. (9), as described in the text. The solid curve is calculated using the parameters listed and the decay portion of Eq. (9).

Figure 9

The guided beam fraction as a function of charge-patch intensity. The data are from Fig. 7. The monopole-to-dipole ratio and surface-charge-decay lifetime parameters used in Eq. (9) to calculate the patch charge, i.e., the guiding charge, are (i) normal configuration: 0.26 pA, 15/85%, and 7 s; 12 pA, 2/98%, and 4.5 s; (ii) reversed configuration: 0.17 pA, 5/95%, and 7 s.

Figure 10

The probability of guiding for various injected currents large enough to result in blocking. In the left figure, the arrows and the question mark at the top indicate the approximate times when blocking occurs for injected currents of 40, 86, 49, 35, and 24 pA. The right figure shows the guiding efficiency vs the capillary voltage. See text for details.