In the discussion of the experimental observations we want to focus on the five following aspects:
- The successful transmission of electrons through all capillary configurations.
- The observed time delay before the start of the transmission
- Blocking of capillary after long-time transmission
- Stable transmission in on-off tests
- Visual observability of guiding process due to cathodoluminescence.
Electron transmission through all four capillary configurations was achieved in all tests with a particle energy of approximately 15 keV. This value was determined from preliminary tests. Other parameters varied: For example the currents that were injected into the capillaries varied from 3.3 µA to 20 µA and the transmission efficiency was found to be between 73% to nearly 100%. Due to a lack of a device to measure the particle energy of the transmitted electrons, it is not possible to clearly define if the particles were transported through the dielectric tubes primarily be elastic scattering, inelastic scattering or the guiding from assembled negative charge patches. Future tests will have to show if there is a minimum kinetic energy for the transmission process.
The irradiation of the capillaries showed a significant time delay before efficient guiding was achieved. One exception was the 270° capillary which was irradiated with two different beam configurations before the current was transmitted. Therefore, no exact charge up phase could be determined for this sample. The time delay before high transmission might be a clear indicator for the build-up of negative charges on the inner capillary surface assisting the electron guiding process. The build-up of a charge distribution leads to the deflection of further incoming particles towards the capillary exit. A long-term test with the 90° capillary showed a stable electron transport over the course of 2.5 hours. An interruption of the electron transport lead to a sudden breakdown of the transmitted current from over 90% to only 15% (see Figure 2). We considered possible blocking effects that might have disturbed the guiding process due to overcharging as well as sudden discharges of a negative patch within the borosilicate glass capillary as observed in . The scenario of electron transmission after a quiet period has been observed in 5,6, where electrons were guided through PET nanocapillaries. However, the current densities were much smaller compared with our experiments. Furthermore, Petukhov et al. 9 mentioned no time delay for the transmission of currents through capillaries with 90° and 180°. The filament electron gun in our experiment is a source of uncertainty. A variable focus was achieved by means of the negative voltage offset created by a pre-resistor of the Wehnelt cylinder. The aperture electrode in front of the capillary inlet provides an additional collimation. But it is unclear, if the local beam current density and beam alignment were similar in all experiments and stable with time. The focus of the electron source could only be significantly changed by changing the pre-resistor, which prevented a dynamic adaption of the focus without switching the source on and off in between.
The current transmitted through the 180° sample showed a more stable behaviour and the quiet period was shorter than for the 90° capillary. It has to be noted, that in this test a much lower current and also a lower current density was injected into the capillary due to misalignment in the setup. These factors appear to have a strong influence on the guiding performance, as the following 270° test showed. Here a focused beam could not be transmitted, whereas an injection with lower current density lead to guiding. This shows that the charge distribution inside macroscopic capillaries also depends on a number of beam parameters e.g. the current density, the angle of injection and the beam divergence which affect the charge distribution on the inner capillary walls.
While a quiet period followed by an instant transmission phase was observed in the 90° and 180° samples, the data of the 360° helix capillary test show an intermediate phase in which the transmission was accompanied by strong noise. This is most likely the phase in which the transmission varies as a result of the dynamic evolution of additional negative charge patches. During the equilibrium the transmission efficiency was at around 74%, which is much lower compared to the previous samples. This might be attributed to the greater capillary length and higher aspect ratio as well as the larger bending angle but has to be examined in further studies.
An overview of parameters used in the presented tests are given in Table 2. A counterintuitive but notable factor is that the duration of the quiet period seems to scale disproportionately with the curve angle. In case of the 360°, the time delay before a significant transmission occurred was only 5 minutes, while for the 90° capillary it was four times the duration. A possible reason for the longer quiet phase inside the shorter capillary might be the usage of a narrow beam whereas a broader beam was injected into the helical capillary. However, a lot of additional work is required to investigate the influence of varying parameters on the guiding performance.
Preliminary on-off tests to investigate the durability of the capillary state were carried out. An example of the corresponding data is displayed in Figure 4 for the 180° capillary. No influence on the guiding performance was observed which indicates that the equilibrium state inside the capillary remained stable to some extent. This was not surprising as the discharge times in highly insulating materials are very high and can even reach days 10.
Furthermore, a blueish glow of the capillaries could be observed in the course of all tests. This is most likely attributed to the cathodoluminescence of glass where impacting electrons lead to the creation of electron-hole pairs in the material which subsequently recombine and emit photons in the visible spectrum 11. Throughout the tests, we were able to observe different glow states which appear to correlate with the electron transport. The 90° capillary and the 360° capillary were chosen for a detailed investigation of this phenomenon. Although the bright patches at the inlet and curved parts of the capillaries could be observed with the naked eye, the photos were taken with high exposure times, which made the glow pattern in the capillaries better visible. An f-number of F/3.5, a shutter speed of 30 s and an ISO value of 100 were used. As far as we know, there are no studies concerning an optical observation of the electron guiding effect yet. In Figure 7 different glow states of the earlier mentioned 90° capillary test are displayed for certain moments after the irradiation was started.
Figure 7a shows the general setup for the 90° capillary as explained earlier including the target, the backflow electrode, the aperture and the electron gun. A narrow beam was injected into the capillary with a primary particle energy of 14.8 keV. In Figure 7b the transmission process in subdivided into different guiding stages. The initial glow state of the capillary during the first 10 minutes is depicted in Figure 7-I. It can be seen, that the whole straight section and a part of the curved section is glowing. A clear and more intense blue spot is visible at the start of the curvature, as this is the region where most of the electrons are likely to impact the capillary wall. This spot disappeared during the next minutes, as depicted in Figure 7-II. Although two smaller spots are visible, the straight entrance section and the beginning of the curvature glow mostly uniformly. This state occurred around 3 minutes before more efficient electron transmission started. The evenly glow might be attributed to the charge up of the capillary, which lead to a more uniform distribution of impacting electrons on the capillary wall. Figure 7-III displays the exciting moment when the transmission efficiency instantly rose and electron guiding occurred. The glow inside the capillary surprisingly reduced almost instantly to an intense glow only at the start of the capillary entrance with an additional very weak spot in the region where the curvature starts. This observation strongly indicates a transport of the particles through the glass capillary nearly without direct particle-wall interaction. This state remained mostly unchanged until the electron transport was interrupted. Right afterwards the glow state was very similar to the one at the beginning of the test with an intense blue spot at the curvature (Figure 7-IV). This appearance slowly reduced into a weaker uniform purple glow in the entrance section without any noticeable spots, as displayed in Figure 7-V. This might correspond to the mentioned blocking state, in which an overcharged capillary hinders further electron transport through the capillary. Afterwards, in this experimental configuration the electron transmission remained low at about 15%. Additional tests in which the primary energy of the injected electron beam was varied, showed a correlation between particle energy and intensity of the emitted light, while the colour remained seemingly unchanged. Hence, additional work is required to examine the reason for the change in colour after the guiding process collapsed.
The 360° capillary was mounted in a way that every section could be observed, as depicted in Figure 8. Before guiding was achieved, a blue glow at the entrance section and the start of the curvature was visible (see Figure 8-I). Unlike in the 90° capillary, there was no intense spot in the bent part of the helix. Instead, the highest intensity was visible at the inlet region of the capillary, which is most likely attributed to the fact that a broadened beam was injected as explained earlier. Figure 8-II shows the change of the visible light formation, when electron transport was achieved at the 5-minute mark. While the intensity in the straight section was strongly reduced, the whole capillary glowed very weakly and evenly, which may be due to low energetic particle wall interactions. While the electron transport was somewhat stable at the beginning, it was accompanied by a growing noise during the next minutes. The strong noise in the current measurements indicated a dynamic evolution of additional negative charge patches before reaching equilibrium. In this stage the entrance region still glowed blue and multiple purple spots slowly formed visibly at different regions in the capillary which could be an optical indicator for the charge distribution. These spots were visible in the first 270 degrees of the capillary while there was no noticeable glow in the last quarter section. The blue glow at the outlet is most likely the reflection of the light in the inlet. When transmission reached equilibrium after around 42 minutes, the spot formation remained mostly unchanged. Figure 8-III shows a picture of the capillary during equilibrium.