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FINAL REPORT

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NASA Grant Number NAG 3-206

IMPROVEMENT OF ION THRUSTER DESIGN

by

Raymon T. Carpenter

Principle Investigator

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Department of Physics and Astronomy

THE UNIVERSITY OF IOWA

Iowa City, Iowa 52242
FINAL REPORT

for

NASA Grant Number NAG 3-206

IMPROVEMENT OF ION THRUSTER DESIGN

by

Raymon T. Carpenter

Principle Investigator
INTRODUCTION

This report covers work done at the University of Iowa under

NASA grant NAG3-206, starting in September, 1981 and continuing

until September, 1984. During this time extensive measurements have

been made on two physically different ion thrusters. One was

supplied by NASA Lewis and is the 17 cm. ion thruster described by

Sovey (Sovey, 1981). This thruster was configure^ with Inxl"x0.42"

SmCo magnets in a line cusp configuration. The second thruster was

constructed at the University of Iowa and is identical in inside

dimensions to the first. It differs in that the iron walls are

somewhat thicker and the conical end section is bolted onto the main

chamber rather than being welded so that it could be easily

exchanged with a flat end section, such as is used in the ring-cusp

configuration. It is equipped with Inxl"x0.25" SmCo magnets and has

been used in both ring cusp and line cusp arrangements. The same

hollow cathode was used with both thrusters. Early measurements

were performed with the NASA thruster but after establishing that

the Iowa thruster had essentially identical plasma properties and

equal or slightly superior performance parameters, all later work

was done on the new device.

It is assumed that the reader is familiar with the general

nature of the ion sources developed at NASA Lewis and no general

discussion of these devices will be given. The papers by Sovey

(Sovey, 1981; Sovey, 1982) and references therein are an excellent
-2-

introduction to this material. Fig. I.I is taken from Sovey's 1981

reference and shows the essential features of both thrusters used in

the work reported here. The hollow cathode assembly originally used

in this thruster was slightly altered and is shown in the

configuration used in the present work in Fig. 1.2. Also it was

found that the new magnets used in the Iowa thruster line cusp

configuration were more difficult to handle. For this reason, and

also to improve the magnet cooling, the magnet rows were encased in

brass channels as shown in Fig. 1.3. The iron pole-faces were

added because previous work at NASA-Lewis had shown a marginal

improvement in performance with such an arrangement (Sovey, 1981).

Measurements of two types were performed. Langmuir probes were

used to measure plasma potential, electron density and electron

temperature in all regions inside the thruster. These data were

obtained for several sets of discharge voltages and currents.

Investigations of the ring cusp configurations were considerably

more extensive than for the line cusp case. This is essentially

because our procedures improved markedly during the course of the

grant period and the ring cusp measurements followed those on the

line cusp configuration. Also both ion and electron currents have

been measured to all parts of the walls and to all parts of the

cathode assembly using collecting plates of various types. These

measurements have also been made for various parameter sets.
-3-

The experimental conditions under which the data to be

described were taken differ in two respects from those at

NASA-Lewis. First, no current regulator was available for the main

power supply. Therefore the discharge was stabilized by inserting a.

one-ohm resistance in series with the power supply. For the runs

where plasma parameters inside the thruster were determined as a

function of position, the discharge current was kept constant so the

series resistance had no effect. However, for runs where data were

taken with fixed probes over a wide range of operating parameters,

the usual method of operation was to set the power-supply voltage

and then vary the discharge current by varying the gas flow in the

hollow cathode. The result of course was that the discharge

voltage, discharge current and flow rate all varied from point to

point, a situation that is not particularly unwanted but which may

make comparison with data taken under different circumstances

difficult. The second difference is possibly more significant. The

vacuum system available was significantly limited compared to those

used at NASA-Lewis. Two systems were used. Early data were taken

with a system pumped with a 6 inch diffusion pump with an overall

pumping speed of about 1000 liters per second. Later data were

taken using a system pumped by a 10 inch pump and an overall speed

of about 4000 liters per second. The result was that at the higher

gas flow rates there was undoubtedly a reflux of gas into the

thruster chamber at rates that were difficult to estimate.

Operationally this is equivalent in every way to introduction of gas
-4-

into the chamber through an inlet separate from the hollow cathode,

as was customarily done at Lewis, so there was no difference in the

physical situation. However, control of the situation was not

possible.

In the following we first discuss some generalities about the

data-taking methods used. All of the data are then summarized and

discussed as it is presented in section 2. The organization. is

approximately chronological. Finally, a discussion is given in

section 3 of the operation of the thruster based on calculations of

ion orbits in the electric and magnetic fields that exist in the

thruster. Other analytic considerations and results are discussed

in this section also. A short final survey is given at the end.

Much of what will be presented here is contained in the

Master's thesis of Mr. Scott Boardsen (Boardsen, 1984) which is

appended to this report in a slightly abbreviated form, to

facilitate reference to this work. The abridgment consists of the

elimination of non-essential introductory comments. Many details

concerning this work are covered there and will not be repeated in

this report. There is, however, considerable overlap between the

two papers so the present report is essentially self-contained.
-5-

Section 1 EXPERIMENTAL METHODS

1.1 Langmuir Probe Measurements

The plasmas encountered in the ton thrusters are dense and hot.

There is considerable density variation inside . the thruster but

typical values range from on the order of 1013/cm3 near the hollow

cathode exit aperture to a tenth or less of this near the walls.

This influences greatly the types and sizes of probes that can be

put into these devices and also the manner in which they can be

employed. Tungsten wires with diameters of .25 mm or .38 mm were

used in most cases with about 2 mm of length exposed to the plasma.

Even with such small areas extreme care was required to prevent

melting when probing the densest regions. A computer was used to

rapidly sweep the prpbe bias and digitally record the resulting

current. The time during which significant electron current was

drawn was kept less than .01 seconds followed by a cooling period

during which the probe was kept at a negative bias. The computer

(an S-100 bus system) and ADC/DAC (Cromemco D+7A-I/0) was capable of

sweeping a 50 volt range with 5 points/volt in .03 seconds. The

Langmuir characteristics were analyzed in the usual way (Chen,1965)

after completion of the experiment. Even with these precautions it

was difficult to obtain data within one cm of the hollow cathode

exit aperture without probe damage. In fact, exactly on axis the

closest possible approach was approximately 6 cm. In these regions
-6-

the electron current had to be kept well below the saturation point

and therefore only the temperature was measured. Two general

classes of probe measurements were made. First, in some of the

earlier work a set of fixed probes was used. For these cases, the

plasma parameters were obtained for several sets of thruster

operating conditions and the object generally was to determine how

the plasma parameters, most importantly the plasma density, were

related to the beam current and to the discharge voltage and

current. In the second class of measurements a movable probe was

used and the object was to determine how the plasma parameters

varied throughout the interior of the thruster chamber for various

fixed thruster operating conditions. These measurements were much

more time,consuming and it was usually possible to acquire data for

only a single set of thruster operating conditions in a day. The

probes were insulated, except for the tips, by alumina ceramic

tubing. The main axial shaft passed through a sliding vacuum seal

which permitted axial motion (variations in z) and rotation

(variations in 6). In turn the seal was on a sliding plate which

permitted variations in r. The probe shaft entered the thruster

through a slit in the end plate, which was a 120 wires per inch

screen grid for some of the runs and a solid sheet for others. For

some of the runs the data were digitized and stored in a computer

for off-line analysis while in others probe saturation current

(proportional to plasma density) was read from an oscilloscope

display of the probe characteristic using a transistor curve tracer.
-7-

1.2 Loss measurements

In principle the measurement of the flux of electrons or of

ions to a given surface involves only the measurement of the current

to an insulated plate placed on the surface and biased at the

original surface potential. In practice both electrons and ions

flow to all surfaces and it is necessary to separate the

contributions from each species. This can be done by obtaining an

I-V characteristic of the plate. The usual situation is that the

original surface is negative relative to the plasma. This is

because the anode is usually the most positive conducting surface in

the plasma and, in a surface confinement discharge plasma, the

plasma is positive relative to the anode by a few electron

temperatures. If the surface were positive, the current to it would

be completely dominated by electrons and the ion current, because of

the low ion temperature and the large ion mass, would be completely

negligible. In this case the actual current measured to the plate

when it is biased at the wall potential is the desired electron

current. The loss plate characteristic, needed when the wall is

negative with respect to the plasma, is identical in form to a usual

Langmuir characteristic. The contribution from the ions is a

straight line region when the plate bias is negative enough to repel

all electrons in the plasma. When extrapolated to the wall

potential this gives the ion current and any residual is the

electron current. Note that in the case of ion losses to the
-8-

cathode, this procedure is unnecessary since the cathode is the most

negative surface in the chamber. Nevertheless, a few

characteristics were taken in this case also to check on any

unforeseen source of high energy electrons.

Several different sorts of probes were used to measure loss

currents to different surfaces in the thruster. These probes

differed from the small- area probes used to map the interior of the

plasma in that they were planar and had much larger areas, on the

order of a few square centimeters since the ion currents were

generally quite small. In the case of the sides of the cathode

assembly, they took the form of tantalum foils, insulated from and

attached to the assembly with Kapton tape. Lead in wires were

spot-welded to the foils. The foils were usually 1 cm wide and a

few cm long, the long dimension being wrapped around the assembly.

Loses to the front of the cathode assembly, excluding the heat fin

attached to the cathode itself, were measured to a disk, with a

concentric hole large enough to allow the actual cathode to

protrude, which covered the entire front of the magnet and magnet

holder outside of the heat fin and again held in place with Kapton

tape. Some loss measurements were made using only a segment of such

a disk. Measurements of ion loss currents to the heat fin were not

made with plane probes, although the region near the heat fin was

extensively investigated with the wire probes described previously.

Measurements of loss currents to the walls were made with foils
-9-

taped to the walls and to the magnets, and also with discs embedded

in the iron pole-faces (which were used when the Iowa thruster was

in the line-cusp configuration) and with a plane probe attached to

the same movable arm used with the wire probes and described above.

Each of these arrangements has its conceptual problems and

advantages. The foils seem in principle to be the best but there is

the problem of lack of mobility and of getting the lead in wires out

of the chamber without altering the plasma. Embedding discs in the

pole-faces certainly provided the least disturbance of the plasma

and the wires were taken out via a slit in the back of the

pole-faces so they were completely isolated from the plasma region.

However. the method unfortunately cannot be used in regions where

such embedding is impractical, such as on the cathode assembly or

between the magnets or in the cusp regions if pole-faces are not

used. The movable probe has the advantage of complete mobility but

probably produces the most severe perturbation of the plasma.

Fortunately, results from all three types of probes were consistent

in cases where they could be compared.

1.3 Scope of the Measurements

The various operating conditions under which the plasma

parameters were measured for the line cusp configuration are shown

in Fig. 1.1. In this figure the dots indicate parameter sets where
-10-

single measurements were made. The open circles are cases where

extensive measurements were made at most points within the chamber.

The sets of thruster parameters for which loss measurements

were made in the line cusp configuration are also shown in Fig.

1.1. The open squares indicate points where relatively extensive

measurements were performed while at the points indicated by open

triangles limited data were acquired. While not identical to the

parameters for which the plasma parameters were mapped, there is

enough overlap that results of the two types of measurements can be

compared without unwarranted extrapolation.

Figure 1.2. illustrates the scope of the measurements for the

ring cusp configuration. The significance of the various shapes for

the points is the same as discussed above for Fig. 1.1. The fact

that the ring cusp case was studied more more intensively than the

line cusp case is not apparent from these figures because the

difference is primarily in the number of interior points that were

investigated in the two cases.
-11-

Section 2 EXPERIMENTAL RESULTS

The optimization of thruster design can be considered as the

maximization of beam current for a given power input, or as the

minimization of power input for a given beam current. It is some

advantage to be able to consider plasma density instead of beam

current in these considerations and this would of course be strictly

possible if these two parameters were in direct proportion. The

relation between beam current and plasma density determined by

Langmuir probe measurements in the line cusp case is shown in Fig.

2.1. The approximate proportionality is obvious. For a given

plasma density, the lower values of beam current correspond to

higher values of discharge current. This effect is believed to be

due to the increased gas flow rate which was used in order to

produce the higher discharge current, which in turn increased the

neutral pressure in the thruster thereby decreasing the beam current

by collisional effects. It is not clear whether this effect would

be as large in an experimental setup with more pumping capacity, but

regardless of the experimental pumping speed, some beam reduction at

high enough gas flow rates must occur since pumping of the chamber

itself will be impeded by the extraction grids and acceleration

electrodes. As a crude approximation, one can imagine the neutral

gas to form a uniform cloud through which the ion beam must

penetrate. In this case the beam current should vary with neutral
-12-

pressure p as exp(-bp), where b is some constant. Fig. 2.2 shows a

semi-logarithmic plot of the ratio of beam current to plasma density

versus neutral pressure, as indicated by the fore-pressure in the

system diffusion pump, for the same data set used in Fig. 2.1.

Assuming constant pumping speed the fore-pressure is proportional to

the neutral pressure in the chamber. The data tend to support a

pressure dependence of the type suggested, but the scatter clearly

indicates the limitations of the model. It is clear that the beam

current depends on the plasma density in the vicinity of the

extraction grid. This density will depend on the rate of diffusion

of ions into the region and the diffusion rate will depend on

gradients in the plasma density and in plasma potential (the

electric field). These gradients should be taken into account in a

complete theory, although their effect seems to be relatively weak.

Some measurements of the spatial variations in plasma density

are shown in Fig. 2.3 for the line cusp case. The gradients

mentioned above are evident. Some measurements of the radial

variation of the density are shown in Fig. 2.4. Clearly the plasma

is approximately one-dimensional except for regions very near the

walls. Various authors have given the results of calculations of

plasma density for both planar and cylindrical geometries and with

various assumptions about the ion production (Tonks and Langmuir,

1929; Kino and Shaw, 1966; Self, 1967). In all cases ion losses

could occur only in one direction along the axis. The density was a
-13-

maximum over some plane and Chen decreased in the loss direction.

In the thruster, losses occur at the extraction grid but also in the

other end of the chamber on the cathode, which presents a surface

with a total area comparable to the extraction port and which is

biased at about the same negative potential as the extraction grid.

The density is therefore a maximum near the center of the chamber

and falls off in both directions. The solid lines shown in Fig.

2.3 are the calculations of Self (Self, 1967) normalized at the

point of maximum density. In these calculations the ion production

is assumed to occur throughout the chamber with a rate proportional

to the electron density, a situation which is probably close to the

situation in the thruster chamber. The agreement would seem

satisfactory. These same calculations show little difference

between the planar case and two dimensional results with cylindrical

geometry. This is not surprising in view of the limited radial

variation predicted in the two dimensional calculations and observed

in the thruster as shown in Fig. 2.4.

Some examples of loss currents observed in the line cusp case

are shown in Fig. 2.5. These are losses in the cusps and were

obtained by measuring currents to disks imbedded in the iron

pole-faces. The ion losses fall off in the half of the chamber near

the grid at about the same rate as the axial decrease in density in

this region. The increased loss to the cusps near the cathode is

not understood however. The variation in electron losses along the
-14-

cusp also is not understood. The fact that the enhancements,

relative to the interior plasma density, in the ion and electron

losses are in opposite directions could possibly be explained by a

force such as that due to an axial electric field very near the

pole-faces (which, it should be remembered, are also the anodes for

the discharge) or due to E x B. However, the necessary fields have

not been observed. The losses between the cusps are very small.

Figure 2.6 shows the azimuthal and radial variation in density,

electron temperature and plasma potential at a fixed axial position

near the center of the chamber. The plasma density approaches zero

at regions near the wall and between the cusps. These and other

potential measurements were undertaken with the expectation of

finding potential islands between the cusps such as have been

observed in other surface cusp-confinement plasmas (Hershkowitz, et

al, 1979). The results show, however, that the islands are not as

well developed in the present case. This is consistent with the

view that the islands form because of the need to equalize electron

and ion losses when the electrons, but not the ions, are confined by

the magnetic fields. The ion gyroradius is expected to be larger

than the electron gyroradius by a factor of 86 for Argon, assuming

the electron temperature is ten times the ion temperature. However,

for the very strong magnets used in the thruster, the field between

the cusps was about 1200 gauss so the ion gyroradius was about 3.5

mm. Thus ions were well confined by the magnetic fields and no

additional electrostatic confinement was needed.
-15-

The ring cusp configuration presents a considerably different

plasma situation. This is because the bulk of the plasma is no

longer in a nearly magnetic field free region, as with the line cusp

case. The radial variation of the magnitude of B measured in the

line cusp case is shown in Fig. 2.7 as the solid lines. The upper

solid line was measured along a radius connecting opposite

pole-faces and the lower solid curve was measured along a radius

between the cusps. The dashed curves show the same thing for the

ring cusp case. The upper dashed curve is for an axial position

corresponding to one of the rings and the lower dashed curve is at

an axial position between rings. The magnetic field in the central

region is larger and less homogeneous in the ring cusp case. One of

the results of this difference is a considerable increase in the

radial density gradients and potential gradients. Enough data were

taken for the ring cusp configuration to allow the construction of

contour plots to display the plasma parameters throughout the

device. Examples are shown in Figs. 2.8, 2.9 and 2.10. The axial

variation in the plasma density is shown in Fig. 2.11. This result

differs from that shown in Fig. 2.3 in two ways. The most obvious

is the large increase in density in the vicinity of the cathode.

Some considerations of the plasma production process will be given

in the next section. For now we note only that this increase in

density is consistent with the visual observation of a very bright

tapered column near the cathode orifice which was not noticed in the

line cusp case. It is clear from this observation and from Fig.2.11
-16-

that much more plasma production occurs along the central column

near the cathode in the ring cusp case. The second difference is

that the agreement with the calculations of Self, shown by the

dashed line in Fig. 2.11, is not as satisfactory. It is clear from

Fig. 2.10 that the situation is very two dimensional now. A

comparison of the radial variation of plasma density would show even

greater disagreement between theory and experiment. This is perhaps

not surprising in view of the reduced homogeneity of plasma

production. The density variations in both the radial and axial

directions could possibly be fit by Self's results, .which assume a

sort of volume production of plasma, superimposed on a large peak

which is centered a few centimeters in front of the cathode and

falls off in all directions, perhaps as a Gaussian, which would

result from relatively localized plasma production near the cathode

orifice. Self's calculations, in which plasma production is

proportional to electron density would be appropriate if such a

Gaussian peak in electron density could be introduced self

consistently.

Two different arrangements of the ring cusps were investigated

in addition to the one discussed above. One of these, which had

four rings instead of five, was found to have extremely poor

efficiency and so no very extensive measurements were made. The

other arrangement was identical to the first except the magnet ring

on the base plate was inverted. This change was suggested by
-17-

calculations of the magnetic field which were performed on various

geometries with the object of increasing the flux which directly

linked the cathode with the extraction grid. Figures 2.12 and 2.13

are of the magnetic field directions in the two cases and show the

increase in flux linkage in the second design. Figures 2.14, 2.15

and 2.16 show the plasma density, plasma potential and the electron

temperature for this case. The axial variation in plasma density

was shown in Fig. 2.12. The increase in density near the cathode

is not as steep as for the first case and the agreement with Self's

calculations is not better. The plasma extends further away from

the center but the radial gradients are still high and the plasma is

still not planar over any appreciable area.

Loss currents in the cusps and to the cathode for the ring cusp

in the first configuration are shown in Figs. 2.17 and 2.18. These

data were obtained with foils fixed to the various surfaces. Figure

2.19 shows a continuous distribution of ion currents over part of

the axial range for the second ring cusp configuration. These data

were obtained with a thin rectangular plate (3.2 mm X 12.8 mm) swept

axially at a radial position 2 mm from the magnet pole-faces.

Figure 2.21 shows representative loss distributions for the second

ring cusp case for several sets of operating parameters. Of the

sets that were investigated, the one indicated by dashed lines had

the lowest beam cost factor (148 watts/amp) and for this case the

losses are significantly lower to rings C, D and E. However, the
-18-

beam-cost factors for the other cases shown vary greatly and there

is no significant difference between the relative losses to the

various rings. These data, and those shown in Fig. 2.18, show

axial variations in ion loss flux quite similar to what was seen in

the line cusp case. In this case, there is a close parallel to the

axial variation in plasma density. The electron losses shown in

Fig. 2.17 also show a correspondence to the local plasma density in

contrast to the observation in the line cusp . case. However, the

magnitude and inhomogeneity of the magnetic field in the interior of

the chamber makes the correlation between losses and density

different in this case. Even in regions where the magnetic field is

weakest the electron gyroradii are less than a millimeter and in

most regions they are less than 0.1 mm. Almost all plasma electrons

are trapped in this case and losses depend on scattering of

electrons into loss cones. Of course the rate of such scattering

depends oh the electron density and so the loss fluxes should depend

on density as is observed. The data shown in Fig. 2.19 show that

there are significant ion losses between the cusps. In fact there

is more total ion flux between rings A and B than there is in either

ring A or B. Overall the ion loss between cusps is between 50% and

100% of the loss in the cusps. The elimination of these

between-cusp losses would seem to be an attainable objective if

further improvements in thruster performance is desired.
-19-

Of the three geometries that were extensively investigated, the

second ring cusp arrangement gave the lowest beam cost factor. The

lowest actual ratio of input power to beam current was 205

watts/amp. The beam current was collected on a screen with a

geometric transmission of 0.36 so if 100% of the beam were extracted

the beam cost factor would be 131 watts/amp. The corresponding best

value with the ring cusps in the first arrangement was 165

watts/amp. In the line cusp arrangement beam cost factors of 180

watts/amp were achieved and in this case the beam was collected on a

solid sheet so no correction was needed. It is likely that further

improvements in the beam cost factor could be achieved by variations

in the positioning of the rings but this has not been attempted.
-20-

Section 3 ADDITIONAL DISCUSSION

Some insight into the nature of the problem of optimizing

thruster design can be obtained by studying the orbits of ions in

the thruster. To this end a program was written to calculate

exactly the orbits in the multi-dipole magnetic field which exists

in the thruster and in an electric field which is obtained from the

experimentally determined potential. The magnetic fields were

calculated analytically by replacing the magnet rings with two

current loops nearly coincident with radii equal to the radius of

the magnet rings and with oppositely flowing currents. The electric

fields were approximated by analytic functions. The experimental

potential for a particular set of plasma parameters was shown in

Fig. 2.15. The analytic potential used in the orbit calculations

is shown in Fig. 3.1. The magnetic field used in the orbit

calculations is shown in Fig. 3.2. This field can be easily

changed by changing the current- loop parameters. The ions were

assumed to be born at various points throughout the thruster

although most of the calculations were performed at points on axis

or just off axis. Various initial energies were assumed for the

ions. In all cases calculations were done for all initial

directions between 0 and 180 degrees in two degree intervals. The

orbits were followed until the ions contacted some surface.
-21-

Some examples of orbits calculated for ions born with very low

energy near the exit orifice are shown in Figs. 3.3 and 3.4. In

plot 3.3a) the source was at an axial position of 17.0 cm and 0.1 cm

off axis. Almost all of the ions are lost to the back plate. They

are forced there by the electrostatic field and are not well

confined by the back-plate magnet ring. The reflections that seem

to occur on the horizontal axis would be simply continuations into

the lower quadrant, but are plotted as shown to conserve space in

the figure. Plot 3.3b shows orbits for a source on axis at a radial

position of 16.9 cm and plot 3.3d has the source at the same radial

position but displaced 0.1 cm from the axis. Considerably more of

the ions get to the extraction grid (10% in plot 3.3b and 13% in

plot 3.3d)). Two conclusions are to be drawn from this: First, a

very slight change in the position the ions are born makes a large

change in the likelihood that the ion will reach the extraction

grid. Second, since very little loss flux is observed to the

back-plate magnet ring (see Figs. 2.18 and 2.21) not many of the

ions are born on the cathode side of the potential maximum near the

cathode (shown in Figs. 2.9 and 2.15). The source in plot c) is at

an axial position of 16.0 cm and .1 cm off axis. There are 46

orbits that hit the extraction grid, 36 that hit the cusp at 5.2 cm

and are not mirrored, and 8 that hit the back plate. Figure 3.4

shows orbits for ions born at 16.0 cm, 0.1 cm off axis, and at 14.0,

12,0 and 9.0 cm, all on axis. The increase in the probability of

being extracted as the point of origin moves toward the grid is
-22-

obvious. Figure 3.5 shows orbits for ions born with energies of 0.4

eV at a) 16.9 cm, b) 16.0 cm, c) 14.0 cm and d) 12.0 cm. Figure 3.6

shows the same thing for ions born with 1.0 eV at the same points.

Ions with 1.0 eV, and even higher energies, can arise from charge

exchange with fast neutrals. The fast neutrals arise from

neutralization at the walls of ions which fall from the central

region where the potential is on the order of 4 volts positive

relative to the walls. These neutrals then travel back into the

central region without further change in energy, except by

collisions, until they either charge exchange with a low energy ion,

creating a fast ion, or drift out of the extraction port. However,

an examination of the various orbits indicates that the dependence

on energy is very slight. The dependence on the position of origin,

relative to the potential, is significant. Although there is not a

monotonic relationship it seems that the nearer to the grid that

ions originate, the better chance they have of being extracted, a

not surprising conclusion. This dependence on the potential points

out what is probably the most important deficiency in this

treatment. In a complete theory the potential would be determined

self-consistently as the structure required to keep charge densities

and fluxes balanced. To impose a potential and then look at

particle orbits can provide the basis for a few generalities, but

can probably not be used as the basis for a quantitative treatment

of the device.
-23-

It is also clear that the magnets are sufficiently strong to

confine the ions, which is consistent with the fact that potential

islands do not occur between the cusps. In almost no cases do any

of the orbits terminate on the side walls between the cusps. This

is contrary to the observation, illustrated in Fig. 2.19, that

total between-cusp losses are comparable to losses in the cusps.

The conclusion is that diffusion plays an extremely important roll

in determining the performance of the thruster. This of course is a

second reason that orbit calculations have limited .quantitative use.

These calculations do, however, show the extreme importance of the

position at which the ions are born.

In view of this, it is clear that considerations of ion

production are at least as important as considerations of ion loss

in calculations of thruster performance. There are two aspects to

this part of thruster operation. First, as the orbit calculations

show, for a given ion production rate, lower beam cost factors will

result if the average ion production position can be moved toward

the extraction grid. Second, it is desirable to optimize the ion

production rate for a given discharge current. In his thesis,

Boardsen shows that bulk ion production due to thermal plasma

electrons can account for only from 10% to 30% of the ion production

(Table 5 in the thesis) . He finds a very hot dense region near the

cathode where apparently most of the ionization occurs. The

temperatures of electrons in this region have been remeasured and we
-24-

find that the extremely high values reported by Boardsen were

probably in error, due to overloading of the electron current

measuring circuit. The temperatures are very high in this region,

however, reaching 7.9 eV at a point on axis and 6 cm from the exit

orifice. It was not possible to make reliable measurements on axis

at points closer to the orifice than this because of probe damage,

even using extreme care. At points just 1 cm off axis, however, the

electron temperature drops to 2 to 3 eV, even 1 cm from the orifice,

and the density is low enough that measurements can be performed.

This implies a jet-like beam of electrons from the cathode which is

well confined by the axial magnetic field in this region. If this

beam were to continue without interaction it would be reflected by

the extraction screen, return to the cathode where it would be

reflected again and possibly make several such loops before being

deflected or making ionizing collisions. However, visual

observations as well as density and temperature measurements make it

clear that the beam is rapidly thermalized within 5 to 10 cm from

the cathode. It is believed that as much as 70% of the ion

production occurs within this region. This extremely efficient

conversion of the energy deposited in the chamber by the discharge

current electrons into ionization may be the principal reason for

the high performance observed in the ring cusp case. The mechanism

for this conversion is not known but is probably connected with an

instability, perhaps associated with the production of electron

cyclotron waves, which could be excited by a beam-plasma interaction
-25-

with electrons accelerated at the cathode exit orifice. Stable

double layers, needed for the strong electric fields required for

such acceleration, are known to exist at points where the plasma

column changes diameter (Andrews and Allen, 1971) and in diverging

magnetic fields (Alport et al, 1986). Both of these conditions

exist at the cathode orifice so the existence of a stable strong

double layer is almost guaranteed. Intense UHF noise has been

observed in the high potential side of similar double layers in

cases where rapid thermalization of the beam .electrons is also

observed (Lindberg, 1982a and 1982b). It might be the case that

various changes in thruster performance observed here and elsewhere

are due, not so much to changes in losses of ions to the walls, but

to changes in ion production rates due to modification of the

environment near the cathode orifice. At any rate, this is an area

that should be thoroughly investigated in future thruster studies.
-26-

FINAL SUMMARY STATEMENT

In spite of the dense hot plasmas that exist in ion thrusters,

it is possible to investigate their plasma properties with simple

modifications of standard techniques. It is found that in the line

cusp configuration the plasma density is essentially as predicted by

existing calculations (e.g. Self, 1967). In particular the

calculations of Kino and Shaw (1966), which were motivated by the

thruster program, give ion currents which should be directly

comparable to the results obtained at NASA-Lewis. In the ring cusp

arrangement the interior of the plasma contains an inhomogeneous and

relatively large magnetic field so the geometry is decidedly

two-dimensional and it is observed that the models of Self (1967)

and of Kino and Shaw (1966) do not agree with experiment. It is

observed in the ring cusp case that ion losses between the cusps are

rather larger than in the line cusp case. It should be possible to

eliminate these losses by electrostatic means and this would permit

a modest increase in the performance with a slight increase in

complexity. These between-cusp losses are not predicted by exact

ion orbit calculations and this indicates that ion- ion and

ion-neutral collisions play a very significant role in actual

thruster performance. A difference between the ring cusp and line

cusp operation is that relatively more of the ion production occurs

in a region near the cathode exit orifice in the ring cusp case. It
-27-

is suggested that changes in ion production characteristics may be

largely responsible for changes in performance figures as various

configurations are tested. Also, this effect cannot be ignored as a

contributor to changes in the beam cost factor when discharge

voltage and current are varied with a given configuration. Further

attempts to understand thruster operation with a view toward

improving performance should undertake the clarification of the role

of ion production processes in this system.
REFERENCES

Alport, M. J., S. L. Cartier and R. L. Merlino, Jour. Geophys. Res. 91, 1599

(1986)

Andrews, J. G., and J. E. Allen, Proc. Roy. Soc. Lond. A.320, 459 (1971)

Boardsen, Scott, Master's Thesis, University of Iowa, Unpublished, 1984

Chen, Francis F. , in Plasma Diagnostic Techniques, ed. Richard H. Huddlestone,

Academic Press, 1965

Hershkowitz, Noah, John R. Smith and Hideo Kozima, Phys. Fluids 22, 122 (1979)

Kino, G. S. and E. K. Shaw, Phys. Fluids 9, 587 (1966)

Lindberg, L., Proc. Int. Conf on Plasma Physics, Gothenberg (1982a)

Lindberg, L., Proc. Symposium on Plasma Double Layers, Riso, (1982b)

Self, S. A., Phys. Fluids 10, 1569 (1967)

Sovey, J. S., Proc. Int. Electrical Propulsion Conference, Las Vegas, paper

number AIAA-81-0745, 1981

Sovey, J. S., Proc. Int. Electrical Propulsion Conference, New Orleans, 1982

Tonks, L. and I. Langmuir, Phys Rev. 34, 876 (1929)
FIGURE CAPTIONS

Fig. I.I The "17 cm" NASA-Lewis ion thruster used in the current work

with the following changes: The ground screen and the shell for ion

optics mounting were not used. The anodes were removed. There were

9 magnet rows of each polarity.

Fig. 1.2 Hollow cathode assembly used in all phases of this work. The

heater which surrounds the front of the cathode was covered with four

or five layers of tantalum foil, tightly wound and spot-welded in place.

This and the entire tube was then covered with two or three layers of

loosely wound tantalum foil. Three tantalum foil discs heat-protected

the magnet in the front. The magnet was tightly fit into a stainless

steel sleeve and held in place with set screws. The back plate which

holds the cathode was held in place with screws and an adjustable

telescoping sleeve.

Fig. 1.3 Magnet holders used in the line cusp configuration. The tabs

cut in the ends of the iron pole faces overlap the brass holders and

retain the magnets.

Fig. 1.1 Sets of discharge voltages and currents where measurements

were performed in the thruster in the line cusp configuration. See

text for the significance of the various symbols.

Fig. 1.2 Sets of discharge voltages and currents where measurements

were performed in the thruster in the ring cusp configuration. See

text for the significance of the various symbols.

Fig. 2.1 Beam current versus plasma density for the line cusp case.

Fig. 2.2 The ratio of beam current to plasma density versus neutral

pressure for the line cusp case.

Fig. 2.3 Plasma density versus position for the line cusp case. The

upper graph is for a discharge voltage of 38.0 V and a discharge

current of 19.6 A. The corresponding values for the lower graph

are 43.6 V and 15.1 A.

Fig. 2.4 Radial variation of plasma density for the line cusp case for

three different sets of operating parameters.

Fig. 2.5 Losses along the cusps in the line cusp configuration. Ion

losses are shown in the upper graph and electron losses in the lower

graph.

Fig. 2.6 Contour plots showing the variation in (a) electron temperature

(b) plasma potential and (c) plasma density as they depend on the

azimuthal position y and distance from the wall x (which is at 150

mm) at a point near the middle of the thruster in the line cusp

configuration.

Fig. 2.7 Radial variation of the magnitude of the magnetic field in

the line cusp case (solid curves) and the ring cusp case (dashed

curves). In both cases the upper curves are along radii through

the cusps and the lower curves are along radii between the cusps.
Fig. 2.8 Contour plot of the electron temperature for the ring cusp

case.

Fig. 2.9 Contour plot of the plasma potential in the ring cusp case.

Fig. 2.10 Contour plot of the plasma density in the ring cusp case.

Fig. 2.11 Axial variation of the plasma density in the ring cusp case.

Fig. 2.12 Magnetic field near the axis of the thruster for the ring cusp

case in arrangement number 1. The lines show the calculated directions

of the magnetic field. The density of lines has absolutely no meaning.

Note that only two of the lines which pass through the extraction

grid connect to the cathode.

Fig. 2.13 Same as Fig. 2.12 except for arrangement number 2. Note the

increase in the number of magnetic field lines that connect the cathode

and the extraction grid.

Fig. 2.14 Contour plot of the electron temperature for the ring cusp case

in arrangement number 2.

Fig. 2.15 Contour plot of the plasma potential for the ring cusp case

in arrangement number 2.

Fig. 2.16 Contour plot of the plasma density for the ring cusp case

in arrangement number 2.

Fig. 2.17 Electron loss currents to the cusps in the ring cusp case,

arrangement number 1. There were no electron currents to the cathode

or to the extraction grid. The letters defining the cusps refer to

the same locations as shown in Fig. 3.2.

Fig. 2.18 Ion loss currents to the cusps and cathode in the ring cusp

case, arrangement number 1. The letters defining the cusps refer to

the same locations as shown in Fig. 3.2.

Fig. 2.19 Ion loss currents to a thin movable strip in the ring cusp

case, arrangement number 2. The letters defining the cusps refer to

the same locations as shown in Fig. 3.2.

Fig. 2.20 Representative ion currents in the ring cusp case, arrangement

number 2, for several operating conditions. The letters defining the

cusps refer to the same locations as shown in Fig. 3.2.

Fig. 3.1 Analytic function used to approximate the potential in order

to calculate ion orbits.

Fig. 3.2 Calculated magnetic field used in the orbit calculations.

Fig. 3.3 Ion orbits for ions born with an energy of 0.1 eV. In each

figure there are 91 orbits corresponding to initial directions from

0 to 180 degrees in 2 degree steps. The four figures correspond to

four different starting points. See text for details.

Fig. 3.4 Same as Fig. 3.3 for four other starting points.
Fig. 3.5 Same as Fig. 3.3 except the initial ion energy is 0.4 eV.

Fig. 3.6 Same as Fig. 3.3 except the initial ion energy is 1.0 eV.
23cm

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The "17 cm" NASA-Lewis ion thruster used in the current work

with the following changes: The ground screen and the shell for ion

optics mounting were not used. The anodes were removed. There were

9 magnet rows of each polarity. '
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Fig. 1.2 Hollow cathode assembly used in all phases of this work. The

heater which surrounds the front of the cathode was covered with four

or five layers of tantalum foil, tightly wound and spot-welded in place.

This and the entire tube was then covered with two or three layers of

loosely wound tantalum foil. Three tantalum foil discs heat-protected

the magnet in the front. The magnet was tightly fit into a stainless

steel sleeve and held in place with set screws. The back plate which

. holds the cathode was held in place with screws and an adjustable

telescoping sleeve.
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Fig. 1.3 Magnet holders used in the line cusp configuration. The tabs

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Fig. 1.2 Sets of discharge voltages and currents where measurements

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text'for the significance of the various symbols.
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Fig. 2.1 Beam current versus plasma density for the line cusp case.
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current of 19.6 A. The corresponding values for the lower graph

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Fig. 2.5 Losses along the cusps in the line cusp configuration. Ion

losses are shown in the upper graph and electron losses in the lower

graph.
(a) ELECTRON TEMPERATURE (b) PLASMA POTENTIAL

-20

150 160 170 180

X-AXIS (mm)

E

E

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160 170

X-AXIS ( mm)

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150 160 170 180

X-AXIS (mm)

Fig. 2.6 Contour plots showing the variation in (a) electron temperature

(b) plasma potential and (c) plasma density as they depend on the

azimuthal position y and distance from the wall x (which is at 150

mm) at a point near the middle of the thruster in the line cusp

configuration.
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Fig. 2.7 Radial variation of the magnitude of the magnetic field in

the line cusp case (solid curves) and the ring cusp case (dashed

curves). In both cases the upper curves are along radii through

the cusps and the lower curves are along radii between the cusps.
A-G84-802

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Fig. 2.8 Contour plot of the electron temperature for the ring cusp

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Fig. 2.9 Contour plot of the plasma potential in the ring cusp case.
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FIELD CONNECTION BETWEEN CATHODE AND GRID

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Fig. 2.12 Magnetic field near the axis of the thruster for the ring cusp

case in arrangement number 1. The lines show the calculated directions

of the magnetic field. The density of lines has absolutely no meaning.

Note that only two of the lines which pass through the extraction

grid connect to the cathode.
FIELD CONNECTION BETWEEN CATHODE AND GRID

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Fig. 2.13 Same as Fig. 2.12 except for arrangement number 2. Note the

increase in the number of magnetic field lines that connect the cathode

and the extraction grid.
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PLASMA POTENTIAL

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Fig. 2.15 Contour plot of the plasma potential for the ring cusp case

in arrangement number 2.
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Fig. 2.16 Contour plot of the plasma density for the ring cusp

in arrangement number 2.

case
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CATHODE E B A GRID

Fig. 2.17 Electron loss currents to the cusps in the ring cusp case,

arrangement number 1. There were no electron currents to the cathode

or to the extraction grid. The letters defining the cusps refer to

the same locations as shown in Fig. 3.2.
900

800

700

600

500

400

300

200

100

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Fig. 2.18 Ion loss currents to the cusps and cathode in the ring cusp

case, arrangement number 1. The letters defining the cusps refer to

the same locations as shown in Fig. 3.2.
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Fig. 2.19 Ion loss currents to a thin movable strip in the ring cusp

case, arrangement number 2. The letters defining the cusps refer to

the same locations as shown in Fig. 3.2.
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number 2, for several operating conditions. The letters defining the

cusps refer to the same locations as shown in Fig. 3.2.
ELECTRIC rOTCMTlM. CONTOURS

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AXIAL POSITION(M)

130

9 10

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Fig. 3.1 Analytic function used to approximate the potential in order

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OF POOR LINES OF MAGNETIC FIELDS

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APPENDIX

This appendix consists of chapters 3, 4 and 5 of the Master's

thesis of Mr. Scott Boardsen together with all of the figures and

tables of that work. It will be recognized that this Final Report

has borrowed heavily from the figures in the thesis and that there

are several duplications. The principle justification for including

this appendix is that certain details are treated in the thesis that

were otherwise omitted from this report. In particular, the Tables

and the discussion that goes with them have considerable technical

interest as an introduction to some quantitative aspects of the

thruster. Also the data-taking program and the magnetic field

calculations are more fully discussed. Further, it is felt that the

discussion, while speculative, is provocative and therefore

potentially useful.
K

CHAPTER III

EXPERIMENTAL METHODS

Langmuir (collecting) probes were used to measure plasma density and potential and electron temperature. Loss fluxes to various

surfaces were determined by measuring the currents to foils attached

to or imbedded in the surface in question. The Langmuir probe data

were acquired using a microcomputer to generate the probe sweep and to

store the resulting digitized probe current. The loss currents were

determined from current vs voltage (I-V) characteristics observed on a

Tektronix type 575 "transistor curve tracer" oscilloscope.

Probe Measurements

A schematic of the probe data system is shown in Fig. 7. The

computer outputs a 256 step ramp. Each step is 0.02 volts, which is

amplified by a factor of ten, yielding a 50 volt ramp. The computer

requires 11 msec per ramp with a 8 msec waiting period after each ramp.

Each ramp consists of 256 output points and reading 256 data points.

Each trace that is recorded is averaged over 10 cycles. Each trace is

stored in a 1 by 256 point array. There is a linear relationship

between array location and voltage applied to the probe whose array

value corresponds linearly to the current drawn at that corresponding

voltage. The stored traces are transferred to a minicomputer where

they are analyzed.
15

The Langmuir probe was cylindrical in nature consisting of the

exposed tip of 10 ndl tungsten wire, whose surface area ranged from

0.012 to 0.02 cm2, collecting no more than 80 milliamps at any time.

Due to the small Debye lengths of approximtely 2 x 10~3 cm compared to a

probe radius of 2.5 *10~2 cm a planar Langmuir probe theory is used in

the analysis. The data analysis is described in Appendix B.

The interior of the device was mapped out by cutting a horizontal

slit in the extraction grid through which a Langmuir probe was inserted,

whose exposed end was at the tip of an elbowed insulating rod. The

insulating rod was lined up with the device axis and could move back and

forth in that direction. The probe also had horizontal motion along the

slit and could be rotated about the axial direction. This allowed

access to any point inside the ion thruster.

Due to the aximuthal symmetry of the ring cusp configuration,

data was taken in axial rows for various radial positions whose range

swept out the device. The probe was moved in 1 cm steps between data

points except in regions with large density gradients where smaller

steps were taken. Programs were constructed that computed various volume intervals of some function of the plasma parameters. The integrals

were computed by fitting the data with cubic splines in the axial direction and with linear interpolation in the radial direction.

Loss Current Measurements

In the ring cusp configuration the measurement of the total current to a given surface was just the reading of an ammeter connected
16

between a foil on the magnet surface and the anode surface. The location and size of these probes are shown in Figs. 8 and 9. To separate

this into electron and ion components, and to correct for voltage drops

in the measuring circuit, it is necessary to obtain an I-V characteristic for the foil. At high positive bias, relative to the surface,

electron saturation current is drawn. The curve is not horizontal,

however, due to IE drops and expansion of the sheath around the foil.

Therefore, the straight, but sloped, line was extrapolated to zero bias

(the point where the foil was at wall potential) to obtain the electron

current to the wall, this was done in the line cusp configuration. The

ion current was similarly obtained by extrapolating the negatively

biased saturation curve back to the wall potential. Some error due to

the slight geometric distortion produced by the foils (Fig. 9) could

not easily be avoided. In one case, the foils were embedded in holes

drilled into the iron pole faces used in the line cusp configuration.

This prevented the foils from extending into the plasma, but instead

distorted the magnetic field somewhat. From these measurements, plus

the extraction grid currents, the total ion production rate can be

determined.
17

CHAPTER IV

EXPERIMENTAL RESULTS

Line Cusp Configuration

The line cusp configuration was mapped out by measuring its

plasma characteristics. The results are discussed in an earlier

paper.8 A summary of the results will be given. The line cusp configuration consists of 18 rows of samarium cobalt magnets, each row

alternating in polarity. This type of configuration tends to push the

magnetic fields away from its axis toward the anode walls. The field

strength in the central axial region is negligible and only has a significant effect within 3 cm of the anode wall. For a given radial

profile the density profile has little variation until the probe is in

the cusp region near the anode, as shown in Figs. 10 and 11, for two

different operating conditions. The potential profiles follow the

density profiles but with a smaller variation. The low central

field strength allows the electrons to mix readily and the electron

temperature is constant to within experimental uncertainties throughout most of the device, except in the cusp regions.

The possible presence of positive potential islands existing

between the cusps was investigated which have been observed8 in similar multicusp plasmas. A detailed map of the plasma characteristics

between the cusp regions was made in the middle of the device. Figs.
18

12-14 are contour maps of electron temperature, plasma potential, and

plasma density. They show decreasing density, decreasing temperatures, and positive potential islands when moving from the device center toward the anode. The decreasing density is due to the magnetic

confinement and slow diffusion rates across field lines. The decreasing electron temperature is due to the cooling of plasma electrons due

to neutral particle collisions. Since the ion temperature is very low

(< 0.1 eV), the potential islands play a role in channeling the ions

into the cusps. This decreases the ion loss width, leading to better

confinement.

Ring Cusp Configuration Design 1

Unlike the line cusp configuration, which has a field free

central region, the central region in the ring cusp configuration has

fields large enough to effect the electron motion. Therefore, in this

case, the constant radial dependence of plasma density and electron

temperature observed in the line cusp configuration is not observed in

the ring cusp configuration.

Fig. 15 is a contour map of the field configuration for ring

cusp design 1, which consists of 5 magnet rings of alternating polarity. The fifth ring lies on the endplate and is of opposite polarity

with the cathode magnet. Fig. 16 is a plot of magnetic field lines

that indicate the field direction. Fig. 17 shows the seven distinct

flux regions into which the field lines are separated. The confinement strength of each region is related to the magnetic flux contained

in that region.
19

To get an idea of the Important physical processes going on in

the main body of the thruster, a detailed picture of the thruster operation will be drawn for one parameter setting. This setting is close

to the maximum efficiency for this particular configuration called

design 1. Table 4 gives the external parameter readings.

Figures 18, 19, and 20 are axial graphs for electron temperature, plasma potential, and plasma density at radial position equaling

0.0 mm. Figure 21 gives a better idea of axial plasma potential including the cathode and grid. The graphs show that electron temperature,

plasma density and plasma potential all vary when approaching the orifice (axial position = 180 mm). The high plasma potential could indicate high plasma production given the large electron temperatures and

their large mobilities. High plasma density and electron temperature

also indicate large ion production.

Figures 22, 23, and 24 are contour maps of the electron temperature, plasma potential, and plasma density, respectively. Notice that

the electron temperature and density contours have a tendency to follow

the field lines which is expected since the collisional mean free paths

are longer than the device length. Also notice the enhanced penetration of the electron temperature contours in the region of magnetic

ring C compared to the penetration into the region of magnetic ring B.

This suggests that a large portion of the power emitted from the cathode orifice ends up in region 1.

Figures 25 and 26 show the electron and ion currents to the magnetic poles, cathode, and grid. A large proportion of the discharge
20

current tends to go to pole C. Minimizing the fraction of discharge

current to pole G would probably lead to higher efficiences.

Figures 16 and 17 indicate why the efficiency is poor for this

configuration. Region 2 is weak and narrow near the orifice, while

the field structure in Region 1 strongly links the cathode orifice

with the anode. To get better efficiencies for the ring cusp configuration, Region 2 must be enhanced, weakening the coupling with pole C.

With this idea a new design was tested which amounted to switching the

polarity on magnet ring E. In design 2, Region 2 is larger in diameter when compared to design 1 as shown in Figs. 27 and 28. The best

efficiencies were achieved in this configuration when compared to the

line cusp configurations tested and other ring cusp configurations.

Ring Cusp Design 2

Figures 5 and 6 are magnetic field strength and direction

plots, respectively, for ring cusp design 2. Note the enhanced axial

field region connecting the cathode orifice with the extraction grid.

Table 4 gives the external parameters close to maximum efficiency for

design 2 which was mapped out.

Figures 29-31 are contour plots of electron temperature, plasma

potential, and plasma density, respectively. Note that the electron

temperature and plasma density contours are different compared to

those of design 1. The high temperature lobular arm extending toward

pole C present in design 1 is no longer present in design 2, which

indicates that the magnetic coupling between the cathode and pole C

has been significantly weakened.
21

Figures 32 and 33 are BCF curves for design 1 and design 2.

Design 2 is much more efficient than design 1 or the line cusp configuration. Enhancing the number of field lines that connect the orifice,

or regions near the orifice, with the grid seems to be an important

factor in reducing the BCF. Enhancing this linkage in the line cusp

configuration is difficult because there are many poles on the anode

close to the cathode and of opposite polarity that provide a strong

magnetic coupling between the cathode and anode. Therefore, the ring

cusp configuration appears to be an inherently better design.

Ring Cusp Calculations

Table 5 gives the values of various volume integrals of physical

quantities averaged over the chamber volume for both design 1 and

design 2. In regions of the device with temperatures above 17 eV those

temperatures were truncated to 17 eV because temperatures above the

primary electron energy seem physically unobtainable. The ion production rate, due to Maxwellian electrons, was calculated by performing a

volume integral throughout the thruster. The neutral density inside

the device must be known to make this calculation and other similar

calculations. The neutral density was determined by mounting an ionization gauge on the thruster endplate. The neutral density is given in

Table 4« Near the endplate* cathode the plasma density is 30$ of the

neutral density. It was assumed that the plasma density, plus the neutral density is constant. This might not be a good assumption. Under

the above assumptions, thermal ionization accounts for roughly 10 to

30$ of the total ion production.
22

Beam-Plasma Observations

Probing the area, around the cathode orifice using an Tektronix

type 575 "curve tracer" oscilloscope indicates the presence of a very

turbulent lobular region of 3-5 cm in size projecting from the cathode

orifice. In this region large amplitude low frequency noise in the

range of 8 KHz to within a factor of 10 was observed. The amplitude

of this noise falls off rapidly as the probe is moved away from the

orifice. Figures 34-37 are Langmuir traces. Their corresponding fits

are taken on the device axis in thruster design 1. Although not shown

in the figures, the base line is flat. Figure 34 is nearest to the

orifice; roughly 1 cm away, while Fig. 37 is the furthest. Figure 34

has the shape characteristic of a primary beam (although the indicated

energy is about a factor of 2 too large), which is rapidly thermalized

as it moves sway from the cathode orifice (Figs. 35-37). If the above

interpretation is correct, the primary electron beam is damped away

within 4 cm of the cathode orifice.

The power input into the thruster main body by the primary beam

can be estimated from the observation that the external current to the

cathode exterior is, in most cases, less than 1 amp. This means that

*Two pressure gauges were used. One was mounted on the thruster and

the other was downstream of the thruster. The flow meter and

downstream gauge give no indication of a change in flow rate after

device ignition, which is not surprising since most of the flow

impedence is due to the gas feed tubing. But the thruster mounted

gauge indicates a pressure drop after ignition. This is probably

because a large proportion of argon atoms are pumped from the

thruster as ions.
23

the primary current is roughly equal to the discharge current. Therefore, the power input is

P! ~ Id

 x *E • (4)

One would expect that the primaries are initially directed

along the magnetic field lines as they leave the orifice. The lines

of magnetic fields in all configurations diverge slowly at the orifice

and range between 0.5 and 1.0 IsG, depending upon the configuration.

The initial primary density can be estimted knowing the area of the

orifice AQ, the primary energy Ep, and Ip. In Table 6 the calculation

is made giving an initial value of primary beam density ng of

1014 cm-3.

Initially, a dense energetic primary beam is impinging on the

main body plasma which has a much lower density np ~ 4 x 1012 cnr3

Instabilities and radial electric fields could lead to a substantial

spreading of the beam downstream of the orifice. There are two important factors that must be understood in the beam-plasma interaction.

1) How the beam yields its energy to the plasma leading to damping and

thermalization of beam particles, and 2) The role beam primaries play

in ion production by direct ionization.

It is observed that these processes occur within a very

turbulent lobular region emanating from the cathode orifice of roughly

3 to 5 cm in size. Outside this region the plasma appears to be close
to Maxwellian in nature with little evidence of the existence of a

primary beam.

There are two processes that contribute to the damping of the

primary beam. 1) Damping due to binary collision between primaries

and other particles, and 2) Collective interactions between the beam

and the plasma leads to strong damping.

Table 7 gives collision cross sections, collision frequencies

and mean free paths for various binary collisions between a 17 eV

primary and another particle. Collisions within the beam and elastic

neutral or ion particle collisions do not change the primary energy

but produce scattered primaries which are capable of producing ions in

sigle step processes. All other types of collisions lead to the rapid

thermalization of the primaries into plasma electrons.

Table 7 indicates that binary collisions play a minor role in

the damping of the primary beam. Collisions within the beam itself

gives the largest contribution of all the binary collisional processes. The beam-beam collisions initially have a small mean free path

but the decay in density due to this type of collision is a power law

decay, not an exponential decay. Further, beam-beam collisions do not

cause the primary beam to damp. What causes the rapid damping of the

beam?

Another riystery lies in accounting for the ion production rate.

As noted earlier, ionization due to the high energy Maxwellian tail of

the plasma electrons accounts for only 10 to 30% of the total production rate. The direct ionization due to primary electrons has an
25

extremely large mean free path but the primaries seem to be rapidly

damped after being emitted from the hollow cathode. Multistep ionization seems to be negligible, assuming a collision cross section of

primaries with excited neutrals of 20 * 10~16 cm2 (probably too

large), an initial primary density of 10ll+/cm3, and a relaxation time

of 10~8 s, the mean time between collisions with primaries for excited

neutrals is 2 * 10~8 s, therefore 1/3 of all excited neutrals would

still be excited during the collision, but the primary density falls

off by at least a factor of 30 within 1 cm of the orifice so this

method of ion production seems negligible.

This suggests that collective interactions in the form of strong

turbulence plays a central role in energy transfer and ion production.

(It is possible, however, that we are not seeing the primaries, many of

which might escape the lobular turbulent region. They could account

for the ion production rate if they are effectively trapped, for

example, by electrostatic trapping between the cathode and extraction

grid or magnetic trapping between the anode pole faces and the cathode. )

High frequency turbulence of large enough amplitude if present,

could cause the primaries to make a random walk in velocity space that

would lead to an enhancement in absolute distance traveled in the turbulent region. This would increase the probability of direct ionization and other binary collisional processes. The turbulence that the

primary beam generates could explain the observed heating of the plasma
26

electrons and ions. In general, turbulence of the proper frequency

and amplitude for a given particle retards the migration of that particle from that region. Without this random walk in velocity space

the distance traveled from a given point is

D = vt (5)

but with it the distance traveled is

D = v/t/^ (6)

where v is the collision frequency due to turbulence. If v£/v » 1,

where Z, is the size of the turbulent region, the particle has a larger

probability of undergoing a binary collision compared to a situation

where the turbulence is not present. The possible presence and nature

of turbulence is thus an important question.
27

CHAPTER V

SUMMARY AND DISCUSSION

Plasma properties were mapped out and various loss currents

were measured for different thruster configurations. Due to the

almost field free interior of the line cusp configuration, the electron

temperature was constant throughout the device and the plasma density

and potential showed little radial variation, except near the anode

walls, between the cusps, where positive potential islands are

present, which are large enough to reduce the ion leak width.

The ring cusp designs tested have fields greater than 0.1 kG

throughout most of the device, therefore the electron motion is

different compared to the line cusp configuration. The radial

dependence of electron temperature and plasma density is no longer

constant but drops off rapidly, moving away from the device axis; and

the electron temperature is no longer constant throughout the device

but varies from region to region. Because of the large variations,

simple soup pot calculations performed on the line cusp configuration7

involving total cusp length, ion and electron leak widths, and loss

areas, which had some success in explaining qualitative and some

quantitative features of the line cusp observations, become ambiguous

in the ring cusp configuration.
28

Applying some soup pot calculations to the ring cusp configuration, leak widths were calculated using average values of plasma density, temperature, and potential (refer to Table 9). This yielded an

ion leak width within a factor of 10 of the ion gyroradius and an

electron leak width within a factor of 10 of the electron gyroradius.

Grid current was calculated from the ring cusp data as an integral of

Bohm velocity times plasma density at z = - 7 mm (Fig. 24) over the

grid area, giving answers within a factor of 2 of the actual currents.

Much higher efficiences have been obtained in the ring cusp

design 2 compared to the line cusp design. Data suggests that the

important factor is the number of field lines connecting the cathode

with the extraction grid. Enhancing the area of this connection seems

to enhance the efficiency. This connection is weak in the line cusp

configuration due to the line cusp topology, suggesting that the ring

cusp configuration is inherently better.

The reason this type of connection enhances efficiency is

strongly dependent on how the primaries generate ions and transfer

their energy, which determines where in the main body the ions are

generated, and, on how effective the magnetic field is in channeling

ions throughout the device.

The interpretation of our data indicates that the primaries are

rapidly damped after leaving the cathode orifice. However, measurements of primary density are difficult and the primaries presence

could go undetected. If the primaries are rapidly damped, the majority of the ions are produced close to the cathode. This implies that
29

the magnetic channeling is important. Ions produced in region 2 move

freely toward the grid while ions produced in region 1 have a tendency

to be magnetically trapped and lost to the anode or cathode. There

are problems with this scenario: 1) If more ions are produced near

the cathode, ion losses to the cathode could be high, which is not

observed. However, the bulk of them are probably produced at least

1 cm away from the cathode where the potential structures channel them

toward the grid. 2) In most regions the relative change of magnetic

field strength over an ion gyroradius is large, which implies that it

is difficult to magnetically trap the ions.

If the primaries are escaping our detection and escape the

highly turbulent region, then the scenario is the following. Beam

primaries in region 2 will tend to be reflected back and forth between

the extraction grid and cathode, losing their energy through inelastic

collisions (mainly ionizing) or elastic collisions with plasma electrons. A large fraction of primaries in region 1 will be in the loss

cone and lost to the anode pole faces. So enhancing region 2 reduces

primary losses in region 1, leading to better plasma production and

thus a lower BCF.

If primaries are attenuated or strongly scattered in the highly

turbulent region near the cathode, this damping cannot be accounted

for by typical mean free path calculations and the nature of this turbulence must be understood.
30

REFERENCES

, M. M. , et al., Proc. of the 8th Symposium on Engineering

Problems of Fusion Research, p. 656, 1979.

2Spencer, E. G. and P. H. Schmidt, "Ion beam techniques for device

fabrication," J. Vacuum Sci. Tech.. 8, 552-570, 1971.

3Byers, D. C., V. K. Raulin, "Electron bombardment propulsion system

characteristics for large space systems;" Paper no. 76-1039, to

be presented at AIAA 12th Electric Propulsion Conference, Key

Biscayne, FL, Nov. 1976.

^Jahn, Robert G., Physics of Electric Propulsion, McGraw-Hill , Inc . ,

New York,

5Sovey, J. S., "Improved ion containment using a ring-cusp ion

thruster," Proceedings of the 16th International Electric

Propulsion Conference, New Orleans, 1982.

6Siegfried, Dan, Xenon and Argon Hollow Cathode Research, NASA Report

No. 168340, 76-121, 1984.

7Hershkowitz, Noah, John R. Smith, and Hideo Kozima, "Electrostatic

self -plugging of a picket fence cusped magnetic field," Phys.

Fluids. 22_{1), 122-125, 1979.

8Carpenter, R. T., S. A. Boardsen, and S. V. Daniels, "Plasma

characteristics of a 17 cm diameter line-cusp ion thruster,"

Proceedings of the 16th International Electric Propulsion

Conference, New Orleans, 1982.
31

APPENDIX A

DISCUSSION OF MAGNETIC FIELD PROGRAM

The magnetic field structure inside the ion thruster plays a

central role in determining the efficiency of the device. It is

important to know how the local and global plasma characteristics correlate with the field structure. A program was developed that determines the field structure of a given ring cusp configuration. This

allows the experimenter to check out the field structure of a design

before the design is constructed.

The idea is to approximate each magnet row with two current

rings with opposite polarity. The field of one current ring can be

given in terms of complete elliptic integrals. The solenoidal cathode

magnet is approximated by a magnetic dipole. Without the iron shell

that composes the anode which serves to complete the magnetic circuit

this program would be a very good approximation to the actual field

structure. The assumption is that to first order the effect of the

shell is to modify the moments of the current rings and dipoles making

them appear larger.

Table 8 gives the measured field values at the pole face and

the measured local maximum on the device axis near the extraction grid

for design 1 and 2. Figures 38, 39, 40, and 41 give graphs of the two
32

field components along the device axis and at a radical position of

100 mm which sweeps across the pole faces. Comparing the two suggests

that the program gives answers that are accurate to within 10$.
33

APPENDIX B

DISCUSSION OF DATA ANALYSIS PROGRAM

The data analysis program is as follows, given an array Y =

Y[X(i)], where Y corresponds to probe current drawn and X(i) corresponds to applied probe voltage. The first derivative at a given point

in the array is found by fitting that point and its four nearest

neighbors with a four degree polynomial as shown in Fig. 42. The

point where the first derivative is a maximum is defined as point B.

Then the trace between points A and B are least squares fit to the

four parameter curve

Y = A + B*X + C*D**X . (Bl)

The procedure is to pick a value for D. Since Y is linear in A, B,

and C, a linear least squares fit can be made holding D constant.

Then D is varied as a systematic way, repeating the above procedure

until a minimum is found in chi-squared. This yields a curve shown in

Fig. 43- l/ln(D) is proportional to the electron temperature. Next,

a linear least squares fit is made on the portion of the probe trace

between points B + DELTA and C. The intersection point of the two

fitted curves is used to determine the plasma potential and plasma

density (Fig. 44).
34

Table 1

Typical exhaust velocities for various chemical fuels.

Propellant type ' Ueg m/sec

Liquid monopropellants 1,700 - 2,900

Solid propellants - 2,100 - 3,200

Liquid bipropellants (fuel and oxidizer) 2,900 - 4,500

"Exotic" bipropellants and tripropellants 4,000 - 6,000
35

Table 2

Table of velocity increments for various

impulsive space missions.

Mission Av, m/sec

Escape from earth surface (impulsive) 1.12 * 101*

Escape from 300-mile orbit (impulsive) 3-15 * 103

Escape from 300-mile orbit (gentle spiral) 7.59 * 103

Earth orbit to Mars orbit and return* 1.4 x lO4

Earth surface to Mars surface and return1" 3.4 x io4

Earth orbit to Venus orbit and return* 1.6 x 101*

Earth orbit to Mercury orbit and return* 3«1

 x

Earth orbit to Jupiter orbit and return* 6.4

 x

Earth orbit to Saturn orbit and return* 1.1 x io5

Values are quoted for typical impulsive missions over minimum

propellant semiellipse trajectories.
36

Table 3

Typical operating parameters for thruster operation.

Operating Parmeter Plasma Parameter

Discharge Voltage VD 20 - 40 volts

Discharge Current ID - 8-30 amps

Grid Voltage VG ~ 50 volts

Extraction Current IQ 0.5-4.0 amps

Plasma Density 1011 - 1012 cm3

Electron Temperature 4 - 5 eV

Debye Length XD - 10~3 cm

Electron gyroradius re ~ 3 x 10"

 3 cm

Ion gyroradius r . ~ 0.5 cm

Lz
37

Table 4

External operating conditions at which measurements

were made in ring cusp design 1.

Design 1 Design 2

ID

IE

VG

Neutral Pressure

Ion Loss Rate

Electron Loss Rate

Neutral Density

BFC

28.96 ±0.3 volts

17.54 ± 0.28 amps

2.09 ± 0.03 amps

52.97 volts

2.81 x 10-* torr

4 amps

22 amps

9.25 x io12 cm3

243

28.33 ± 0.05 volts

16.5 ± 0.2 amps

2.65 ± 0.05 amps

49.20 volts

3.9 x lO'4 torr

not measured

not measured

12.84 x 1012 cm3

176
38

Table 5

Various calculations for ring cusp design 1 and design 2.

Method Design 1 Design 2

Ion Production

Rate Rj

Electron Production Rate RE

Number of Ions

in Device Nj

Average Plasma

Density np

Average Electron

Temperature

Electron Confinement

Time ice

Ion Confinement

Time Tel

Neutral ColIsions and

Electron

Undergoes

Rate of lonization due to

Thermal Plasma

Electrons

measured

measured

/ np d3x

/npTe d3x

ce

iei =

ce

d

3

4 amps

22 amps

1.24 x 1015

2.74 x 1011 cm3

3.63 eV

1.1 x 10-5

5.0 x io-5 s

0.8 amps

> 2.67 amps

> 16.5 amps

> 4.8

insufficient data

3.90 eV

insufficient data

1.4 amps
39

Table 6

Calculation of initial primary beam density

as it leaves the orifice.

Area of Orifice A,., 0.00454 cm2

Ep

Flux Conservation

VB

17 amps

17 eV

nB = B

= 2.45 cm/s

= 9.55 x 1013/cm3
Table 7

Binary collisional information between 17 eV

primaries and other particles.

Particle

Neutral

Argon Atom

Neutral

Argon

Atom

Neutral

Argon

Atom

Plasma

Electron

Other

Primary

Collision

Type •

elastic

inelastic

ionizing

Collision

Cross Sec.

(10-16cm2)

~ 21

~ 0.3

~ 0.2

.769

130

Mean Free

Path

(cm)

51.48

3.6 x 103

5.4 x 103

4.3 * 103

0.8 cm

Primary Collision Frequency with Particle

(Hz)

4.75 x 106 Hz

6.8 x id4 Hz

4.5 x 104 Hz

5.7 x io4 Hz

8.5 x 107 Hz

Note:

^ = 9.25 x 1012/cm3

np = 3 x 1012/cm3

Tp = 1.3 eV

nB = 10llt/cm3
Table 8

Measured magnetic field values at anode pole faces and

orifice; axial maximum near grid for ring cusp

design 1 and design 2.

Pole Face

A

B

C

D

E

Cathode Orifice

Axial Maximum

(near grid)

Design 1 (kG)

2.7

2.5

2.5

2.3

2.8

1.0

0.11

Design 2 (kG)

2.1

2.5

2.5

2.3

2.1

0.5

0.11
41

Tatle 8

Calculated leak widths compared to gyroradius

and ion current to grid.

Particle

Electron

Ion

Leak Width (cm)

0.017

0.88

Ctyroradius (cm)

0.0024

0.1 *

ion leak width = I±/lc J±

electron leak width = Ie/lc Je

Ji = 1/2 e np~

Je = 1/2 e np exp(-

fe" = 3.63 eV

rip" = 2.74 x iQll cm-3

Ij_ = ion current to anode = 1.7 Amps

Ic = electron current to anode = 22 Amps

Ic = cusp length = 290 cm

<j>P = 3-43 volts

1 —^—^^—

Ion grid current = / 75- e np/Te/mi dA = 1.29 Amps compared to

grid ^

measured value of 2 Amps.

Ion energy was assumed to be 0.1 eV in a 2.4 kG field.
42

Table 9

Calculated leak widths compared to gyroradius

and ion current to grid.

Particle

Electron

Ion

Leak Width (cm)

0.017

0.88

Qyroradius (cm)

0.0024

0.1 *

ion leak width = Ii/lc Ji

electron leak width = Ie/lc Je

J± = 1/2 e 5p~

Je = 1/2 e np exp(-

T7 = 3-63 eV

np" = 2.74 * 1011 cm-3

!•£ = ion current to anode = 1.7 Amps

Ic = electron current to anode = 22 Amps

Ic = cusp length = 290 cm

<(>P = 3-43 volts

Ion grid current = / -~ e np/Te/nu dA = 1.29 Amps compared to

grid *

measured value of 2 Amps.

Ion energy was assumed to be 0.1eVina2.4kG field.
8-084-701

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50

LOCATION OF PROBES

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