In this section, an experiment is performed in order to demonstrate the capability of the probe to measure forces as vectors. For this purpose, the force is generated in a vacuum chamber by a mixed Ar/Ar ^{+} beam that impinges at variable angles of incidence *α* at the probe target, see Fig. 6a [12].

The force probe is mounted on a turnable platform driven by a step motor with an angular resolution of *Δ**α*=1.8°. The cantilever coincides with the vertical rotational axis of the turnable platform, so that the target remains at the symmetry axis of the ion beam when the probe is rotated. The beam is provided by a broad-beam ion source with grid system [17, 26]. The distance from the beam source to the target is 88 cm. At this distance from the grid system of the broad-beam ion source (diameter 125 mm), inhomogeneities of the beam can be neglected (compare [11], where the target was bigger and the distance from the source was shorter).

The plasma in the ceramic source chamber, from where the ions are extracted, is generated by a 2.45 GHz electron cyclotron resonance microwave discharge at an Ar gas flow of 5 sccm. The potential of the source plasma is anchored by means of an anode at a potential of *U*_{a}=+1200 V in order to accelerate the extracted ions in the grid system, which separates the source chamber plasma at the high potential from the target chamber plasma at a low potential. The kinetic energy of the accelerated ions in the target chamber is therefore approximately *E*_{kin}=1.2 keV. A more detailed discussion of the kinetic energies in the beam can be found in [9].

The vacuum chamber is a stainless steel cylinder with an inner diameter of 65 cm and a length of 160 cm, see Fig. 6. The argon gas pressure in the target chamber is 2×10^{−2} Pa achieved by a turbo molecular pump (pumping speed 500 l s ^{−1}) in combination with a rotary vane pump (60 m^{3} h ^{−1}).

Each force measurement consists of a previous reference measurement when the beam is off and a subsequent main measurement during beam operation. Thereafter, the beam is switched off, and the displacement is measured again. The time series of such a measurement procedure for the two axes are displayed in Figs. 7a and b. The deflections of the two axes are unequal in Fig. 7a because of the oblique angle of incidence, which is *α*=45° in this case.

For the determination of the displacements in the three periods of time, the respective averages are calculated (the data closer than 0.2 s to the switching time points are excluded from the averaging). The average displacements are indicated in Figs. 7a and b by horizontal lines. The difference between the two averaged reference displacements is related to the repeatability of the individual measurement and is displayed as error bars in Fig. 8.

Figure 7c and d demonstrate the effect of the eddy current damping. In case of the removed damping system, an overshooting and subsequent persistant oscillations occur at every switching. The amplitude of the overshooting and the oscillations is comparable to the causal signal itself, i.e. the signal-to-noise ratio is here about unity.

In case of the time series shown in Fig. 7, the probe target is a copper foil, so that sputtering and a release of momentum together with the outgoing particles (repulsion) is to be expected. Consequently, the measured force is larger than the force that a perfectly absorbing and not sputtering material experiences. Carbon has a low sputtering yield and is therefore often used for beam dumps in test chambers. Moreover, the effective sputter yields can be reduced even more by means of an appropriate topography of the surface. Carbon fiber velvet (produced by the Energy Science Laboratories, Inc.) is such a material; it consists of approximately 2.2 mm long and 7 *μ*m thin carbon fibers that arise perpendicularly from a plane base. Figure 6b shows a scanning electron microscopy image of the fibers. The geometry, which resembles a brush with extremely thin bristles, allows the ions to enter deeply into the carbon fiber velvet. Consequently, sputtered carbon from one fiber is re-deposited at other fibers with high probability, and reflected ions likely undergo more than one contact with the fibers before they leave the material.

Now, measurements at variable angles of incidence *α* are performed with the copper foil and the carbon fiber velvet. Figure 8a shows the measured displacements *d*_{1}(*α*) and *d*_{2}(*α*) for the angles *α*=−10°⋯+100°, while Fig. 8b displays the forces *F*_{1}=*k* *d*_{1} and *F*_{2}=*k* *d*_{2} transformed into a more practical coordinate system: One component, *F*_{normal}, points along the inward directed target normal, and the other one, *F*_{in-plane}, is the projection of the force vector onto the target surface. The transformations of the components are

$$\begin{array}{@{}rcl@{}} \qquad & F_{\text{normal}} & = \sqrt{\frac{1}{2}} \, (F_{1} + F_{2}) \\ \text{and} \qquad & F_{\text{in-plane}} & = \sqrt{\frac{1}{2}} \, (F_{1} - F_{2}). \end{array} $$

(3)

Note the equality of the displacements, *d*_{1}=*d*_{2}, for the angle *α*=0°, and that the axes change roles when *α* changes its sign due to the symmetric setup (Fig. 8). For increasing oblique incidence angles *α*>10°, the flux onto the target becomes more and more reduced, and one could expect that the flux vanishes for extremely grazing incidence, *α*≈90°. However, due to the finite diameter of the ion source and the beam divergence, some beam particles strike the probe target even at *α*>90°. This explains the not vanishing deflections for *α*≥90°.

Before we discuss the difference between the two targets, we come back to the hypothetical case of a perfectly absorbing and not sputtering material. In this case, the beam particles transfer their entire momentum to the target, and no further momentum exchange occurs. The angle-of-incidence dependent two force components *F*_{1} and *F*_{2} can be described by the functions

$$\begin{array}{@{}rcl@{}} \qquad & F_{1}(\alpha) & = F_{0} \, \cos \alpha \, \cos (\alpha - 45^{\circ}) \\ \text{and} \qquad & F_{2}(\alpha) & = F_{0} \, \cos \alpha \, \cos (\alpha + 45^{\circ}), \end{array} $$

(4)

where *F*_{0} is the magnitude of the force vector at perpendicular incidence, i.e. \(F_{0} = \sqrt {{F_{1}^{2}}(0^{\circ}) + {F_{2}^{2}}(0^{\circ})}\). The Eqs. (4) account by their cos*α* terms for the reduced flux at oblique incidence and express by the second cosines the projection of the force vector onto the respective directions of the displacement sensors. These theoretical functions are plotted (as the corresponding displacements) in Fig. 8a, where the amplitude *F*_{0} was taken from the measurement with the carbon fiber velvet at perpendicular incidence (*α*=0°).

The measurements with the carbon fiber velvet roughly follow the model of pure beam absorption, the small deviations can be summarized in two observations: First, both force components vanish at *α*=90° according to the discussion above; and second, the measured force components tend to be slightly more positive than the theoretical ones. The latter can be attributed to an imperfectly inhibited sputtering that still causes additional repulsion directed at some angle into the target.

In case of the copper target, the deviations from the pure absorption case are much more pronounced. Most obviously, the forces (displacements) at perpendicular incidence (*α*=0°) are significantly, by 44%, enhanced. Moreover, the force measured by the second sensor does not vanish at *α*=45°, it rather has a magnitude of approximately 0.4 of the *F*_{2} value at *α*=0°. At this oblique angle of incidence, the second sensor is directed perpendicularly to the beam direction, so that the measured force can only be caused by particles that leave the target with momentum.

Finally, we introduce an optional component that becomes necessary for measurements in environments where it is not feasible to repeatedly switch the beam on and off for the reference measurements. For this purpose, a beam shutter can be placed directly in front of the probe target. The shutter shown in Fig. 6c consists basically of a blade iris that has a maximum aperture of 36 mm and can be closed completely. A small direct-current motor drives the blades for quick opening and closing. Measurements in the plume of a Hall thruster have recently been performed and are planned to be published soon.