starship-design: Interplanetary Propulsion (was VASIMR)

["L. Clayton Parker" <lparker@cacaphony.net>]

The Grand Challenge: A New Plasma Thruster
Samuel A. Cohen and Michael A. Paluszek

Manned Mars mission. The top plot shows total vehicle mass including the
100,000-kilogram payload. The second plot shows the maneuver duration and
the bottom plot shows the thrust generated by the thruster. The minimum
mission duration is obtained with a specific impulse near 3000 seconds.
Other figures referenced in text can be found in the print version of
Launchspace Magazine.





Visionary leaders at NASA have set "Grand Challenge" goals for America's
space program. Among the ambitious candidate missions are comprehensive
explorations of the solar system and manned ventures to remote planets. For
these types of missions to be practicable, rocket engines are required to
have larger exhaust velocities, greater efficiencies and more reliability
than those currently available. A novel plasma thruster design offers great
promise for providing these revolutionary advances in propulsion technology.
Advanced electric propulsion systems, both ion and plasma thrusters, have
been developed over recent years because of their high propellant exhaust
velocity, ue. The presently available high-ue systems, however, produce too
low a thrust for many of the Grand Challenge missions. Here, we describe
technical features that make a new plasma thruster design a revolutionary
step beyond the existing systems and able to provide a propulsion method
scaleable to more demanding Grand Challenge missions.

The primary innovative technical features are the wave-heating mode,
thrust-generation mechanism and the technique for decoupling the exhaust
plume from the engine. These are predicted to result in more than an
order-of-magnitude increase in thrust, while also significantly extending
specific impulse, Isp = ue /g (where g is the gravitational acceleration,
9.8 m2/s), thruster life and reliability.

Electromagnetic waves heat a fully ionized gas that is confined by a
super-conducting magnetic coil and expelled through a magnetic nozzle. The
novel nozzle in this design is a constriction in the plasma flow channel set
by shaping (tapering) the magnetic field rather than a material surface.
Magnetic fields strongly inhibit charged particle motion perpendicular to
them while allowing easy flow parallel to the field lines. This reduces
plasma contact with nearby materials, considerably extending their lifetime.
Plasma expanding through the magnetic nozzle is accelerated to supersonic
speed by a strong electric field that develops in the nozzle. In the
expansion process, plasma cooling occurs; if sufficiently rapid, the plasma
will recombine into a supersonic stream of neutral gas. Neutral particles
are free of the magnetic force. Proper shaping of the magnetic nozzle
subsequent to the recombination zone will generate a small angle exhaust
plume, increasing thrust efficiency. This propulsion concept can lead to
high-thrust, high-specific-impulse propulsion systems that could grow in
capability over a 40-year period. A fusion power reactor could be
incorporated as the direct-drive power source, if scientists are able to
produce a working fusion reactor.

Before describing these technical features in more detail, we give a
comparison of the parameters of this novel thruster with existing electric
propulsion methods. Figure 2 shows the thrust, T, and specific impulse, Isp,
of various electric propulsion methods, including the proposed wave-heated
thruster (WHT).

In terms of thrust and power capability, the closest competitor to the WHT
is the Magnetoplasmadynamic (MPD) thruster. In MPD thrusters, strong
currents flow between electrodes in the plasma. The most promising fuel for
MPD thrusters is lithium. However, lithium presents a contamination problem
to the rest of the spacecraft. Even though lithium is the best of all fuels
in this regard, plasma contact with the electrodes causes them to degrade,
limiting the thruster lifetime and mission duration. Hall thrusters, now
used on satellites, have somewhat less severe electrode degradation but
produce lower thrust. These two configurations use magnetic fields to
increase the plasma density. Their magnetic fields are oriented
perpendicular to the plasma exhaust; electrical currents are driven along
the magnetic field, between electrodes, to heat and accelerate the plasma.
This is a surface power input method, a major difference from the WHT and
one reason why these thrusters are difficult to scale to the higher powers
needed for certain Grand Challenge missions.

In the WHT, plasma flow and thrust are generated by the plasma pressure
gradient parallel to the magnetic field. There are no electrodes in contact
with plasma to degrade. The magnetic field forms an insulating barrier
between the plasma and the surrounding material surfaces. (The "thermal
insulation" provided by this magnetic field shape exceeds that of
Styrofoam.) The WHT can potentially produce higher thrust/specific impulse
products than the other systems on the graph, to a large degree, because of
the high densities achievable with the confinement properties of the
specific magnetic field configuration of the method, a wave-heated magnetic
mirror configuration.

Maximizing Thrust

Many wave-heated plasma systems have operated with similar magnetic geometry
to that in the WHT. None has employed a feature essential for space
propulsion applications: a method for decoupling the plasma exhaust from the
magnetic field. Without this feature, plasma expelled from the rear of the
spacecraft will follow magnetic field lines back to the nose of the
spacecraft, counterbalancing the thrust. In this specific WHT design, the
decoupling is achieved by causing plasma cooling and recombination - ions
combining with electrons to produce neutral atoms - in the expansion zone of
the magnetic nozzle. Other decoupling methods may be possible, such as
asymmetric magnetic nozzles, but analyses of these predict lower
efficiencies in converting input energy into thrust.

The main advantages of the WHT are: higher power capability, because of
volumetric heating; higher plasma density, because of better plasma
confinement produced by the magnetic geometry; and ability to use a magnetic
nozzle for plasma cooling and recombination, because of the linear
magnetic-field geometry.

An important consideration for Grand Challenge missions is the power
available to the thruster. Large thrust and high specific impulse require
high power. Power levels up to 20 kW will be available on near-term
commercial satellites. Power levels up to hundreds of kilowatts may be
feasible using multijunction and concentrator solar photovoltaic technology
or solar dynamic systems using heat engines. If the power source is solar,
then large solar collector areas, and possibly high pointing accuracy and
tight figure control of the solar collectors, are required.

Megawatt power levels could be supplied for extended periods by an external
fission or fusion reactor. Both make consideration of radiation and
environmental effects essential. In an internal fusion-powered option, the
application of high-power RF would ionize the mixture in the WHT chamber,
form a reversed-field configuration (FRC) there and heat the fuel to fusion
temperatures.

The FRC is an intrinsically high-beta plasma, favorable to the use of
advanced (neutronless) fuels. (Beta, b, is the ratio of plasma thermal
energy to magnetic field energy.) Recent research has shown more potential
for p-11B fusion than earlier predicted. In an optimal FRC fusion reactor, a
mixture of boron and hydrogen is injected into the FRC. Fusion creates
energetic helium, which further heats the fuel, sustaining the burn. Plasma
crosses the FRC's closed flux surface, flows along the open magnetic field
lines to the nozzle and exits there, providing thrust, as shown in Figure 3.
The FRC requires a solenoid-shaped magnetic field, the same geometry needed
by the wave thruster and the magnetic nozzle. These factors make the FRC the
most attractive fusion reactor from an engineering perspective. Many of the
components are common to both the nearer (non-fusion) and longer-term
(fusion) propulsion systems. As a consequence, development of the
wave-heated plasma thruster will create technology that will be directly
applicable to future fusion propulsion systems.

Wave-heated plasma propulsion

This novel thruster differs from earlier wave-heated thermal thrusters in
that it employs a confined, fully ionized warm plasma, a strong axial
magnetic field and a magnetic nozzle with large expansion. Wave heating in
this field geometry is a volumetric method; that is, waves launched from
antennas at the plasma's edge propagate deep within the plasma before their
energy is absorbed. This reduces the power loads on and losses to the
surrounding structures.

Five different frequency ranges are candidates for wave heating: electron
cyclotron (EC), lower hybrid (LH), helicon, ion cyclotron (IC) and rotating
magnetic field (RMF). Although a thruster must produce high-velocity ions,
apparently favoring the IC method, acceleration in the proposed thruster
design is caused by the nozzle's electric field. This converts electron
thermal energy into directed ion momentum. Thus, there is no clear reason
yet for selecting one candidate from the others. Indeed, the optimal choice
may change with each mission's specific requirements. For thruster
parameters noted in Figure 2, a plasma density of 5 x 1014 cm3 is needed at
an electron temperature of ~20 eV. For hydrogen propellant, this would
provide a thrust of about 2 x 104 N per m2 of nozzle area.

The magnetic field required by each is similar, between 1 and 5 kG. The low
end is set by the plasma b requirements. The upper end may be more practical
by easing antenna design. The nozzle magnetic field strength is about 10
times higher than that needed by the heating method. Even 50 kG field
strengths are readily achievable by present-day superconductor technology.
High-temperature superconductors would improve the attractiveness of the
engines by reducing the cooling requirements.

Table 1: Candidate RF and mwave modes for heating plasmas for thruster
applications
Mode EC LH Helicon RMF IC
Approximate frequency (GHz) 2.5-10 0.5-2.5 0.1-0.5 0.3-100 0.03-10
Temperatures achieved (eV) 20 5 3 20 5
Densities achieved (cm-3 ) 5 x 1012 1 x 1014 1 x 1014 1 x 1014 1 x 1013
Ionization fraction (%) 50 90 50 10 10


The LH system has achieved more than 90% ionization, primarily because of
the high density and controlled startup procedures. This is desirable for
improved fuel utilization efficiency. (The RMF has yet to achieve a high
ionization fraction because of the low magnetic fields used and the high
fill pressures necessary with the traditional plasma formation procedures.)
With improved operational techniques, all the candidate frequencies are
likely to produce full ionization at high power. The main question is
whether they can also produce the proper electron temperatures within the
plasma - temperatures that produce high thrust without compromising the
recombination properties of the nozzle.

The achieved parameters shown in Table 1 were at relatively low power,
typically 0.5-3 kW. The only exception was RMF, which needed higher power
because of the enhanced losses and high fill pressure. Extending the
database for each heating mode to higher power is needed and one of the
technical objectives to be addressed by research and development efforts.
Scalability, i.e., achievable plasma parameters versus nozzle radius, is
another subject that must be addressed by R&D.

The overall energy efficiency of this method will depend on the product of
the usual factors: the efficiency for converting power from the spacecraft
power source to the wave power supply; the coupling of the wave power to the
plasma; the power lost to the thruster structures by radiation and plasma
conduction; and the frozen-in power loss. The choice of propellant is
particularly important for determining the frozen-in losses.

Magnetic nozzle: thrust and plasma recombination

The axial magnetic field used by these wave-heating methods allows both ions
and electrons to be exhausted along B. As noted, the nozzle generates the
thrust by converting random electron thermal motion into directed ion motion
in the nozzle's electric field. Strong electric fields have been found in
many mirror machines, such as studied in the fusion program. Potential drops
of kilovolts were obtained, very good for ion acceleration. As we shall soon
see, this was too large to allow recombination. Contrary to Mae West's
statement, too much of a good thing was too much.

In 1995, a steep electric field of approximately the proper strength, ~ 10
eV/cm, was discovered in a linear plasma device in our Princeton University
laboratory. This was accomplished by collision cooling of the plasma
electrons, rather than by magnetic expansion cooling. The remarkable
observation associated with this modest electric field was rapid plasma
recombination to neutral gas, something not attained in the hotter fusion
magnetic mirror experiments.

This brings us to the major conceptual leap provided by the magnetic nozzle.
The question arose, how can the plasma exhaust be decoupled from the strong
magnetic field? In an axially symmetric magnetic nozzle, the plasma is
constrained to follow the field lines, even for high plasma dielectric
constant, 8pmnc2/B2. (This is in contrast to the flow of a plasma slab
across a magnetic field with simple, one-dimensional curvature.) A
resolution to this vexing problem is to cause sufficient plasma cooling in
the nozzle expansion that recombination transforms the plasma exhaust into a
supersonic stream of neutral gas. Figure 4 shows that cooling to
temperatures below ~ 1 eV (11,600 K) is necessary to get rapid
recombination.

Expansion from a nozzle results in cooling and acceleration. There is a
direct relation between the cooling and the Mach number achieved by a
nozzle. Our calculations show that the recombination rate coefficient
increases with Mach number approximately proportional to M3 for g=5/3 and
proportional to M5 for g=2, where g is the usual ratio of specific heats. By
examining the calculated Mach number as a function of magnetic field
expansion we predict that nearly complete recombination can be generated by
a magnetic expansion of 50 for g=2 or 1000 for g=5/3 (g is expected to be
between 5/3 and 2 for a magnetized monatomic plasma of initial density 1 x
1014 cm-3).

How did the Princeton experiment show extensive recombination? The plasma
appeared as different as night from day. Recombining plasmas are
characterized by emission of intense light with a special spectral
signature. Warm plasma, viewed through a window of the linear apparatus,
flows from left to right. As the plasma cools from 50,000 K to 10,000 K, its
brightness dramatically increases. Detailed analysis of the spectrum showed
this could be quantitatively explained by three-body recombination.

A critical aspect of the thruster design is the selection of the fuel. At Te
< 1 eV, helium has the most rapid three-body recombination rate of all the
singly charged monatomic ions. However, its high ionization potential
unfavorably increases the frozen-in losses. Other inert gases like xenon are
much better in that regard, but have relatively low second-ionization
potentials. The optimal fuel will depend on the overall plasma temperature
and plasma confinement time. R&D are essential for selecting the optimal
electron temperature, hence wave-heating method and plasma shape.

Propulsion system designs

Two candidate WHT operating points are described to illustrate the potential
of this engine. The first, at 30 kW power, is for a reusable transfer orbit
vehicle for low Earth orbit operations. The second, at 30 MW power, is for
interplanetary and trans-lunar operations. The 30 kW mission is an orbit
transfer mission from a 400-kilometer orbit to a 2000-kilometer orbit,
including a return mission with the full payload. The low Earth mission is
shown in Figure 7. A thruster with this power level could also be used as a
drag makeup thruster on the International Space Station. It would be
difficult to perform the drag makeup mission or the reusable upper stage
with other electric thrusters due to their relatively short lifetimes. Two
missions are shown for the 30 MW thruster. One is a manned Mars mission.

The second is a near-sun flyby for an interstellar mission. The Mars mission
assumes a 100,000-kilogram payload, including the propulsion system. The
minimum one-way travel time is about two months, which is a reasonable
amount from an operational cost and radiation dose standpoint. The power for
this mission would need to come from a nuclear reactor, which could be the
internal fusion reactor described above. The spacecraft for the interstellar
mission is inserted into an elliptical heliocentric orbit with its perigee
close to the sun. The idea is to perform all of the delta-V near perigee to
get an additional boost due to the sun's gravity well and to take advantage
of the high solar flux at that distance. The plots show a numerical
simulation of the mission in which the propulsion system produces a 40
km/second delta-V. The final velocity is in excess of 100 km per second and
it passes the orbit of Jupiter 160 days after injection into the elliptical
Earth/sun transfer orbit. The specific impulse is held constant at 2500
seconds and the thrust is allowed to vary up to the limit of the available
power. This trajectory is by no means optimal, nor does it account for
thruster limitations.

Numerous advanced electric propulsion concepts have been developed over
recent years because of higher propellant exhaust velocity, me, compared to
chemical systems. The wave-heating method, thrust-generation mechanism,
decoupling of plasma from magnetic fields and scalability make the WHT
system a significant advance over existing electric thruster concepts.
Wave-heated plasma propulsion is a revolutionary concept that could be used
in the short term to produce a high-thrust, high specific-impulse electric
thruster and could incorporate a fusion propulsion, if a practical one is
ultimately developed. It is in an early stage of development. Considerable
effort will be required before a prototype is ready for flight.


Samuel A. Cohen received a Ph.D. in Physics from MIT in 1973. He has been at
the Princeton University Plasma Physics Laboratory ever since, now serving
as a lecturer with rank of professor in the Astrophysical Sciences
Department and director of the Program in Plasma Science and Technology in
the School of Engineering and Applied Science.

Mr. Michael Paluszek is the founder of Princeton Satellite Systems, Inc. He
received his S.B. degree from MIT in Electrical Engineering in 1976 and his
E.A.A. and S.M. degrees from MIT in Aeronautics and Astronautics in 1979. In
1986 he joined GE Astro Space, where he led the design of the attitude
control systems for GPS IIR, Inmarsat 3, GGS Polar Platform and the Mars
Observer Delta-V mode. His current research includes collaborative work with
the Princeton Plasma Physics Laboratory on advanced plasma thrusters and the
development of artificial intelligence techniques for embedded systems.




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