Stabilizing the ion-beam transmission through tapered glass capillaries

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 how 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%.

Figure 1

Profile of the inner and outer glass-vacuum interfaces of the capillary. Black solid lines stand for the grounded conducting electrodes. $R_b=0.4\mathrm{mm}$ is the radius of the hole in the grounded collimator plate in front of the capillary. Setup INS and GND differ by the 3 mm short grounded electrode that covers the tip (circled) and which is absent in setup INS.

Figure 2

Ion trajectories (black) at three different moments, identified by the injected charge $Q$ or in brackets by the injection time ($Q/I_{\text{in}}$). Beam intensity is $I_{\text{in}}=1\mathrm{pA}$. Configuration INS was used and the profile of the inner surface of the capillary are shown in violet. Below each panel showing the trajectories, the electric potential, normalized with respect to the potential of the ion source $U_s$, is given.

Figure 3

Ion trajectories (black) after 6000 pC have been injected. Configuration GND was used and the profile of the inner surface of the capillary are shown in violet. Below we show the electric potential normalized with respect to the potential of the ion source $U_s$

Figure 4

Evolution of the transmitted fraction as a function of the injected charge for various beam intensities $I_{\text{in}}\in [0.05,1.8]\mathrm{pA}$. Injected beam emittance was ${\epsilon }_{\text{rms}}=0.36\mathrm{mm}\mathrm{mrad}$. Top panel used configuration INS and bottom panel configuration GND. Note the x-log scale.

Figure 5

(a) Evolution of the transmitted fraction as a function of the injected charge $Q$ for various beam intensities $I_{\text{in}}\in [1.6,2.6]\mathrm{pA}$. Configuration GND is used but with a grounded tip electrode which is 8 mm long. (b), (c) and (d) show the trajectories at different moments indicated by the injected charge $Q_{\text{in}}$, for the case $I_{\text{in}}=2.4\mathrm{pA}$.

Figure 6

Modeling of the beam emittance. Positions of projectiles are uniformly sampled on the source disk and emitted at a given angle, normally distributed. Trajectories that miss the entrance (red dotted arrow) are discarded. The green arrows are the trajectories that enter the capillary.

Figure 7

Evolution of the transmitted fraction as a function of the injected charge for various emittances $\epsilon \equiv {\epsilon }_{\text{rms}}\in [0.3,1.6]\mathrm{mmm}\mathrm{rad}$. The chosen configuration is shown in the top left corner. Intensity of the injected current was 1 pA.