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Micropropulsion Technologies 249

I B V B V B
h ¼ ¼
E
I B V B þ I D V D þ P 0 V B þ « B þ P 0
I B (11:21)
I D V D
« B ¼
I B
We can see from the following equation that the propellant utilization, h u ,is
directly proportional to the beam current, JB, and the total propellant mass flow
rate given by:

I B m i
h ¼ (11:22)
u
m T e
where m i is the mass of an ion and e is the charge of an electron. This relation does
not account for the effect of multiply charged ions, which may be neglected for first
order approximations and performance comparisons. An effective way of determin-
ing chamber performance is to plot the beam ion energy cost, versus the propellant
utilization efficiency. To assess the relative performance of multiple thruster con-
figurations, it is also important to compare their total efficiency values. The total
efficiency of an ion thruster may be expressed as:

T 2
h ¼
T
2m T P E
r ffiffiffiffiffiffiffiffiffiffi (11:23)
2eV B
where T ¼ m T h
u
m i
11.2.5.2 System Requirements
While in principle, the miniaturization of the ion engine is possible, there are some
problems that make the realization of a small system difficult. The chamber walls
are at anode potential, which implies that electrons that are emitted from the
cathode get lost to the chamber. In a very small chamber, the travel distance and
thus the travel time are decreased, which limit the possibility of the electrons
producing ions. One way of increasing travel time is to use magnets to insulate
the anode magnetically. The magnets, however, become a mass liability. As with all
ion thrusters, the positive ions that exit the thruster through the grids represent a
sufficient current of positive ions to the ambient environment. This will cause the
thruster and craft to quickly obtain an overall negative charge. As a result, a
neutralizer cathode has to be placed near or in the beam to emit electrons into the
positive ion beam. Although this will add additional mass, it is important to note
that this neutralization process creates a benign, uncharged exhaust, especially in
the case of noble-gas propellants such as xenon.
Care must be taken to ensure that electrical discharges do not occur across the
closely spaced acceleration grids. Such discharges could seriously damage the
thruster. A micro-ion thruster also requires the development of appropriately
sized power conditioning units and propellant feed system. Due to the high voltages

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