In this section, the measurements in the two sensor positions denoted in Fig. 5(a), i.e. beside the energetic ion beam and in the idling ion beam, are presented.
Outside the beam
In these experiments, RPA and LP measure outside the beam, i.e. in the position marked as “Pos. 1” in Fig. 5(a).
Plasma potential and ion energies
For the following measurements, the potential of the secondary plasma, from where the charge-exchange ions stem, is modified in a controlled way. The shift of the plasma potential is achieved by variations of the bias voltage of the cathode. In the test environment, the cathode is a 2.5 cm long 100- μm tungsten wire heated by a current of 1.7 A. The positive pole of the current supply is connected to a voltage supply, which allows biasing from −35 V to +35 V. The heated wire is placed 14 cm below the beam axis and 3.5 cm shifted laterally (toward “Pos. 1”) at a distance of 23 cm from the screen (see Fig. 5).
First, some examplary RPA data is shown before the combined use of both diagnostics will be presented. Figure 7 represents two measurements with the RPA for the bias voltages +10 V and +35 V.
In the current plots, Fig. 7 (a) and (b), one can clearly distinguish two regimes: First, the regime of higher collector currents for screen grid potentials some volts below a certain threshold, and, second, the regime of almost vanishing currents for potentials some volts above that respective threshold. The first derivatives, shown in Fig. 7 (c) and (d), can be interpreted as the ion energy distribution function (IEDF): The retarding potential in volts corresponds to the energy of the singly charged ions in eV. The most abundant energy is where the derivative peaks are. (Note that the first derivatives with the unit nA/V are a measure of the rate at which ions of a given energy interval impinge on a surface, i.e. ions per m2, s, and eV, which is different from the number density per energy interval in a volume element, i.e. ions per m3 and eV.)
One can clearly notice the shift of the curves on the discriminator voltage axis. The IEDFs exhibit narrow peaks, which indicates that the ions that reach the RPA are approximately monoenergetic. The energy of the ions shifts from 8.0 eV to 22.5 eV. We will gain a somewhat deeper understanding of the effect of the cathode bias when we come to the combined use of RPA, LP, and the additional cylindrical Langmuir probe.
First, however, we look at the raw characteristics obtained by the LP. The three characteristics in Fig. 8 result from cathode potentials of −10 V, +10 V and +35 V. For each curve, the “ ×” markers indicate the inflection point, which is taken as at the plasma potential, and the “ ∘” symbols mark the roots of the curves, i.e. the floating potentials. Note that the characteristics are shifted toward positive voltages for increasing cathode potentials, where the shift is notably less than the increase of the hot cathode potential. We will look into this correlation in more detail.
Figure 9(a) shows the plasma potential measurements with the two Langmuir probes. The cylindrical probe was placed at the other side of the beam at the same distance to the beam axis as the plasma sensor, i.e. 18 cm. Because of the symmetry of the chamber, we expect similar plasma conditions at the positions of both Langmuir probes, which is confirmed by the two data sets: Both probes measure nearly the same plasma potentials.
More interesting is the dependence of the plasma potential on the cathode bias voltage: For <0 V at the cathode, the plasma potential remains stable at (8.8±0.4) V. This means that the injected electrons, which fall from the negative hot filament potential into the attractive plasma, do not affect much its potential. The emitted electrons traverse the plasma and are absorbed by the walls: The hot filament and the walls act like a thermionic diode. In this case, plasma and filament can maintain different potentials. The situation changes for cathode potentials ≥0 V, at which the electrons are trapped in the chamber, because the electric field in the plasma sheaths reflects them. Now, the hot filament is “connected” to the plasma via the plasma electrons (not the thermionic electrons): The filament in the plasma resembles a second diode, whose forward direction is for positive filament voltages with respect to the plasma potential. In this regime, the plasma potential increases linearly with the cathode bias voltage with a slope of approximately 0.7 for both probes. Finally, the plasma sheath at the chamber walls acts as a diode, too: For shifted plasma potentials U below the undisturbed plasma potential, the electron current across the sheath increases exponentially with the potential shift (the current is proportional to the Boltzmann factor exp(eU/kBTe)). This effectively prevents plasma potentials from being shifted below approximately +8 V.
Figure 9(b) displays the ion energies obtained from the quasi-simultaneous RPA measurements. Here, the behavior is similar: The energy profile is roughly flat at (8.3±0.5) eV for the negative cathode bias voltages and linearly increasing with increasing positive cathode bias voltages (0.56 eV per V). However, the transition between the two regimes seems to be shifted by approximately 10 V in the positive direction. This could find an explanation in the different plasma potentials at the hot filament position and at the beam positions where the ions are created by charge-exchange collisions.
We learned from these preliminary experiments that the application of positively biased hot filaments is a simple and efficient method to shift the plasma potential in the beam and to rise the energies of the secondary ions. On a spacecraft, such potential shifts may occur unintentionally for various reasons [10].
Variation of the repeller grid voltages
These measurements aim at a correct or optimal choice of the RPA repeller voltages. The two repeller grids are driven by the same voltage supply and connected to each other in the sensor housing; a common wire in the harness connects them to the electronics box. Figure 10 shows IEDFs for the 1.2 keV Xe ion beam with the plasma sensor still in the position “Pos. 1” in Fig. 5(a). The following can be observed:
First, the determined peak ion energy (most abundant ion energy) only weakly depends on the repeller voltage; the peak energies remain within ±1 V about the energy determined with our default repeller voltage of −20 V. This is the most important result because the main purpose of the RPA is to determine the energy of the ions that return to the satellite.
Second, the peak heights and widths reach their maximum and minumum values, respectively, at a repeller voltage of only −15 V. The peak width saturates at its lowest half width (0.6 eV) for the repeller voltages from approximately −16 V to −8 V. The finding, that already moderate repeller voltages are sufficient for preventing the plasma electrons from passing through the outer repeller grid, reflects the fact that the electron temperatures are small under the given beam conditions, namely below 1 eV in Fig. 6(c). However, the capability of the hardware to change the repeller voltages can be used for an in-flight fine tuning of the RPA.
One has to keep in mind that the ion beam is not monoenergetic, so that the minimum measured widths of less than ±1 eV can be used as a conservative estimate of the resolution.
In the idling beam
In the following, the RPA is moved into the beam, where it is exposed to the primary ions from the ion source. However, as described in “The test environment: setup and methods”, the anode voltage of the ion source is 0 V, so that only the plasma potential in the source relative to ground potential accelerates the ions.
Two ion populations
The RPA is facing directly the ion source, but is laterally moved out of the central position “Pos. 2” marked in Fig. 5(a). The panel in Fig. 11 shows collector currents and resulting IEDFs for three different positions: on the beam axis, at the edge of the beam, i.e. 40 mm away from the axis, and 100 mm away from the axis. The current profiles exhibit three discriminator grid voltage regimes separated from each other by two negative flanks, one at a low energy below 10 eV and another one above 100 eV. The flanks result in IEDFs with two peaks. The two peaks mean two ion populations, one at (6.5±2.0) eV and one at (107±5) eV, which can clearly be distinguished since they have small widths compared to their distance. This double-humped ion energy distribution function can easily be understood: The population with higher energies are the primary ions from the “idling” ion source, and the population with lower energies are the secondary, charge-exchange generated ions.
Note that the primary ions are most abundant in the center, Fig. 11 (a) and (d), reduced to less than half of that value at the edge, (b) and (e), and only marginally represented outside the beam, (c) and (f). This reflects the beam profile, to which we come back in connection with the absolute calibration of the RPA. In contrast, the secondary ions approximately stay at the same rate; this seems to be a rather complicated result of the respective “drainage volume”, the volume from where the RPA collects these ions.
Directivity of the RPA
The following test assesses the directivity, or angle dependent sensitivity, of the RPA. The RPA is placed in the central position “Pos. 2” marked in Fig. 5(a), i.e. at the beam axis, where it is rotated up to approximately 25∘ in both directions.
Figure 12 shows the currents measured by the collector segments at the different angles of incidence for the low energy ion beam. Two major results can be extracted from the data. First, the sensitivity of the RPA decreases within 15∘ to less than one half. (The effect of the cosine of the angle is less than 4%.) Second, the outer collector segments are very sensitive to the angle of incidence. For example, the segment 3, which is oriented in the direction in that the spot on the collector plate is shifted, reaches its maximum current value at an impact angle of approximately −15∘. The other two segments point 60∘ upward and downward due to the trisection of the outer segments. Therefore, segments 1 and 2 reach their respective maxima already at smaller angles of incidence than +15∘. The up–down asymmetry between the segments 1 and 2 seems to be due to the broken symmetry of the setup in the vertical direction. For example, the translation stages and the cathode are in the lower half of the cylindrical chamber, while the upper half is essentially empty.
Calibration of the RPA
This test aims at a calibration of the RPA currents by means of an additional Faraday cup (see Fig. 5). The currents measured by the RPA are significantly smaller than the currents that arrive at the plane of the outer grid. A part of the ions and electrons ends at one of the four grids, and another small part, depending on the angle of incidence, reaches the collector plate beyond the collector segments.
Moreover, the trajectories not only depend on the ion energies and directions, but also on the current density [28]. Especially the ion population with energies corresponding to the descriminator grid potential slows down to very low speeds in the vicinity of the discriminator grid. Hence, the ion density increases there significantly, which can result in a high space charge and a local potential above the discriminator grid potential. At low ion current densities, as a result of lower plasma densities, the latter effect can be neglected. In conclusion, the measured currents and the derived absolute heights of the obtained IEDF are to be interpreted with caution. (Note that this warning does not refer to the measured ion energies, but to the absolute values.)
Nevertheless, the here described method provides a conversion factor that allows a rough estimate of the ion current density from the actually measured collector currents at vanishing discriminator potentials.
Figure 13(a) shows the total current at a discriminator grid voltage of 0 V as a black curve. In this case, all ions can, at least in principle, reach one of the collector segments. The red curve depicts the total current at a discriminator grid voltage of +40 V. In this case, only ions with kinetic energies that exceed 40 eV can pass through the discriminator grid. The difference between both, i.e. the ions with kinetic energies less than 40 eV, is plotted as the blue curve.
The ions with low energy (below 40 eV) exhibit only minor variations along the path at which the RPA was moved. This reflects the presence of charge-exchange ions at all these positions. In contrast, the ions with high energy (above 40 eV) are concentrated about the beam axis and vanish completely at a distance of 100 mm from the axis. Remember that the aperture of the screen has a radius of 40 mm. The width of the Gaussian best-fit curve for the total current is approximately 40 mm, too. The energetic ions can therefore be identified as the primary ions from the ion source.
The second part of the calibration method consists of Faraday cup measurements at the same positions where the RPA measured under the same conditions. To this end, the translation stage with the two diagnostics is moved twice through the beam, the first time with the RPA directed toward the beam, and a second time, on the way back, after a rotation by 45∘, with the Faraday cup directed toward the beam.
Figure 13(b) shows the resulting current densities. In case of the Faraday cup, we simply calculate the current density from the measured current and the cross section of its aperture. The profile resembles the total current measured by the RPA in that it has an inner Gaussian part for the radii up to 50 mm and a broader outer part. From the discussion of the RPA measurement, we conclude that the inner part is dominated by the energetic ions from the ion source and the outer part consists only of charge-exchange ions created in the plume.
The Gaussian best-fit curve for the Faraday cup data results in a width of approximately 50 mm. This is one quarter broader than in case of the RPA. The reason could be found in the much greater acceptance angle of the Faraday cup. At radii somewhat larger than 40 mm, which is the core radius of the beam cylinder, there are still beam ions due to the beam divergence, which we assume for an ion energy of 1.2 keV in the order of magnitude of a few degrees, probably less than 10∘ [24, 29]. These oblique energetic beam ions fully contribute to the current measured by the Faraday cup, but they are significantly attenuated by the ion optics in the RPA.
Therefore, such a calibration of the RPA currents makes only sense for perpendicularly incident ions and vanishing discriminator voltages. Taking the peak values of 0.33 μA for the RPA and 2.5 μA cm −2 for the Faraday cup at the beam axis, we obtain a calibration constant of 7.6 cm −2. Multiplying the RPA currents for a discriminator voltage of 0 V and assuming merely perpendicular incidence yields a rough estimate of the current density.
We repeated this measurement with Ar instead of Xe and found the same calibration constant of 7.6 cm −2.