magnetoplasmadynamic thrusters

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Magnetoplasmadynamic Thrusters

Mariano AndrenucciDepartment of Aerospace Engineering, University of Pisa, Pisa, Italy

1 Introduction 12 The Nature of the Lorentz Force 2

3 The Ideal Self-Field MPD Thruster 5

4 Real Self-Field MPD thrusters 7

5 The Onset Riddle 10

6 Applied-Field MPD Thrusters 13

7 Lithium Propellant MPD Thrusters 14

8 Survey of Major R&D Efforts 15

9 Future Prospects 18

References 20

1 INTRODUCTION

Theessenceof what was later to becomeknown as themagne-

toplasmadynamic, or MPD, thruster, emerged from the flurry

of research and development activities that characterized the

field of propulsion among others in the feverish, post-

Second World War era. Research on arc thrusters came about

almost naturally from work on conventional rockets, as an

alternative way to heat the propellant, as opposed to the use

of the heat released by chemical reactions. Heating the work-

ing gas by means of an electric arc offered the additional

bonus of making it possible to adjust the power input inde-pendently of the mass flow rate. Extensive research activities

were started in many public and private laboratories, which

brought, in a relatively short time, to the experimentation of

a wide variety of configurations and operating regimes.

Encyclopedia of Aerospace Engineering.Edited by Richard Blockley and Wei Shyyc 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-68665-2

It was just in the midst of one such arcjet-related activ-

ity that the evidence of an acceleration mode differing fromthe expected conventional gasdynamic mechanism was gath-

ered, quite serendipitously, by Adriano Ducati at the Giannini

Scientific Corporation of Santa Ana, California (Ducati,

Giannini and Muehlberger, 1965). In the words of one of

its major discoverers (Jahn, 1968), in an empirical series

of experiments with a conventional short arcjet device it

was found that by drastically reducing the propellant gas

flow. . . the exhaust velocity of the hydrogen flow could be

increased to values of the order of 100000 m s1, and the

overall efficiency reached 50%. The ensuing supposition

was that the high current densities in the arc were generating

self-magnetic fields within the chamber sufficiently intenseto produce substantial electromagnetic acceleration of the

flow.

The device experimentally demonstrated by Ducati (Fig-

ure 1) was the MPD arc thruster with a self-induced magnetic

field. This discovery led to a burgeoning of activity in plasma

thruster research. The new acceleration mode was referred

to with a variety of names such as the high-impulse arc,

thermoionic accelerator, magnetic annular arc, and Hall arc

accelerator, and it took some time for the term Magnetoplas-

madynamic to become accepted as the standard name for this

new class of device.

This is how MPD thruster work began in the USA. Activ-

ities along similar lines were sprouting up in the meantime in

the former Soviet Union, and based on what would become

known only decades later, the dimension of these efforts

soon exceeded the levels reached in the USA and, later on,

in Germany and other western countries. The main lines of

the subsequent evolution of the MPD concept and the main

results achieved are shortly reviewed later. First we shall

focus on the concept itself and its physical bases, which


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2 Alternative Propulsion

1958

Anode

Anode Plasma

Uniform exhauststream

Very high Isp core

Low Isp envelope(a) (b) (c)

Cold propellantinlet

Cathode

Cold

propellantinlet

Cathode

1959 1960

1961 1963

Figure 1. (a) The elimination of the supersonic nozzle has been our first effort. This was a difficult idea to accept at that time;however, nozzles are gradually disappearing as one can observe in a comparison of contemporary geometries used in the adoptionof this principle; (b) uniformity of thermo-ionic vs conventional arc-jet. Adopted from Ducati, Muehlberger and Giannini (1964) cAIAA.

were for some time considered rather elusive. The discover-ers themselves noticed (Ducati, Muehlberger and Giannini,

1964): Many questions still remain unanswered. One can

call the thruster thermo-ionic, electro-thermal, J-cross-B,

Hall-Current, or cyclotron resonance, or any otherdescriptive

name, but still no onecan explain completely its mechanism.

It is to the clarification of this mechanism that the next section

is dedicated.

2 THE NATURE OF THE LORENTZ

FORCE

Under the physical conditions typical of high-power arc

devices we can assume the working fluid to be in the state

calledplasma. The most important implication of this is for

such a fluid to behave as an electrically conductive medium

that remains quasi-neutral at all scales comparable with the

size of the device or experiment of interest. This can be

statedin terms of number densitiesof thecomponent charges,

electrons and ions, as:

|ne ni| ne ni = n (1)

The consequences of this assumption, as well as a numberof other features that are usually associated with the term

plasma, are extensively covered in many excellent textbooks

(Chen, 2006; Bittencourt, 1986; Lieberman and Lichtenberg,

1994; Spitzer, 1964; Mitchner and Kruger, 1992) and will not

be dealt with here. MPD thrusters, as well as other types of

electric thrusters such as Hall-effect thrusters, fit in a category

that can be designated as plasma thrusters. This definition

entails the idea that apart from local effects such as the

sheaths positive and negative particles never get separatedthroughout all phases of the acceleration process (differently

from what happens in gridded ion thrusters).

To analyze the nature of the MPD acceleration process,

we shall start by describing the dynamical equilibrium at

any point of the flowfield produced in a generic thruster

microscopically. As is largely known, the analysis of the

motion of an ensemble of particles is the realm of kinetic

theory. The behavior of an ensemble of particles can be thor-

oughlydescribed by thekinetic equation known asBoltzmann

equation. But as we are interested in the global, collective

behavior of the various components of the working medium,

a description in terms of average behavior of particles of anyspecies is normally sufficient. This is usually done by taking

the first three velocity moments of the Boltzmann equation,

thus obtaining the mass, momentum, and energy conservation

equations for each species.

As we deal with a general problem of thrust generation,

for the purpose of the present discussion we shall focus on

the momentum equation for each of the species constituting

the working medium. We shall limit our attention to a simple

case that will permit us to reach some general conclusions

without unnecessary complications.

Let us hence adopt the following main simplifica-

tions (other assumptions should become obvious from the

context):

we shall assume the working medium to be com-

posed of two species only: electrons and singly-charged

ions;

as mentioned, we shall assume the fluid to remain quasi-

neutral at all times:ne ni = n;


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Magnetoplasmadynamic Thrusters 3

we shall neglect viscous effects which are usually very

small in typical situations of our interest;

we shall neglect the momentum storing capability of the

electron fluid due to the smallness of the electron mass as

compared to that of the ions.

Under the above assumptions the momentum conservation

equations for the ionic and the electronic components at any

point of the thruster channel can be simply stated as

mindui

dt= n e (E + ui B) pi + Pi e (2)

0 = n e (E+ ue B) pe + Pe i (3)

where mi is the ion mass, n the common number density

of electrons and ions, ui and ue the ion and electron fluid

velocities in the laboratory frame, E and B the local electric

and magnetic induction field vectors, p i andpe the ion and

electron pressures, and Pieand Peithe momentum gain of the

ion fluid caused by collisions with electrons and vice-versa.

The term on the left in the ion equation describes the time

change in momentum of the ion fluid in a frame moving with

the fluid. It represents theconvective derivative

d

dt=

t+ u (4)

which combines the time change in momentum seen by a

static observer plus the change produced as the observer

moves with thefluid into a region of differentmomentum. Theterms on the right side relate such total momentum change

with the effects of the forces applied. Under the simplifying

assumptions listed above, only the electromagnetic force and

those associated with pressure gradients and collisions are

accounted for.

This is where the Lorentz force comes into play. Named

after the Dutch physicist who discovered it, the Lorentz force

law states that a chargeqmoving with velocity u in the pres-

ence of an electric field E and a magnetic field B will not

only feel a forceqE due to the electric field but also a force q

(u B) associated with the magnetic field. Alternately, we

could say that the charge will feel an overall electric fielddiffering in magnitude and direction with respect to the field

Eseen by a static charge by a component u B. This gives

for both electrons and ions the expressions given in equations

(2) and (3).

As for the collision terms, they describe in this case only

collisions between electrons and ions. The characteristicsand

effects of collisions between charged particles in a plasma are

very different from the strong, typically inelastic, collisions

involving neutrals, in that the interaction takes place at a

distance, by means of the Coulomb electric field forces sur-

rounding all the nearby charged particles (glancing collisions

or Coulomb collisions). It takes a large number of such glanc-

ing collisions combining casually to produce effects similar

to those induced by a head-on collision. This process can be

described in terms ofrandom walk, so as to define an equiva-

lent collision cross section, a collision frequency, a mean free

path,and so on, allowing collisions between charged particles

to be described in analogy with ordinary strong collisions.

To understand the nature of the Lorentz force it is not

necessary to enter into the details of the collision terms. It is

sufficient to recognize that under the two-fluid idealization

assumed here it is simply

Pi e = Pe i (5)

so that we can cancel the collision terms between equations

(2) and (3), to find

mindui

dt= n e (E + ui B)

pi n e (E+ ue B) pe (6)

which, with the following further definitions

p = pe +pi = min (7)

gives

d ui

d t= n e (ui ue) Bp = j B p (8)

where the difference between electron and ion velocities has

been expressed in terms of current density

j= n e (ui ue) (9)

Thus, in equation (8)everythingfinally reduces to thefamiliar

Lorentz force termj B (apart from the pressure gradient

contribution).

Thesituation canbe illustratedas shown in Figure2. Leav-

ing aside the effects of pressure gradients, the primary causeof acceleration is the electric field. Electrons are accelerated

by the field but transfer all of the momentum acquired to ions

through collisions. Ions, in turn, are also accelerated by the

electric field and the ensuing momentum increase combines

with that received from the electrons. Also evident is the fact

that the increase in momentum felt by the electrons can be

subdivided in a part that would be felt if the electrons where

moving at the same velocity of the ions and a second part due


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Figure 2. The Lorentz force.

to their differential velocity with respect to ions. The former

part is equal andoppositeto themomentumincreaseimparted

by the electric field on ions so that when this is transmitted by

the electrons to ions through collisions the two terms cancel

each other. The only effect left is therefore the effect of the

electric field on the electrons due to the velocity difference

of electrons with respect to ions externally seen as current

and transferred to the ions themselves (i.e., to the fluid)

through collisions. By choosing to represent the electric field

in a frame moving with the ions, E, we are dispensed from

referring to any specific ion velocity, thus making the picture

more general.

To obtain further insight into the character of the accel-

eration process we need to be more specific about the form

of the collisional term. Assuming the electron-ion collision

process to correspond to an equivalent collision frequency

i e, in the two-fluid idealization assumed here we can write

Pi e = Pe i = i emen (ue ui) = n e

j (10)

where we have introduced the conductivity

=n e2

i eme(11)

Making use of equation (10), (2) and (3) can be restated as

mindui

dt= n e (E+ ui B) pi

n e

j (12)

0 = n e (E+ ue B) pe +n e

j (13)

The latter can also be written as:

j=

E+ ue B+

1

n epe

=

E+ ui B+

1

n epe

1

n ej B

(14)

which can be recognized as the generalized Ohms law

describing the relationship between fields and current in the

plasma. Solving the above equation for the electric field E

we obtain

E = ui B+1

n ej B

1

n epe +

j

(15)

where we can recognize, from right to left, the Ohmic com-

ponent (last), the field-equivalent of the pressure gradient, the

field associated with the electron relative motion (current) in

the presence of the magnetic field (Hall term) and the fieldassociated with themagnetic force exerted on theions. This is

the so-calledself-consistent electric fieldexpressing an equi-

librium that must exist at any point of the channel between

the local values of the fields and the other physical quantities.

To see how effectively the momentum exchange between

electron and ions can result in increasing the flow directed

kinetic energy let us derive the dot product of the momentum

equations for the two species, equations (8) and (9), with ui


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and ue respectively:

uidui

dt= piui + n eEui

n e

jui (16)

0 = peue n eEue +

n e

jue (17)

being the work of the magnetic force on the moving particles

of course equal to zero. The last term in equation (17) can

now be decomposed by use of equation (9). With obvious

further passages we obtain

d

d t

u2i

2

= piui + n eEui

n e

jui

(18)

0 = peue n eEue +

n e

jui

j2

(19)

where the dashed boxes now highlight the collisional terms

describing the frictional power exchange between electrons

and ions associated with the collisional friction force density.

Not surprisingly, the rate at which directed energy is

acquired by the electrons due to collisions with the ions is

simply minus the rate at which energy is acquired by the ions

due to collisions with the electrons. But the electron energy

change includes another term, j2/, which represents the

conversion of the ordered motion of the electrons, relative to

the ions, into random motion (i.e., heat) via collisions with

the ions. Note that this term is positive definite, indicating

that the randomization of the electron ordered motion gives

rise to irreversible heat generation. This is the term usually

calledohmicorJoule heatingterm.

Addingup equations(18) and(19) andremembering equa-

tion (9) the collisional terms cancel out, and we are left with

d

d t

u2i

2

= piui peue +Ej

j2

(20)

If we want to make the role of the Lorentz force in equation

(20) more explicit, we can go back to equation (15), and

scalarly multiply with j, thus obtaining

Ej= (ui B) j1

n epej+

j2

(21)

Considering that it is

(ui B) j= (j B) ui (22)

we can write

Ejj2

= (j B) ui

1

e npej

= (j B) ui pe (ui ue) (23)

so that equation (20) can be finally put in the form

d

d t

u2

2

= pu+ (j B) u (24)

whereu uiis the mass-averaged plasma velocity. Equation

(24) could also be obtained directly from equation (8) by

scalar multiplication with u.

The above analysis shows that the acceleration mechanism

based on the Lorentz force is inherently dissipative in that it

is based on a collisional momentum transfer between elec-

trons and ions that inherently entails frictional dissipation. Inthis regard MPD thrusters are necessarily less efficient than

thrusters in which the acceleration of the ions is obtained

from electrostatic forces, and hence conservatively (apart

from other real-life loss mechanisms). The above analysis,

as noted before, described the equilibrium at a generic point

of the acceleration channel of a generic thruster. To correlate

this with the behavior of the thruster as a macroscopic device

implies integrating fluid equations under appropriate bound-

ary conditions expressing the operating conditions applied to

the thruster. Although this could only be made on the basis

of a detailed description of any specific device, some impor-

tant scaling laws can be obtained that express quite general

behavioral trends.

3 THE IDEAL SELF-FIELD MPD

THRUSTER

In its basic form, the MPD thruster consists of two metal

electrodes separated by an insulator: a central rod-shaped

cathode, and a cylindrical anode that surrounds the cathode

(Figure 3). A high-current electric arc is driven between the

anode and cathode so as to ionize a propellant gas to create

plasma. A magnetic field is generated by the electric cur-rent returning to the power supply through the cathode. This

self-induced magnetic field interacts with the electric current

flowing from the anode to the cathode (through the plasma)

to produce the electromagnetic Lorentz force that pushes the

plasma out of the engine, creating thrust. MPD thrusters are

usually classified either in the self-fieldvariety, which is fully

based on the pure self-field mechanism said above, or in

the generally lower-power applied-fieldversion, where


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Figure 3. Schematic of MPD thruster.

an external coil is used to provide additional magnetic field

to help stabilize and accelerate the plasma discharge. For the

moment we shall concentrate on the basic, selffield version

of the concept.

The basic analysis of MPD thruster operation is usually

prompted by simple one-dimensional idealizations (Figure

4a). For a coaxial channel of external radiusre and internal

radius ri, integration of the distributed Lorentz body-force

over the discharge volume leads to the following expression

for the thrust (Maecker, 1955):

T=1

2LJ2 =

0

4ln

re

riJ2 (25)

whereL is the channel inductance per unit length and Jis

the thruster current. In a more complex channel geometry and

taking into account finite cathode length and pressure effects

on the cathode tip, the above expression can be generalized

with the inclusion of a corrective term as follows

T=0J

2

4ln

re

ri+ A

(26)

For instance, in the case of a conical cathode tip involvinga combination of radial and axial current attachment (Figure

4b and c) one would find A= 3/4.

In more realistic configurations the relationship between

thrust and current squared would depend on the details of

electrode geometry and current attachment; but the electro-

magnetic component of the thrust would still follow a law of

the type

T= b J2 (27)

with b representing a factor of a mainly geometrical char-

acter. Values ofb for typical geometries are about (23) 107 N/A2.

Based on the above analysis, in an ideal device the thrust

would appearto dependon the discharge current only, regard-

less of the propellant mass flow rate m. The effective exhaust

velocityve would therefore scale with the inverse of m

ve =T

m= b

J2

m= b k (28)

where we have introduced the characteristic parameter k =

J2/m, which is reminiscent of the electrical power deposited

in the channel per unit propellant mass flow-rate. As we shallsee later, the importance of this parameter in characterizing

an MPD device cannot be overemphasized. Equation (28)

shows that, apart from the b factor, theJ2/m ratio is equiv-

alent to the effective exhaust velocity; that is, to the specific

Figure 4. Idealized MPD channel models: (a) uniform radial current; (b) radial current into conical cathode; (c) uniform axial current.Modified from Jahn (1968) cMcGraw Hill.


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impulse. Attempts to obtain higherIsp are therefore equiva-

lent to trying to operate the thruster at larger ratiosJ2/m. As

will be discussed later, beyond a certain limit this turns out

to be prohibitively difficult.

Based on equation (28), the ideal kinetic power associated

with the thrust can be written as

PT =1

2m u2e =

b2k

2J2 (29)

so that we can define a dynamic impedance associated with

the useful power spent in accelerating the fluid as

ZT =b2k

2(30)

Finally, we can express the overall input power as the sum

of the useful power associated with the thrust plus losses

Pi = PT + PL (31)

The power associated with losses can also be related to an

equivalent impedance

ZL =PL

J2 (32)

We can therefore write a general expression for the thrust

efficiency as follows

T =PT

PT + PL=

ZT

ZT + ZL=

b2k2

b2k2 + ZL

=1

1 + 2ZLb2k

(33)

An ideal MPD thruster with thrust scaling quadratically

with the current would therefore obey the following laws of

dependence of power and voltage with the current

Pi =b2

2 mTJ4 (34)

V=Pi

J=

b2

2 mTJ3 (35)

In conclusion, the behavioral trends of an ideal MPD

thruster could be summarized as

T J2 V J3 P J4 (36)

4 REAL SELF-FIELD MPD THRUSTERS

Information on how real thrusters behave is obtained through

experimental activities. Self-Field MPD thrusters are natu-

rally relegated to high power operation, as the self-induced

magnetic field is relatively week unless very high currents ofO (10 kA) are applied. Unfortunately, steady-state testing

at the MW level is difficult, and the most experimental data

collected over decades in various laboratories have been gath-

ered with thethrusterworkingin the Quasi-Steady(QS) mode

(Clark and Jahn, 1970). In this mode, the thruster is operated

for current pulse lengths ofO (1 ms), and data so obtained

are expected to be representative of its steady-state perfor-

mance. Unfortunately, this may appear questionable. From

direct comparison of geometrically identical thrusters oper-

atedin continuousmode and QS pulsed mode, Auweter-Kurtz

etal. (1994)havedrawn indication that results of QS thrusters

cannot be plainly extrapolated to the steady operation case.

Were this so, most QS results obtained in the past decades

would be irrelevant to characterizing the real behavior of

steady-state high-power thrusters. However, this is the data

available at present and nothing better can be expected until

MW level steady-state testing becomes feasible or practical.

Let us return to the ideal MPD thruster model outlined

in the previous section. Given its high degree of idealiza-

tion, some discrepancies in the behavior of real thrusters

with respect to the model presented above were of course

to be expected. Several factors conspire to make the real situ-

ation different and in particular: the geometrical shape of the

thruster, the pattern of current flow lines and fields, various

subtle aspects of ion and electron dynamics not included inthe simple model, losses taking place at various levels.

Even in a simple coaxial configuration the situation would

depart from the assumed patterns of orthogonal electromag-

netic fields, currents and gas flow pictured in Figure 4. Due to

the Hall effect, under typical conditions existing in an MPD

thruster channel and especially in the anode sheath region,

the current tends to flow with a strong axial component (Fig-

ure 5). In addition to complicating the current flow pattern,

this also brings about a radial component of the Lorentz force

resulting in a depletion of chargecarriersnear the anode, with

detrimental effects that we shall discuss later.

Another factor that complicates the picture is the back-EMF due to plasma motion through the self-field. This

voltage gradient given by thevector product of theflow veloc-

ity andthe magnetic field strengthuB, tends to discourage

the current from flowing in the intermediate region of the

channel, where bothuandBare large (Figure 6). This results

in a current density increase at the two ends of the electrodes

with possible consequencesin termsof enhanced erosion, and

which can even entail a full conduction crisis in the event


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Figure 5. Conceptual illustrationof current flow in an MPDthrusterwith Hall effect. Modified from Hoyt (2005) c IEPC.

the back-EMF becomes comparable to the thruster driving

voltage (we shall return to this later).

Such and other effects concur in making the real situation

different from the idealized one. This implies, in particu-

lar, that the thrust formulas presented in the previous sectionare inadequate to provide anything better that an order of

magnitude appraisal of the expected thrust level. Various

attempts have been made to work out more complex expres-

sions enabling to improve the thrust prediction capability

(Choueiri, 1998), but the expressions worked out seem hardly

applicable to different configurations or operating regimes,so

that in the end the simple expression of equation (26) remains

preferable for a general use.

Unfortunately, depending on the thruster operating point,

other real-world effects of a more elusive and malign nature

come into play to complicate the picture. This can be bet-

ter illustrated by looking at the electrical characteristic; that

200

100

00 10000 20000 30000

Discharge current, A

Voltag

e,

V

Mass flow rate, g s1 4 5

6

(III)

(II)

(I)

Full ionization

Figure 7. Voltage-Current characteristic of a self-field MPDThruster.

is, the curve describing the terminal voltage as a functionof the arc current (Figure 7). Based on the ideal model, at

constant mass flow rate this curve should display a cubic

dependence on current. But since the earliest experiments

with MPD thrusters it was shown (Boyle, Clark and Jahn,

1976) that, at lower current regimes, for all mass flow rates

the voltage tends to scale linearly with the current and the

exhaust velocity remains nearly constant. It is only beyond a

certain point that the dependence of thethrust on thesquare of

the current starts to be recognizable, giving the characteristic

curve the expected cubic shape.

Unfortunately, at yet higher currents a new unexpected

deviation from the normal behavior is encountered that

Figure 6. Effects of the back-EMF (a) vs. idealized model (b).


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Figure 8. Experimental V-I characteristics for typical self-field MPD thrusters (a) comparison between different anode shapes; and(b) comparison between different cathode lengths. Reproduced from Andrenucciet al. (1992); see also Figure 17.

appears to be associated with the onset of a variety of

disturbing phenomena, including severe fluctuations of the

terminal voltage (voltage hash) and increased electrode ero-

sion. Simultaneously, the anode losses tend to increase,

leading to a reduced efficiency. Once this conditionis reached

the characteristic curve tends to revert to a linear dependence

onJ.

This behavior, which in time became known as the onset

phenomenon, or simply onset, is confirmed by a large amount

of experimental data gathered in many laboratories world-

wide. For example, in Figure 8 the voltage vs. current data

referring to self-field MPD thruster prototypes of different

configurations and operating conditions are shown. Such data

were obtained in Pisa in a series of experimental activities

carried out in the early 1990s (Andrenucci et al., 1992).

How can we explain such deviations from the theoreticalcubic dependence? As to the linear dependence observed at

lower currents, experiments showed thatthe rangeover which

this behavior takes place coincides with current regimes

insufficient for full ionization of the propellant flow. This

has prompted a physical interpretation related to theCritical

Ionization Velocity(CIV) phenomenon described by Alfven

(Alfve n, 1960; Choueiri,Kelly andJahn,1985;Turchi,1986)

according to which, as long as ionized particles move in

the presence of significant amount of non-ionized particles,

the maximum velocity that can be achieved by the ionized

component is limited to

vac = (2 e i/mi)1/2 (37)

(beingi is the ionization potential of the involved species)

and all of the excess power fed into the thruster goes into

ionizing the remaining low-velocity neutrals rather than

further accelerating the ionized fraction. Values of the crit-

ical ionization velocity for various substances are shown in

100000

10000

1000

1 10 100

Atomi weight

AlfvenCIV(m

s1)

1000

H2

He

N2 Ne

A

Kr

XeNa

Li

K

Cs

Figure 9. Alfven CIV for various substances.

Figure 9.

It is only after reaching the full ionization condition that

the thruster starts complying with the cubic voltage law. But

when the onset phenomenon starts manifesting itself the char-

acteristic swerves again toward a linear dependence. This is

easily interpreted as correlatedwith the entrainment of eroded

mass adding to the discharge, possibly as a consequence of

heavy erosion. Eroded mass canbe expected to ablateat a rate

proportional to the square of the current, so that the self-field

thrust relation of equation (28) implies that exhaust velocitiesremain constant; and indeed velocity measurements at those

regimes indicate that the exhaust velocity is independent of

current.

This phenomenon was first reported by Malliaris et al.

(1972) at the AVCO Corporation. In the attempt to increase

the current level at constant mass flow rate, they iden-

tified a critical value, (J2/m), above which the thruster

started exhibiting a noisy voltage signal and enhanced ero-


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sion of thruster components. They also determined (J2/m)

to depend on propellant atomic weight as M1/2 and to be

smaller for larger values of the anode-to-cathode radius ratio.

Boyle, Clark and Jahn (1976) were the first to use the term

onset.

Based on a long series of experiments with argon propel-lant carried out mostly in Princetonon theso called Full Scale

Benchmark Thruster(FSBT) a lower bound for the onset cri-

terion was initially estimated to be (Choueiri, Kelly and Jahn,

1987):

k =

J2

m

40kA2 s g1 (38)

Values more than 2.5 times as large for thrusters of the

same type were documented in later studies. A more general

onset criterion includingthe dependence on propellantatomic

weightwas proposed by Hugel (1980)on thebasisof different

sources:

k =

J2M1/2a

m

(15 33)1010 A2 s kg1 (39)

This expression, graphically represented in Figure 10, is in

good agreement with the previous one for argon propellant.

The limit on the viable (J2/m) in real thrusters is a

problem in many senses. First of all, as already noted, it

limits the specific impulse attainable. In addition, this limit

implies being confined to low efficiency operation, a prob-

lem that has plagued MPD thrusters for decades hindering

their introduction into flight applications. Most experimental

MPD thrusters have typically exhibited efficiencies of 25

35%, particularlyat themoderate(2000 s) specific impulses

Babkin

Cory

Malliaris

Hgel

IRS33.1010

15.1010

He Li Ne Ar Kr

40

20

10

8

6

4

2

1

1 10 100 1000

Atomic weight

K

*(1010A

2skg1)

Xe

Figure 10. Onset criterion. Reproduced with permission fromHugel (1980) c DFVLR.

of interest to most near-term missions. This low thrust effi-

ciency results primarily from frozen flow losses and from the

powerfractiondeposited in theanodevoltage drop that devel-

ops in the vicinity of the anode surface (Gallimore, 1992;

Myers and Soulas, 1992). Exceedance of this limit is typi-

cally associated with increased anode losses, that for typical

MPD devices can reach as much as 50 to 90% of the input

power (Gallimore, Kelly and Jahn, 1993), not to mention

the erosion effects which would curtail the thruster lifetime.

As we shall see, frozen flow losses can be reduced by using

low ionization energy propellants such as lithium. However,

enabling an MPD thruster to provide the high-efficiency oper-

ation needed for real mission usage will require methods to

significantly reducethe fraction of powerwasted in theanode.

This explains why so much time and ingenuity was dedi-

cated over the years in the attempt to clarify and overcome

the onset problem. A brief review of these efforts is made in

the following sections.

5 THE ONSET RIDDLE

Following the work of Malliaris, contributions to the clarifi-

cation of the onset phenomena came from a host of authors

in the subsequent decades. A detailed review of the enor-

mous body of literature that was developed on the onset

over the years can be found in Uribarri (2008), Appendix D.

The sections below summarize the most significant findings

regarding onset phenomenology and the theories proposed to

explain its nature.

5.1 Onset phenomenology

Once the onset threshold is exceeded the magnitude of the

voltage noise (hash) increases slowly at first and then more

conspicuouslywith rising (J2/m). At even highercurrentsthe

hash is also noted to fall again (Rudolph etal., 1978; Rudolph,

1980). The characteristic frequency of the hash has been fre-

quently described as hundreds of kHz (Hugel, 1973; Kuriki

and Iida, 1984; Kurtzet al., 1987). The erosion of all thruster

components, and in particular that of the anode, rises steadily

with increasing current, not exhibiting the rise-and-fall trendof the voltage hash (Ho, 1981). Spotsapparently associated

with current concentration and local melting appear on the

anode at discrete points.

The mostprominentphenomenon signalingthe onset is the

voltage hash. An example of voltage trace taken at different

current levels is given in Figure 11. The presence of char-

acteristic frequencies in the noisy voltage traces associated

with the onset has been taken for granted until recently. The


11/22


Figure 11. The quasi-steady voltage traces for m = 3 g s1 argon, at two currents, showing the emergence of the voltage hash at highercurrent, and a 100s portion of the same traces. The currents correspond to k= 26 and 123kA2 s g1, respectively. Modified from Uribarri(2008).

first author to relate anode spots to voltage oscillations was

Hugel (1973) who estimated the main frequency of volt-

age fluctuations at approximatley 230 kHz. Similar results

were documented by many other authors afterwards (Boyle,

Clark and Jahn, 1976;Vainberg, Lyubimov and Smolin, 1978;

Kuriki and Iida, 1984; Wagner, Kaeppeler and Auweter-

Kurtz, 1998).

Recently Uribarri (2008) has questioned this picture. First

he has proved theoretically and experimentally (Uribarri and

Choueiri, 2008)that MPD thruster voltage measurements can

be affected by resonance of the electrical feeding lines; volt-

age measurements should be taken as close as possible to

thruster body in order to avoid corruption of the real sig-

nal. In addition he has shown that power spectra of voltage

measurements taken close to the thruster do not show anypreferred frequency of oscillation, but reveal that the volt-

age signal has the nature of a Brownian motion; that is, it is

the time integration of a random signal (Figure 12). What is

even more important is that voltage hash statistics are very

similar for anodes made of deeply different materials (lead,

copper and graphite were used), thus showing that voltage

fluctuations are presumably driven by a fundamental plasma

mechanism and not by anode erosion.

Thus, according to Uribarri (2008), previous detections of

peculiar frequencies in the voltage hash are to be attributed to

either a misinterpretation of the fluctuations, or. . .a source

of corruption such as the power supply.As regards the thruster components erosion phenomena,

starting at onset conditions all thruster components suffer

from intense ablation and degradation, particularly the anode,

thus reducing thruster lifetime. Anode damage, melting and

discoloration, are traces of the transition taking place in the

current pattern from a diffuse fashion to a spotty one. Urib-

arri has shown that the severity of anode damage depends

essentially on anode material, even if a general increase in

Figure 12. Power spectrum of voltage signals taken on the

Princeton Benchmark Thruster revealing a 1/f trend operation atk= 69kA2 s g1, beingk* 60kA2 s g1. Modified from Uribarri(2008).

damage severity is observed with increasing (J2/m). Indeed,

lead anodes show severe damage also at (J2/m) values much

lower than those at which intense voltage hash begins to be

observed, while anodes made of graphite present no evident

marks of damage also after several firings at (J2/m) values

much greater than critical ones.

5.2 Onset theories

The majority of theories developed to explain the onset phe-

nomena fall into two categories: anode starvation andplasma

instabilities. These two perspectives are indeed compatible

to some extent, in that starvation is often seen as a triggering

mechanism for plasma instability.


12/22


5.2.1 Anode starvation

By anode starvation or anode crisis we mean a decrease in the

density of charge carriers near theanodeup to a point at which

the anode can no longer collect the total current imposed

by the external source. The anode starvation model argues

that with increasing current levels, a condition is reached inwhich the current collected at the anode becomes sheath-

limited. The value of the sheath-limited current is taken to

correspond to the random thermal flux of electrons across the

sheath. Attempts to conduct current greater than the sheath-

limited current result in onset phenomena (Baksht, Moizhes

and Rybakov, 1974; Korsun, 1974; Vainberg, Lyubimov and

Smolin, 1978; Kurtzet al., 1987).

The total current collected at the anode is given by the

integration of charge carrier fluxes; that is, current densities,

over its surface. At low current operation, well below k,

the anode sheath is slightly electron-repelling and the local

current density can be expressed as

j=en

4vthexp

esh

kBTe

(40)

nbeing the particle density in the neutral region outside the

sheath, athe magnitudeof the anode sheath potentialbarrier,

Te the electron temperature, kB the Boltzmann constant and

vth the electron average thermal velocity

vth =

8 kBTe

me(41)

As long as the anode barrier is retarding, the current can be

increased if the barrier is lowered. But once the barrier has

vanished, the local current density cannot exceed the ran-

dom thermal flux of electrons, usually called the electron

saturation current:

jsat =en

4vth (42)

Trying to drive more current than that resulting from the

integration of the electron saturation current density over the

entire anode surface leads to a reversal in the sign of theanode sheath from negative, or electron repelling, to posi-

tive, or electron attracting. If the particle density near the

anode decreases, a large anode fall voltage develops because

the anode potential needs to increase to the level required for

ion generation. But under such conditions a diffuse anode

attachment becomes impossible and the current breaks down

to discrete anode spots with local anode vaporization. This

transition, with all its associated detrimental phenomena,

which include various possible instabilities in addition to spot

formation, is identified with the onset.

The decrease of particles density near the anode, that the

model indicates as the root cause for the onset, is mainly due

to the Hall effect, that is, to the Lorentz-force pinching com-

ponent deriving, as noted in Section 4, from the interaction

of the axial component of current density with the azimuthal

component of self-induced magnetic field. This also prompts

the idea that any increase in the anode-adjacent particle den-

sity, through propellant species or geometry changes, should

delay starvation.

5.2.2 Plasma instabilities

The second great branch of theoretical models trying to

explain onset phenomena is related to plasma instabilities.

These theories basically state that, at critical operation, con-

ditions are created in thruster channel for the development of

a variety of unstable oscillation modes.

One such type of instabilities most frequently evoked are

the so-called drift instabilities, which are excited by large

relative velocities between electrons and ions; that is, large

currents. The criterion for this instability is taken to coincide

with a critical drift velocity which the electrons attain when

the driven current exceeds a threshold (Shubin, 1976; Wagner,

Kaeppeler and Auweter-Kurtz, 1998).

Other authors have also shown that MPD thrusters are

prone to the development of a variety of microinstabili-

ties, among which the Bunemann instability, the generalized

lower hybrid drift instability, the electron cyclotron drift

instability, the ion-acoustic instability and the drift cyclotroninstability (Tilley et al., 1996; Choueiri, Kelly and Jahn,

1990, 1991, 1992; Choueiri, 2001) the space charge or

Pierce instability (Maurer, Kaeppeler and Richert, 1995;

Wagner, Kaeppeler and Auweter-Kurtz (1998, 1998)), the

Wardle instability (Di Vita et al., 2000). Actually most

of such results, while not particularly enlightening about

onset phenomena, seem much more useful to the explanation

of a variety of anomalous transport and energy absorption

effects.

5.2.3 Other onset theories

Besides the onset theories reviewed above, a number of addi-

tional theories exist in the literature.

In some of these theories onset is induced by back EMF. As

wasshown earlier (Section 4), the backelectro-motive forceis

responsible forreducingthe effectiveelectric field seen by the

plasmain thecentralpartof theacceleration channel, andcon-

sequently the electrode current attachment zone. According

to Lawless and Subramaniam it is possible for the acceler-


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ator plasma to flow quickly enough to impede current from

flowing between the electrodes; they hence hypothesize that

this mechanism is at the base of the onset phenomenon (Law-

less, 1987; Subramaniam and Lawless, 1987; Subramaniam,

1991).

Some of the theories developed to explain the onset

have put the blame on macroscopic rather than micro-

scopic instabilities. The onset of rotating disturbances in the

interelectrode region and exhaust jet of an MPD arc had

been experimentally observed since early studies (Larson,

1968;Allario, Jarrett Jr. and Hess, 1970). Schrade, Auweter-

Kurtz and Kurtz (1985) and Schrade, Wegmann and Rosgen

(1991) have suggested that onset may result from a macro-

scopic instability in a current-carrying channel originating at

the tip of the cathode.

Joint work along similar lines was carried at Centrospazio

(now Alta), Pisa, and at Consorzio RFX, Padova (Zuinet al.,

2004a, 2004b). They attributed the observed oscillations in

terminal voltage as well as in temperature and magnetic fieldmeasurements above certain values of total current to the

inception of MHD kink instability, both in self-field and

applied-field MPD thrusters.

These theories are generally lacking in oneway or another,

in that they seem applicable to specific configurations or

operating conditions rather than addressing the fundamen-

tal origin of onset in the most general sense. In addition,

although sometimes proving reasonably capable at predict-

ing values of (J2/m)

, none of the above theories can

fully explain the appearance of the voltage hash or the

spotty current attachment taking place near or beyond the

onset.Sometimes, the existence of anode spots is simply

assumed without attempting to explain their origin; the

voltage hash is then explained as a result of the forma-

tion, extinction, and movement of anode spots. The work of

Diamant, Choueiri and Jahn (1998) provided useful insights

along this line of thought.

More recently, Di Vita et al. (2000) and Uribarri (2008)

have hypothesized that spot generation can follow from a

plasma instability known as the filamentation instability,

which causes the current to fragment into many channels,

irrespective of the anode material. Current filamentation is

strongly reminiscent of the anode spots phenomenon, and

it has been observed in other plasma-pinch devices that

present analogies with MPD thrusters (Feugeas and Pamel,

1989;Milanese, Niedbalski and Moroso, 2007). Thus, the fil-

amentation approach may represent a promising clue to the

understanding of the onset.

6 APPLIED-FIELD MPD THRUSTERS

A related technology, perhaps more amenable to near-term

application, is the so-called applied-field MPD thruster (Fig-

ure 13). In this type of thruster, an external solenoid produces

a field with meridional lines of force,arrangedso as to diverge

in a nozzle fashion toward the exit (Krulle, 1998; Auweter-

Kurtz and Kurtz, 2002). The self-induced field is often of the

same order of magnitude as the field applied, so that the mag-

netic field lines are twisted in a helical fashion. The strong

axial component of the magnetic field hinders the electron

flow to the anode forcing the current to follow trajectories far

downstream of the thruster exit. The thrust fraction generated

within the channelis therefore quitesmall and Lorentz actions

mainly result here in a swirling effect. In the region where

current stream lines bend to assume a more marked radialcomponent, the Lorentz actions exhibit an azimuthal compo-

nent which sustains the swirling and a meridional component

which provides a blowing and a pumping contribution, both

contributing directly to the thrust.

The thrust in an Applied-Field MPD thruster can thus be

visualized as a combination of different components:

Figure 13. (a) Self-field MPD thruster; (b) applied field MPD thruster.


14/22


the interaction of the azimuthal (Hall) component of the

discharge current with the applied magnetic field yields

axial and radial Lorentz forces, that can both provide a

direct or indirect contribution to the thrust, TH;

the interaction between the radial component of the dis-

charge current and the self-induced azimuthal magnetic

field results in a thrustcomponent Tsfsimilar to that occur-

ring in self-field MPD devices;

the interaction of the radial component of the discharge

current with the axial component of the magnetic field

results in an azimuthal force component that causes the

plasma to rotate. The energy recovered from this swirl

motion canpartially give rise to an axial thrust component

Tsw;

finally, a gasdynamic component similar to that found in

arcjets,Tgd is generally present.

The overall thrust produced by an applied-field MPD

device can thus be expressed as

Taf= TH + Tsf+ Tsw + Tgd (43)

The azimuthal electron drift current is akin to that found

in Hall thrusters, although here the collisionality is higher.

Typical values of the Hall parameters in this type of thruster

are about 3 to 5.5. This type of thruster therefore exhibits abehavior that is intermediate with respect to self-field MPD

and Hall thrusters and may justify expectations for more effi-

cient operation and a lesser sensitivity to instabilities and

erosion compared to the former. Because of this, efficient

operation at lower powers is easier to obtain. On the other

hand, the combination of several types of effects makes the

physics of this thruster more difficult to understand and to

optimize. In addition, the fact that the discharge extends

considerably downstream does not favor accurate vacuum

chamber testing. Development has been hindered as a con-

sequence. Test results obtained with noble gases have not

been encouraging, while hydrogen (again, at high specificimpulses) has provided levels of efficiency of over 50%

(Krulle, Auweter-Kurtz and Sasoh, 1998). Recent work on

lithium-fed AF-MPD thrusters has yielded over 40% at only

130 kW, with Isp up to 3500 s. A critical review of the state

of the art of Applied-Field MPD thrusters, with a detailed

compilation of the performance levels attained by AF-MPD

devices of many different types and propellants, has been

performed by Kodys and Choueiri (2005).

7 LITHIUM PROPELLANT MPD

THRUSTERS

Lithium Lorentz Force Accelerator (LiLFA) is the name

adopted to designate a variety of MPD thruster that has come

of age in the mid-nineties (Figure 14). Its operating prin-ciple is essentially identical to that of the self-field MPD

thruster. The new designation was probably intended as a

way to refresh the image of this type of device, weary with

prolonged and sometimesfrustrating development efforts.

But the use of lithium vapor as a propellant, and the hollow-

cathode design of the center electrode may perhaps justify

the adoption of a specific name.

The choice of a low-ionization energy propellant (lithium)

in place of inert gas propellants as used by traditional MPD

thrusters, such as argon, helium, and hydrogen reduces the

power loss associated with propellant ionization, which can

represent almost 50% of the total input power especially forpower levels lower than 200kW, and is therefore beneficial in

terms of thrust efficiency. The use of lithium also offers addi-

tional advantages in terms of reduced system complexity and

storing capability. However, no space-qualified feed system

exists for lithium propellant. As for the multi-channel design

for the central electrode, this has been proved to improve effi-

ciency and increase thruster life-time by reducing electrode

erosion (Ageyev and Ostrovsky, 1993).

The LiLFA concept has also been implemented in the

applied-field version (AF-LFA), which aims to increase

the efficiency of Lithium-fed MPD thrusters at power lev-

els lower than 200kW. With the addition of an external

solenoid to enhance the magnetic field, efficient electro-

magnetic acceleration can be obtained at current levels too

low to induce a sufficiently large magnetic field. The AF-

LFA offers the advantage higher efficiencies ( 40%) at

lower power (


15/22


while maintaining exhaust velocities (1035 km s1) that are

comparable. Potential applications of the AF-LiLFA include

missions requiring relatively high thrust-to-power ratios,

such as orbit transfer, N-S stationkeeping, and drag com-

pensation (Sankaranet al., 2004).

8 SURVEY OF MAJOR R&D EFFORTS

Initially investigated in the 1960s, MPD thrusters have been

the objects of periodically funded research in the USA,

achieving slow but significant improvements in performance.

Most of the related activities were initiated and conducted for

many years at the Electric Propulsion Laboratory of Prince-

ton University (now EPPDyL). A multi-decade experimental

activity undertaken in the early 1960s was focused on a

basic model of self-field, gas-fed, coaxial, quasi-steady MPD

thruster that came to be known as the benchmark thruster

(Figure 15).

Activities carried out in Princeton have provided most

of the available knowledge on this class of device. This

information has been collected and made available to the

community in the form of a Quasi-steady Magnetoplasmady-

namic Thruster Performance Database (Choueiri and Ziemer,

2001).Also from Princetoncame fundamental insights on the

involved physicalphenomena, starting from the seminal work

of Robert G. Jahn (1968), through the efforts of a generation

of EP specialist graduated there, up to more recent contribu-

tions to the clarification of the onset phenomena. Many sig-

nificant examples of these are cited in the previous sections.

Another huge contribution to this field since theearlyyearsof development was given by German researchers, especially

from Stuttgart University. In time, the Institute of Space

Systems (IRS) group at Stuttgart performed testing activi-

ties on a large class of devices, ranging from simple arcjets,

to Applied-field and Self-field MPD thrusters. Steady-state

MPD Arcjets were extensively studied and tested at power

levels ranging from a few kilowatts to several hundred kilo-

watts, providing valuable insight on the operation of this type

of devices. Figures 16 and 17 showtwo of the thrusters tested

at IRS. For the ZT3 thruster, no indication of instability could

be detected up to 12700 A, where a (J2/m)

value of more

than 8 1010 A2 s kg1 was reached, whereas for the nozzle

type MPD thruster a critical value of ca 2.7 1010 A2 s kg1

had been found, with argon propellant, with all thrusters of

the DT series (Auweter-Kurtz and Kurtz, 2008).

Researchers from Stuttgart also carried out extensive

theoretical work on the onset problem, with important contri-

butions on the anode-starvation theory and both microscopic

and large-scale instabilities; some of the most relevant of

these are included in the cited references.

In Japan, research on MPD/QSdevicesbecame very activesince the late seventies. Important contributions were given

on the theoretical ground (e.g., Kuriki, Kunii and Shimizu,

1983) while R&D activities quickly achieved the space

demonstration level. An MPD thruster was tested onboard

the Japanese Space Flyer Unit (Figure 18) as a part of elec-

tric propulsion experiment (EPEX) launched in 1995 and

retrieved by space shuttle mission STS-72 in 1996 (Toki,

Shimuzu and Kuriki, 1997). To date, this is the only opera-

tional MPD thruster to have flown in space. A database of

measured quasi-steady thruster performance has been com-

piled in Japan by Sasoh and Arakawa (1992).

In Italy, work on MPD thrusters was started in the eight-ies focusing on experiments on ring-anode thrusters similar to

Princetons benchmark thruster. Test campaigns on geometry

Figure 15. The princeton benchmark MPD thruster: rc= 0.95cm, ra= 5.1 cm, rao= 9.3 cm, rch= 6.4 cm, ta=0.95cm, and lc=10 cm.Reproduced with permission from Burton, Clark and Jahn (1983) c AIAA.


16/22


Figure 16. Schematic and test firing of the DT2 nozzle type MPD thruster of the IRS, Stuttgart. Adopted from Auweter-Kurtz and Kurtz(2008).

Figure 17. Schematic and test firing of the ZT3 cylindrical thruster of the IRS, Stuttgart. Adopted from Auweter-Kurtz and Kurtz (2008).

Figure 18. Integration of the EPEX experiment on the Space Flyer Unit and the MPD thruster.

and scale effects (Figure 19) were carried out with heated

cathode quasi-steady MPD thrusters. Cathode heating was

aimed at assessing the impact of cathode temperature on

cathode phenomena, onset characteristics and performance

levels of the thrusters tested. Joint work on a Hybrid Plasma

Thruster - an MPD thruster with a pre-ionization chamber,

windowed anode and short cathode was carried out in Pisa in

collaboration with the Moscow Aviation Institute (Tikhonov

et al., 2000; Paganucciet al., 2001). Also, the Pisa group at

Centrospazio/Alta and Consorzio RFX, Padova, jointly per-

formed theoretical and experimental work for the study of

macroscopic instabilities of the helical kink type.

A hugevarietyof MPD thruster conceptswere investigated

in the then Soviet Union, starting in the late fifties (Gorshkov


17/22


Figure 19. Geometries of the Pisa thrusters and one of the thrusters during test.

etal., 2007). The scale of the efforts produced there is impos-

ing and the number of contributors so large to defy any

attempt to cite them here. R&D work was conducted at dif-

ferent institutions, and in particular at the Keldish Research

Center (Figure 20), RSC Energia and DB Fakel (Figure 21)

and the Moscow Aviation Institute (Figure 22). Thrusters

tested included Self-field and Applied-field devices, steady-

state devices with power levels up to MW and all types of

propellants, with lithium vapor providing the most efficient

performance (Table 1).It was the Russians who demonstrated the advantages

obtainable by the use of Lithium. Lithium-fed MPD thrusters

were operated at power levels of several hundred kilowatts,

with efficiencies of 45 percent and plasma exhaust veloci-

ties approaching 50 000 m s1. Tests of up to a 500h firing

duration at 500 kW were successfully completed. A several-

thousand hour life capability was projected, sufficient for

most of the space missions this thruster was cenceived for.

In 1996 the RIAME/MAI team lead by Professor Viktor

Tikhonov started a new investigation of Li-MPD thrusters

under NASA contract to demonstrate the level of the Russian

technology for further research. Laboratory model, applied-

field Li-MPD thrusters with power levels of 30 kW and

200 kW were built and tested. Following this activity, facili-

ties to investigatelithium-fed MPD thrusters were established

in the United States at Princeton University and the NASA

Jet Propulsion Laboratory (Goebelet al., 2005). A 200kW

version of the lithium-fed MPD thruster called the lithiumLorentz force accelerator (Li-LFA, Figure 23) tested at the

EPPDyL laboratory in Princeton, has been claimed to have

achieved erosion-free operation over 500 h of steady thrust-

ing at 12.5 N, 4000 s Is, and 48% effciency (Choueiriet al.,

1996).

Based on such activities, JPL started a program to develop

a 500 kW Li-LFA. The conceptual design of the thruster,

the 250 kW ALPHA2 thruster, is illustrated in Figure 24.


18/22


Figure 20. Self-field (a) and applied field (b) MPD thrusters of the Keldish Research Center. Reproduced with permission from Gorshkov

et al.(2007) c IEPC.

Figure 21. Lithium thrusters tested at Energiya (a) and Fakel (b). Adopted from Gorshkov et al. (2007) c IEPC.

This thruster, featuring a flared anode geometry incorporat-

ing Lithium heat pipes, a multichannel hollow cathode and

applied-field solenoid was targeted at achieving an efficiency

level in excess of 60% at Ispof 6200 s for a projected lifetime

of more than 3 years (Goebelet al., 2005).

9 FUTURE PROSPECTS

As of the end of the first decade of the twenty-first century

and almost fifty years after its conception, MPD propulsion

can hardly be said to have fulfilled the expectations of its

inventors. This is certainly dueto a variety of adverse circum-

stances. Since high efficiencies (>30%) are only reached at

high power (>200 kW), MPD thrusters require power levels

that are an order of magnitude higher than those typically

available on current spacecraft in order to be competitive

with other propulsion concepts. Therefore, research on MPD

propulsion has been left aside in recent years, in favor of

thrusters offering higher efficiencies at lower power levels.As a technology inherently suited for high power applica-

tions, it could hardly find opportunities in the scant mission

scenarios of the post-Apollo era.

But apart from external factors, it must be said that this

so promising concept has shown in time its own draw-

backs. The factors preventing achievement of performance

levels suitable for mission usage, onset in particular, have

proved particularly impervious to penetrate, understand and


19/22


Figure 22. A 200 kW thruster tested at RIAME/MAI. Reproduced with permission from Gorshkov et al.(2007) c IEPC.

Table 1. Russian experience in Li-fed MPD thrusters (Gorshkovet al.(2007)).

Organization Power (kW) Current (kA) Specific Imp. (s) Efficiency (%) Typical Duration Notes

NIITP 3001000 615 35005000 4060 5 min NIITP designFakel 300500 69 35004500 4060 30 min Energiya design

Energiya 300500 69 35004500 4060 30 minEnergiya 500 9 4500 55 500 hours Endurance testEnergiya 250500 58 30004500 3555 3060 min Cathode failureMAI 300500 69 35004500 4060 30 min Energiya design

Figure 23. The Li-LFA thruster tested in Princeton and at JPL. (a): Reproduced with permission from Choueiri and Ziemer (2001) cAIAA. and (b): Goebel et al(2005).


20/22


Figure 24. Conceptual designof theALPHA2 LFA thruster. Repro-duced from Goebelet al. (2005).

circumvent, despite an impressive amount of efforts invested

in this attempt.

Testing is another critical issue. Steady-state testing at the

megawatt level is difficult, and to date all data in the 1

6 MW range has been taken in quasi-steady mode. So far,

steady-state data is limited to less than 1 MW. The NASA-

GRC test facility had the capability to operate at steady-state

power level of up to 600 kW. Facilities to investigate lithium-fed MPD thrusters have been established in the United

States at the NASA Jet Propulsion Laboratory and Princeton

University.

Despite all shortcomings, the MPD thruster has proved to

be the only type of electric thruster capable of processing

megawatts of electrical power in a small, simple, compact

device with thrust densities of the order of 105 N m2. NASA

is currently researching both pulsed and continuous forms

of MPD thrusters with hydrogen or lithium as a propellant.

Lithium-fed thrusters in the power range of 0.5 to 1 MW

would be ideal for near-term applications requiring Isp lev-

els of 40006000 s, such as orbit transfer and Mars cargoapplications. One to 5 MW lithium thrusters may be suitable

to fulfill mid-term propulsion requirements, such as initial

piloted Mars missions. For even higher power levels, the ter-

minal voltage with lithium seems too low to process the high

power levels involved; hydrogen should be capable of provid-

ing the required efficiency at Isps of 1000015000 s, paving

the way for piloted missions to Mars and the outer planets

(Polk, 2005).

In conclusion, while no present operational spacecraft

employs MPD propulsion systems, ongoing and future R&D

activities may result in further improvements in the per-

formance and lifetime of steady-state MPD thrusters. As

research continues, the efficiency of MPD thrusters will

gradually increase, hopefully achieving levels compatible

with the requirements of future space missions. Once higher

power levels are available in space, MPD thrusters could then

becomethe methodof propulsion that carries humansto other

planets in our solar system.

REFERENCES

Ageyev, V.P. and Ostrovsky, V.G. (1993) High-current stationary

plasma accelerator of high power. 23rd International ElectricPropulsion Conference, Seattle, WA, USA. IEPC-93-117.

Alfven, H. (1960) Collision between a nonionized gas and a mag-

netized plasma.R. Mod. Phys.,32(4), 710713.

Allario, F., Jarrett, O. Jr.,and Hess, R.V. (1970) Onset of rotatingdisturbance in theinterelectrode region andexhaust jetof an MPDarc.AIAA J.,8(5), 902907.

Andrenucci, M., Paganucci, F., Grazzini, P. and Pupilli, F. (1992)Scale and Geometric Effects on the Performance of MPDThrusters. 28th AIAA/ASME/SAE/ASEE Joint Propulsion Con-ference, Nashville, TN, USA. AIAA Paper 92-3159.

Auweter-Kurtz, M., Boie, C., Kaeppeler, H.J., Kurtz, H.L., Schrade,H.O., Sleziona, P.C., Wagner, H.P. and Wegmann, T. (1994)Magnetoplasmadynamic thrusters: design criteria and numericalsimulation.Int. J. Appl. Electromagn.Mater.,4, 383401.

Auweter-Kurtz, M. and Kurtz, H. (2002) Arc devices for space

propulsion. ISU/AAAF Short Course: Introduction to SpacePropulsion, Versailles, France.

Auweter-Kurtz, M. and Kurtz, H. (2008) High-power and high-thrust-density electric propulsion for in-space transportation, inNuclear Space Power and Propulsion Systems, (ed. C. Bruno)

(2008) AIAA Progress in Astronautics and Aeronautics Series,vol. 225, Chapter 4, Reston, VA.

Baksht, F.G., Moizhes, B.Y. and Rybakov, A.B. (1974) Criticalregime of a plasma accelerator. Sov. Phys. Tech. Phys., 18(12),16131616.

Bittencourt, J.A. (1986) Fundamentals of Plasma Physics. Perga-mon Press, Oxford.

Boyle, M.J., Clark, K.E. and Jahn, R.G. (1976) Flowfieldcharacteristics and performance limitations of quasi-steadymagnetoplasmadynamic accelerators. AIAA J., 14(7), 955962.

Burton, R.L., Clark, K.E. and Jahn, R.G. (1983) Measured perfor-mance of a multimegawatt MPD thruster. J. Spacecraft Rockets,20(3), 299304.

Chen, F.F. (2006) Introduction to Plasma Physics and ControlledFusion. 2nd edn, vol. 1, Springer, New York.

Clark, K.E. and Jahn, R.G. (1970) Quasi-steady plasma accelera-tion.AIAA J.,8(2), 216220.


21/22


Choueiri, E.Y., Kelly, A.J. and Jahn, R.G. (1985) The Manifes-tation of Alfvens Hypothesis of Critical Ionization Velocity in

the Performance of MPD Thrusters. 18th International ElectricPropulsion Conference, Alexandria, VA., USA, September-October 1985. AIAA Paper 85-2037.

Choueiri, E.Y., Kelly, A.J. and Jahn, R.G. (1987) MPD Thruster

Plasma Instability Studies. 19th International Electric Propul-sion Conference, Colorado Springs, CO, USA. AIAA Paper87-1067.

Choueiri, E.Y., Kelly, A.J. and Jahn, R.G. (1990) Current-DrivenPlasma Acceleration Versus Current-Driven Energy DissipationPart I: Wave Stability Theory. 21st International Electric Propul-sion Conference, Orlando, FL, USA. AIAA Paper 90-2610.

Choueiri, E.Y., Kelly, A.J. and Jahn, R.G. (1991) Current-DrivenPlasma Acceleration Versus Current-Driven Energy DissipationPart II: Electromagnetic Wave Stability Theory and Experiments.22nd International Electric Propulsion Conference, Viareggio,Italy. AIAA Paper 91-100.

Choueiri, E.Y., Kelly, A.J. and Jahn, R.G. (1992) Current-DrivenPlasma Acceleration Versus Current-Driven Energy Dissipation

Part III: Anomalous Transport. 28th AIAA/ASME/SAE/ASEEJoint Propulsion Conference, Nashville, TN, USA. AIAA Paper92-3739.

Choueiri, E.Y., Chiravalle, V., Miller, G.E., Jahn, R.G., Ander-son, W. and Bland, J. (1996) Lorentz Force Accelerator withan Open-ended Lithium Heat Pipe. AIAA 32nd Joint PropulsionConference, Lake Buena Vista, FL, USA. AIAA Paper 96-2737.

Choueiri, E.Y. (1998) Scaling of thrust in self-field magnetoplas-madynamic thrusters.AIAA J. Propul. Power,14(5), 744753.

Choueiri, E.Y. (2001) Instability of a current-carrying finite-betacollisional plasma.Phys. Rev., E,64(6), 066413.

Choueiri, E.Y. and Ziemer, J. (2001) Quasi-steady magnetoplasma-dynamic thruster performance database.AIAA J. Propul. Power,

17(4), 520529.Diamant, K.D., Choueiri, E.Y. and Jahn, R.G. (1998) Spot mode

transition and the anode fall of pulsed magnetoplasmadynamicthrusters.AIAA J. Propul. Power,14(6), 10361042.

Di Vita, A., Paganucci, F., Rossetti P. and Andrenucci, M.(2000) Spontaneous Symmetry Breaking in MPD Plasmas.AIAA/ASME/SAE/ASEE 36th Joint Propulsion Conference,Huntsville, AL, USA. AIAA Paper 2000-3538.

Ducati, A.C., Muehlberger, E. and Giannini, G.M. (1964)High Spe-cific Impulse Thermo-ionic Acceleration. AIAA 4th InternationalElectric PropulsionConference, August-September. AIAA PaperNo. 64-668.

Ducati, A.C., Giannini, G.M. and Muehlberger, E. (1965) RecentProgress in High Specific Impulse Thermo-ionic Acceleration.

AIAA 2nd Aerospace Sciences Meeting. AIAA Paper 65-95.

Feugeas, J.,and Von Pamel, O. (1989) Current distribution duringthebreakdown in a coaxial electrodesystem.J. Appl. Phys., 66(3),1080.

Gallimore, A.D. (1992) Anode power deposition in coaxial mpdthrusters. PhD thesis, Princeton University.

Gallimore, A.D., Kelly, A.J. and Jahn, R.G. (1993) Anode powerdeposition in magnetoplasmadynamic thrusters. AIAA J. Propul.Power,9(3), 361368.

Goebel, D.M., Katz, I., Ziemer, J., Brophy, J.R., Polk, J. and John-son, L. (2005) Electric Propulsion Research and Development

at JPL. 41st AIAA/ASME/SAE/ASEE Joint Propulsion Confer-ence, Tucson, AZ, USA. AIAA Paper 2005-3535.

Gorshkov, O.A., Shutov,V.N., Kozubsky, K.N., Ostrovsky, V.G. andObukhov, V.A. (2007) Development of High Power Magnetoplas-

madynamic Thrusters in the USSR. 30th International ElectricPropulsion Conference, Florence, Italy. IEPC-2007-136.

Ho, D. (1981) Erosion studies in an MPD thruster. Masters thesis,Princeton University.

Hoyt, R.P. (2005) Magnetic Nozzle Design for High-Power MPDThrusters. 29th International Electric Propulsion Conference,Princeton, NJ, USA. IEPC-2005-230.

Hugel, H. (1973) Flow Rate Limitations in the Self-Field Accel-erator. AIAA 10th Electric Propulsion Conference, Lake Tahoe,NEV, USA. AIAA Paper 73-1094.

Hugel, H. (1980) Zur Funktionsweise der Anode im Eigen-feldbeschleuniger, DFVLR-FB 80-30.

Jahn, R.G. (1968) Physics of Electric Propulsion, McGraw-Hill,

New York.Kodys, A.D. and Choueiri, E.Y. (2005) A Critical Review of the

State of theArt in thePerformanceof Applied-fieldMagnetoplas-madynamic Thrusters. 41st AIAA Joint Propulsion Conference,

Tucson, AZ, USA. AIAA Paper 2005-4247.

Korsun, A. (1974)Currentlimitingby self magnetic field in a plasmaaccelerator.Sov. Phys. Tech. Phys.,19(1), 124126.

Krulle, G., Auweter-Kurtz, M. and Sasoh, A. (1998) Technologyand application aspects of applied field magnetoplasmadynamicpropulsion.J. Propul. Power,14(5), 754762.

Kuriki, K., Kunii, Y. and Shimizu, Y. (1983) Idealized model forplasma acceleration in an MHD channel. AIAA J., 21(3), 322326.

Kuriki, K. and Iida, H. (1984) Spectrum analysis of instabilities inMPD arcjet. 17th International Electric Propulsion Conference,

Tokyo, Japan. IEPC-84-28.

Kurtz, H.L., Auweter-Kurtz, M., Merke, W.D. and Schrade, H.O.(1987) Experimental MPD Thruster Investigations. 19th Inter-national Electric Propulsion Conference, Colorado Springs, CO,USA. AIAA-87-1019.

Larson, A.V. (1968) Experiments on current rotation in an MPDengine.AIAA J.,6(6), 10011006.

Lawless, J. and Subramaniam, V.V. (1987) Theory of onset inmagnetoplasmadynamic thrusters. J. Propul. Power, 3(2), 121127.

Lieberman, M.A.and Lichtenberg, A.J. (1994) Principlesof PlasmaDischarges and Materials Processing, Wiley, New York.

Maecker, H. (1955) Plasmastromungen in lichtbogen infolge eigen-magnetischer kompression. Zeitschrift fur Physik, Bd. 141,198216.

Malliaris, A., John, R., Garrison, R. and Libby, D. (1972) Perfor-mance of quasi-steady MPD thrusters at high powers. AIAA J.,

10(2), 121122.

Maurer, M., Kaeppeler, H.J. and Richert, W. (1995) Calculation ofnonlinear drift instabilities in magnetoplasmadynamic thrusterflows.J. Phys. D: Appl. Phys.,28, 22692278.


22/22


Myers, R.M. and Soulas, G.C. (1992) Anode Power Deposition inApplied-Field MPD Thrusters. 28th AIAA/ASME/SAE/ASEE

Joint Propulsion Conference, Nashville, TN, USA. AIAA Paper92-6463.

Milanese, M.M., Niedbalski, J.J. and Moroso, R.L. (2007) Fila-ments in thesheathevolution of thedense plasmafocusas applied

to intense auroral observations. IEEE Trans. Plasma Sci.,35(4),808.

Mitchner, M. and Kruger C.H., Jr. (1992) Partially Ionized Gases,Wiley, New York.

Paganucci, F., Rossetti, P., Andrenucci, M., Tikhonov, V.B. andObukhov, V.A. (2001) Performance of an Applied Field MPD

Thruster. 27th International Electric Propulsion Conference.Pasadena, CA, USA. IEPC Paper 01-132.

Polk,J. (2005)Lithium-fuelled electromagnetic thrusters for roboticand human exploration missions. Space Nuclear Conference, SanDiego, CA, USA.

Rudolph, L. (1980) The MPD thruster onset current performancelimitation. PhD thesis, Princeton University.

Rudolph, L., Jahn, R.G., Clark, K. and von Jaskowsky, W. (1978)Onset Phenomena in Self-Field MPD Arcjets. 13th InternationalElectric Propulsion Conference, San Diego, CA, USA. IEPC-78-653.

Sankaran, K., Cassady, L., Kodys, A.D. and Choueiri, E.Y. (2004)A survey of propulsion options for cargo and piloted missions toMars.Astrodyn., Space Missions, and Chaos. The Annals of theNew York Academy of Science, 1017, 450467.

Sasoh, A. and Arakawa, Y. (1992) Electromagnetic effects in anapplied-field magneto plasmadynamic thruster. AIAA J. Propul-sion Power,8(1), 98102.

Schrade, H.O., Auweter-Kurtz, M. and Kurtz, H. (1985) Stabil-ity Problems in Magneto plasmadynamik Arc Thrusters. AIAA18th Fluid Dynamics, Plasma dynamics and Lasers Conference,

Cincinnati, Ohio, USA. AIAA-85-1633.Schrade, H.O., Wegmann, T. and Rosgen, T. (1991) The Onset

Phenomena Explained by Run-away Joule Heating. 22nd Inter-national Electric Propulsion Conference, Viareggio, Italy. AIAAPaper 91-022.

Shubin, A. (1976) Dynamic nature of critical regimes in steady-statehigh-current plasmaaccelerators. Sov. J. PlasmaPhys., 2(1),1821.

Spitzer, L. Jr. (1964) Physics of Fully Ionized Gases, Wiley, NewYork.

Subramaniam, V.V. (1991) Onset and Erosion in Self-field MPD

Thrusters. 22nd International Electric Propulsion Conference,Viareggio, Italy. AIAA Paper 91-021.

Subramaniam, V.V. and Lawless, J.L. (1987) Onset in Magne-toplamadynamic Thrusters with Finite Rate Ionization. 19th

International Electric Propulsion Conference, Colorado Springs,CO, USA. AIAA-87-1068.

Tikhonov, V.B., Antropov, N.N., Dyakonov, G.A., Obukhov, V.A.,Paganucci, F., Rossetti, P. and Andrenucci, M. (2000) Investi-

gation on a New Type of MPD Thruster. 27th EPS Conferenceon Controlled Fusion and Plasma Physics. Budapest, Hungary,

ECAVolume 24B, pp. 8184.

Tilley, D.L., Choueiri, E.Y., Kelley, A.J. and Jahn, R.G.(1996) Microinstabilities in a 10-kilowatt self-field magneto-plasmadynamic thruster. J. Propul. and Power, 12(2), 381389.

Toki, K., Shimuzu, Y. and Kuriki, K. (1997) Electric PropulsionExperiment (EPEX) of a Repetitively Pulsed MPD Thruster Sys-tem Onboard Space Flyer Unit (SFU). 25th International ElectricPropulsion Conference, Cleveland, OH, USA. IEPC-97-120.

Turchi, P.J. (1986)Critical speed and voltage-current characteristicsin self-field plasma thrusters.AIAA J. Propul. Power,2(5), 398401.

Uribarri, L. (2008) Onset voltage hash and anode in quasi-steadymagnetoplasmadynamic thrusters. PhD thesis, Princeton Univer-sity.

Uribarri, L. and Choueiri, E.Y. (2008) Corruption of pulsedelectric thruster voltage fluctuation measurements by trans-mission line resonances. AIAA J. Propul. Power, 24(3), 637639.

Vainberg, L., Lyubimov, G. and Smolin, G. (1978) High-currentdischarge effects and anode damage in an end-fire plasma accel-erator. Sov. Phys. Tech. Phys.,23, 439443.

Wagner, H.P., Kaeppeler, H.J.and Auweter-Kurtz,M. (1998a) Insta-bilities in MPD thruster flows: 1. space charge instabilities inunbounded and inhomogeneous plasmas.J. Phys. D: Appl. Phys.,

31, 519528.Wagner, H.P., Kaeppeler, H.J. and Auweter-Kurtz, M. (1998b)

Instabilities in MPD thruster flows: 2. investigation of drift andgradient driven instabilities using multi-fluid plasma models. J.Phys. D: Appl. Phys.,31, 529541.

Zuin, M., Cavazzana, R., Martines, E., Serianni, G., Antoni, V.,Bagatin, M., Andrenucci, M., Paganucci, F. and Rossetti P.(2004a) Critical regimes and magnetohydrodynamic instabili-ties in a magnetoplasmadynamic thruster. Phys. Plasmas, 11(10),47614770.

Zuin, M., Cavazzana, R., Martines, E., Serianni, G., Antoni, V.,Bagatin, M., Andrenucci, M., Paganucci, F. and Rossetti P.

(2004b) Kink instability in applied field MPD thrusters. Phys.Rev. Lett.,92, 225003.

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