Temperature control of ion guiding through insulating capillaries

Guiding of highly charged ions through tilted capillaries promises to develop into a tool to efficiently collimate and focus low-energy ion beams to sub-micrometer spot size. One control parameter to optimize guiding is the residual electrical conductivity of the insulating material. Its strong, nearly exponential temperature dependence is the key to transmission control and can be used to suppress transmission instabilities arising from flux fluctuations of incident ions which otherwise would lead to Coulomb blocking of the capillary. We demonstrate the strong dependence of transmission of Ar${}^{7+}$ ions through a single macroscopic glass capillary on temperature and ion flux. Results in the regime of dynamical equilibrium can be described by balance equations in the linear-response regime.

Figure 1

Schematic illustration of the electrical circuit for measuring the bulk conductivity (solid lines) as well as surface conductivity (dashed lines). The glass sample (blue, center) is covered on one side with a circular electrode (black, top). On the bottom side, a ring electrode (red, right and left) is surrounding a central circular electrode (green, center).

Figure 2

Time dependence of the measured bulk electrical conductivity ${\sigma }_b\left(t\right)$ (different symbols correspond to different applied voltages). The time $t=0$ corresponds to the time the voltage is turned on.

Figure 3

Temperature ($T$) dependence of the specific electrical conductivity of Duran glass. Triangle (square) symbols denote results for bulk (surface) conductivity measurements. Measurements in vacuum (filled symbols) are compared to corresponding measurements under ambient air (open symbols) conditions. For comparison bulk conductivity values for Pyrex (Type 7740 [33], another borosilicate glass) are shown as black circles (solid line).

Figure 4

Setup for guiding experiment. The ion beam impinges from the left. It hits the capillary entrance aperture or the reference aperture depending on the $z$ position of the manipulator. Behind the capillary heating unit, containing the sample, the beam is passing a set of vertical deflectors (for charge-state analysis). Approximately 18 cm behind the capillary, a position sensitive micro-channel-plate detector is mounted. Inset: geometry of macrocapillary.

Figure 5

Normalized transmission curves $I(\varphi ,T)$ for 4.5 keV Ar${}^{7+}$ ions guided through a glass capillary for different temperatures ranging from $-25{}^{\circ }$C to $75{}^{\circ }$C (248–348 K). The flux of the incident projectiles was kept constant at about 5000 counts on the PSD in the $\varphi =0^{\circ }$ direction. Gaussian fits through the data points are shown as solid lines. The shaded area indicates the geometric limit of transmission in the absence of guiding.

Figure 6

Center-of-gravity motion of an Ar${}^{7+}$ beam transmitted through a glass capillary at $T=35{}^{\circ }$C (left) and $T=-25{}^{\circ }$C (right). In both cases the capillary was tilted by $2^{\circ }$. The elapsed time is indicated by colors: from $t=0$ (blue) to $t=6000$ s (red).

Figure 7

Intensity of the 4.5 keV Ar${}^{7+}$ projectile ions transmitted through a single glass capillary at room temperature as a function of capillary tilt angle for different incident current densities $j_{\mathrm{in}}$. Gaussian fits through the data points (normalized to 1 in forward direction) are shown as solid lines. The hatched region indicates the geometric opening of the capillary. The incident current is normalized to the transmitted flux in forward direction ($\varphi =0^{\circ }$, no guiding) in units of kilocounts per second.

Figure 8

Relative transmission as a function of total charge in the capillary. Incoming projectiles have a kinetic energy of 1.5 keV (red diamonds), 2.5 keV (green circles), and 3.5 keV (blue triangles). The thin solid line is a fit of the data at 2.5 keV to Eq. (9) (cf. text). The incidence angle is $\varphi =2^{\circ }$, $T=25{}^{\circ }$C.

Figure 9

Transmission function $f$ visualized as the fraction of the entrance cross section of the capillary (diameter 200 nm) through which projectiles must enter to be transmitted (area labeled B) for the three charging values $Q_i(i=1,2,3)$ indicated in Fig. 8. Green (grey) dots indicate points within the entrance cross section from where trajectories of projectiles leading to transmission start. Light grey (area A): Projectiles hitting the capillary surface as the Coulomb force of the primary charge patch is not strong enough to deflect them along the capillary axis. Red (dark grey) dots (area C): Projectiles hitting the opposite capillary wall ($j_s$). (a) Transmission at the maximum of the transmission function ($Q_1$; cf. Fig. 8), (b) reduced transmission ($Q_2$, center), and (c) trajectories ending at the capillary wall finally blocking the transmission (charge $Q_3$, right).