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Brittany Albrandt, Donny Newsom
Colorado State University
The NASA Origins Program, which seeks an understanding of the origin of the universe,
requires deep space (interstellar) exploration. The Interstellar Probe Mission is a part of this
program, which will require delivery of a spacecraft to a location 250 astronomical units from the
Earth in 10 years. One mission scenario would involve launch around 2007 and subsequent
interstellar travel sustained by a Nuclear Electric Propulsion (NEP) package. The NEP scheme
involves the production of electrical power from a nuclear heat source and consumption of the
power in one or more ion thrusters. This paper will describe ion thruster operation and explain
why NEP with ion thrusters yields performance superior to that of conventional chemical
thrusters in this application. The selection of krypton propellant and an ion acceleration voltage
of 13 kV will be justified. Detailed numerical analyses will be presented that show the
trajectories of ions as they are extracted through electrodes (the ion optics) and accelerated to the
high exhaust velocities (high specific impulses) at which the thrusters must operate to perform
this mission efficiently. Results obtained from these analyses will be used to define the ion optics
geometry that will assure proper thruster operation over the full 10-year mission lifetime and
spacecraft acceleration to the desired terminal velocity of the probe.
The origins program seeks to answer two enduring questions. Where do we come from?
Are we alone? “NASA’s Origins Program has a goal (by ~ 2040) of imaging and remote sensing
the potentially Earth-like planets around other stars out to approximately 40 light years.” i The
program is based on a family of missions. These missions include some ground-based
observatories and some spaced-based observatories. The spaced-based observatories are broken
up into four groups of missions; Precursor missions, First-generation mission, Second-generation
mission, and Third-generation mission. The early missions are designed to determine which
planets have the capability of sustaining life. Subsequent missions are designed to study these
planets in greater detail. An example of one of the first precursor missions was the Hubble Space
Telescope (HST). The Interstellar Probe mission, expected to launch in 2007, is designed to
travel to a distance of 250 astronomical units in 10 years. An astronomical unit is defined as the
mean distance between the sun and the earth, which is 1.496x1011m. The goals of the Interstellar
Probe are to examine the characteristics of some of these planets while developing the technology
for later missions.
Some options for propulsion systems include nuclear electric propulsion and chemical
rockets. NEP involves an electric power generator powered by a nuclear fission heat source.
Thrust is produced by acceleration of ions through the device. An examination of chemical
propulsion system versus a NEP system follows. The basis of this analysis is Equation (1).
 Vvelocity 
mi  m f exp 
 Ue 
Where mi is the initial mass of the rocket, including propellant (kg); mf is the final mass
of the system (kg); Vvelocity is the change in spacecraft velocity (m/s) required to
accomplish the mission; and Ue is the exit velocity of the propellant (m/s). The law of
conservation of energy, expressed as Equation (2), can determine the exit velocity for the
NEP propellant:
Vvoltage * q 
* m *U e
Where Vvoltage is the difference in voltage through which a positively charged propellant
ion is accelerated through (V); q is the charge of an ion (C); m is the mass of the
propellant ion (kg); and Ue is the exit velocity (m/s). Solving the above equation for Ue:
Ue 
2 * Vvoltage * q
For example, if the discharge chamber is charged to 13,000V and krypton (atomic weight
= 83.8) is used for the propellant, the average exit velocity of an ion would be:
Ue 
2 *13000V *1.61  10 19 C
83.8 *1.66  10 27 kg
Ue  180,000m/s
This result assumes that all of the propellant atoms are ionized and then accelerated to
produce thrust. Laboratory work has shown that not all atoms are ionized to contribute to
the thrust. The true mean exit velocity, as a consequence, is reduced. In the present case,
this means the true exit velocity is expected to be 140,000 m/s. Equation (2) also
demonstrates why krypton, and not xenon, is the propellant of choice for this mission. In
order to achieve the same exit velocity (180,000m/s) for xenon (atomic weight = 131),
the voltage must be larger than 13,000V. Thus, krypton was chosen to obtain lower
voltages that present less challenging design issues. It also should be noted that the
Vvelocity term is different for the ion thruster and the chemical rocket. One of the main
differences between a chemical rocket and an ion thruster is that a chemical rocket thrusts
intensely for a short amount of time, where as an ion thruster thrusts continually at low
level for the duration of the mission. Figure 1 shows a typical velocity distribution for a
chemical rocket and ion thruster.
Figure 1. Velocity vs. Time for Chemical Rocket & Ion Thruster
For the chemical rocket, the average Vvelocity can be approximated by equation (3).
Vvelovity _ avg 
Where Vavg is the average change in velocity (m/s) for a chemical rocket; s is the
distance traveled (m); and t is the mission duration (thruster time) (s). For a typical
chemical rocket, traveling a distance of 250AU at a constant velocity:
Vchemical 
250 AU * (1.496  1011 m / AU )
10 yr * (365d / y ) * (86400s / d )
Vchemical = 1.19x105 m/s
Using this value in equation (1) and assuming a final mass of 1,000 kg and an exhaust
velocity (for a typical chemical rocket) of 4,000 m/s:
 1.19  105 m / s 
mi  1000kg * exp 
 4000m / s 
mi = 8x1015 kg
Nearly all of this initial mass is propellant required to produce the needed thrust. This
mass is so great that it makes the mission impractical.
The NEP system thrusts throughout the entire mission and must still realize the
same average velocity as the chemical system. The Vvelocity value for the NEP becomes:
VNEP = 2Vchemcial
Using the V found for the chemical rocket:
VNEP = 2*1.19x105 m/s
VNEP = 2.38x105 m/s
The initial required mass can then be calculated by assuming a final mass of 1,000 kg
payload, a 9,000 kg mass for the nuclear power plant, and an exit velocity of 140,000
m/s, Equation (1) becomes:
 2.38  105 m / s 
mi  10000kg * exp 
 140000m / s 
mi = 50,000 kg
This comparison clearly shows the benefits of NEP. For a mission to 250AU, chemical
propulsion is not a viable option due to the excessive propellant mass required to
accelerate the payload. The initial mass for the nuclear electric propulsion is a reasonable
amount of mass.
Figure 2. Schematic of Typical Ion Thruster
The operation of an ion thruster is a fairly simple process that involves simple
electrostatic forces. Propellant, typically xenon or krypton, enters the ionization
chamber. Inside the chamber, the propellant is bombarded by energetic particles to form
positively charged ions. Both the screen grid and the acceleration grid are made up of
thousands of small, round holes. As the positive ions are accelerated through the grids by
the potential difference between the two electrodes, a thrust is produced. The ionization
chamber is typically charged to some large positive voltage. For the Interstellar Probe
Mission, the chamber and the screen grid are charged to approximately 13,000V. The
positively charged ions, or discharge plasma, are then accelerated out of the chamber and
through the screen grid and the acceleration grid. Negatively charged electrons produced
from each ionization event are collected at the anode and removed via a power supply to
the neutralizer. From there they are emitted into space at the same rate as the ions being
produced. The acceleration grid is sufficiently negative compared to the neutralizer and
discharge plasma to prevent electrons from being drawn upstream through the holes into
the discharge plasma.
A key performance indicator of a propulsion system is its specific impulse, or
thrust produced per unit of propellant consumption. The specific impulse is determined
from the mean exhaust velocity of the propellant (Ue) by the expression (5):
I sp 
Where g is the acceleration due to gravity (m/s2). For the case of the ion thruster where
the exhaust velocity is 140,000m/s then:
I sp 
140,00m / s
9.81m / s 2
Isp  14,000s
The higher the specific impulse of the ion thruster compared to that of the chemical
rocket (400s) indicates its more efficient performance.
Figure 3. Grid Schematic
Figure 3 shows a cross-section for one of the hole sets in grids. The upstream screen
grid, as well as the discharge chamber and plasma is charged to a potential of 13,000V.
The accelerator grid is charged to –500V. The diameter or the screen grid holes (ds),
diameter of the acceleration grid hole (da), thickness of the screen grid (ts), thickness of
the accelerator grid (ta), and the distance between grids (lg) must all be analyzed in order
to design an efficient thruster system.
A major design requirement is that the ion thruster grids must have a lifetime of
more than 10 years. The grids erode rapidly when ions strike them and sputter away the
grid materials. Figure 4 illustrates a one way in which this can occur.
Figure 4. Direct Impingement
Screen Grid
Accelerator Grid
Figure 4 shows a schematic of direct impingement. This phenomenon occurs when too
much current is forced through the acceleration grid holes. The schematic shows the
upper half on one grid hole. The lines represent trajectories of individual ions as they
traverse the length of the thruster. As the figure shows, ions collide and will erode the
grids over long mission durations. As the grid material erodes, small bits of material may
become dislodged and create a short between the grids. A second factor influencing the
lifespan of the grid is cross-over erosion, which is also a form of direct impingement.
Figure 5 shows this schematic:
Figure 5. Cross-Over Erosion
Screen Grid
Accelerator Grid
In this scenario, the ions impinging the accelerator grid originate from other half of the sheath.
This can also cause grid erosion. Figure 6 shows an optimized ion thruster without any form of
Figure 6. Ion Thruster
Screen Grid
Accelerator Grid
Another design criterion is the minimum voltage at the centerline of the grid must be –30V. This
negative voltage insures that the electrons from the neutralizer and downstream plasma do not
turn around and reenter the plasma chamber. Figure 7 shows these design criteria graphically.
Figure 7. Voltage Criteria
Where Vn is 13,000V and Vt is 500V. The minimum, labeled as “Potential Through Apertures,”
represents the design criteria of –30V.
Nuclear electric propulsion, although more effective than chemical propulsion for
interstellar missions, does have some political drawbacks. The ion thruster system is powered by
a nuclear reactor. Although the Soviet/Russian space programs have been using nuclear reactors
is space exploration for quite some time, nuclear power carries a stigmatism. Some people feel
that nuclear power is dangerous not only to human beings but also to the environment, both here
and in space. Also, nuclear power is strictly regulated in the United States. In order for a nuclear
reactor to be launched into space by the United States, the president must sign off on the nuclear
reactor prior to launch.
Considering all the geometry and design criteria an optimal design can be selected. For this case,
a potential of 13,000 volts for the plasma, accelerator grid voltage of –256 volts, and a centerline
voltage of –30, the optimal geometry is:
Grid Spacing 9 mm
Screen Hole Diameter 9mm
Acceleration Grid Hole 4mm
Acceleration Grid Thickness 4mm
Screen Grid Thickness 1.5mm
Hole-to-Hole Distance 9.5mm
Normalized Perviance per Hole 1-1.5
These results are based on laboratory tests performed in another undergraduate research study.
The designs tested were direct results of the analysis discussed in this paper.
Nuclear electric propulsion is the future of space exploration. It provides a more
effective propulsion system than traditional chemical systems. Careful analysis of the ion optics
leads to an optimized design for the Interstellar Probe Mission.
Patterson, M.J., R.F. Roman, and J.E. Foster. “AIAA 2000-3811: Ion Engine Development for
Interstellar Precursor Missions.” NASA Glenn Research Center: July 16-19, 2000.