NASA CR-174621 

ION EXTRACTION CAPABILITIES OF 

TWO-GRID ACCELERATOR SYSTEMS 

(LASA-CE- 1740L1) iuti iXThACTIICh bi 84- 19468 

CAPAdILITXL> OF TiD-GBiD ACCLLLRAZCR SYSlERS 

n.s. Ttesis tcoiurado state UELV.) I i 1 i; 

nc A~VY~ ~131 CSCL 21c unclas 

G3/~0 11913 

PREPARED FOR 

LEWIS RESEARCH CENTER 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

Grant NGR-06-002-112 

by 

Dean C. Rovang 

Approved by 

Paul .J , Wilbur 

Feb. 1984 

Department of Mechanical Engineering 

Colorado State University 

Fort Collins, Colorado 
1. Report No. 

NASA CR 176621 

4. Title nd Subutta 

ION EXTBACTIOI CAPABILITIES OF WID ACCELERATOR SYSTEMS 

7. Authorlst 

Dean C. Bavang and 

Paul J. Wilbur 

e. WorMngolgwum~NMlandAddrera 

Department of kchadeal Engineering 

Colorado State University 

Fort Collins, Colorado 80523 

3. Ranplent'r Catalog No I 

5. Rce~ Oalc 

Feb. 1984 

6. Wormmg Organization cade 

8. Psrtorming Orgamzation Report No. 

10. Work UNI No. 

11. Contram or Grant No 

NGR-06-002-112 

7. Kev Words (Suggasred bv Authafs)) 

Electrostatic Thruster 

Ion Acceleration 

National Aeronautics and Space Administration 

Washington, D.C. 20546 

18. Distribution Statamem 

Unclassified - Unlimited 

I 

15. supplemaw NotarGrant Moultor - William Kerslake. NASA Levis Research Center. Cleveland, Ohio 44135. 

This report is a reproduction of the H.S. Thesis of Dean C. Bovang. 

sponsor and to the distribution list in this form both as a presentation of the technical material, 

and as an indication of the academic program supported by the grant. 

It is submltted to the 

. 

19. Security Classif. lot this report) 

Unclassified 

16. 

Ao experimental investigation into the ion extraction capabilities of two-grid accelerator 

This work resulted in a large body 

lesults suggest that the 

Impingement-limited performance is shown to depend most strongly on grid separation 

systems combon to electrostatic ion thrusters is described. 

of experimental data which facilitates the selection of the accelerator system geometries and 

operating parameters necessary to maximize the extracted ion current. 

impingement-limited perveance is not dramatically affected by reductions in screen hole diameter 

to 0.5 mn. distance, accelerator hole diameter ratio, the discharge-to-total accelerating voltage ratio. and 

the net-to-total accelerating voltage ratio. Results obtained at small grid separation ratios 

suggest a new grid operating condition where high beam current per hole levels are achieved at a 

specified net accelerating voltage. It is shown that this operating condition is realized at an 

optimum ratio of net-to-total accelerating voltage ratio which is typically quite high. 

apparatus developed for this study is also shown to be well suited for measuring the electron 

backstreaming and electrical breakdown characteristics of two-grid accelerator systems. 

The 

20. %curity Classif. (of this paw) 21. No. of Pap 22 Price' 

Unclassified 109 

NASAC-IO (Rev. 10-75) i 
TABLE OF CONTENTS 

Chapter Page 

I . 

I1 . 

111 . 

IV . 

v . 

INTRODUCTION ...................... 1 

ION BEAM FORMATION ................... 3 

Accelerator System Operation ... .......... 3 

Phenomena . Limiting Proper Grid Operation ........ 6 

Theoretical Considerations ............... 7 

Ion Extraction .................. 7 

Electron Backstreaming .............. 8 

Electrical Breakdown ............... 11 

APPARATUS AND PROCEDURE ................ 13 

Apparatus ....................... 13 

Procedure ....................... 17 

EXPERIMENTAL RESULTS .................. 22 

Ion Extraction ..................... 22 

Definition of Impingement-Limited Operation .... 22 

Effect of Net-to-Total Accelerating Voltage Ratio . 24 

Effect of Discharge-to-Total Voltage Ratio .... 28 

Effect of Accelerator Aperture Diameter ...... 30 

Effect of Grid Thicknesses ............ 33 

Effect of Screen Grid Hale Size .......... 35 

Application to Design ............... 42 

Other Considerations ............... 54 

Electron Backstreaming ................. 61 

Electrical Breakdown .................. 67 

CONCLUSIONS ...................... 73 

REFERENCES ....................... 77 

APPENDIX A . A Design Example ............. 80 

APPENDIX B . Impingement-Limited Perveance Data .... 93 

APPENDIX C . Electron Backstreaming Data ........ 100 

APPENDIX D . Electrical Breakdown Data ......... 104 

ii 
Figure 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

LIST OF FIGURES 

Page 

Two-Grid Acceleration System .............. 

Ion Source Instrumentation Schematic .......... 

Variable Grid Spacing Apparatus ............ 

Characteristic Impingement-Limiting Curve ....... 

Effect of Net-to-Total Accelerating Voltage Ratio 

on Ion ixtraction Performance ............. 

Effect of Discharge-to-Total Accelerating Voltage 

Ratio on Ion Extraction Performance .......... 

Effect of Total Voltage on the Ion Extraction 

Performance for a Specified Discharge-to-Total 

VoltageRatio ..................... 

Effect of Accelerator Hole Diameter Ratio (d /d ) 

on Ion Extraction Performance ............. as 

Effect of Accelerator Grid Thickness Ratio (ta/ds) 

on Ion Extraction Performance ............. 

Effect of Screen Grid Thickness Ratio (ts/ds) on 

Ion Extraction Performance ............... 

Effect of Screen Grid Hole Diameter on Ion 

Extraction Performance (small accelerator hole 

diameter ratio: 

Effect of Screen Grid Hole Diameter on Ion 

Extraction Performance (large accelerator hole 

diameter ratio: 

Effect of Screen Grid Hole Diameter on Ion 

Extraction Performance (medium accelerator hole 

diameter ratio: da/ds = 0.81) ............. 

Cross Plot of Impingement-Limited Perveance as a 

Function of Net-to-Total Accelerating Voltage Ratio . . 

da/ds = 0.66) ............. 

d,/ds = 1.00) ............. 

4 

14 

16 

23 

25 

29 

31 

32 

34 

36 

37 

38 

39 

44 

iii 
Figure 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

A. 1 

A.2 

A. 3 

Comparison of Impingement-Limited Current Levels 

as a Function of Grid Separation and Net-to-Total 

Accelerating Voltage Ratio ............... 

Effect of Net-to-Total Accelerating Voltage Ratio 

on the Baseline Impingement Level ........... 

Comparison of Impingement-Limited Current Levels as a 

Function of Accelerator Hole Diameter Ratio and 

Net-to-Total Accelerating Voltage Ratio ........ 

Effect of Changes in the Definition of the 

Impingement-Limited Operating Condition on the 

Ion Extraction Performance Results ........... 

Effect of Propellant Flow Rate on Ion 

Extraction Performance ................. 

Characteristic Scatter in Ion Extraction 

Perfomance Results Before Implementing Improved 

Experimental Technique ................. 

Characteristic Scatter in Ion Extraction 

Performance Results After Implementing 

Improved Experimental Technique ............ 

Effect of Perveance on Electron Backstreaming Limit . 

Effect of Net Accelerating Voltage on Electron 

Backstreaming Limit Operating Near the 

Impingement Limit ................... 

Correlation of Electron Backstreaming Limits for all 

2.0 mm Diameter Screen Grid Aperture Geometries 

Operating Near the Impingement Limit .......... 

Effect of Screen Grid Thickness on the Electric Field 

at Electrical Breakdown ................ 

Comparison of Predicted Current Density Levels as a 

Function of Electrical Breakdown Limit and Screen 

Grid Hole Diameter for a Total Accelerating 

VoltageoflOOOV ................... 

Minimum Grid Separation Variation ........... 

Impingement-Limited Current Density as a Function of 

Normalized Grid Separation for R = 0.5 ......... 

Maximum Impingement-Limited Current Densities 

Predicted for a Screen Aperture Diameter of 2.0 mm ... 

Page 

45 

49 

52 

55 

57 

59 

60 

62 

63 

66 

69 

71 

82 

84 

86 

iv 
Page 

1.4 Comparison of the Maximum Impingement-Limited 

Current Densities Prediced for Different Screen 

Grid Hole Diameters . . . . . . . . . . . . . . . . . . 88 

V 
I. INTRODUCTION 

To reduce the number of electrostatic ion thrusters required for a 

space propulsion mission and hence the cost and mass of the thruster 

subsystem, it is generally desirable to increase the thrust densities 

of these devices above those attainable with currently available ion 

thrusters. To keep the thrusters operating at their optimum specific 

impulse this should be accomplished by increasing the ion beam current 

density extracted through the ion optics system without increasing the 

exiting ion velocity. To this end in recent years many experimental 

and theoretical investigations have been conducted to determine the ion 

beam extraction Lharacteristics of accelerator systems used on electrostatic thrusters. *-lo Because of the complexity of the theoretical 

considerations involved, the theoretical models used to date are 

generally considered to be useful for predicting general trends only. 

The experimental investigations on the other hand although considered 

more quantitative, have focused primarily on the ion beam divergence 

characteristics of these accelerator systems rather than the phenomena 

which limit extractable ion current density. The present investigation 

was therefore undertaken in an attempt to provide a more complete 

understanding of the phenomena which limit the ion extraction capabilities of two-grid accelerator systems. This investigation deals with 

the effects of variations in the accelerator system geometry and operating conditions of the ion thruster on these ion extraction limiting 

phenomena. It is believed that a more complete picture of the ion 
2 

extraction capabilities of two-grid accelerator systems is provided 

because of the extended range of geometries and operating conditions 

over which these limiting phenomena are investigated. 

Most of the data presented here were collected using screen holes 

having a 2 mm diameter which is typical for present day accelerator 

systems. A substantial amount of data is presented, however, that 

suggests that the basic relationships defining the ion extraction 

capabilities of ion optics systems are valid for screen hole diameters 

as small as 0.5 mm. This differs from previous experimental 

results 8911-13 which have suggested that there might be a reduction in 

the ion extraction capabilities of accelerator systems utilizing grids 

with small screen hole diameters ((2.0 nun). 
11. ION BEAM FORMATION 

Accelerator System Operation 

The essential components of a two-grid accelerator system are 

shown in Fig. la. Although the side view of a single circular aperture 

pair is depicted it should be noted that a multi-aperture system is 

implied. The accelerator system, consisting of a screen grid and an 

accelerator grid, is positioned so the screen grid is adjacent to a 

discharge chamber containing a low density plasma at a potential a few 

tens of volts above that of the screen grid. A plasma is generated in 

the discharge chamber by electron-bombardment of neutral propellant 

a toms. 

Around each screen hole a plasma sheath forms which defines the 

boundary between the discharge plasma and the ion acceleration region. 

Fotentials applied to the grids produce an electric field that accelerates the ions and repels the electrons coming into the sheath from the 

discharge plasma. Figure lb illustrates the variation of electric 

potentials associated with the grid geometry of Fig. la. The solid 

line shows the potential variation through the grids themselves. This 

potential variation approximates but is not the same as that actually 

encountered by the ions. Under normal operating conditions, the dotted 

line shows the potential variation which the ions experience as they 

are accelerated through the extraction system. The ions are first 

accelerated from a high positive plasma potential to a negative potential near the potential applied to the accelerator grid. They are then 
SCREEN HOLE SCREEN ACCE L E RATOR 

PLASMA SHEATH GRID GRID 1 

a) GRID GEOMETRY 

t 

-I 

Iz 

W 

Ia - 

B 

SCREEN HOLE PLASMA SHEATH POTENTIAL DROP 

1 

I 

POTENTIAL 

THROUGH APERTURES 

(BACKSTREAMING ) 

GROUND 

POTENTIAL 

THROUGH 

GRIDS - 

~ ~~ 

b POTENTIAL VARIATION 

Figure 1. Two-Grid Acceleration System 
5 

decelerated as they pass from the plane of the accelerator grid to the 

region downstream that is held near ground potential. In this latter 

region electrons are supplied to maintain charge neutrality in the 

plasma associated with the ion beam. The potential difference between 

the plasma potential and ground potential is referred to as the net 

accelerating voltage (V ) and it determines the exiting ion velocity. 

Because the discharge chamber plasma potential is near anode potential, 

the potential drop across the screen hole plasma sheath is approximately equal to the discharge voltage (VD). The net accelerating 

voltage used herein is therefore defined as the sum of the discharge 

voltage and the screen voltage 

N 

VN = VD + vs . 

The total accelerating voltage applied to the accelerator system is 

defined as the sum of this net accelerating voltage and the absolute 

value of the potential applied to accelerator grid, 

or 

VT = v + vs + IVA/ . (2b) 

The ratio of the net accelerating voltage to the total accelerating 

voltage (R) is defined as 

D 

R=- vN . 

"T 

(3) 
6 

Phenomena Limiting Proper Grid Operation 

In normal operation the concave shape of the sheath similar to 

that shown in Fig. la is observed. Experimental evidence obtained by 

Aston" showed that as the plasma density and consequently the ion flux 

to the sheath increases, the sheath moves closer to the hole and begins 

to flatten out. Eventually, an operating point is reached where the 

sheath is sufficiently flat or even slightly convex so that ions 

passing through the accelerator grid are no longer focused properly and 

they begin to impinge directly upon the accelerator grid. The direct 

impingement by these high velocity ions causes sputter erosion of the 

accelerator grid and this process can result in rapid destruction of 

this grid. The onset of this direct ion impingement thus limits the 

extractable ion current for a particular grid geometry and set of 

operating voltages. 

Another phenomenon which can limit the operating range of the ion 

acceleration system is electron backstreaming. Electron backstreaming 

occurs when electrons in the downstream ion beam plasma find a path 

along which they can be accelerated through grid apertures directly 

into the discharge chamber. This condition occurs when the potential 

variation through the apertures is similar to that shown by the centerline in Fig. lb. When this type of potential profile exists, the 

electrons in the beam plasma are no longer repelled by the negative 

potential on the accelerator grid and they are therefore able to backstream into the discharge chamber. This backstreaming electron current 

is undesirable primarily because it represents a power loss for the 

accelerator system and thus decreases the electrical efficiency of the 

thruster subsystem. 
7 

A final phenomenon which is generally considered to limit the 

operating range of the accelerator system is electrical breakdown 

through the region between the grids. Electrical breakdown occurs when 

the electric field strength that exists in the region between the grids 

exceeds the local electrical breakdown limit. When this happens large 

electron currents, typically sufficient in magnitude to be destructive, 

flow between the grids. 

The remainder of this thesis deals with the specifics of how these 

three phenomena 

1) direct ion impingement onto the accelerator grid 

2) electron backstreaming 

3) electrical breakdown 

directly or indirectly limit ion extraction capabilities of a two-grid 

accelerator system. 

Theoretical Considerations 

Ion Extraction 

Because the ion flow is space charge limited, there exists a limit 

to the amount of ion current that can be extracted from an accelerator 

system of this kind. The general relationship which describes these 

space charge effects is g'ven by Poisson's equation 

V2V = -P/E0 (4) 

where V is the electrostatic potential, p is the charge density and 

is the permittivity of free space. Solving this equation numeilcally in 

two or three dimensions is beyond the nature and scope of this study. 

.er 

- .'. 

Probably the most concentrated effort in solving this problem numerically has been conducted by those people interested in neutral beam 

heating of fusion plasmas. Further details on investigations of this 

kind can be found in the literature. 14-16 
8 

Considerable physical insight into the ion current density extraction 

capabilities of these accelerator systems, however, can be gained by 

considering the equation which results from a one-dimensional solution 

to the ion acceleration problem 

This equation, commonly referred to as Child's law,I7 describes the 

one-dimensional space charge limited current density, j, which can be 

drawn between two flat, parallel surfaces. Here q is the ion charge, 

m is its mass and Q represents the length +.hrough which the ions 

are accelerated by the potential difference applied between the surfaces (VT). Applying Child's law to the three-dimensional geomeLry of 

the accelerator system requires an assumption concerning the accelerai 

tion length Q. In past theoretical and experimental investigations 5 98 

the physical acceleration length used to correlate the performance of 

various grid geometries that are not truly one-dimensional is the 

effective acceleration length Q shown in Fig. la. For the geometry 

of this figure 

e 

hhere represents the grid separation distance and is the 

screen hole diameter. Substituting this effective acceleration length 

into the one-dimensional Child's law, and setting the beam current 

g dS 

density (j) equal to 

screen grid hole, Eq. 

the beamlet current (J) divided by the area of a 

5 can be written 
9 

The collection of parameters on the left side of this expression is 

known as the normalized perveance per hole and it will be used in this 

thesis to correlate the performance of accelerator grid systems as a 

function of the various grid geometries and the operating conditions 

investigated. Of particular interest will be the impingement-limited 

normalized perveance per hole defined as the perveance per hole at the 

onset of excessive accelerator grid ion impingement. It should be 

noted that the right-hand side of Eq. 7 has a fixed value for a particular propellant. In the case of argon, the propellant used in this 

study, this value is 6.8 x lo-’ A/w. This value represents a 

theoretical limit to the maximum obtainable normalized perveance per 

hole and is indicative of the perveance expected at the impingement 

limit. 

Electron Backstroaming 

The dotted line of Fig. lb shows the potential variation along the 

centerlines of grid aperture pairs that are operating normally. As the 

negative potential on the accelerator grid is reduced, however, the 

potentials through the accelerator grid become less and less negative 

until eventually a condition is reached where the potentials at all 

points along the centerline become positive (shown by the centerline in 

Fig. lb). When this occurs electrons downstream of the accelerator 

grid in the beam plasma are free to backstream fhrough the grid holes 

arid into the discharge chamber. For a fixed net accelerating voltage 

the reduction in the magnitude of the accelerator grid potential that 

causes this transition from the dotted line to the centerline in 

Fig. lb corresponds to an increase in the ratio of net-to-total accelerating voltage (R). The ratio of net-to-total accelerating voltage at 
ORIG$JA!, PACE [s 10 

OF POOR QUALITY 

which electron backstreaming is initiated is referred to as R 

max * 

Using an analytical expression for the potential variation through an 

idealized accelerator system geometry, l9 Kaufman” first proposed the 

following relationship between the maximum allowable ratio of the 

net-to-total accelerating voltage ratio and the effective acceleration 

length normalized to the accelerator hole diameter, 

Based on the numerical results obtairied by Latham,l Kaufman” then 

modified the above expression to include the effect of accelerator grid 

thickness, 

le 1 

(1-R ) = exp 

a 

ma x 

More recently in order to include the data from his own more extensive 

numerical analy~is,~ Kaufman altered Eq. 9 slightly by changing the 

constant on the right hand side of the expression from (1/2 n) to 0.2, 

and obtained 

e [- 4 R 

(l-Rmax) j- = 0.2 exp 

a 

or 

=IRma x 

a 

Using this expression for unfortunately, did not provide a 

satisfactory correlation of the experimental results obtained in this 

study. It was found, however, that a fairly good correlation of the 

experimental results was obtained when the maximum allowed ratio of 

Rmax * 
11 

net-to-total accelerating voltage (Rmax) was plotted simply as a 

function of an effective normalized length represented by the quantity 

- 

Rmax - *max (> a exp [>I) . a 

Other correlations using different normalized effective lengths were 

attempted and even though these more complex empirical models appeared 

to facilitate improved correlations, the effective normalized length 

(le/da exp[ta/da]) was ultimately chosen as the correlating parameter 

because of its simplicity and also because of its historical and 

theoretical basis. 

Elect r ica 1 Breakdown 

The electrical breakdown or "sparking" characteristics of ion 

thruster accelerator systems are generally considered not tt) be 

governed by Paschen's rulez1 relating electrical breakdown to the gap 

and pressure between two surfaces across which a potential difference 

is applied. The reason for this is that the large gaseous mean free 

paths associated with the typical low operating pressures of these 

accelerator systems are several orders of magnitude larger than the 

grid separation or "gap". Rather, the processes considered critical to 

determining the electrical breakdown characteristics of these systems 

are field emission of electrons and secondary electron emission resulting from ion bombardment of the negatively charged surface. Based on 

these considerations and utilizing the experimental and theoretical 

results of several other investigators, Kilpatrick developed the 

following criterion for electrical breakdown between two electrodes in 

a vacuum, 

22 
12 

W E* exp[-17O/E] = 1.8 x IO6 . (12) 

In this expression W is the upper limit on the energies of the ions 

that are present (eV) and E is the maximum permissible electric field 

strength (kV/mm). More recently, two empirical relationships have been 

published by people working with neutral beam injection systems for 

These are 

‘2 E = 19/2 

8 

and 

E = 10 (14) 

where E has the units of kV/mm and 2 represents the electrode gap 

expressed in terms of millimeters. The above expressions predict 

higher maximum field strengths than those typically associated with ion 

thruster accelerator system operation (-2-6 kV/mm). 25-29 The reason 

for this disparity is unknown, but it is noteworthy that these above 

expressions were developed for accelerator systems with geometries and 

operating conditions that differ from those of typical ion thrusters 

for space applications and these differences may account for a part of 

this discrepancy in maximum permissible electric field strengths. 

From a practical standpoint achieving higher electric fields is of 

interest to ion thruster operation because, for a given set of accelerator system operating voltages, a higher maximum permissible field 

strength permits operation at a closer grid separation which, in turn, 

generally facilitates operation at a higher current density. 

g 
111. APPARATUS AND PROCEDURE 

Apparatus 

All testing has been conducted on an 8 cm diameter by 10 cm long 

ion source with a mildly divergent magnetic field. The magnetic field 

was derived from a long solenoidal winding wrapped around the outside 

of the thruster body. A cylindrical copper anode was used and apart 

from this, nonmagnetic stainless steel construction was employed 

throughout the source. Refractory tungsten filaments were used for 

both the neutralizer and cathode emitters. The emission levels for 

both of these was controlled by adjusting the current flowing through 

the filaments from their ac power supplies. This source design was 

selected because it provided the high current density capability needed 

to assure a proper test of the grids, and it provided a stable discharge. Figure 2 shows a schematic of the basic ion source design with 

associated power supplies and instrumentation. 

The grids were made from thin sheets of amorphous graphite. The 

grid aperture pattern used was a nineteen hole hexagonal array with a 

center-to-center hole spacing of 2.5 mm. The extraction region of the 

grids was masked down to a small area (-1 cm2) near the axis of the 

source. This was done to help ensure ion extraction at each hole from 

a uniform plasma. The geometries of the grids were varied by selecting 

different diameter drills with which to machine the hole patterns in 

various thicknesses of graphite sheets. Each of the grid geometries 
14 

/ MAGNET WINDING /I 

- 

0. C. 

/ DISCHARGE CHAMBER L 

CATHODE NEUTRALIZER 

I 

GRIDS rn $, HEATER 

Figure 2. Ion Source Instrumentation Schematic 
15 

investigated in this study was operated over a wide range of grid 

separations using the variable grid spacing apparatus described next. 

Because the grid separation distance was a very important parameter 

in this study, the test apparatus was designed so the grid separation 

could be varied while the ion source was being operated. This was 

accomplished, using the apparatus shown schematically in Fig. 3, by 

moving the fork-shaped wedge in the manner suggested by the large 

arrow. As this wedge is moved toward the grids it forces the accelerator and screen grid support plates apart and hence the screen and 

accelerator grids attached to these plates are also separatcd. All 

materials used in the construction af this apparatus are capaLle of 

withstanding high temperatures. Graphite was used for both the grids 

and grid support plates to minimize the differential thermal expansion 

between these components that could cause grid warpage. The distance 

between the points at which the grids were attached to the support 

plates was also minimized to minimize the effects of grid warpage and 

deflection due to the attractive electrostatic forces between the 

grids. Initial alignment of the grids was accomplished manually by 

positioning and clamping each grid and then checking the alignment 

visually beneath a large illuminated magnifying glass. This alignment 

is maintained during operation by the boron nitride guideposts shown in 

Fig. 3. Electrical isolation is assured by the sheet of isomica 

between the screen grid support plate and the wedge. The wedge is 

mecttG.iLcally connected to a micrometer used to measure and adjust its 

translation from the qutside of the vacuum system. 

Immediately after each period of data collection, while the source 

was still hot, the grid separation distance was reduced until the 
16 

ORIGINAL PAGE a 

OF POOR QUALm 

FORK- SHAPED 

SECTION A - 9 

Figure 3. Variable Grid Spacing Apparatus 
17 

measured electrical resistance between the grids went essentially to 

zero. This reference point on the micrometer (assumed to correspond to 

zero separation) along with the geometry of the wedge could then be 

used to calculate the grid spacing from the micrometer readings 

recorded during the testing. Because this procedure for defining the 

reference point was conducted while the grids were hot, this further 

minimized any error of grid separation that might have been caused by 

thermal warpage. 

Procedure 

The ion extraction performance of each grid geometry was 

investigated over a large range of net-to-total accelerating voltages 

and grid separations. A summary of the parameters varied in these 

tests is provided in Table 1. The grid geometries have been normalized 

with respect to the screen hole diameter (ds). Similarly, the discharge voltage (V,) has been divided by the total accelerating voltage 

(0;) to make it non-dimensional. 

After allowing the source to warm up, data collection was begun 

with the accelerator system operating at a large grid separation and 

high ratio of net-to-total accelerating voltage, typically R = 0.8. 

The propellant flow rate was adjusted to the minimum flow rate at which 

the source operated stably over the full range of beam currents investigated. The conduct of the tests involved increasing the cathode 

emission current in steps to induce increases in the beam and impingement currents. These currents were recorded manually from high accuracy digital gauges at each step. This process continued until the 

impingement current reached a high vslue (:lo% of the beam current). 

At this time, the cathode emission current was reduced to a low value 
18 

*0.81 0.25 

0.81 0.25 

0.81 0.25 

0.81 0.25 

0.81 0.25 

0.81 0.13 

0.81 0.38 

0.66 0.25 

t 1.00 0.25 

Table 1 

Test Conditions 

dS da/ds ta/ds "D/"T R 

(mm) ~ 

0.25 

0.25 

0.25 

0.13 

0.38 

0.51 

0.25 

0.25 

0.25 

0.25 

-~ ~- 

0.05 

0.10 

0.15 

0.10 

0.10 

0.10 

0.10 

0.10 

0.10 

0.10 

~ ~- 

0.1 - 0.8 

0.1 - 0.8 

0.1 - 0.8 

0.1 - 0.8 

0.1 - 0.8 

0.1 - 0.3 

0.1 - 0.8 

0.1 - 0.8 

0.1 - 0.8 

0.1 - G.8 

1.5 0.66 G.25 0.25 0.10 0.2, 0.5, 0.8 

1.5 1 .oo 0.25 0.25 0.10 0.2, 0.5, 0.8 

1.0 0.66 0.25 0.25 0.10 0.2, 0.5, 0.8 

1 .o 1 .oo 0.25 0.25 0.10 0.2, 0.5, 0.8 

0.5 -0.81 0.25 0.25 0.15 0.2, 0.5, 0.8 

*Standard Configuration 
19 

and the ratio of net-to-total accelerating voltage was lowered to the 

next value of interest. The procedure of increasing the beam and 

impingement currents was then repeated; keeping the propellan'. flow 

rate the same. After the range of net-to-total accelerating voltages 

of interest had been investigated, the grid separation was reduced 

slightly and the above procedure was repeated. Reductions in grid 

separations continued until very close grid separations were obtained. 

For all of the testing described here the magnet current was held 

constant at 12 amperes. This magnet current resulted in a magnetic 

field strength of approximately 35 gauss at the screen grid and 

45 gauss near the upstream end of the discharge chamber. The bell jar 

pressure was primarily 3 filnction of the propellant flow rate and it 

varied within the range of 1.0 - 5.0 x Torr for the tests. Also, 

unless stated otherwise, the discharge voltage was maintained at 

45 volts. 

The collection of backstreaming data for each grid geometry was 

accomplished by reducing the magnitude of the accelerator grid potential (IVAl = VT - VN) while watching for the rather sudden increase in 

beam current that is indicative of electrons backstreaming into the 

discharge chamber. Care was taken to try to identify as closely as 

possible the exact accelerator potential at which even the slightest 

detectable increase in beam current was observed as a result of electron backstreaming. Beam current increases of one percent were generally sufficient to ensure the occurrence of electron backstreaming. 

At each test point, using the procedure just described, the accelerator 

grid voltage at which electron backstreaming initiated was double 

checked. As a general rule the magnitude of these voltages agreed to 
within one or two volts. The average of these accelerator grid 

voltages was used along with the net accelerating voltage (V,) to 

ca 1 cula te 

Since the 

ing value 

the backstreaming limit (R 1, ma x 

V.. 

- 

Rmax - 

Backst reaming 

(15) 

grid separation and grid geometry were known, the correspondof the effective length (gelda * exp[ta/da]) could be calculated. It will be shown later chat the electron backstreaming limit is 

somewhat dependent on beam current or normalized perveance per hole. 

However, because the value of the maximum allowable net-to-total accelerating voltage ratio (Rmax) at the impingement limited perveance is 

probably of the greatest interest, most of the backstreaming data was 

collected at or near this operating condition. The net accelerating 

voltage was also observed to have a minor effect on electron backstreaming, but most of the backstreaming data presented here were 

obtained operating at a constant net accelerating voltage of 400 V. 

Because of the potentially destructive nature of the electrical 

breakdown phenomenon. the electrical breakdown characteristics of each 

of the graphite grid pairs were measured after the perveance/impingement characteristics and electron backstreaming data had been obtained. 

The data were collected by establishing a given grid spacing with the 

ion source operating at a moderate beam current. The screen and accelerator voltage were then increased in magnitude until electrical 

breakdown occurred. These tests indicated that either the screen or 

accelerator voltage could be increased to induce breakdown, i.e. the 

magnitude of the electric field was the critical variable in determining when breakdowr occurred. The electric field at electrical breakdown 
21 

is defined then as the sum of the screen voltage (V ) and the absolute 

value of the accelerator voltage (V,) divided by the grid separation 

S 

(ag) 

- "s + iVAl 

g 

Ebrea kdawn -a (16) 
IV. EXPERIMENTAL RESULTS 

Ion Extraction 

Definition of Impingement-Limited Operation 

Figure 4 displays a typical curve showing how impingement current 

(normalized to beam current) was obs :ved to vary as a function of beam 

current. At low beam currents, the curve is horizontal and the ratio 

of impingement to beam current is constant at a baseline impingement 

level determined by the rate at which charge exchange ions* strike the 

accelerator grid. As the beam current is increased it is seen that the 

curve in Fig. 4 begins to depart from the baseline level and the 

impingement current begins to rise abruptly. This increase in impingement curr-?t above the baseline level is due to the direct impingement 

of high velocity ions on the accelerator grid. Instead of presenting 

all performance data in the form shown in Fig. 4, it is more convenient 

and more meaningful for comparison purposes to define an impingementlilnited beam current, i.e. the beam current at which the direct accelerator grid impingement current becomes excessive. For this paper, the 

impingement-limited condition is said to occur when the onset of direct 

*A charge exchange ion results from a slow moving neutral atom which 

gives up an electron to a beam ion. Because of this dependence on 

neutral density, the baseline impingement current is primarily a function of the background (bell jar) pressure. 
23 

OJ2- 

0.10 

038 

0.06 

0.04 

0.02 

04 

ORIGINAL PAGE Is 

Of POOR QUALlW 

ARGON d3 52.0 mm 

v0=45 v %=0.54 

~450 V - 

R =0.8 !h =0.81 

2 =0.25 

ds 

= 

- 

IMPINGEMENT 

- 

- 

-- 

1 

0.5 I .o 1.5 

' 

n 

3 

\ 

. 

m 

< 

0 

F 9 

I2 

E 

3 

Figure 4. Characteristic Impingement-Limiting Curve 
24 

ion impingement results in an increment of 0.005 rn the ratio of 

impingement to beam current above the baseline impingement level. The 

magnitude of this incremental increase, although somewhat arbitrary, 

was selected as a compromise between two competing considerations. 

First of all, it should be large enough to ensure that the increase in 

impingement current was indeed due to direct ion impingement and not a 

result of impingement current noise. On the other hand, because excessive direct ion impingement is undesirable, it should be as small as 

possible. The selected increment of 0.005 appeared to be an appropriate compromise which yielded consistent results. The beam current 

associated with this impingement-limited condition is denoted by the 

dashed line in Fig. 4. 

For a given test, the total accelerating voltage, the grid 

separation distance and the hole size are known. The impingementlimited beam current ran be therefore divided by the number of apertures to obtain the current per hole. The impingement-limited normalized perveance per hole can then be calculated using Eq. 7. The 

normalized perveance based on this definition will be used to make 

comparisons of the ion extraction capabilities of the various grid 

geometries over a large range of operating conditions. 

Effect of Net-to-Total Accelerating Voltage Ratio 

When results like those of Fig. 4 are obtained over a range of 

separation distances and then impingement-limited normalized perveances 

are computed in the manner just described, one obtains curves like 

those shown in Fig. 5. In this figure, the impingement-limited normalized perveance per hole is plotted as a function of the grid separation 

normalized to the screen hole diameter for various ratios of the 
25 ORlolNAL PAGE 18 

OF POOR QUALITY 

ARGON 

v,=45 v ds =2.0 mm 

Vr = 450 V 

vO=O.l 

VT 

!Q =0.81 

dS 

!A =0.25 

ds 

t =0.25 

as 

R 

0 0.1 0 0.5 

0 0.2 b 0.6 

a 0.3 b 0.7 

v 0.4 0.0 

I I I I I I I I I I I I 

0.4 0.0 I .2 

NORMALIZED GRID SEPARATION [ eo/d,] 

Figure 5. Effect of Net-to-Total Accelerat. ng Voltage Ratio 

on Ion Extraction Performance 
net-to-total accelerating voltage ratio. Each of the curves in Fig. 5 

corresponds to a different net-to-total accelerating voltage ratio (R). 

It is observed that at close grid separations increases in the ratio of 

net-to-total accelerating voltages always results in increased perveances (improved extraction performance). However, it is seen at larger 

grid separations that all the curves tend to converge to a single 

perveance. If the impingement-limited normalized perveance per hole 

was a perfect normalizing parameter over the complete range of grid 

separation and net-to-total accelerating voltage ratio, all of the 

curves would be coincident horizontal lines. Figure 5 shows ;hat this 

tends to occur only at large grid separations. It is therefore argued 

that departures from this single value at close grid separations represent departures from the one-dimensional model on which the normalized 

perveance per hole is based. It is also believed that the reduction in 

perveance at low values of R is related to the poor focusing at lower 

values of R observed by Aston.8 Although Aston reported large variations in beam divergence with R, his data did not indicate such a 

dramatic effect of R on the impingement-limited perveance per hole as 

that suggested by the results of Fig. 5. The main reason for this is 

considered to be due to the fact that Aston's investigation was conducted primarily at the larger grid separation ratios where single 

values of perveance are obtained. 

In summary, the results shown in Fig. 5 indicate that the ion 

optics of two-grid accelerator systems are complex and are not adequately described by the one-dimensional model for space charge limited 

ion flow. In the one-dimensional model the acceleration length and 

potential difference through which the ions are accelerated are very 
27 

well defined. Obviously, based on the results shown in Fig. 5 this 

does not appear to be true for two-grid accelerator systems, especially 

at smaller grid separation ratios. Also, in the one-dimensional model, 

ion trajectories are assumed to be one-dimensional. This is not a good 

assumption in the case of the two-grid accelerator system. Possible 

improvements to the one-dimensional model might be realized by selecting a new effective acceleration length. Such an effective acceleration length should represent a better physical description of the 

actual acceleration length encountered by the ions. For example, it 

might account for changes in the plasma sheath location that accompany 

changes in the extracted ion current density. It should still include 

the grid separation and also might include all or part of the grid 

thicknesses. Defining a new acceleration length was beyond the scope 

of this present study, however. As mentioned previously, a large body 

of experimental and theoretical ion extraction performance data already 

exist which utilize the present definition of the effective acceleration length (Eq. 6). Based on this historical usage, this effective 

acceleration length (I ) seemed to be the most appropriate for correlating the ion extraction performance data collected in this present 

work. It should be noted that regardless of the suggested improvements 

in the definition of the acceleration length, there would still be an 

effect of net-to-total accelerating voltage ratio on ion extraction 

performance at small grid separation ratios. Modeling the effect of 

the net-to-total accelerating voltage ratio on ion extraction performance represents a possible goal for future investigations. 

e 

The set of curves in Fig. 5 characterizes the ion extraction 

performance of the particular accelerator system geometry defined by 
28 

the parameters da/ds, ts/ds, ta/ds, ds and ratio of discharge to 

total voltage (V /V ) The effect of variations in these parameters on the ion extraction performance will be 

considered in the following sections. Instead of trying to compare the 

ion extraction performance using all of the ratios of net-to-total 

accelerating voltage shown in Fig. 5, a high ratio (R = 0.8), a medium 

ratio (R = 0.5) and a low ratio (R = 0.2) have been selected to 

indicate general trends. 

noted at the top of Fig. 5. DT 

Effect of Discharge-to-Total Voltage Ratio 

The effect of the ratio of discharge-to-total voltage on ion 

extraction performance is shown in Fig. 6. At large ratios of net-tototal accelerating voltage (E = 0.8) it is seen that lower ratios of 

discharge-to-total voltage result in increased perveances over the 

entire range of grid separations investigated. Similar trends hold 

true for the lower values of R, but it is observed that at closer grid 

separations the curves converge onto a single curve. In general 

though, lower ratios of discharge-to-total voltage result in improved 

ion extraction performance. This trend has been reported previously by 

Aston8 and explored in more detail by Kaufman. 30 Kaufman3' theorized 

that the relative effects of the discharge and total accelerating 

voltage on the plasma sheath cause the sheath to flatten out at high 

ratios of discharge-to-total voltage and thus result in the onset of 

impingement at lower perveances. Sheath profile data obtained by 

Aston18 confirm this relative effect of discharge voltage on the 

contour of the sheath upstream of the screen hole. 

It was of interest to determine whether or not the ion extraction 

performance data obtained at a particular ratio of discharge-to-total 
29 

3RIGINAL PAtM l@ 

OF POOR QUALITY 

n 

0 I I111 11111 IJ 

6 io" 

Rr0.5 P 

- 

3- 

P 

- 

0 111 111111 111 

- "0 

"1 

0 0.05 

0 0.10 

A 0. I5 

ARGON 

ds =2.0 mm 

h= 0.25 Rt0.2 ds 

!A= 0.25 

ds 

0 0.4 0.8 1.2 

NORMALIZED GRID SEPARATION [ U,/d,] 

Figure 6. Effect of Discharge-to-Total Accelerating Voltage 

Ratio on Ion Extraction Performance 
30 

voltage was independent of the total accelerating voltage. If so, then 

the ion extraction performance data obtained at one total voltage would 

apply for any total voltage as long as the ratio of discharge-to-total 

voltage remained the same. To make this determination tests were 

conducted at total accelerating voltages of 350, 450, and 550 volts 

with the discharge voltage set in each case so the discharge-to-total 

accelerating voltage ratio was 0.1. Figrire 7 shows the impingementlimited normalized perveance per hole data collected in these tests. 

It is seen that the curves of constant net-to-total accelerating 

voltage ratios are relatively independent of the discharge and total 

accelerating voltages for this case where their ratio is held constant. 

Recently this invariance of the impingement-limited perveance with 

total voltage for a fixed geometry and discharge-to-total voltage ratio 

was verified in an independent investigation. 31 

Effect of Accelerator Aperture Diameter 

In Fig. 8, the effecc of variations in the accelerator hole 

diameter ratio (d /3 ) on impingement-limited perveance i- shown. In 

general, it is observed that larger accelerator holes facilitate operaLion at higher perveances and therefore higher beam currents. The 

largest differences are seen over the entire range of grid separations 

for a net-to-total accelerating voltage ratio equal to 0.8. At this 

same net-to-total accelerating ratio of 0.8 it is observed that the 

curve for the largest accelerator hole diameter ratio (d /ds = 1.0) 

does not extend to very low grid separations. It was not possible to 

operate at grid separation ratios below -0.4 in this case because of 

the occurrence of electron backstreaming. It should be noted that some 

of the other geometries were ne3r the electron backstreaming limit at 

as 

a 
31 

URlGlNAL PAGE S 

OF POOR QUALlrV 

n 

Rt0.8 

R=0.2 

"0 0.4 0.0 I .2 

NORMALIZED GRID SEPARATION [ @g/ds] 

vD 'T 

0 35 350 

045 450 

a55 550 

ARGON 

ds = 2.0 mm 

d-a= 0.81 

dS 2 = 0.25 

!!z = 0.25 

ds 

Figure 7. Effect of Total Voltage on the Ion Extraction Performance 

for a Specified Discharge-to-Total Voltage Ratio 
32 

0 

a 1.00 

R=0.5 0 0.81 

0 0.66 

R = 0.2 

NORMALIZED GRID SEPARATION [ eg/ds] 

ARGON 

de =2.0 mm 

=0.25 ds 

!il t0.25 

ds 

Figure 8. Effect of Accelerator Hole Diameter Ratio (d,/ds) 

on Ion Extraction Performance 
33 

very close grid separations when operating at a net-to-total 

accelerating voltage ratio of 0.8. However, it should be emphasized 

that caution was exercised not to include any data in the ion extraction performance results that might have been noticeably influenced by 

electron backstreaming. 

The data of Fig. 8 also show for R = 0.8 that the perveance for 

the smallest accelerator hole diameter ratio (0.66) remained relatively 

constant as a function of grid separation instead of increasing to 

larger perveances of close grid separations as was the case for the 

medium ratio of d /d = 0.81. It is noteworthy that a similar trend to 

larger perveances at close grid separations was observed for the 

smallest accelerator hole diameter ratio (d /d = 0.66) but only at 

ratios of discharge-to-total voltage below the 0.1 value appropriate to 

the data of Fig. 8. 

as 

as 

The trend of decreased ion extract; 3n performance with decreased 

accelerator hole diameter was expected and has been reported in previous experimental and theoretical investigations .5 '8 There is, however, an exception that is of particular interest. At close grid separations for R = 0.5 it is seen that the impingement-limited perveance 

for the largest accelerator hole diameter ratio tested (da/ds = 1.0) 

falls slightly below that for the medium ratio (da/ds = 0.81). This is 

believed to be a real effect and will be discussed in greater detail in 

a later section. 

Effect of Grid Thicknesses 

Figure 9 shows the effect of accelerator grid thickness ratio on 

the impingement-limited perveance. The only significant effect on ion 

extraction performance is observed at close grid separations for a 
34 

Rs0.8 

3 F 

F.,,,,,,,,,.. 0 

W 

N3 o a* 

RzO.5 

!Q 

ds 

0 0.13 

0 0.25 

A 0.38 

0 0.51 

3 c 

NORMALIZED GRID SEPARATION c 3 

=2.0 mm 

=0.8 I 

= 0.25 

Figure 9. Effect of Accelerator Grid Thickness Ratio (ta/ds) 

on Ion Extraction Performance 
net-to-total accelerating voltage ratio of 0.8. Even then, there is no 

consistent trend, except it is seen that the perveance levels of the 

thickest accelerator grid lies substantially below the others. This is 

consistent with the results obtained by Aston' who reported significant 

decreases in ion extraction performance only at fairly large ratios of 

accelerator grid thickness (ta/ds L 0.6). 

Figure 10 shows the effect of screen grid thickness racio on the 

impingement-limited perveance. At large grid separations and high R 

values it is seen that operation with thinner screen grids facilitates 

operation at higher perveances. For the medium and low ratios of 

net-to-total accelerating voltage ratio, however, this difference 

disappears at close grid separations. It is noteworthy that previous 

investigators operating at fixed grid separations have reported similar 

general trends of decreased perveance levels with increased relative 

screen grid thicknesses. 8,20 

Effect of Screen Grid Hole Size 

A major consideration of this study was the investigation cf the 

effect of operating with screen grid hole diameters below 2.0 mm on ion 

extraction performance. In Figures 11-13 the impingement-limited 

perveance levels obtained with screen grid hole diameters smaller than 

2.0 mm are compared to those obtained with 2.0 mm diameter holes. 

Figures 11 and 12 compare the performance of 1.0, 1.5 and 2.0 mm diameter holes for the accelerator hole diameter ratios, of 0.66 and 1.00 

respectively. These figures do not appear to show any consistent 

trends that would indicate a decrease in performance with decreasing 

hole size. Similarly, this observation has been verified recently in 

an independent investigation for screen grid hole diameters as small as 
36 

‘i 3 

10-9 

c 

- t 

R=0.2 

-71 I I I 

-0 0.4 0.8 1.2 

NORMALIZED GRID SEPARATION [ eg/ds] 

!a 

% 

0 0.13 

0 0.25 

A 0.38 

ARGON 

=0.25 

d8 

Figure 10. Effect of Screen Grid Thickness Ratio (ts/ds) 

on Ion Extraction Performance 
R =0.8 

NORMALIZED GRID SEPARATION [%Ids] 

d6 (mm) 

0 1.0 

0 1.5 

h 20 

ARGON 

- VO =o. I 

"T 

ds 43 =0.66 

Figure 11. Effect of Screen Grid Hole Diameter on Ion Extraction 

Performancp (small accelerator hole diameter ratio: 

da/ds = 0.66) 
R =0.8 

R =O.2 

i IO'' 

NORMALIZED GRID SEPARATION [ Og/ds] 

6 5 io" 

R =O.2 

3- 

OOfi"' 0.4 'I Ifi 0.8 I I .2 ' 

NORMALIZED GRID SEPARATION [ Og/ds] 

d, (mm) 

0 1.0 

0 1.5 

h 2.0 

ARGON 

- "0 =O.I 

"1 

4 !!Q= 1.0 

la = 0.25 

dS 

!Q = 0.25 

dS 

Figure 12. Effect of Screen Grid Hole Diameter on Ion Extraction 

Performance (large accelerator hole diameter ratio: 

da/ds = 1.00) 
39 

3- 

0 

ORIGINAL PAGE IS 

OF POOR QUALlW 

- 

- 

L 

L 

1111l1 11111 I 

RtO.8 

3- 

0 

Rt0.5 w 

w 

- 

- 

1111 It II Ill1 

3- 

ds (mm) 

0 0.5 

0 2.0 

R =0.2 - 

- 

- 

- I, m, 

ARGON 

- = 0. I5 VD 

VT 

3 = 0.25 

2 =0.25 

d8 

Figure 13. Effect of Screen Grid Hole Diameter on Ion Extraction 

Performance (medium accelerator hole diameter ratio: 

da/ds = 0.81) 
40 

1.0 01111. 32 It should be noted that the grids with 1.0 mm and 1.5 mm 

diameter screen grid holes were manufactured and aligned in a similar 

fashion to those with 2.0 m diameter holes. Using this conventional 

method of construction and alignment, attempts were made to extend the 

operation to screen grid hole diameters of 0.5 mm. These results 

suggested a decrease in ion extraction performance below the levels 

obtained for the larger diameter holes. The inability to align these 

smaller hol.%s was suspected to be the cause of the poor performance. 

In order to ensure alignment, in a separate test the accelerator grids 

were ion machined in situ. This machining process yielded a slight 

spread (k0.05 m) in accelerator hole diameters with an average diameter of 0.4 mm. In Fig. 13 the perveance levels obtained in this test 

are compared to those of the 2.0 mm diameter holes for an accelerator 

hole diameter ratio of 0.81 and a discharge-to-voltage ratio of 0.15. 

The similarity of perveance levels shown in Fig. 13 suggest that accelerator system operation without reductions in ion extraction performance is possible with screen grid hole diameters as small as 0.5 nun. 

This observation differs from what was expected based on previous 

experimental investigations that reported a decrease for screen grid 

hole The reason for this disparity 

remains uncertain. However, based on the results and observations made 

during this investigation, certain possibie explanations can be 

theorized. 

diameters below 2.0 nun. 8p11-13 

It was noted above that only after hole alignment was ensured for 

the 0.5 nun diameter screen grid holes did the performance return to the 

levels obtained with the larger diameter holes. Based on this observation, it is proFosed that misalignment of the screen and accelerator 
41 

holes represents a possible explanation for the reductions in 

performance observed previously. Lt is also noteworthy that the conventional hole alignment technique used in this study differed somewhat 

from that of the previous investigations reporting reductions in performance for screeii grid hole diameters below 2.0 m. The variable 

grid spacing apparatus used in this study allowed the holes to be 

aligned with the grids touching and then later separated for testing. 

In the previous investigations, the grid systems required alignment of 

the holes with grids separated. This improvement in alignment technique might account for part of the reason why in this investigation 

normal grid operation could be extended to screen grid holes as small 

as 1 mm in diameter before encountering apparent alignment problems. 

8 Another consideration is that, except for the one conducted by Aston, 

the other investigations were conducted with large diameter accelerator 

systems with thousands of holes. Their complexity makes the alignment 

of smaller holes more difficult. In any case, it should be emphasized 

that hole alignment is considered crucial to the success of operating 

with small screen hole diameters. 

Another factor which was found to influence the ion extraction 

performance was the stability of the discharge chamber plasma. During 

a segment of the tests the discharge chamber was changed to a design 

that operated less stably (arc discharge noise being apparent on an 

oscilloscope). The onset of high impingement currents occured at lower 

perveance levels with this design than it did with the more stable one. 

In light of this observation, previous attempts to operate with smaller 

holes and higher current densities may have resulted in decreased 

performance due to unstable discharge chamber operating conditions. 
42 

As a final note, in this study when considering the ion extraction 

performance of the different screen grid hole diameters, only those 

results obtained with similar normallzed grid geometries (2 /d g s’ da/ds’ 

ts/ds, ta/ds) and similar operating conditions (V /V R) were compared. This is important because it has been shown that the ion 

extraction performance is a function of those parameters. 

D T’ 

Application to Design 

Although the impingement-limited normalized perveance per hole is 

useful for correlating data, it is not easy to use directly to decide 

at what grid separation ratio and ratio of net-to-total accelerating 

voltage one should operate in order to maximize the beam current or 

beam current density for a specified net accelerating voltage. This 

information can, however, be obtained from curves similar to those 

shown in Fig. 5, if one assumes that for a particular ratio of 

discharge-to-total voltage these same curves would be obtained at other 

total accelerating voltage levels. Fortunately, this independence of 

the impingement-limited normalized perveance curves from the total 

accelerating voltage has been demonstrated (Fig. 7). Thus for source 

operation at the minimum flow rate required for stable operation, the 

impingement-limited normalized perveance per hole (P ) is primarily a 

function of the net-to-total accelerating voltage ratio, the ratio of 

the discharge-to-total voltage and the grid geometry, i.e. 

I 

or 

2 dt ts vD 

‘T s S 

,e 2 ft) = PI (R, - ’ A d ’ ds’ ds ’ 
43 

Dividing Eq. (17b) by R3I2 and [<r , yields, 

The term on the left, which will be referred to as the impingementlimited current parameter, is useful because it facilitates a comparison of the maximum current per hole obtainable as a function of the 

net accelerating voltage as opposed to the total accelerating voltage. 

The reason for this is mainly due to the fact that the impingementlimited normalized perveance per hole is normalized with respect to the 

total accelerating voltage and not to the net accelerating voltage. 

Figure 14 shows a cross plot of data taken from Fig. 5 at three different grid separation ratios. In this figure the impingement-limited 

normalized perveance per hole is plotted as a function of the ratio of 

net-to-total accelerating voltage. This figure also includes additional data collected at net-to-total accelerating voltage ratios of 

0.45, 0.55, 0.65 and 0.75. Using Eq. 18, the values of impingementlimited normalized perveance per hole found along the curves shown in 

Fig. 14 can be used to calculate the impingement-limited current parameter. The data of Fig. 14 have been replotted in Fig. 15 with the 

impingement-limited current parameter rather than the impingementlimited normalized perveance per hole as the dependent variable. 

Figure 15 shows the highest beam currents per hole are achieved at the 

lowest net-to-total accelerating voltage ratios and that the magnitudes 

of these currents are relatively independent of grid separation. At 

small grid separation ratios high current levels are also achieved at 

an optimum ratio of net-to-total accelerating voltage. The peaks in 
44 

ARGON 

=O.I 

VT 

IO” 

d8 = 2.0 mm 

5 =0.81 

d8 

!& = (2.25 

t -2 = 0.25 ds 

d8 

5.0.42 

ds 

0.65 

I I I I I I I I I I 

OO 0.5 1.0 

NET-TO-TOTAL ACCELERATING 

VOLTAGE RATIO [R] 

Figure 14. Cross Plot of Impingement-Limited Perveance as a Function 

of Net-to-Total Accelerating Voltage Ratio 
45 ORIGINAL PAGE !% 

OF POOR QUALIW 

30- 

CI 

E 

> 

\ 

a 

Y 

25- $ 

\ 

. 

7 

ti 

g 20- 

c 

a 

z 

c 

ARGON 

- vo =O.I 

VT 

5 15 

a 

z 

II 

w = IO 

r 

W 

(3 

2 

E 

z 

0 

w 

k 

J 

- 

- 

5 

ds = 2.0 mm 

I I I I 1 I I I I 1 

!A = 0.25 

!!l = 0.25 

d8 

d8 

Figure 15. Comparison of Impingement-Limited Current Levels as 

a Function of Grid Separation and Net-to-Total 

Accelerating Voltage Ratio 
46 

the curves of Fig. 15 at these optimum R values represent the maximum 

currents achievable at close grid separations and high ratios of netto-total accelerating voltage. It should be noted that even higher 

beam currents could presumably be realized at the peak by further 

reducing the grid separation and operating at R values above -0.70 

where the ll /d = 0.2 curve peaks. The grid separation could presumably continue to be reduced until the onset of electron backstreaming 

or electrical breakdown occurred. 

8s 

For operation at high beam current density levels the results of 

Fig. 15 seem to suggest the choice of operating at low ratios of netto-total accelerating voltage or at high ratios of net-to-total accelerating voltage and small grid separation ratios. However, because of 

some other considerations, this observation is not as straight-forward 

as it may first appear, To illustrate, a design example using the 

results of Fig. 15 is considered. 

The results of Fig. 15 suggest that similar values of the 

impingement-limited current paramter (-22.5 x A/V3l2) would be 

obtained by operating either at the peak of the curve for 

where R Z 0.7 or at a net-to-total accelerating voltage ratio of 

0.15. The interesting thing to note about operation at R = 0.15 is 

that for the range of normalized grid separation appropriate to Fig. 15 

(0.2 < R /d < 0.65) the impingement-limited current parameter appears 

to be independent of the grid separation ratio. Because of manufacturhg and mechanical design constraints, one of the first dimensions 

usually specified in the design of a large diameter accelerator system 

is the grid separation distance necessary to maintain a minimum spanto-gap ratio. Under the constraint of maintaining this design limited 

Yds = OS2 

8s 
47 

grid separation distance, operation at larger grid separation ratios 

could be accomplished by selecting smaller screen grid holes. These 

smaller screen grid holes would facilitate more holes per unit area of 

the grids and thus higher beam current densities. In the particular 

case under consideration here, for a fixed grid separation distance, an 

increase in the grid separation ratio from 0.2 to 0.65 translates 

roughly into a screen hole diameter three times as small. Since the 

area of the hole scales with the square of hole diameter, this means 

that approximately nine times as many holes could fit into the same 

size accelerator system and, as a result, a nine fold increase in 

current density could be achieved. From the standpoint of obtaining 

higher densities, the preceding comparison suggests that when the grid 

separation distance is fixed, it is advantageous to operate with 

smaller holes at low ratios of net-to-total accelerating voltage and 

large grid separation ratios as opposed to high ratios of net-to-total 

accelerating voltage and small grid separation ratios. This statement 

presumes that the impingement-,-,nited current parameter is not a function of screen grid hole size. Because the impingement-limited current 

parameter is based directly on the impingement-limited normalized 

perveance per hole, it is argued that the observed invariance with hole 

size demonstrated in these tests for perveance therefore applies similarly to the impingement-limited current parameter. 

Besides current density, there are still other considerations that 

need to be addressed when trying to decide between operating at a high 

value of R or at a low value of R. When operating two-grid accelerator systems at low ratios of net-to-total accelerating voltage one 

observes : 
48 

1) Higher total voltages. For a fixed net accelerating voltage 

lower ratios of net-to-total accelerating correspond to 

higher total voltages. To avoid electrical breakdown these 

higher total voltages may require operation at larger grid 

separations. It is conceivable that eventually these 

increased grid separations would result in decreased beam 

current per hole. This would tend to reduce the increased 

current densities noted above for operation at low ratios of 

net-to-total accelerating voltage and large grid separation 

ratios. 

2) More divergent beams. Aston8" found that decreasing the 

net-to-total accelerating voltage ratio generally increases 

overall ion beam divergence. These more divergent beams 

result in a thrust loss due to off-axis velocity components 

of the ions. 

3) Rapid rise to excessive impingement. At very low ratios of 

net-to-total accelerating voltage (R < 0.3), the rate of 

increase to high impingement levels with increases in beam 

current was observed in these tests to be more dramatic than 

it was at higher ratios. This increased sharpness of the 

"knee" on the characterstic impingement-limited curve (Fig. 

4) could present problems for a thruster operating near the 

impingement limit because a small fluctuation in thruster 

operating conditions might cause a dramatic and undesirable 

increase in impingement current. 

4) Higher baseline levels of impingement. In Fig. 16, representative data showing how the baseilne ratio of impingementto-beam current was observed to increase with decreasing 
49 

NET-TO-TOTAL ACCELERATING VOLTAGE RAT IO [ R] 

Figure 16. Effect of Net-to-Total Accelerating Voltage Ratio 

on the Baseline Impingement Level 
50 

ratios of net-to-total accelerating voltage is shown. The 

increase in baseline impingement current levels is not 

believed to be attributable to increases in bell jer pressure 

be(-ause it remained the same €or all of the data shown in 

Zig. 16. Part of the increase in impingemefir current 

observed at the lower valges of R can be attributed, however, 

to larger collisional cross sections for charge exchange. 

Using the empirical relationship developed by Robinson33 for 

the cbarge excharge crov section of argon, calculations show 

that changing from a net accelerating voltage of 315 V 

(R = 0.81, to 45 V IR = 0.1) would o~!ly result in a 20% 

increase in the charge exchange cross section. Although, it 

is in the right direction, this illcrease in cross section 

only accounts for a small fraction cf the increase in 

impingement current suggested bv the data shown in Fig. 16. 

The reason for the remainder of the increase in impingement 

current remains uncertain. It is speculated that at the very 

low ratios of net-to-total accelerating voltage, the ion 

focusing has deteriorated to the point where a measurable 

amount of direct ion impingement is evidenced at all beam 

current levels. If this is so, then decreased thruster 

efficiency and decreased accelerator grid lifetimes would ',e 

expected. 

5) Higher energy charge exchange ions. As the ratio of net-tototal accelerating voltage is reduced the negative potential 

on the accelerator grid increases. This results in an 

increase in the energies of charge exchange ions striking the 
51 

accelerator 

increased 

1 i fet imes . 

grid. These higher energy ions would result in 

erosion rates and shorter accelerator grid 

All of these disadvantages must be weighed against the advantage 

b~ dbtaining higher beam current densities by operating with low ratios 

of net-to-tc*nl accelerating voltage and large grid separation ratios 

as compared to operating at high ratios of net-to-total accelerating 

voltage and small grid separation ratios. The only perceived disadvantage to Qyerating at high ratios of net-to-total accelerating voltage 

as opposed to low ratios is the greater likelihood of electron backst-reaming at higher ratios. 

fhe usefulness of the impingement-limited current parameter as a 

design tool is further demonstrated in Fig. 17. In this figure the 

impingement-limited current parameter is plotted as a function of the 

ratio of net-to-total accelerating voltage for three different accelerator hole diameter ratios operating at the same normalized grid separation. The most interesting point to be made concerning the results 

shown in Fig. 17 is that at larger ratios of net-to-total accelerating 

voltage the highest impingement-limited current levels are obtained not 

with the largest accelerator hole diameter but rather with the second 

largest. This is an important result because it is preferable from the 

discharge chamber viewpoint to operate with stnailer accelerator grid 

holes in order to minimize the loss of unionized propellant. Heretofore, it was generally accepted that grids should be operated with the 

largest possible accelerator grid holes (da/ds = 1.0) to achieve the 

highest beam currents. Herce, the objectives for high beam currents 

and low neutral propellant loss were in conflict. However, the results 
52 

CI 30 

> 

\ 

a 

m 

Y 

25 

;* 

\ 

7 

U 

a 

W 

H 

L 20 

8 

a 

a 

Iz 

a 15 

a 

3 

V 

0 

W 

II 

- J IO 

Iz 

W 

z 

W 

(3 

2 

h 

I 

r5 

ARGON d, = 2.0mm 

Pg /dS = 0.22 

"T ts /ds = 0.25 

to 1 ds = a25 

- "O = 0.1 

- do ~0.81 P= 

XIO-~ 

I I I I I I I I I I 

0 0.5 I .o 

NET-TO-TOTAL ACCELERATING VOLTAGE RATIO [ R ] 

Figure 17. Comparison of Impingement-Limited Current Levels as 

a Function of Accelerator Hole Diameter Ratio and 

Net-to-Total Accelerating Voltage Ratio 
53 

of Fig. 17 suggest that at small grid separations ratios d?d medium to 

high ratios of R, it is sometimes unnecessary and even self-defeating 

to try and achieve higher beam currents by utilizing very large accelerator hole diameter ratios (da/ds = 1.0). It should be noted that the 

data point for da/ls = 1.0 and R = 0.8 was not included in Fig. 17 

because of the occurrence of electron backstreaming. 

The observed reduction in impingement-limited current for the 

accelerator hole diameter ratio of unity is inconsistent with the trend 

toward higher current levels that are generally expected for larger 

accelerator hole diameter ratios. It is postulated that increases in 

the accelerator grid hole diameter ratio cause the potential difference 

between the center of the accelerator grid hole and the accelerator 

grid proper to become larger. This results in increased defocusing in 

the region of the accelerator grid. It is argued that at close grid 

separations with large accelerator holes this reduced ion focusing is 

communicated upstream into the screen grid hole in a manner that causes 

the onset of direct ion impingement at reduced beam currents. 

In earlier sections the effects of variations in accelerator 

system geometry and operating conditions on the impingement-limited 

perveance were examined at selected ratios of net-to-total accelerating 

voltage (R = 0.2, 0.5, 0.8). It should be noted, however, that a 

complete tabular listing of the experimental results for the entire 

range of ratios investigated, from R = 0.1 to 0.8 for 2.0 mm diameter 

screen holes can he found in Appendix B. Thr data contained in Appendix B represent design data which can be used to make comparisons 

similar to those shown in Figs. 15 and 17. Because the ion extraction 

performance was demonstrated to be relatively independent of the screen 
Y 

54 

grid hole size, it is argued that the data contained in Appendix B can 

be applied to any screen grid hole size as long as the normalized 

geometrical parameters are the same. 

Other Cons idera t ions 

The effects of variations in accelerator system geometries and 

operating conditions considered thus far in this thesis represent the 

main focus of this investigation. There are, however, some other 

effects and considerations that should be taken into account when 

considering ion extraction performance results and their application to 

accelerator system design. 

As mentioned previously, for the data analysis used herein, the 

impingement limit was based on a very modest increase in impingement 

current above the baseline level. To be precise, it was defined at the 

point where direct ion impingement of the accelerator grid resulted in 

an increment of 0.005 in the ratio of impingement-to-beam current above 

the baseline impingement level, (6(J /J ) = 0.005). -- Because this 

definition was somewhat arbitrary, it is worthwhile to consider the 

sensitivity of the results to this definition. Figure 18 shows how 

allowing operation of higher levels of direct ion impingement generally 

resulted in increased perveance levels. It is seen, however, that the 

shapes of the curves at each ratio of net-to-total accelerating voltage 

remain qualitatively the same. The proximity of the curves to one 

another gives a rough indication of the relative sharpness of the 

"knee" on the impingement-limiting curve. The proximity of the curves 

shown for a net-to-total accelerating voltage ratio of 0.2 verify the 

statement made earlier concerning the rapid rise to excessive impingement levels observed for very low values of R. It was also observed 

IB 
XIO-9 

6- 

- 3- 

E 

> 

a 

\ 

_- 

- 

I 

- 

- 

111 I I I I 

Figure 18. Effect of Changes in the Definition of the ImpingementLimited Operating Conditions on the Ion Extraction 

Pe I: f o ma nce Re su 1 t s 

0 

I 

w 

Q 

a 

w 

0 3- 

2 

a 

w 

> 

Q: 

W a0 

0 0.020 

- 0 0.005 R 4.5 

- 

ARGON 

- =O.I 

ds =2.0rnm 

- VO 

VT r 

I 111111 Ill 11 
w 

56 

during these experiments that impingement versus beam current curves 

obtained with smaller ratios of discharge-to-total voltage characteristically had sharper knees. The most important point to make concerning 

the results of Fig. I8 is that the obtainable perveance levels are 

somewhat dependent on the definition of the impingement limit. Consequently, knowledge of how impingement-limited operation is defined is 

important when applying ion extraction performance results to accelerator system design. 

Figure 19 shows the Effect of propellant flow rate on the 

impingement-limited normalized perveance per hole. Each of the flow 

rates shown represents a multiple of the minimum propellmt flow rate 

required to maintain stable source operation over a complete range of 

beam currents. The circular symbols represent tne minimum required 

flow rate which was also the standard flow rate used *broughout this 

investigation. It is seen from Fig. 19 that for the most part 

increases in the flow rate by a factor of 2 and 3 did not have a 

dramatic effect on the ion extraction performance. An interesting 

distinction, however, can be made between the results obtained for a 

net-to-total accelerating voltage ratio 0.5 and those results obtained 

for the ratio of 0.8. At close grid separation for R = 0.8 it is 

seen that increases in flow rate resulted in decreased perveance 

levels, while the opposite appears to occur for R = 0.5. 

During the early part of this investigation other factors related 

to the discharge chamber operation were determined to influence the ion 

extraction performance. One of the parameters identified was the cleanliness of the anode surface. Before measures were taken to ensure the 

cleanliness of the anode surface, fairly large unexplained fluctuations 
57 

"i IO'" 

R =0.8 

OO 3i 0.4 Q.F I .2 

NORMALIZED GRID SEPARATION [ Eg/ds ] 

m 

m,f 

ARGON 

"0 

"T 

- =O.I 

.!A = 0.25 

db 

Figure 19. Effect of Propellant Flow Rate on Ion 

Ext K;! ct ion Perf o rmancc 
58 

An the impingement-limited perveance would result. The results of 

Fig. 20 give an indication of the magnitude of the observed fluctuations in the impingement-limited normalized perveance per hole for a 

net-to-total accelerating voltage of 0.8. After implementing procedures to ensure a clean anode rurface at the start of each experiment, 

the reproducibility of the ion extraction data improved to the level 

suggested by Fig. 21. Another discharge chamber related effect was the 

reduction in impingement limited perveance levels observed with a less 

stable discharge. 

Considering the effects of the aforementioned discharge chamber 

parameters on ion extraction performance, the application of the ion 

extraction performance results of this investigation to thrusters 

incorporating different discharge chamber designs might be questioned. 

Because considerable effort was taken to minimize the changes in these 

discharge chamber parameters during the investigation of the effects of 

variations in the accelerator system geometries and operating conditions, it is reasoned that those results are self-consistent and that 

similar qualitative conclusions based on those results would be drawn 

regardless of the discharge chamber design. However, it is believed 

that slight quantitative differences can be expected between different 

discharge chamber designs. The exact mechanisms by which each of these 

different discharge chamber parameters affect the ion extraction performance are not presently understood and their investigation were 

beyond the scope of this present study. Changes in the discharge 

chamber design or operating co.iditions may cause changes in the bulk 

plasma properties such as plasma potential, electron temperature, and 

the ratio of primary to Maxwellian electron densities. These changes, 
59 

; 10-9 

c8 

OO 0 

0 

0 

ARGON 

vo 

- =O.l 

VT 

R =0.8 

8 

O0 %o 

OO. 0 

0 0 

0 

0 

d, = 2.0 mm 

= 0.25 

ds 

!Q =0.25 

ds 

CD 

00 

cBo 

0 

0 0 

0 

0 

I I I I I I I I I I I I 

0.4 0.8 I .2 

NORMALIZED GRID SEPARATION [ Ug/ds] 

Figure 20. Characteristic Scatter in Ion Extraction Performance 

Results Before Implementing Improved Experimental 

Technique 
ARGON ds = 2.0 mm 

= 0.25 

I I I I I I I I I I I J 

0.4 0.8 

NORMALIZED GRID SEPARATION [ &g/da] 

I .2 

Figure 21. Characteristic Scatter in Ion Extraction Performance 

Results After Implementing Improved Experimental 

Technique 
61 

in turn, alter the shape of the sLreen grid hole plasma sheath which 

affects the ion focusing. It is proposed that understanding these 

mechanisms more thoroughly represents a potential area of investigation 

for future studies. 

Electron Backstreaming 

Because the variable grid spacing apparatus facilitated operation 

over .i wide range of grid separations, this apparatus was found to be 

well suited for measuring the electron backstreaming characteristics of 

the various grid pairs used in this investigation. The effect of the 

ion beam current or perveance on the electron backstreaming limit 

(R ) is shown in Fig. 22 where these quantities are plotted for three 

different grid separations. The data of Fig. 22 were obtained with the 

standar, !-id geometry. It is seen that at each grid separation lower 

perveance levels facilitate operation at higher ratios of net-to-total 

accelerating voltage before electron backstreaming occurs. This effect 

is even more pronounced at closer grid separations. The data points at 

the maximum perveance for each of the curves in Fig. 22 represents 

operation near the impingement-limited condition. Most of the experimental electron backstreaming data in this study were collected with 

the accelerator system operating near this impingement limit because it 

represents the worst case and also because ion thrusters would typically operate near that condition. In Fig. 23 the effect of variations 

in the net accelerating voltage on the backstreaming limit are shown as 

a function of the normalized grid separation. It. is seen that only at 

close separations and net accelerating voltages below 400 V do changes 

in net accelerating voltage cause a significant change in the backstreaming limit. The effects of variations in the net accelerating 

max 
62 

0.7 

- 

- 

- 

- 

- 

Vo.45 v ds = 2.0 mm 

V~=400 V 

= 0.8 

ds 

= 0.25 

= 0.25 

dIB 

d8 

x 10-9 

Figure 22. Effect of Perveance on Electron Backstreaming Limit 
- 0 300 

I .op 

- 

Y 

0 

. 

2 0.9' 

k 

3i 

J 

(3 

- 

- 

z 

a 

a 

Y 0.81 

m 

(r: 

Y 

0.7 

45 v 

- 

" 

rds = 2.0 mm 

%l= 0.81 

ds 

!& = 0.25 44 

b-= 0.25 

d8 

Figure 23. Effect of Net Accelerating Voltage on Electron 

Backstreaming Limit Operating Near the Impingement Limit 
64 

voltage on the electron backstreaming limit are not believed to be 

caused so much by the voltage changes themselves as by the induced 

chauges in impingement-limited perveance levels. Smaller net accelerating voltages cmrespond to sealler total accelerating voltages. 

These smaller total accelerating voltages result in higher dischargeto-total voltages and it was demonstrated earlier in this work that 

higher ratios of discharge-to-total voltage generally result in lower 

levels of impingement-limited perveance. This indirect effect of the 

net accelerating voltage on electron backstreaming may explain in part 

vhy the cf fect of net accelerating voltages on electron backstreaming 

is more pronounced at lower accelerating voltages. For lower net 

accelerating voltages equivalent changes in the net accelerating voltage produce larger changes in the ratio of discharge-to-total voltage 

than they would at higher net accelerating voltages. Assuming that 

changes in the ratio of discharge-to-total voltage cause proportivnal 

changes in perveanlz, these larger changes in the discharge-to-total 

voltage ratio would produce larger changes in the perveance and therefore have a greater effect on backstreaming. Another contributing 

factor is suggested by the results of Fig. 22 where it is observed that 

the effect of perveance on the backstreaming limit appears to be more 

pronounced at lower perveance levels. Because lower net accelerating 

voltages generally result in lower perveance levels, it is reasoned 

that the electron backstreaming limit would be expected to be more 

sensitive to changes in the net accelerating voltage at low net accelerating voltages than it would at kizi. net accelerating voltages. Itis noteworthy that this reduced effect of perveance on backstreaming at 

higher perveances is in general agreement with results obtaiiled by 

5 Kaufman using numerical techniques. 
c 

65 

All of the experimental electron backstreaming data obtained with 

the different grid geometries for a screen grid hole diameter of 2.0 mm 

are correlated in Fig. 24. These data were cbtained at a net accelerating voltage of 400 V operating at beam currents near the impingement 

limit. In Fig. 24 the beckstreaming limit, is plotted as a 

function of the effective normalized length mentioned previously. 

Considering the wide range of geometries included in the data of 

Fig. 24, the effective length, gelda exp[t /d 1, appears to correlate 

the backstreamirg data reasonably well. Because the data were collected over a wide range of operating conditions and because the geometric effects seem to be reflected properly in the effective length 

parameter, Fig. 24 can be used as a design curve. Accelerator system 

operation without electron backstreaming could be expected by operating 

in the area below and to the right of the experimental curve or above 

it would probably allow electron backstreaming to occur; remembering, 

of course, that roduced perveance levels would permit operation at 

slightly higher ratios of net-to-total acce! erating voltage than those 

indicated ia Fig. 24. Accordingly, those changes in the discharge or 

net accelerating voltage that cause reductions in the impingementlimited perveance levels would be expected to shift the design curve up 

toward higher ratios of net-to-total accelerating voltage. However, 

based on argument: presented previously in this section, changes 

resulting in higher pervearlce levels would not be expected to change 

the position of the curqe significantly. As a matter of information, 

it should be mentioned tha', during these tests the screen grid hole 

size was also determined to have a minor effect on electron backstreaming. It was observed that grid pairs utilizing smaller screen grid 

Rmax , 

aa 
66 

n 

X 

0 

E 

U 

Q= 

I 

J 

VD'45 v 

V~'400 V ~0.66 - 1.00 

ds 

.h = 0.1 3 -0.38 

dS 

tO.13 -0.51 

dS 

f .o 

EXPER 1MENTAL 

0.9 

0.8 THEUREflCAl DESIGN 

CURVE, Eq. 10b 

0.7 - 

t111#111111 I I8J 

0 i .Q 2.0 3.0 

EFFECTIVE NORMALIZED LENGTH exp (to 11 

da 43 

Figure 24. Correlation of Electron Sackstreaming Limits for all 

2.0 rms Diameter Screen Grid Apenure Geometries 

Operating Near the Impingement Limit 
Y 

67 

holes tended to allow operation at slightly higher ratios of net-tototal accelerating voltage before electron backstreaming occurred. It 

was also observed that the magnitude of increases in the electron 

backstreaming limit only became significant (above the spread of data 

shown in Fig. 24) for screen hole diameters below 1.5 nm. The explanation for this effect with hole size remains uncertain at this time. It 

is possible this trend toward higher backstreaming limits with decreasing hole size might be related to an increase in grid webbing area 

between the holes which accompanied reductions in screen hole diameter 

in the present experiments. This occurred because the hole-to-hole 

spacing was held fixed while the diameter varied. It is also possible 

that this observed effect of hole size on backstreaming might somehow 

be related to the plasma sheath thickness downstream of the accelerator 

grid. ce between the accelerator grid and neutralization surface did not scale proportionally with 

the dimensions of the smaller grid geometries. 

It is speculated that possibly th: dis' 

In Fig. 24 a coaparison is made to the theoretical design curve 

proposed by Ka~fman.~ Qualitatively, the experimental and theoretical 

curves have the same shape. At valiies of the effective normalized 

length above -0.8 the theoretical curve is seen to be more conservative. It should be noted that, to the author's knowledge, the experimental results of Fig. 24 represent the most extensive experimental 

investigation of electron backstreaming to date. A tabular listing of 

all the experimental data shown in Fig. 24 can be found in Appendix C. 

Electrical Breakdown 

Electrical breakdown tests were conducted on each of the different 

screen and accelerator grid pairs used in this investigation. The 
4 

68 

electrical breakdown characteristics of each of the different grid 

pairs, although sometimes dramatically different from one another, were 

observed to be fairly constant over the range of grid separations 

investigated (Q < 0.25 am). The ocly significant trend observed with 

accelerator system geometry is shown in Fig. 25 where the electrical 

field at electrical breakdown is plotted as a function of the screen 

grid thickness. This figure shows that the thicker screen grids 

(ts L 0.5 mol facilitated operation at larger electrical fields than 

those obtained with thinner screen grids. It might be expected that 

the thinner grids were deflected more due to the electrostatic and 

thermal loads enrountered and this resulted in the lower observed 

electric fields. Deflection analysis calculations confirmed this 

suspicion and showed that deflection of grids due to electrostatic 

attraction may have indeed caused the lower electric field at breakdown 

with the thinner grids. Computations showed a 0.25 arm thick grid would 

deflect 0.029 m while a 0.50 mm grid would deflect 0.0036 mm and a 

0.75 mm grid would deflect 0.0011 m at a total accelerating voltage of 

450 volts and a grid separation of 0.1 mm. It should be noted that an 

improvement to the gricl support system was made prior to testing of the 

thinnest grid for which data are shown in Fig. 25 (ts = 0.13 m). This 

improvement involved moving the support points of the grid hold down 

systeni closer to the grid apcrtures. This may account for part of the 

reason why the trend toward lower electric fields with decreased grid 

thickness did not continue for the thinner grids. 

h 

8 

In view of this possible grid deflection, the validity of the ion 

extraction performance results obtained with the thinner grids might be 

questioned. Computations showed that grid deflection due tc electrostatic forces becolros substantial only at the closest grid separations. 
c 

ORIGINAL PAGE W’ 

OF POOR QUALtTY 

69 

0 

SCREEN GRID THICKNESS [tt] (mm) 

Figure 25. Effect of Screen Grid Thickness on Electric Field 

Stress at Electrical Breakdown 
70 

For example, increasing the grid separation from 0.1 mm to 0.25 mm for 

the 0.25 mm thick grid operating at a total voltage of 450 V would 

reduce the deflection from 0.029 lllia to 0.0045 mm. Therefore, it is 

argued that the majority of the ion extraction results were unaffected 

by grid deflection. In any case, it should be emphasized that although 

the grid deflection may have affected the electrical breakdown results, 

it is felt that they did not affect the ion extraction performance 

results sufficiently to change the conclusions based on those results. 

All of the electrical breakdown data obtained in this 

investigation occurred at electric fields higher than 2 kV/mm. A limit 

of 2 kV/mm has been accepted generally for many years as a design 

criterion for ion thruster accelerator systems. Most of the existing 

electrical breakdown data for ion thrusters suggest, however, that a 

limit of 2 kV/mm is probably conser~ative.~~-~~ It appears that the 

results of this investigation support that observation since the 

majority of electrical breakdown data obtained lie substantially above 

2 kV/m. It should be emphasized that the results obtained in this 

study were for graphite grids and argon propellant. Other grid 

materials and propellants might be expected to give somewhat different 

results. Finally, it should be noted that no special effort was made 

to ensure the quality of the finishes on the grid surface and it is 

believed that this may have caused some of the scatter in the elec 

cal breakdown limits encountered in these tests. A tabular list 

all the electrical breakdown data obtained can be found in Appendi ';. 

An appreciation of the importance of operating with large electric 

fields and small screen grid holes to realize increased current densities can be gained by considering Fig. 26. This figure shows the 
500- 

0 “E 

-a 

ZE 

4- 

1- 100, 

50, 

c 

c 

t 

71 ORIGINAL PAGE 19 

OF POOR QUALITY 

ARGON 

\ 2 kV/mm’ 

.h ~0.81 

dS 

‘S 

dS 

- ~0.25 

0 I .o 2 .o 3.0 

SCREEN GRID HOLE DIAMETER [ds] (mm) 

Figure 26. Comparison of Predicted Current Density Levels as a 

Function of Electrical Breakdown Limit and Screen 

Grid Hole Diameter for a Total Accelerating Voltage 

of 1000 v 
72 

projected levels of impingement-limited current densities that one 

might expect as a function of the screen grid hole diameter and maximum allowed electric field. The current density levels shown in 

Fig. 26 were calculated by scaling the impingement-limited perveance 

values obtained with the 2.0 mm diameter screen grid hole for a 

discharge-to-total voltage ratio of 0.05 and a net-to-total accelerating voltage ratio of 0.75. It siould be noted that the current densities of Fig. 26 pertain to a total accelerating voltage of 1000 V and 

were calculated by dividing the impingement-limited beam current per 

hole expected ht that voltage by the area of the screen grid hole. 

Fig. 26 shows that for large screen grid holes, increases in the maximum allowable electric fields would not yield substantial increases in 

current density. This does not hold true, however, for the smaller 

screen grid hole diameters where large increases in current density 

levels are suggested by the difference between the curves for 2 kV/mm 

and 6 kV/mm. Also, it is seen in Fig. 26 that for the range of screen 

grid hole diameters considered therein, operating at electric fields 

above 6 kV/mm would not be expected to produce substantial increases in 

current densities. Although the results suggested by Fig. 26 are based 

n experimental results, it should be mentioned that similar qualitative conclusions could have been drawn using a simple Child's law 

analysis to predict expected current densities as a function of hole 

size and electric field strength. 
V. CONCLUSIONS 

An apparatus has been developed which is well suited to the 

evaluation of the impingement-limited ion extraction capabilities, the 

electron backstre 3ming and electrical breakdown characteristics of 

two-grid accelerator systems. The following conclusions are drawn 

based on this study of these phenomena. 

1) The basic relationships defining the current extraction 

capabilities of ion optic systems appear to be valid for 

screen grid hole diameters as small as 0.5 mm. It is expected 

that these relationships would be valid for even smaller 

holes provided the accelerator systems is mechanically sound 

and proper hole alignment and grid separation are maintained. 

Also, the ion source must be capable of supplying a high 

current density to the accelerator system while maintaining a 

stable discharge. 

2) The results show the ion extraction performance of two-grid 

accelerator systems is a function of the net-to-total accelerating voltage ratio and grj4 separation ratio. Tests show 

at large grid separation ratios the impingement-limited 

perveance per hole at which the grids can be operated is 

relatively independent of the neL-to-total accelerating 

voltage ratio. At small grid separation ratios, however, it 

was found that the impingement-limited perveance levels 

increased as the ratio of net-to-total accelerating voltage 
74 

increased. When the impingement-limited normalized perveance 

per hole is plotted over a large range of net-to-total accelerating valtage ratios, as a function of grid separation 

ratio, the resulting set of curves characterize the ion 

extraction performance of a particular accelerator system 

geometry described by the accelerator hole diameter ratio 

(d /d 1, the screen grid thickness ratio (ts/ds), and the 

as 

accelerator grid thickness ratio (t /d ). Results also show 

that these characteristic performance curves are dependent on 

the ratio of the discharge-to-total voltage (V,/V,) but 

appear to be independent of the total accelerating voltage. 

Tests show that impingement-limited normalized perveance per 

hole at which the grids can be operated degrades as the ratio 

of discharge-to-total accelerating voltage increases. 

as 

3) Using the data from a set of characteristic performance 

curves, an empirical model of the current that can be 

extracted from a grid aperture as a function of net-to-total 

accelerating voltage ratio and grid separation ratio is 

developed. This model shows that high beam current per hole 

levels are realized at a specified net accelerating voltage 

at low net-to-total accelerating voltage levels for all grid 

separation ratios. The model also suggests, however, that at 

small grid separation ratios there is another high beam 

current per hole operating point. This high beam current 

condition is realized at an optimum net-to-total accelerating 

voltage ratio in the range R = 0.5 to 0.8. 
75 

4) As expected, results show a general trend toward higher 

perveance levels with increases in the accelerator hole 

diameter ratio (da/ds). However, in this btudy an interesting exception to this trend has been observcd. When operating in the range of medium to high ratios of net-to-total 

accelerating voltage ratio at small grid separation ratios, 

results show that the current levels obtained with an accelerator hole diameter ratio of da/ds = 1.0 actually fell below 

the levels obtained with a smaller accelerator hole diameter 

ratio, da/ds = 0.81. This observation implies that an optimum accelerator hole diameter ratio exists. Grid operation 

at accelerator hole diameter ratios larger than this supposed 

optimum ratio would result in decreased impingement-limited 

perveance levels. 

This work resulted in a large body of experimental data which 

can be used in the design of high beam current density accelerator systems. An example of how the ion extraction performance data might be used for design is discussed in 

Appendix A. 

5) 

6) The electron backstreaming data obtained in this study 

resulted in a simple design curve which can be used to design 

accelerator systems in such a fashion as to avoid e1ec'-r-: 

backstreaming. 

7) Electrical fields greater than 2 kV/m were obtained before 

electrical breakdown occurred between the pairs of graphite 

grids tested. This limit of 2 kV/m is considered somewhat 

conservative since the average electric field at electrical 

breakdown was near 6 kV/mm. 
76 

Future work should focus on the effect of variations in discharge 

chamber conditions on ion extiaction performance. Also, because of the 

importance of operating at higher electric fields in order to take full 

advantage of the increased current densities obtainable with smaller 

screen grid holes, a more detailed investigation of the electrical 

breakdown phenomenon is recommended. 
REFERENCES 

1. Lockwood, D. L., Michelson, W., and Hamza, V., "Analytical SpaceCharge Flow and Theoretical Electrostatic Rocket Eqine Performance," 1st Electric Propulsion Conference, Berkeley, Calif., 

March 14-16, 1962. 

2. Hyman, J., Eckhardt, W. O., Knechtli, R. C., and Buckey, C. R., 

"Formation of Ion Beams from Plasma Sources: Part 1," AIM 

Journal, Vol. 2, Oct. 1964, pp. 1739-1748. 

3. Bogart, C. D. and Ri:hley, E. A., "A Space Charge Flow Computer 

Program," NASA Tech. Note TN-D3394, 1966. 

4. Lathem, W. C., "Ion Accelerator Designs for Kaufman Thrusters," 

Journal of Spacecraft and Rockets, Vol. 6, Nov. 1969, p. 1237. 

5. Kaufman, H. R., "Accelerator System Solution for Broad-'2am Ion 

Sources," AIAA Journal, Vol. 15, July 1°;7, pp. 10; 1-1034. 

6. Alterburg, W., Freisinger, J., Hau,er, J., Seibert, N., and Loeb, 

H. W., "Beam Formation in RF-Ion Thrusters," AIAA Paper No. 

75-426, New Crleans, La., 1975. 

7. Aston, G. and Kaufman, H. R., "The Ion-Optics of a Two-Grid 

Electron Bombardment Thruster," AIM Paper No. 76-1029, Key 

biscayne, Fl., 1976. 

8. Aston, G., Kaufman, H. R. and Wilbur, P. J., "Ion Beam Di:,*rgence 

Characteristrcs of Two-Grid Accelerator Systems," AIAA _I_- - Journal, 

Vol. 16, No. 5, May 1978, pp. 516-524. 

9. Astsn, G. and Kaufman, H. R., "Ion Beam Divergence Characteristics 

of lhree-Grid Accelerator Systems," AIAA Journal, Vol. 17, No. 1, 

Jan. 1979, pp. 64-70. 

10. Homa, J. B. and Wilbur, P. J., "Ion Beamlet Vectoring by Grid 

Translation," AIAA Paper No. 82-1895, Nov. 1982. 

11. Kerslake, W. R. and Paulik, E. V., "Additional Studies of Screen 

and Accelerator Grids for Electron-Bombardment Ion Thrusters," 

NASA Technical Note D-lCl1, 1963. 

12. Rawlin, V. K., Banks, B. A,, and Byers, D. C., "Dished Accelerator 

Grids on 30-ern Ion Thruster," Journal of Spacecraft and Rockets, 

Vol. 10, Jan. 1973, pp. 99-35. 
78 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23 - 

24. 

25. 

2;. 

27. 

Rawlin, V. K., "Studies of Dished Accelerator tirids for 30-cm Ion 

Thrusters," AIM Paper No. 73-1086, Oct./Nov., 1973. 

Whealton, J. H. and Tsai, C. C., "Influence of Chrometic Aberrations on Space Charge Ian Optics," Review of Scientific Instruments -' Vol- 49, No. 4, April 1978, pp. 495-498. 

Whealton, J. H., Jaeger, E. F., and Whitson, J. C., "Optics of Ion 

Beams of Arbitrary Perveance. Extracted from a Plasma," Journal of 

Computational Physics, Vol. 27, 1978, pp. 32-41. 

Wooten, J. W., Whealton, J. H., McCollough, D. H., McGaffrey, 

R. W., Akin, J. E., acd Drooks, L. J., "Ion Extraction and 

Optics in 3D," Journal of Computational Physics, Vol. 43, 1981, 

pp. 95-111. 

Child, C. D., "Discharge from Hot CaO," Physical Review, Vol. 32, 

1911, pp. 492-511. 

Aston, G. and Wilbur, P. J., "Ion Extraction from a Plasma," 

Journal of Applied PhysLcs., - Vol. 52, No. 4, April 1981. 

Spangenberg, K. H., Vacuum Tubes, 1948, pp. 348-349. 

Kaufman, H. R., "Technology of Electron Bombardment Thrusters," 

Advances - in Electronics and Physics, Vol. 36, Ecademic Press Inc., 

San Francisco, 1974. 

Cobine, J. D., Gaseous Conductors: Theory and Engineeriog Applications, 1st Ed., Dover Publications Inc., New York, 1958, p. 164. 

Kilpatrick, W. D., "Criterion for Vacuum Sparking Designed to 

Inciude Both rf an4 dr:," Review of Scientific Instruments, 

Vol. 28, No. 10, October, 1957, pp. 824-826. 

Coupland, J. R., Green, T. S., Hammond, D. P., and Riv-ere. A. C., 

"A Study of Ion Beam Intensity and Divergence Obtained frcm a 

Single Aperture Three Electrode Extraction System," Review of 

Scientific Instruments, Vol. 44, No. 9, September 1973. 

Green, T. S., Inst. Phys. Conf., Ser. 54, Bristol, 1980, p. 271. 

Kersiake, W. R., "Charge-Exchange Effects on the Accelerator 

Impinqement of an Electron-Bombardment Ion Rock c," NASA Tech. 

Note 'rN D-1657, May 1963. 

Byers, D. C., "An Experisental Investigation of a High-Voltage 

Electron-Bombardment Ion Thruster," J. Electrochem. SOC., 

Vol. 116, Jan. 1969, pp. 9-17 

Beattie, J. R., c.an Poeschel, R. I., "Extended Performance 

Thruster Technology Evaluation," AIAA paper 78-666, April 1978. 
79 

28. Rawlin, V. K., "Extended Operating Range of the 30-cm Ion Thruster 

with Simplified Power Processor Requirements," AIAA P-ser No. 

81-0692, April 1981. 

29. Aston, G., Yon Acceierator Systems for High Power 30-cm Thruster 

Operation," AIAA Paper No. 82-1893, Nov. 1982. 

30. Kaufman, H. R., "Ion Source Design for Industrial Applications," 

AIM Journal, Vol. 20, No. 6, June 1982, pp. 745-760. 

31. Brophy, J. R., "Effect of Screen Grid Potential on Perveance," 

appears in "Advanced Ion Thruster Research," NASA CR-168340, Feb. 

1984. 

32. Tsuchiya, I. and Masuzawa, T., "Study on Low Energy Ion-milling 

Equipment," International Ion Engineering Congress, Kyoto, Japan, 

September 12-16, 1983, pp. 765-770. 

33. Robinson, R. S., "Physical Processes in Directed Ion Beam Sputtering,*' NASA CR-159567, March 1979, p. 51. 
APPENDIX A 

A Design Example 

The purpose of this design example is to illustrate a po-sible 

technique for using the ion extraction petformance data obtained in 

this study. To do this, the following design problem is posed: 

Given a maximum design electric field of 4 kV/mm and a desisad net 

accelerating voltage of 500 volts, determine what ratio of net-to-tot81 

accelerating volta.*e yields the highest beam current aensity. Also, 

examine the effect of screen grid hole size on impingement-limited 

current density. 

For this particular example, the ion extraction performance data 

collected with the standard grid geometry (d /ds = 0.81, ts/ds = 0.25 

and ta/ds = 0.25; operating at discharge-to-total voltage ratio of 0.05 

will be used. The appropriate experimental data are found on the first 

page of Appendix B. 

a 

Because the desired net accelerating voltage has been specified, 

selection of a ratio of net-to-total accelerating voltage determines 

the total voltage, 

"N VT = - R- (A- 1) 

Under the design constraint of not exceeding a maximum electric field, 

this total voltage at each value of R can be used to determine the 

minimum grid separation a1 lowed 
81 

or 

R 

g=--. 

g Emax 

(A-2a) 

(A-2b) 

Substitution of the known quantities for this design example intc 

Eq. A-2b yields the following expression 

(1 - 0.05) o.llo 

4000 -R 

-- it a= 

g 

(A-3) 

where !2 has the units millimeters. Figure A.l shows how the grid 

separation is observed to vary as a function of R according to Eq. A-3. 

To use the ion extraction performance data, it is still necessary 

to select a screen grid hole diameter (d ). For now, a screen hole 

diameter of 2.0 m will be assumed. With the screen hole diameter 

specified, for each value of R the respective value of the minimum 

normalized grid separation (2 /d ) is now also defined 

g 

S 

gs 

A=-=- a 0.119 0.06 

d ds-R R . S 

(A-4) 

With the two independent variables, R and !2 /d thus defined, it is 

now possible to use the ion extraction performance curves to determine 

the impingement-limited normalized perveance per hole (P ). At each 

ratio of net-to-total accelerating voltage, the respective pelveance 

(P,) 

8 s' 

I 

can be used to calculate the current density {j):. where 

*All of the current densities referred to in this appendix and elsewhere in the thesis are based on the screen grid hole area, i.e. the 

current density 1s defined as the current per hole divided by the area 

of the screen grid hole. 
82 

ORIGINAL PAGE rs' 

OF POOR QUALITY 

h 

I Y - 

cdw 

u 

= 1.0 9 

tI\ I \ 

a 

W 

v) 

0 

Q 

cc 

a 

r 

0-5l 0 0 

VN = soov 

E =4kV/mm 

- VD = 0.05 

VT 

J I 1 I I I I I I I J 

0.5 1.0 

NET-TO-TOTAL ACCELERATING VOLTAGE RATIO [ R] 

Figure A.l. Minimum Grid Separation Variation 
83 

or 

-x10 5 - 

PI . (33/2 

22 j= 

n (ds)2 [k) + 0-25] 

(A-5b) 

Here, j has units mA/cm2 and ds is expressed in millimeters. There 

is another factor that needs to be considered, namely wher. to determine 

the maximum current density obtainable at each value of R. The current 

density appropriate to the minimum normalized grid separation does not 

always result in the h-’;hest current denity for each value of R. This 

is because in some cases the impingement-limited current density 

decreases (contrary to usual situation) as the grid separation is 

reduced below a certain value of normalized grid separation. A typical 

example of this effect is shown in Fig. A.2 where the impingementlimited current density i5 plotted as a function of normalized grid 

separation f-r 

conditions and 

pertain co the 

value of the m 

R = 0.5. It should bL> merationed that the operating 

normalized grid geometries appropriate to Fig. A.2 

present design example. For this design example the 

nimum normalized grid separation for R = 0.5 is 0.12. 

Figure A.2 shows that higher current densities could be obtained by 

o~erating at normalized grid separations larger than 0.12. Of particular interest here is the maximum current density shown in Fig. A.2. 

For those values of R where higher current densities can be obtained by 

operating it normalized grid separation ratios larger than thP minimum 

grid separation ratio, tte value of the maximum obtainable current 

density should be used for comparison purposes. If higher currents 
84 

ORIQINAL; PA@ a 

OF POOR QUAL^ 

ARGON 

VN = 500 V d, = 2.0 mrn 

R = 0.5 do 

-= 0.81 

ds 

ds 

-!h= 0.05 

"T to = 0.75 

NORMALIZED GRID SEPARATION [ eg Ids ] 

Figure A.2. Impingement-Limited Current Density as a Function of 

Normalized Grid Separation for R = 0.5 
85 

cannot be obtained at larger normalized grid separation ratios, the 

current density associated with the minimum grid separation ratio is 

used. The current densities determined in the aforementioned fashion 

for various values of net-to-total accelerating voltage ratio are shown 

plotted in Fig. A.3. This figure shows that the highest current. densities would be expected at very low ratios of net-to-total accelerating 

voltage. It also shows, however, that high beam current densities can 

be obtained at the higher ratios of net-twtotal accelerating voltage. 

The choice between these two high beam current density operating conditions, very low values of R or tLgh values of R, should be based on 

several considerations. First of all, there are the disadvantages of 

operating at very low ratios of R discussed earlier (pgs. 48 to 51). 

There is, however, an advantage to operating at lower values of R that 

needs to be discussed. Because of their higher total voltages smaller 

ratios of net-to-total accelerating voltage necessitate operation at 

larger grid separations. Using present grid manufacturing techniques, 

these larger grid separations facilitate operation with 'J, : diameter 

discharge chambers which are generally considered to be capable of 

producing ion beams more efficiently than smaller diameter discharge 

chambers. If at some point in the future smaller diameter thrusters 

can be designed t3 produce ion beams as efficiently as large diameter 

thrusters, then this advantage of operating at very low values of R 

could be negated. Another possibility is that maybe at some point in 

the future an improvement in grid design will allow accelerator systems 

of any desired diameter to be constructed with very close grid 

separations. 
\ 

\ 

86 

ARGON 

VN = 500 V ds=2.0 mm 

Emax= 4 kV/mm 

VO dS 

- = 0.05 

VT 

%= 0.81 

!A= 0.25 

q= t a 0.25 

NET-TO-TOTAL ACCELERATING 

VOLTAGE RATIO [R] 

Figure A.3. Maximum 1mpingem:at-Limited Current Densi"es Predicted 

fcr a Screen Apertlrre Diameter of 2.0 mm 
87 

It shoidd be mentioned that the higher ratios of net-to-total 

accelerating voltage shown in Fig. A.3 were checked for the possible 

occurrence of electron backstreaming. Based on tht design curve shown 

in Fig. 24, the net-to-total accelerating voltage ratio of 0.8 was 

found to be near the electron backstreaming limit. After incorporating 

a safety factor to ensure grid operation free of electron backstreaming, operation at a ratio of net-to-total accelerating voltage less 

than R = 3.75 is recommended. 

Curves similar in nature to that shown in Fig. A.3 can be obtained 

by repeating the above procedure for other screen grid hole diameters. 

In Fig. A.4 a comparison of the predicted current densities obtainable 

with screen grid hole diameter smaller than 2.0 mm is made. Fig. E.4 

shows that smaller screen grid hole diameters facilitate operation at 

higher beam current densities. From a practical standpoint, mechanical 

design considerations and the need for efficient ion beam production 

will most likely limit the extent to which the screen grid hole diameter can be reduced. One reason for this is that to maintain similar 

normalized grid thicknesses (t /d t /d ) as the hole size is reduced, s s' a s 

the grid thicknesses must also be reduced. These reduced grid thicknesses mean less mechanical stiength and in general shorter grid lifetimes. Using present accelerator system designs, reduced strength 

necessitates smaller diameter accelerator systems and smaller thrusters. A possible alternative to this would be to maintain the same grid 

thicknesses as the screen grid hole size is reduced. One problem with 

this alternative is that the results of Fig. 10 show that increases in 

the screen grid thickness ratio generally result in reduced perveance 

levels. Another problem is that increases in the screen drid thickness 
88 

200- 

100 

- E s 

5 2 50- 

?E 

I2- 

w *- 

1- 

5-20- kb g!z 

CGi! ZW 

3b =E 

=z 

a 10: 

Ea 

a a 5- 

2- 

ORIQJNAL P,FtGZ 73 

OF POOR QUALITY 

- - 

- 

- 

- 

d,= 1.0 mm 

- 

- 

ds= 1.5mm 

ds = 2.0 mm 

- 

- 

- 

- 

- 

I I I I 1 1 I I I I 

ARGON 

da VN = 500 V 

Emax= 4 kV/mm ds= ***’ 

/ ds =0.5 mm 

Figure A.4. Comparison of the Maxinlum Impingement-Limited Current 

Densities Predicted for Different Screen Grid Hole 

Diame t e r s 
20 ratio cause significant reductions in beam ion production efficiency. 

Also, from a mechanical design viewpoint, the increased precision 

required to maintain proper hole alignment for the smaller holes might 

limit the extent to which the screen grid hole size can be reduced. 

As a final note, in this design example the ratio of discharge-tototal voltage is artificially maintained at a value of 0.05. This 

facilitated the use of only one set of experimental data. However, in 

practice, the discharge voltage is usually held fixed and does not vary 

with changes in total voltage. In this operating mode, the expected 

current densities would differ slightly from those shown in Figs. A.3 

and A.4. The reason for this is that it has been demonstrated that 

changes in the discharge-to-total voltage ratio generally effect 

changes in the impingement-limited perveance levels (Fig. 6). Based on 

the results shown in Fig. 6, slightly higher beam current densities 

would be expected for operation at discharge-to-Lotal voitage ratios 

less than the value appropriate to Fig. 28 (VD/VT = 0.05). Similarly, 

slightly lower beam current densities would be expected at dischargeto-total voltage ratios greater than 0.05. For a fixed discharge 

voltage, this effect of the discharge-to-total voltage ratio on beam 

current densities would tend to favor the lower values of R where 

higher tcrtal voltages are observed. 
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OF POOR QUALITY 

APPENDIX C 

Electron Backstreaming Data 

For all data contained in this Appendix: 

ds = 2.0 am VD = 45 v VN = 400 V 

R 

4 Re Re -. exp (TI ta

da a J/V;l2 RlUi3X 

S 

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ds 

0.74 e L 

0.63 S - = 0.25 

dS 

0.52 

- 0.25 0.41 ta 

dS 

(Standard 0.29 

Configuration) 

0.18 

_- 

0.07 

3.01 

3.07 

3.08 

3.10 

3.31 

3.41 

3.55 

3.98 

4.64 

5.69 

0.953 

0.947 

0.940 

0.936 

0.924 

0.909 

0.894 

0.866 

0.836 

0.791 

2.01 

1.84 

1.68 

1.51 

1.36 

1.22 

1.09 

0.98 

0.9c 

0.85 

1.09 

0.98 

0.87 da 

- = 0.81 

dS 

0.76 

- = 0.25 0.64 

0.53 

dS 

0.42 ta 

ds 

- = 0.13 

0.30 

0.19 

0.08 

2.91 

3.08 

2.94 

3.01 

3.10 

3.25 

3.52 

3.68 

4.32 

4.33 

0.936 

0.928 

0.921 

0.912 

0.900 

0.883 

0.859 

0.827 

0.780 

0.737 

1.74 

1.59 

1.45 

1.31 

1.18 

1.05 

0.94 

0.85 

0.77 

0.73 
ORIGINAL PAGE I8 

OF POOR QUALITY 101 

a 

-8 

(nanopervs/hole) 

1.11 

1 .oo 

0.89 

0.77 

da 

= 0.81 

S 

0.66 tS 

dS 

- = 0.25 

0.55 

0.43 

0.32 

ta 

dS 

- = 0.38 

0.21 

0.10 

2.64 

2.98 

3.08 

3.00 

3.17 

3.19 

3.27 

3.62 

4.17 

4.91 

0.960 

0.955 

0.950 

0.34: 

0.940 

0.931 

0.920 

0.901 

0.881 

0.851 

2.41 

2.20 

2.01 

1.82 

1.64 

1.46 

1.31 

1.17 

1.07 

1.01 

1.10 

0.99 

0.87 

0.76 

0.65 

0.54 

da 

dS 

tS 

ds 

- = 0.81 

- = 0.25 

0.42 ta 

ds 

- = 0.51 

0.31 

0.20 

0.09 

2.62 

2.69 

2.66 

2.78 

2.85 

2.95 

2.94 

3.06 

3.45 

4.23 

0.964 

0.962 

0.958 

0.954 

0.951 

0.943 

0.933 

0.925 

0.906 

0.890 

2.79 

2.56 

2.33 

2.11 

1.89 

1.69 

1.51 

1.36 

1.24 

1.17 
102 

ORIGJNAL PAGE r9 

01: POOR QUALITY 

a 

dJ. 

(nanopervs/bole) 

1.11 

1 .oo 

0.89 da 

ds 

- = 0.81 

0.77 

0.66 

0.55 

= 0.25 0.43 

0.32 

tS 

dS 

- ta 

dS 

- = 0.13 

0.21 

0.10 

3.46 

3.77 

3.79 

3.91 

3.94 

3.98 

4.41 

4.79 

5.47 

5.82 

0.946 

0.941 

0.935 

0.928 

0.916 

0.901 

0.881 

0.852 

0.817 

0.775 

2.06 

1.88 

1.72 

1.55 

1.40 

1.25 

1.12 

1.00 

0.92 

0.86 

1.14 

1.03 

0.92 da 

dS 

- = 0.81 

0.81 c L 

0.69 s 

- = 0.38 

ds 

0.58 

ta 

dS 

- = 0.25 0.47 

0.36 

0.24 

0.13 

0.07 

2.52 

2.58 

2.63 

2.63 

2.72 

2.78 

2.73 

2.94 

3.33 

3.70 

3.86 

0.956 

0.951 

0.946 

0.940 

0.933 

0.923 

0.908 

0.892 

0.859 

0.832 

0.819 

2.11 

1.94 

1.77 

1.60 

1.44 

1.29 

1.16 

1.04 

0.94 

0.87 

0.85 
103 

ORIGINAL PAGE 19 

Of! POOR QUALITY 

(nanopervs/hole) 

1.09 

0.98 

0.86 da 

- = 0.66 

dS 

0.75 

0.64 ts 

- = 0.25 d 

S 

0.52 

0.41 

0.30 

ta 

- = 0.25 

dS 

0.19 

0.07 

1.75 

1.77 

1.79 

1.87 

1.88 

1.84 

1.99 

1.86 

1.76 

1.94 

0.962 

0.959 

0.955 

0.950 

0.945 

0.936 

0.927 

0.914 

0.901 

0.883 

2.66 

2.44 

2.22 

2.01 

1.80 

1.61 

1.44 

1.30 

1.19 

1.13 

1.11 

0.98 

0.89 da 

dS 

- = 1.00 

0.7? 

= 0.25 0.66 - ts 

ds 

0.55 

+ 

c 

0.43 a 

- = 0.25 

dS 

0.32 

0.21 

0.10 

4.23 

4.32 

4.07 

4.34 

4.50 

4.72 

4.96 

4.94 

4.52 

3.69 

0.919 

0.912 

0.908 

0.893 

0.874 

0.852 

0.824 

0.785 

0.758 

0.711 

1.57 

1.44 

1.31 

1.19 

1.07 

0.96 

0.85 

0.77 

0.70 

0.66 
104 

0.14 

0.10 

1 0.05 

APPENDIX D 

t 

ORIGINAL PAGE 18 

OF POOR QUALITY 

Electric Breakdown Data 

2.0 0.81 0.25 0.25 0.16 8.03 

0.11 8.17 

0.07 8.71 

0.02 9.76 

I 0.13 0.17 8.81 

0.12 8.07 

0.07 6.99 

I 0.03 6.31 

0.09 6.60 

I 1 0.04 8.11 

I 0.51 0.18 8.31 

0.13 7.68 

0.09 7.46 

t 0.04 7.17 

0.13 0.25 0.19 

0.14 

0.10 

1 0.05 

3.77 

3.27 

2.73 

2.01 

0.38 0.16 9.00 

0.12 8.35 

0.07 7.32 

0.03 10.58 

~~ ~ 1 0.66 0.25 I 0.16 8.03 
ORIGINAL PAGE 

105 OF POOR QUALW 

1-00 

-- 

$4 da - ts a 8 EBREAKDowN 

ds a- S 

a- (-1 (kV/m) S (-2 

2.0 0.66 0.25 0.25 0.11 8.17 

Y 

I 1 0.07 i 0.02 

8.71 

9.76 

0.15 6.35 

0.10 5.95 

0.06 5.25 

0.01 7.01 

1.5 0.66 0.22 4.76 

0.18 4.19 

0.13 4.01 

0.09 3.36 

0.04 3.85 

0.19 

0.15 

0.10 

0.06 

0.01 

5.13 

4.47 

4.30 

4.35 

5.95 

1 .o 0.66 0.19 5.85 

0.14 5.48 

0.10 5.15 

0.05 5.07 

0.19 5.97 

0.15 4.94 

0.10 3.89 

I 1.00 I i 

I 0.06 4.15 

I 

I 

0.5 0.8 0.25 0.25 0.19 4.18