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242 MEMS and Microstructures in Aerospace Applications

With the radius of curvature of such a cone being approximately 10 –7 m and the
electrodes being 1 mm apart, voltages of the order of kilovolts are sufficient to obtain
the necessary high electric fields. Applying voltages of few kilovolts (5–7 kV) results
in ion currents of 10–100 mA from a single needle source with low energy spread.
The thrust can be calculated directly (for Gallium) from the following equa-
tions:
T ¼ _ mmv (11:12)

m Ga
_ m m ¼ I E (11:13)
e
r ffiffiffiffiffiffiffiffi
eV
v ¼ (11:14)
m Ga
r ffiffiffiffiffiffiffiffi
m Ga p ffiffiffiffi
) T ¼ I E V (11:15)
e
where
T ¼ thrust (N),
m ˙ ¼ mass flow (kg/sec),
v ¼ velocity (m/sec),
I E ¼ emission current (A),
V ¼ extraction voltage (V),
e ¼ 1.6 10 –19 C, and
m Ga ¼ 1.16 10 –25 kg

While this calculation does not account for the beam spread it will nevertheless
result in a close (80%) estimate of the thrust produced. Small thrust noise and very
stable operation are characteristics of this propulsion system. High mass efficien-
cies for FEEP thrusters can be obtained at small extraction currents on the order of a
few microamperes. At higher extraction voltages, which translate into higher
currents, droplets and clusters are formed, which obtain significantly smaller
exhaust velocities and, therefore, lead to lower system efficiency.

11.2.3.2 System Requirements
The FEEP thruster is a very capable low-thrust, low-noise system. Reported
efficiency and thrust-to-power ratios are high and the possibility of MEMS-produced
ion sources exist. These MEMS structures are based on the usage of a large number of
emission sites. First concepts have been evaluated using microtips immersed in liquid
metal as emission sites as shown in Figure 11.9. Another approach involves the use of
small tubes that lead the liquid metal with the help of capillary forces from a bulk
reservoir to the emission site. Highly accurate manufacturing is necessary as small
geometrical differences result in the formation of so-called hot spots, where individ-
ual pixels attract the majority of the emission current, which can lead to unwanted

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