American Institute of Aeronautics and Astronautics1

Half Mirror Wave Heating Plasma Propulsion System

Stelu Deaconu†

Abstract

The paper introduces the conceptual

design of a new, magneto-plasma propulsion

system suitable for Earth orbit transfer and

interplanetary missions. The new system (SE-II)

is a pulsed rocket motor with a theoretical

performance envelope of 103-104 seconds of

specific impulse and 10-200N thrust levels at 1 -

10MW. The thruster can operate at high impulse

levels with light gases like hydrogen or helium or

it can deliver higher thrust levels with a variety of

heavier species like nitrogen or argon, while

incurring a penalty on specific impulse. The

operational principle of the SE-II thruster points

to (a) a possibility to vary thrust and specific

impulse levels while operating at maximum

efficiency, and (b) a simple, robust, and light

hardware design.

Introduction

Magnetoplasmadynamic (MPD)

propulsion systems offer the highest thrust levels

of all electric propulsion systems (tens to

hundreds of newtons1), while achieving specific

impulse and efficiencies comparable to ion

thrusters.

________________________________________† Currently with CFD Research Corp.

From the operational standpoint the MPD

thrusters can be continuous or pulsed. The

common feature of these devices is the utilization

of the magnetic field for confinement and

acceleration of plasma particles. Two widely used

schemes for confinement and acceleration are the

magnetic mirror, and the half-mirror or “the

magnetic nozzle, respectively. The magnetic

mirror was proposed initially (by E. Fermi) as a

solution to the confinement problem of fusion

plasmas. However, in an asymmetric

configuration, the magnetic mirror may become

an effective accelerator of plasma particles. The

loose end of the asymmetric mirror is, in effect, a

magnetic nozzle since it allows highly energized

particles to escape confinement along its axis.

The magnetic nozzle is used to direct the flow of

particles in applied-field MPD thrusters2, FRC

based fusion propulsion concepts3, Princeton

EPPDyL’s ion-accelerator by beating of

electrostatic wave4 (BWX), and NASA’s own

Variable Impulse Magnetoplasmadynamic Rocket

(VASIMR)5, 6. The main difference between these

systems is the method chosen for plasma heating.

Thus, in most MPD thrusters the energy is

provided by DC arc discharges, while in BWX

and VASIMR, the energy is provided by helicon

(RF) waves.

39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit20-23 July 2003, Huntsville, Alabama

AIAA 2003-4887

Copyright © 2003 by Stelu Deaconu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

American Institute of Aeronautics and Astronautics2

Figure 1. The StarEngine-II

The SE-II is a pulsed inductive thruster, designed

to convert electrical energy stored into a capacitor

bank into kinetic energy of a plasma stream by

coupling an ion-wave plasma heating scheme with

a half mirror magnetic configuration (i.e.

magnetic nozzle). The energy transfer is

intermediated by low frequency, ion acoustic and

whistler mode plasma waves. Schematically, the

SE-II engine layout is shown in Figure 1.

At the heart of the system is a loosely

wound, wave excitation coil mounted inside a half

mirror magnetic field configuration. At the mirror

end of the half-magnetic mirror is the gas delivery

system, and a strong, rare-earth permanent

magnet, see Figure 1. The gas system comprises a

high pressure gas reservoir (not shown) and an

injection tube. The gas is delivered periodically

by the opening and closing of a fast acting electro-

valve. The design of the gas injection tube is such

that the gas exiting it is sonic. The capacitor bank

is comprised of several high-energy density, high-

voltage capacitor units, arrayed around one end of

the thruster in a star pattern, designed to minimize

the inductance of the electric supply lines. The

current switching mechanism (trigger) has two

electrodes situated on the symmetry axis of the

magnetic mirror, and inside the wave excitation

American Institute of Aeronautics and Astronautics3

coil. One electrode (the cathode) is mounted in

the gas delivery tube and has a ring geometry.

The second electrode (the anode) has a blunt-

conical shape and is mounted at the other end of

the wave excitation coil facing the hollow

cathode. The trigger is connected in series with

the wave excitation coil and the capacitor bank.

The entire SE-II system is enclosed in a protective

cowling, which is also featured in Figure 1.

The Principle of Operation

After the capacitor bank is charged, the

fast-acting valve opens for a predetermined time

interval, (0.5-1msec) allowing a certain quantity

of gas in the injection tube. The difference of

pressures between the reservoir and the tube

results in a sonic wave front propagating toward

the tube exit. At the exit, the gas expands further

through a series of Prandtl-Meyer expansion fans.

The supersonic flow hits the conical electrode

(anode) before diffusing into the low-pressure

environment around the excitation coil. The result

is a flow structure with good circumferential

symmetry developing in the inter-electrode

region. The presence of the gas particles is

essential to the discharge onset (triggering) and

the generation of plasma in SE-II.

Electrically, the potential difference

between the two electrodes is the same with the

charging voltage of the capacitor bank since the

resistance of the wave excitation coil is negligible.

The two electrodes are separated by a stand-off

distance, which is sufficiently large to prevent gap

breakdown if the gas is not present. As the gas is

admitted in the inter-electrode gap, the

characteristic electric field to particle density ratio

(see for instance Raizer7) of the region decreases

below the breakdown threshold and the discharge

is initiated. The sharp increase in current through

the coil circuit generates a magnetic shock, and is

accompanied by a large induced electric field in

the inter-turn spaces of the loosely wound coil.

The process is similar to plasma formation in

pulsed inductive thrusters (PIT). The electric field

forms a double layer potential, which, if

sufficiently high, can fully ionize the gas. After

the gas is fully ionized, the slower decaying

magnetic field will efficiently couple with the

plasma filling the region. It was argued by

Deaconu8, that in these conditions most of the

discharge energy is spent on heating the plasma,

and that plasma heating is intermediated by ion

acoustic waves propagating along magnetic field

lines. The wave excitation coil and the plasma are

located inside the asymmetrical field of the

magnetic mirror. The magnetic field of the mirror

is opposite in direction from the field created by

the excitation coil. For the short period of the

discharge, 1-2msec, the strong field of the

excitation coil is pushing the plasma radialy

outward, distorting the field of the mirror and

creating a concentric magnetic neutral region. As

the energy stored in the capacitor bank is

depleted, the magnetic field of the coil is decaying

rapidly, and the magnetic field of the mirror starts

pushing back on the plasma, stopping its

expansion. The asymmetry of the magnetic field

also forces the plasma to move forward to regions

American Institute of Aeronautics and Astronautics4

of lower magnetic field strength, and away from

the wave excitation coil. The hot plasma, now in

a region of high magnetic field inside the

magnetic nozzle, starts moving axially toward the

mirror exit, as dictated by the conservation of

magnetic moment9. The result is a directed stream

of particles being accelerated axially toward the

exit of the engine. The length of the half mirror is

chosen such that the particles (now with the

energy source exhausted) have enough time to

recombine as they approach the exit. Thus, as

they recombine, the particles become electrically

neutral and no longer feel the effect of the

magnetic field. In these conditions, the

undesirable case of having ionized particles

follow curved trajectories (as they follow the

magnetic field of the mirror) is prevented.

SE-II A Case Study

Consider the case of a SE-II system with

the following parameters, capacitor bank C =

1000µF, charging voltage U = 4000Volt, and a

wave excitation coil of inductance L = 5µH, and

total wire length lw = 2.5m. The energy stored in

the capacitor bank is 8kJ. With the parameters

chosen, and a time average resistance of the

discharge of 0.05-0.1Ω, the discharge time is

about 1msec, and the average discharge power is

10MW/pulse. Also, consider that the working gas

is hydrogen, and that 5mg is injected during one

injection pulse. These parameters are

representative for the system proposed and allow

for a simplified qualitative analysis.

(I) Discharge Onset and Current Switching

As shown by Deaconu8, when an external

current switching device (e.g. a triggerable spark-

gap) is used, a large fraction (40-60%) of the

energy is lost as Joule heating in the trigger. The

SE-II employs a gas trigger, hollow-cathode

current switch that is an integral part of the

plasma discharge. There are two advantages: (1)

the gap breakdown is initiated by the gas flow,

and the system does not require a separated trigger

signal and the supporting hardware, and (2) a

large fraction (80-90%) of the energy that is

usually lost in the external trigger is used to

preheat and ionize the plasma. The sonic gas flow

along the hollow cathode tube of the SE-II current

switch has also the role of stabilizing the

discharge10, (by preventing the formation of

cathode directed streamers and hot points on the

surface of the cathode) thus increasing the lifetime

of the system.

(II) Gas Ionization, Wave Heating and Ion

Acceleration

The variable magnetic field of the

excitation coil induces an electric field with the

amplitude directly proportional to the applied

capacitor charging voltage. The electric field

generates a double layer potential in the plasma,

which ionizes the gas. Experimental data8 shows

that the double layer potential is (depending on

system inductance) 5-10% of the applied voltage.

For a 4kV charging voltage, the double layer

potential may reach 0.2-0.4kV and is sufficiently

American Institute of Aeronautics and Astronautics5

high to fully ionize and heat any gas injected in

the coil space. As the initial strong magnetic

shock (at discharge onset) ceases, the energy

transfer to the plasma for the remaining discharge

time is mediated by the onset of waves, see for

instance Ohyabu11 et al., Stenzel and Gekelman12,

or Deaconu8. Wave generation is most efficient if

the axial frequency of the coil is matched by the

frequency of one of the oscillation modes of the

plasma system13. This condition is the equivalent

of impedance matching for resonant RLC circuits,

and is referred to as coupling resonance. Based

on this argument it is concluded that the wave

excitation coil will favor the particular plasma

frequency that match its own impedance.

Additionally, lower amplitude harmonics of the

basic plasma frequency may be observed.

Generally, the coil behaves as a classic quarter-

wavelength resonator with a basic frequency of fp

= vw/λc where vw is the wave phase velocity, and

λc = 4⋅lw = 10m is the coil wavelength.

Experimentally, it was observed that the

frequencies of the generated waves are in the

acoustic range, 2 – 5kHz at lower discharge

voltages8, and may reach hundreds of kilohertz, up

to the lower hybrid frequency for 20-30kV

excitation voltages12. The propagation of these

waves along magnetic field lines is the classic

whistler mode9. Taking a conservative view and

replacing an average 10kHz frequency in the

above formula, the wave phase velocity is vw =

100km/sec. In order for the particles (here ions)

to gain energy from the wave, their mean thermal

speed must match the wave speed. At the time

wave dissipation becomes the dominant

dissipation mechanism, the ions are already highly

energized by collision with the hot electrons in the

fully ionized plasma. The wave starts energizing

the ions in high-end tail of the ion energy

distribution function. As the discharge

progresses, there is a statistical redistribution of

ion energies (due to collisions, and wave

turbulence11), and as the wave loses energy, the

overall mean ion speed (i.e. energy) is necessarily

lower than 100km/sec. However, the waves are

storing most of the discharge energy transferred

into the plasma, and in the end, this energy must

be dissipated as heat into the magnetically

confined plasma. Thus, one can conservatively

assume that in the conditions of this discussion the

(hydrogen) ions are energized to mean

speeds/energy of 40-60km/s (20-30eV). The

electrons also gain energy from the electric field

but since the wave is slow compared to plasma

frequency, the electrons are for all intents and

purposes undisturbed by the wave and thus,

maxwellian. Assuming for instance an average

ion temperature of 25eV, the axial velocity of the

ions leaving the mirror is 50km/sec, and the

specific impulse of the SE-II operating with

hydrogen is 5000sec/pulse. At this exhaust

velocity, a power level of 10MW/pulse will

provide a 250N/pulse of thrust by accelerating

5mg H2/pulse. Equivalently, at a pulse rate of

100pulses/sec, the total power required is 1MW,

and the thruster produces an average thrust of 25N

by accelerating 0.5g H2/sec. These values show

that SE-II compares well with the VASIMR

American Institute of Aeronautics and Astronautics6

theoretical performance at similar power levels,

see Ref. [14].

Summary and Final Considerations

The Star-Engine-II is an innovative

plasma propulsion concept that emerged as a

direct result of the experimental research

undertaken by the author at the University of

Alabama in Huntsville, during his Ph.D program.

SE-II takes advantage of the natural behavior of

the plasma during interaction with strong

magnetic and electric fields. Thus, it is an

established fact that in situations involving

transfer of energy from fast varying magnetic

fields to an ionized fluid, the most probable

processes are the generation of waves and ohmic

heating, rather than direct, one directional particle

acceleration. The SE-II efficiently transfers

electrical energy from an external storage unit to

directed kinetic energy of a plasma stream by

combining a wave plasma generator with a half

mirror magnetic field configuration. The

simplicity of the operating principle has the

additional advantage of simple system hardware,

robustness, and longer operating lifetime.

The SE-II system can be versatile from

the point of view of being able to control the

average effective thrust and specific impulse over

sustained periods of time by varying the pulse

rate, and/or the charging voltage of the capacitors,

and the energy input (capacitor values). Another

remarkable feature of the system is a possibility of

in-flight switching between high-impulse, high-

thrust regimes, simply by changing the working

gas.

Although there are no obvious theoretical

limitations on the size, gas flowrate or amount of

power that can be channeled through an SE-II

system, the author considers that any operating

point in the 3000-5000sec specific impulse and

10-50N thrust range can be attained with currently

available energy generation and storage

technologies. The SE-II system operating at this

performance level is well suited for Earth orbit

transfer missions, as well as longer interplanetary

excursions, and thus could become one of

NASA’s thruster of choice for a variety of

unmanned and manned missions within the solar

system.

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/AFMPD/e_af-mpd.html3 Schaffer, M. J., Considerations For Steady State FRC

Based Fusion Space Propulsion, General Atomics

Internal Report, GA-A23579, December 2000.4 Spektor, R., and Choueiri, E., Y., Design of an

Experiment for Studying Ion Acceleration by Beating

Waves, AIAA Paper 2002-3801, July 2002.5 Chang, D. F. R., et. al, The Development of the

VASIMR Engine, Proc. Of International Conf. On

Electromagnetics in Adv. Appl. (ICEAA’99),

September 1999, Torino, Italy, (1999) 99-102.6 Chang, D. F. R., The VASIMR Engine Approach to

Solar System Exploration, Proc. 39-th AIAA

Aerospace Science Meeting and Exhibition, January

2001, AIAA paper 2001-0960.

American Institute of Aeronautics and Astronautics7

7 Raizer, Y. P., Gas discharge physics, Springer Verlag,

Berlin, 1991.8 Deaconu, S, Experimental study of plasma

energization at magnetic neutral points, Ph.D

dissertation, UAH 2002.9 Chen, F. F., Introduction to plasma physics and

controlled fusion, Vol. I: Plasma physics, second. ed.,

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Experimental characterization of a thermionic-arc

discharge ionization device for flowing gases, Rev. Sci.

Instrum., Vol. 73, No. 1, pp. 91-97, January 2002.11 Ohyabu, N., Okamura, S., and Kawashima, N.,

Strong ion heating in a magnetic neutral point

discharge, Phys. Fluids, Vol. 17, No. 11, pp. 2009-

2013, 1974.12 Gekelman, W., Stenzel, R. L., and Wild, N.,

Magnetic field line reconnection experiments 3. Ion

acceleration, flows, and anomalous scattering, J.

Geophys. Res., Vol. 87, No. A1, pp. 101-110, 1982.13 Stix, T., H., The theory of plasma waves, Advanced

Monograph Series, McGraw-Hill, NY, 1962.14http://spaceflight.nasa.gov/mars/technology/propulsio

n/aspl/vasimr.html.