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NASA Contractor Report 4483 



Discrimination of Ionic Species 
From Broad-Beam Ion Sources 



J. R. Anderson 

Colorado State University 

Fort Collins, Colorado 



Prepared for 

George C. Marshall Space Flight Center 

under Grant NGT-50370 _.. 



(NASA-CR-A483) DI SCft I MINAT ION OF N93-18140 

IONIC SPECIES FROM BROAD-BEAM ION 

SOURCES (Colorado State Univ.) 

123 p Unc1as 

Hl/72 0145555 



NASA 

National Aeronautics and 
Space Administration 

Office of Management 

Scientific and Technical 
Information Program 

1993 



TABLE OF CONTENTS 



Chapter 



V. 
VI. 



Page. 



I. INTRODUCTION 1 

n THEORY OF ION EXTRACTION AND MASS 

DISCRIMINATION SYSTEM OPERATION 5 

m. PRELIMINARY EXPERIMENTS 15 

Experimental Apparatus }* 

Experimental Procedure 20 

Experimental Results 22 

IV. THREE-GRID OPTICS/RF MASS DISCRIMINATOR . ... 30 

Experimental Apparatus 32 

Experimental Procedure ^ 

Experimental Results (Argon and/or Krypton) 40 

Experimental Results (Oxygen) " 



CONCLUSIONS 58 

FUTURE WORK 60 

REFERENCES ^ 

APPENDIX A - A One-Dimensional Model of the Intra-Grid 

Acceleration Process 67 

APPENDIX B - Electron Induced Errors in Probe Data ... 86 

APPENDIX C - A Fourier Series Technique for 

Differentiating Experimental Data 94 

APPENDIX D - Nomenclature 112 



li 1NKNU0NAUJ ttLANk PRCC€0!NG PAGE BLANK NOT FILMED 



LIST OF FIGURES 

Figure Pa^ 

1 Single-Stage Bennett Mass Spectrometer 6 

2 First-Order Energy Spread Parameter 10 

3 Species Selection Using Single-Stage Bennett Mass Spectrometer ... 12 

4 Experimental Apparatus for Single-Stage Bennett 

Mass Spectrometer 16 

5 Retarding Potential Analyzer 19 

6 Faraday Probe 21 

7 RPA Trace and Energy Distribution for Krypton-Argon 

Ion Beam 24 

8 Current Balance for 1 mA Current to Single-Stage Bennett 

Mass Spectrometer 26 

9 Current Balance for 3 mA Current to Single-Stage Bennett 

Mass Spectrometer 29 

10 Experimental Apparatus for Three-Grid Optics/RF Mass 

Discriminator 31 

1 1 Retarding Potential Analyzer (for Three-Grid Optics/RF Mass 
Discriminator) 35 

12 Faraday Probe (for Three-Grid Optics/RF Mass Discriminator) ... 36 

13 ExB Probe Schematic Diagram 38 

14 Typical RPA Data 42 

15 Comparison of Theoretical and Experimental Stopping 

Potentials for Argon 45 



Iv 



Figure 



Page 



16 Comparison of Theoretical and Experimental Stopping 

Potentials for Krypton 4 ° 

17 Comparison of Stopping Potentials for Krypton and Argon 47 

18 ExB Data Demonstrating Krypton Filtering for Krypton- Argon 

Ion Beam 49 

19 ExB Data for Argon After Krypton is Stopped 50 

20 ExB Data Demonstrating Argon Filtering for Krypton- Argon 

Ion Beam 52 

21 Theoretical Stopping Potentials for Atomic and 

Diatomic Oxygen 54 

22 ExB Data Demonstrating Filtering of Diatomic Oxygen 55 

23 Atomic Oxygen Current Density Data for 19 Hole Grid System ... 57 

24 Envisioned Configuration for a 5 eV Atomic Oxygen Source .... 61 

Al Geometry and Boundary Conditions for the Single-Stage 

Bennett Mass Spectrometer and the Three-Grid Optics/RF Mass 
Discriminator 68 

A2 Non-dimensional Geometry and Boundary Conditions for the 
Single-Stage Bennett Mass Spectrometer and the Three-Grid 
Optics/RF Mass Discriminator 73 

Bl Raw RPA Data for a Krypton-Argon Ion Beam 88 

B2 RPA Currents Flowing During Single-Stage Bennett Mass 

Spectrometer Testing 89 

CI Step Function and Fourier Sine Series Approximation 102 

C2 Fourier Sine Series Approximation to Step Function Derivative ... 104 

C3 Fourier Series Approximation to Exponential Function and 

its First Two Derivatives 106 

C4 Third Derivative of Exponential Function Using 

128 Coefficients 107 

C5 Third Derivative of Exponential Function Using 64 Coefficients ... 109 

C6 Fourier Sine Series Approximation to Higher Order Derivatives 

of the Step Function 1 10 



Fi gure Page 

C7 RPA Trace and Corresponding Ion Energy Distribution 

Function Ill 



VI 



T JST OF TABLES 

Table 2ag£ 

Al Definition of Non-Dimensional Variables 71 



vii 



T. INTRODUCTION 

Satellites in low-Earth-orbit, about 200-400 km altitude, encounter a rarified 
atmosphere which consists primarily of atomic oxygen, produced by solar radiation 
induced photo-dissociation of diatomic oxygen, and diatomic nitrogen. Since the 
gases are in thermal equilibrium, the speed distribution of the less massive atomic 
oxygen is skewed to higher speeds than the more massive diatomic nitrogen. As a 
result, only a small fraction of the most energetic diatomic nitrogen can reach 
elevations accessible to atomic oxygen. Therefore, the main constituent of the low- 
Earth-orbit atmosphere is atomic oxygen. 

In order to be serviced by the space shuttle, the proposed space station 
Freedom, which is intended to operate for several years, must be placed in low-Earth- 
orbit. There is concern about how the chemically active atomic oxygen will affect the 
exposed surfaces of the space station. This concern arises because tests, conducted in 
low-Earth-orbit, have demonstrated that high-energy oxygen atoms strike the surfaces 
of spacecraft at a sufficiently high rate to cause some spacecraft materials to erode 
rapidly [1,2]. The speed of these atoms relative to the spacecraft, which is 
determined by the spacecraft orbital speed, corresponds to an atomic oxygen kinetic 

energy near 5 eV. 

In order for the space station to operate for many years in low-Earth-orbit, 
protective coatings or materials resistant to atomic oxygen attack must be used for the 
exposed surfaces. To evaluate the suitability of various spacecraft materials that 
might be exposed to this oxygen flux, it is desirable to have an earth-based facility 
that can produce a broad beam of 5 eV atomic oxygen at low-Earth-orbit flux levels 



(10 14 to 10 16 oxygen atoms per second per square centimeter [3]). 

Several approaches have been used in attempts to simulate the low-Earth-orbit 
environment [4]. Reference [4] lists thirty-three facilities and gives a brief 
description of the methods used in each. There are two basic types of systems: 
thermal and electric. In the thermal systems diatomic oxygen is heated and some of it 
is dissociated with either a laser or an electric discharge. The gas is then expanded 
through a nozzle and directed onto the material being tested. The major drawback of 
these systems is that the kinetic energies achieved are less than 1 eV. Also diatomic 
oxygen is mixed in with the atomic oxygen. 

In the electrical systems, atomic and diatomic oxygen ions are produced in 
either an arc discharge or a microwave discharge. To achieve energies greater than 
1 eV these ions are accelerated electrostatically. Because it is difficult to control 
beams with ions having kinetic energies in the few eV range, many of the systems 
direct beams having tens to several thousand eV energies onto the sample of the 
material being tested. 

In the simplest schemes both atomic and diatomic ions are directed onto the 
sample. More sophisticated systems either charge neutralize the ions or filter out the 
diatomic ions before directing the beam onto the sample. The most sophisticated 
systems either try to produce a pure atomic oxygen ion plasma or filter out the 
diatomic ion component of the beam and then charge neutralize the atomic oxygen to 
produce a pure oxygen-atom beam. 

Before describing schemes for separation of diatomic and atomic oxygen ions, 
charge neutralization will be discussed briefly. Charge neutralization of atomic 
oxygen can be accomplished using grazing incidence impact with a polished metal 
surface [5,6,7]. If ions approach the metal plate at incidence angles of less than 
2°, 40 to 50% of the ions can pick up an electron and reflect off the surface with 



virtually no loss of kinetic energy [5]. It is also possible to charge neutralize ions 
approaching a metal plate at larger incidence angles, but these ions will lose kinetic 
energy while interacting with the surface. Theoretical computations have estimated 
the percentage of atomic ions impinging normal to a metal plate which are reflected 
and charge neutralized to be between 40 and 60% at incident energies between 10 and 
50 eV [8]. These calculations also predict that ions approaching a molybdenum plate 
at normal incidence with a kinetic energy of 15 eV will be reflected at energies 
ranging from zero to 11 eV with the peak of the distribution at 6 eV. 

Typically, separation of the atomic and diatomic ions is accomplished with a 
magnetic lens. Magnetic lenses are often used in ion accelerators [9,10,11] 
where ions have keV energies. Such systems tend to be large and ions must travel 
relatively long distances between the ion source and the target. These systems are 
designed to focus ions at or near the center of the beam onto the target; however, ions 
near the edges of the beam or ions on divergent trajectories will be lost. The 
performance of a magnetic lens is expected to be worse at low energies because ions 
take longer to travel from the source to the target. This would allow the mutually 
repulsive forces between ions to act for a longer time and this would cause increased 
beam divergence, resulting in larger loses. 

This dissertation describes the experimental investigation of an alternative 
concept for separating diatomic and atomic oxygen ions. The alternative mass 
discrimination scheme is based on a single-stage Bennett mass spectrometer [12] 
which uses a radio frequency (RF) voltage signal to accomplish mass separation. 
First, a theoretical description of the single-stage Bennett mass spectrometer which 
predicts the energy of ions being extracted from it is given. Then experimental 
results, which demonstrate that the single-stage Bennett mass spectrometer operation 
agrees essentially with the theoretical predictions, are described. However, problems 



with efficient extraction of ions using the single-stage Bennett mass spectrometer 
prompted design changes. The resulting device, which combines the function of a 
three-grid optics system [13] and the single-stage Bennett mass spectrometer, has 
been named the three-grid optics/RF mass discriminator. Next, experiments 
demonstrating that diatomic oxygen ions can be filtered out of the beam in the three- 
grid optics/RF mass discriminator are discussed. In addition, atomic oxygen ion 
energy, current density and beam divergence data are also presented. Finally, a 
configuration which could incorporate the charge-exchange process into the three-grid 
optics/RF mass discriminator is proposed. 



IT. THEORY OF TON EX TRACTION AND MASS 
msrRTMTNATION SY STEM OPERATION 

Before describing the three-grid optics/RF mass discriminator system, it is 
instructive to discuss how a single-stage Bennett mass spectrometer might be used to 
accomplish mass discrimination. A single-stage Bennett mass spectrometer has three, 
equally-spaced grids and is configured as shown in Fig. la. All three grids are held 
at a prescribed mean electric potential and a sinusoidal, RF voltage like the one 
illustrated in Fig. lb is applied to grid 2. In order to understand the principle of 
operation of the device, consider the effect of this RF signal on an atomic and a 
diatomic ion represented, respectively, in Fig. la by the smaller and larger circles. 
Assuming both ions are drawn from the same ion source (i.e. accelerated through the 
same potential difference), the more massive diatomic ion will enter the system at a 
lower velocity, as its velocity vector suggests. Consider the case where both ions 
pass through grid 1 at time zero when the RF voltage on grid 2 begins to go positive. 
The electric field set up between these grids will cause the ions to decelerate as they 
travel toward grid 2. If the radio frequency is selected so that the atomic ion reaches 
grid 2 one-half cycle later as the voltage goes negative, the electric field between 
grids 2 and 3 will cause it to continue to decelerate as it travels toward grid 3. 
However, the diatomic ion, which is travelling slower, will not have reached grid 2 
after half an RF cycle; therefore, after the potential on grid 2 goes negative, it will 
see an accelerating field until it reaches grid 2. The diatomic ion will also accelerate 
for a portion of the time it is between grids 2 and 3. As a result, at these particular 
conditions, the atomic ion will lose more kinetic energy than the diatomic one does 



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GRID 3 



• GRID 2 



ATOMIC ION 



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-© GRID 1 



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OXYGEN IONS — ^ 

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ENERGY ' 

(BOTH SPECIES) 




DIATOMIC OXYGEN IONS 



r\ 






i \ 

t \ 

i \ 

t i 

J. i. 



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1 2 3 

NON-DIMENSIONAL TIME 



c. Energy of Ions Exiting Grid 3 



Fig. 1 



Single-Stage Bennett Mass Spectrometer 



during its passage through the grids. Although the operating conditions just described 
are not the optimum conditions for separating atomic and diatomic oxygen, this 
tendency for atomic and diatomic ions to experience different kinetic energy changes 
is exploited to effect mass discrimination. 

In operation, a steady stream (or beam) of atomic and diatomic ions is fed into 
the single-stage Bennett mass spectrometer. Depending on the phase of the RF signal 
when an ion enters the spectrometer, it could emerge at grid 3 with more, the same, 
or less kinetic energy than it had when it entered. Figure lc shows the energies of 
atomic and diatomic oxygen ions as a function of the time at which they emerge from 
the third grid. In order to determine this time variation of the energies of the 
emerging ions, a simple, one-dimensional model of the intra-grid acceleration process 
has been developed (Appendix A). The model enables one to compute the kinetic 
energy at which ions emerge from the third grid, which is referred to as the terminal 

ion energy. 

The model is cast in terms of non-dimensional variables which are convenient 
to describe the system. The non-dimensional kinetic energy (£) is the actual ion 
energy divided by the energy that ions have when they arrive at grid 3 when no RF 
signal is applied. When the RF signal is not applied, there are no time varying 
voltages so the system operates in a steady-state condition. During non-steady 
operation the kinetic energy will oscillate about the steady-state value. Non- 
dimensional voltage (p) is the actual voltage divided by the difference between 
discharge chamber plasma potential (i.e. the potential at which ions are created) and 
the mean potential applied to grid 2. Non-dimensional frequency (F) is the actual 
frequency multiplied by the time it takes a diatomic oxygen ion to travel between 
grids 1 and 2 when the system is operated at steady-state. Non-dimensional time (T) 
is the actual time divided by the time it takes a diatomic oxygen ion to travel between 



7 



grids 1 and 2 during steady-state operation. Non-dimensional ion mass (M) is the 
actual ion mass divided by the mass of a diatomic oxygen ion and non-dimensional 
charge (Q) is the actual charge divided by the magnitude of the electron charge (e). 

Before continuing the discussion, it is noted that these non-dimensional 
variables will be used throughout the dissertation. Unless otherwise stated, it is to be 
implicitly understood that the non-dimensional values are being referred to when 
energy, potential, frequency, mass, charge and time are used. 

One additional parameter, the effective frequency for a particular species, is 
also useful. The effective frequency for a given species is defined as the mean 
number of cycles an ion experiences as it travels between grids 1 and 2. This is 
equal to the frequency (F) multiplied by the time it takes an ion of the species being 
considered to travel from grid 1 to grid 2 at steady-state (r) 1 . In Appendix A it is 
shown that this transit time is related to the charge-to-mass ratio through 

t -]q • (I) 

Since the charge- to-mass ratio is 1 for singly ionized diatomic oxygen, the frequency 
(F) is equal to the effective frequency (Ft) for diatomic oxygen. When the 
spectrometer is operating, the frequency (F) is held fixed; however, because each 
species has a different charge-to-mass ratio, their velocities are different resulting in 
different transit times for each species. Consequently, the effective frequency is 
different for each species travelling through the system. 

A first-order model, using the RF voltage as a perturbation to the steady-state 
solution, has been developed to determine the terminal ion energy (Appendix A). The 



! Since the single-stage Bennett mass spectrometer grids are equally spaced and at the 
same mean potential, the time it take an ion to travel from grid 2 to grid 3 at steady-state 
is also t. 



first-order solution for the terminal ion energy is 

€ = 1 + vrf iKFt) sin[2xFT + 5(Fr)] < 2) 

where tf, the energy spread parameter, depends on the effective frequency (Fr) for a 
given species. The phase shift between the sinusoidal RF signal and the terminal ion 
energy, which is also a function of the effective frequency for a particular species, is 
denoted by 5. The equations for both $ and 5 are given in Appendix A. Since the 
sine function varies between ± 1, the product of the function ^ and the RF voltage 
("rf> g ives » t0 first order ' * e maxirnum variation of the terminal ion energy. 
The energy spread parameter \p is plotted as a function of the effective 
frequency (Ft) in Fig. 2. If a single-stage Bennett mass spectrometer is to be used to 
separate atomic and diatomic oxygen ions, the system is operated so that the effective 
frequency for diatomic ions is unity and that for atomic ions is \ 0.5 as labeled in 
Fig. 2. Since r=l for singly ionized diatomic oxygen, the frequency is fixed at unity 
(F = l). From the plot in Fig. 2 it is evident that ^(1.0) = 0. Plugging this into Eq. 
2 shows that, to first order, the diatomic oxygen ions emerge from the system as a 
mono-energetic group with an energy of unity. The reason the diatomic ions emerge 
as a mono-energetic group is that, to first order, all the diatomic ions take two full 
RF cycles to travel between grids 1 and 3. Because of this they experience the same 
amount of acceleration and deceleration, causing them to emerge with same energy 
they had when they entered the system 2 . Since atomic oxygen has half the mass of 
diatomic oxygen, the mass-to-charge ratio for singly ionized atomic oxygen ions is 
0.5; therefore, the effective frequency for atomic oxygen ions is J 0.5 (-0.71). 
From Fig. 2 it is seen that ^(0.71) = 0.57. Using this value and an RF voltage (v^) 
of 0.25 in Eq. 2, the terminal ion energies of the atomic oxygen ions are seen to 



^e model assumes that a mono-energetic group of ions enters the system. 

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vary, to first order, between 0.86 to 1.14. The reason that atomic ions have a spread 
induced in their energies is that they do not experience an integer number of RF 
cycles through the single-stage Bennett mass spectrometer. Consequently, some of 
the ions experience more acceleration and some more deceleration, depending on the 
phase of the RF signal when they enter the system. As a result, a significant spread 
of atomic ion energies is induced in the system. 

Figure lc shows a plot of the terminal energy for atomic and diatomic ions, 
predicted by the first-order solution, as a function of the time at which they emerge 
from the system. This plot was made assuming that a mono-energetic group of ions 
begins entering the single-stage Bennett mass spectrometer at time zero. Since, to 
first order, diatomic ions take two RF cycles to travel through the system, the first 
diatomic ions emerge after two periods. The atomic ions, however, take about 0.7 
periods to travel between each pair of grids. Therefore, the atomic ions that entered 
the single-stage Bennett mass spectrometer at time zero emerge after about 1.4 
periods. Ions that enter the system later also exit at later times and the variation of 
their terminal energies with time are shown in Fig. lc. It is evident that the atomic 
ions have a significant energy spread when they exit, while the atomic ions emerge as 

a mono-energetic group. 

In order to understand how the energy dispersion introduced to the atomic ions 
can be used to effect mass discrimination, consider Fig. 3a. This figure shows the 
single-stage Bennett mass spectrometer connected to a filtering grid and power supply 
which can be used to adjust its potential. A mono-energetic beam of atomic and 
diatomic oxygen ions with an energy of unity enters the single-stage Bennett mass 
spectrometer where their energies are perturbed before they travel on to the filtering 

grid. 

Figure 3b shows the effect of filtering potential on time-averaged, filtered- 

11 



FILTERED 
BEAM 



PERTURBED ATOMIC 
AND DIATOMIC IONS 



ATOMIC AND 
DIATOMIC IONS 



a. Physical System 

TIME 

AVERAGED 

FILTERED 

BEAM 
CURRENT 
DENSITY 



ttttt 



ttttt 



FILTERING 
GRID 



FILTERING 
POTENTIAL 



SINGLE-STAGE 
BENNETT MASS 
SPECTROMETER 



ttttt 

* = 1 



TOTAL IONS 

ATOMIC IONS 



DIATOMIC IONS 




NON-DIMENSIONAL 
FILTERING POTENTIAL 

b. Frequency Selected to Perturb Atomic 
but not Diatomic Ions 



Fig. 3 Species Selection Using Single-Stage Bennett Mass Spectrometer 



12 



beam current densities 3 when the operating conditions for the single-stage Bennett 
mass spectrometer of Fig. 3a are selected to induce a significant energy change in the 
atomic ions while not perturbing the energies of the diatomic ions. Shown are the 
atomic, diatomic and combined (or total) time-averaged, filtered-beam current 
densities that would be measured downstream of the filtering grid as a function of the 
potential applied to it. Diatomic oxygen accounts for most of the current because, 
typically, atomic oxygen accounts for less than 30% of the ions extracted from an arc 
discharge [14]. At low filtering potentials all of the ions are able to pass through 
the filtering grid. However, as the filtering potential increases, a point is eventually 
reached where the kinetic energies of the atomic ions that decelerate the most in the 
single-stage Bennett mass spectrometer are insufficient to overcome the adverse 
potential and they are removed from the filtered beam. Further increases in filtering 
potential cause the fraction of atomic ions removed from the beam to increase. 
Because the diatomic ions are a mono-energetic group, they are removed abruptly at a 
filtering potential of unity. At filtering potentials above that needed to stop the 
diatomic ions, the time-averaged, filtered-beam current density is due to atomic ions 
only. (This would be the desired operating condition if this system configuration 
were to be used in the 5 eV atomic oxygen source.) Further increases in filtering 
potential cause the time-averaged atomic ion current density to decrease and 

eventually drop to zero. 

Two obvious drawbacks to the mass discrimination scheme just described are 
1) at most half of the atomic ions drawn from an ion source will pass through the 
filtering grid onto a sample being tested and 2) the ions that do reach the sample will 
have an energy spread rather than having the preferred 5 eV mono-energetic 



3 Time-averaged, filtered-beam current density is the charge flowing through a unit 
of the filtering grid per RF cycle divided by the period of the cycle. 



area 

13 



distribution. The energy spread on the ions can be minimized by reducing the 
amplitude of the radio-frequency voltage, but some energy spread will always occur 
in a properly operating system. The great advantage of this discrimination concept is 
that it utilizes a compact combination of optics and mass discrimination system 
elements. This should minimize the divergence losses that plague magnetic field- 
induced mass discrimination systems. 



14 



TTT. PttFIJMlNAgY FXPERTMENTS 

Experimental Apparatus 

The experimental apparatus used to conduct the preliminary investigation of 
the single-stage Bennett mass spectrometer is shown schematically in Fig. 4. Ions 
were generated in the 8 cm dia mildly-divergent-magnetic-field discharge chamber 
shown at the bottom of the figure. The discharge chamber was made with non- 
magnetic stainless steel and a magnetic field was induced with a solenoidal winding 
extending the length of the discharge chamber. Additional windings were placed at 
the back of the discharge chamber so that the magnetic field at the back of the 
chamber was 1.6 times stronger than it was at the screen grid. This discharge 
chamber could be run on a variety of source gases which were introduced through 
two gas injectors placed at the rear of the chamber. The discharge chamber bias 
supply could be used to bias the chamber with respect to ground. The cylindrical 
anode was biased with respect to the discharge chamber so that electrons emitted from 
the heated, tungsten filament cathode acquired the kinetic energy they needed to 
ionize the gas being used in the chamber. More information on this type of discharge 
chamber can be found in the literature [15,16,17,18]. 

Two different grid systems were used to study the single-stage Bennett mass 
spectrometer; one was a single aperture grid set (shown in Fig. 4) and the other was a 
19-hole grid set. With the single aperture grid set, ion acceleration was accomplished 
using an optics system consisting of a sheath-constraining [19] screen grid and an 
accel grid. The accel grid could be biased up to 2 kV negative of ground to facilitate 
ion extraction at a reasonable beam current density level. The sheath-constraining 



15 



STAINLESS-STEEL 

WIRE MESH 

(3 PLACES) 



i s^sfti" n 



T 



RF SUPPLIES 



GRID SPACING 



<\j 






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GENERATOR GRID SPACING 



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T> W " 



DC 



ACCEL 

GRID 

SUPPLY 



GRID 3 



GRID 2 



GRID 1 



SINGLE-STAGE 
BENNETT MASS 
SPECTROMETER 



ACCEL GRID 

32553 



ANODE 
POWER 
SUPPLY 

+ 
DC 



rv ^?T 



• SHEATH-CONSTRAINING 
MESH 



SCREEN GRID 



DC 



Ti 



ANODE 



CATHODE 

mm 



HI- 



DC — • 



HI- 



DISCHARGE 
CHAMBER 

— MAGNET WINDINGS 



r 



GAS 
INJECTOR 



DC 



DISCHARGE CHAMBER CATHODE 
BIAS SUPPLY HEATER 



ELECTRO-MAGNET 
POWER SUPPLY 



Fig. 4 Experimental Apparatus for Single-Stage Bennett Mass Spectrometer 



16 



screen served to control the sheath shape and hence beam divergence under optics 
system operating conditions where the accel grid was biased very negative. Both the 
screen and accel grids were made of 1.6 mm thick, 8.9 cm dia stainless steel disks 
with 2.9 cm dia holes machined at their centers. The sheath-constraining mesh was 
made by spot welding 0.25 mm dia tungsten wire to form a square mesh with 2 mm 
wire-to- wire spacing. The mesh was contoured to form a spherical segment over the 
2.9 cm dia aperture, as suggested in Fig. 4. 

Energy dispersion was induced in the single-stage Bennett mass spectrometer 
subsystem shown downstream of the accel grid in Fig. 4. The mean potential applied 
to all of the single-stage Bennett mass spectrometer grids was ground potential. The 
spectrometer grids were also made of 1.6 mm thick, 8.9 cm dia stainless steel disks 
with 2.9 cm dia holes machined in their centers. The grids were evenly spaced and 
grid spacing is defined at the distance between the adjacent faces of neighboring 
grids. To provide a planar, uniform potential across each of the apertures, stainless- 
steel wire mesh with a transparency of about 0.8 was spot welded over the aperture of 
each of the spectrometer grids. The radio-frequency signal applied to grid 2 was the 
amplified output of a sine-wave signal generator; an RF signal up to 100 V peak-to- 
peak could be applied. 

One drawback to the single-aperture grid set was that about 20% of the current 
arriving at each of the single-stage Bennett mass spectrometer grids impinged on the 
wire mesh. Since there was stainless wire screen over three grids, a total of about 
half (1-0.8 3 ) of the ions supplied to the spectrometer were lost. In order to eliminate 
this impingement loss, a 19-hole grid set with matching 2 mm dia apertures was made 
of 0.25 mm thick graphite. Each grid had 19 holes arranged in a hexagonal close- 
pack pattern with 2.5 mm center-to-center spacing and the grids were aligned 
coaxially. The grids were used in the same configuration as the single-aperture grid 

17 



set; however, a sheath-constraining mesh was not placed over the screen grid holes 
and wire mesh was not placed over the single-stage Bennett mass spectrometer grid 
holes. It was anticipated that this would result in lower impingement loses because 
the ions should have been focused through the holes instead of being lost to the wire 
meshes. 

Two pieces of diagnostic equipment were used during preliminary 
experiments. A retarding potential analyzer (RPA) was used to measure energy 
characteristics of the beams extracted from the single-stage Bennett mass 
spectrometer. A Faraday probe was used to measure current-density profiles of these 
beams. The RPA, shown in Fig. 5, was used to measure total-time-averaged beam 
current density as a function of the retarding potential applied to the collector. As 
this figure suggests, the beam ions passed through a 2 mm dia aperture in the Faraday 
cage and struck a molybdenum collector. The time-averaged current of these ions 
was determined by measuring the current of electrons through the ammeter required 
to neutralize them. The Faraday cage was biased sufficiently far below ground so 
that electrons in the ambient plasma, which had a Debye length [20] near 1 cm, 
should have been unable to reach the collector through the 2 mm dia aperture. 
Although electrons were not expected to pass through the aperture, a small electron 
current was still measured when the retarding potential was high enough to stop all of 
the ions. It is believed that these were secondary electrons which were emitted when 
ions repelled by the collector struck the inside surfaces of the Faraday cage. This 
secondary electron current was subtracted off the raw RPA data using the method 
developed in Appendix B. It should be noted that the RPA collector served the 
function of the filtering grid shown in Fig. 3a and discussed in the related text. Thus, 



RETARDING 
POTENTIAL 




DC 



FARADAY 
CAGE 
BIAS 



DC 



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n-rr 






COLLECTOR - £ 
RPA SUPPORT ^^*L^t) 



FARADAY 
CAGE 



COLLECTOR 
CURRENT 



©■ 



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p 



2 mm DIA 
APERTURE 



ttttt 



ION BEAM 



Fig. 5 Retarding Potential Analyzer 



19 



„4 



the retarding potential applied to the collector and time-averaged current density 4 
correspond, respectively, to filtering potential and time-averaged, filtered-beam 
current density. 

The Faraday probe was used to measure time-averaged, beam-current-density 
profiles which could be integrated to determine the total, time-averaged ion current 
extracted from the single-stage Bennett mass spectrometer. The Faraday probe shown 
in Fig. 6 was similar to the RPA of Fig. 5. As with the RPA, beam ions passed 
through the 2 mm dia aperture and impinged on the collector. However, the collector 
was held at ground potential and the Faraday probe was swept through the beam in a 
plane downstream of and parallel to the single-stage Bennett mass spectrometer grids. 
The current arriving at the collector was measured as a function of position using the 
position-sensing potentiometer. The Faraday cage was biased negative enough to stop 
plasma electrons from entering the aperture and impinging on the collector. 
Experimental Procedure 

Preliminary experiments designed to investigate the performance of the single- 
stage Bennett mass spectrometer were conducted using argon and krypton ions 
because they yielded a simple beam (essentially Ar + and Kr + ions only) with energy 
characteristics that could be analyzed readily and compared to theoretical predictions. 
Additional reasons for selecting these gases were that they are chemically inert, their 
mass ratio (84 a.m.u. to 40 a.m.u.) is about the same as the diatomic-to-atomic 
oxygen mass ratio and they have similar ionization cross sections (3.67 A 2 for 
krypton and 2.49 A 2 for argon [21] at the 45 eV discharge voltage used in all 
testing). 



''The time-averaged current density is equal to the time-averaged ion current 
impinging on the collector divided by the area of the 2 mm dia aperture in the Faraday 
cage. 



20 



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Faraday Probe 



21 



One set of preliminary experiments involved demonstration that a single-stage 
Bennett mass spectrometer could induce a spread in the energies of one species while 
introducing a minimal spread in the energies of the other species. In order to obtain 
results that could be interpreted readily, the tests were conducted using beams 
extracted with about a 50% -50% mixture of krypton and argon ions. The exact 
proportions of each gas were controlled to assure operation with approximately equal 
krypton and argon current densities. This testing was done using the single-aperture 
grid set and the RPA was used to obtain current density v. retarding potential traces. 

The Faraday probe was used, in another set of preliminary experiments, to 
measure currents extracted from the 19-hole grid set while a time-averaged current 
balance was performed to determine the magnitude of impingement losses. The 
system was set up with ammeters so that the time-averaged current to each of the 
single-stage Bennett mass spectrometer grids could be measured and the Faraday 
probe was swept through the beam downstream of the grid system. The current 
density profiles obtained with the Faraday probe were integrated to determine the total 
current extracted from the spectrometer. In addition, the effect of frequency on 
impingement currents were studied. All of these tests were conducted using argon 
only. 

All experiments were conducted with the discharge chamber, grid systems and 
probes located inside a 30 cm dia pyrex vacuum bell jar. Power and the gas being 
used were fed into the vacuum system with feed-throughs from supplies located 
outside the bell jar. The bell jar was pumped by a 15 cm dia oil diffusion pump 
backed by a mechanical pump. Pressures in the bell jar during experiments ranged 
between 10* 5 to 10^ Torr. 
Experimental Results 

Experimental results are presented in terms of non-dimensional frequency, 

22 



energy and voltage. However, to identify the actual operating conditions, a pair of 
dimensional values will be listed on figures where experimental data are shown. One 
of the dimensional values is the kinetic energy that ions would have when they reach 
the third grid under steady-state operating conditions; this is termed the mean ion 
energy. The other dimensional value given is the grid spacing. As discussed in 
Appendix A, for the single-stage Bennett mass spectrometer, the dimensional 
operating conditions can be deduced from these two values if the ion species is 
known. Therefore, both these parameters, along with the source gas used to produce 
ions, will be listed on figures showing data obtained with the single-stage Bennett 
mass spectrometer. 

Figure 7 shows a typical comparison between theoretical (solid line) and 
experimental (dashed line) RPA traces and corresponding distribution functions for the 
50% krypton-50% argon mixture. The frequency of the signal used in the single- 
stage Bennett mass spectrometer is selected so the effective frequency for krypton 
ions is unity. Because krypton has a mass 2. 1 times that of argon, the effective 
frequency for argon is about 0.69 (J 1/2.1). Theory predicts that the time-averaged 
current density measured by the RPA remains constant for retarding potentials below 
about 0.87. Above this, the current begins to drop off as the argon ions that have lost 
energy in the single-stage Bennett mass spectrometer begin to be repelled by the 
retarding potential applied to the collector. At retarding potentials near unity, the 
current drops sharply as krypton ions are repelled from the collector. Further 
increases in retarding potential cause the theoretical current density to again decrease 
gradually as the argon ions that gained energy in the single-stage Bennett mass 
spectrometer are repelled. 

The ion energy distribution function is proportional to the negative of the first 
derivative of the RPA trace and inversely proportional to the square root of the ion 

23 



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THEORETICAL 

EXPERIMENTAL 



SOURCE GASES - ARGON AND KRYPTON 
MEAN ION ENERGY - 110 eV 
GRID SPACING = 6.0 mm 
NON-DIMENSIONAL RF VOLTAGE = 0.23 
EFFECTIVE FREQUENCY FOR KRYPTON = 1 .0 
EFFECTIVE FREQUENCY FOR ARGON = 0.69 



A ' N «— 



a. RPA Data 



0.7 0.8 0.9 1.0 1.1 1.2 1, 
NON-DIMENSIONAL RETARDING POTENTIAL 



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1.4 



b. Energy Distribution Function 



Fig. 7 RPA Trace and Energy Distribution for Krypton-Argon Ion Beam 

24 



energy [22]. In order to differentiate the RPA traces, a Fourier series is fit to the 
data and the Lanczos convergence factor (described in Appendix C) is used to assure 
convergence of the derivative of the Fourier series. 

The theoretical energy distribution function shown in Fig. 7 is characterized by 
a relatively constant magnitude with two peaks at the ends and a large spike at unity. 
The spike at unity is due to the krypton ions and the rest of the distribution function 
represents the argon ion energy distribution. The experimental RPA trace and 
distribution function shown in Fig. 7 are seen to follow the same trends as the 
theoretical curve. The spike at unity in the experimental distribution function is wider 
than the theoretical one. This may be due to a krypton ion energy spread at the 
entrance to the single-stage Bennett mass spectrometer that is broader than the mono- 
energetic distribution assumed in the theoretical model. Peaks, although they are not 
as sharp as those predicted theoretically, are observed at the two ends of the argon 
ion distribution. It is interesting that both peaks appear at ion energies slightly 
greater than those predicted theoretically. The reason for this displacement has not 
been determined; however, this trend is also observed at other RF voltages. 

The experimental results of Fig. 7 and other similar data obtained at a variety 
of grid spacings, ion energies and effective frequencies [23] are considered very 
important. They suggest that the single-stage Bennett mass spectrometer can indeed 
be used to discriminate between two ionic species with about a 2-to-l mass ratio in a 
moderate current density application. They do not, however, show conclusively that 
only argon ions are present at energies above unity because the RPA measures current 
but does not differentiate between the charge carrying species. Demonstration that the 
two species can be separated will be deferred until the three-grid optics/RF mass 
discriminator is discussed. 

Figure 8 shows time-averaged impingement current data obtained with the 

25 




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19-hole, graphite grid set. Shown are the total current supplied to the single-stage 
Bennett mass spectrometer by the optics system as well as the currents to each of the 
grids and the extracted current determined by integrating Faraday probe traces. The 
sum of the impingement currents and the extracted current should equal the total 
current supplied to the single-stage Bennett mass spectrometer; generally they agree to 
within less than 15%. The data in Fig. 8 are obtained while the system is being 
operated at a condition that results in a minimum total impingement current (i.e. sum 
of the currents to each of the single-stage Bennett mass spectrometer grids is 
minimized). Figure 8 shows typical current data obtained with an RF voltage of 0.06 
applied over a range of effective frequencies. These data show that the impingement 
currents going to grids 1 and 2 account for less than 25% of the total impingement 
current and over 75% of the impingement current goes to grid 3. These data show 
that impingement currents remain nearly constant over the range of effective 
frequencies investigated. At the operating conditions of Fig. 8, about 85% of the 
total current supplied was extracted from the 19-hole grid set which represents an 
improvement over the 50% extraction rate obtained with the wire mesh covered, 
single-aperture system. 

One concern is whether the extracted current density is in the 0.016 to 
1.6 mA/cm 2 range needed to simulate the low-Earth-orbit environment. A spatially- 
averaged current density can be estimated by dividing the extracted current by the 
grid area through which current is extracted. The area of a hexagon circumscribing 
the 19 holes through which the current is being extracted is about 0.85 cm 2 and the 
extracted current is about 0.85 mA which gives a spatially-averaged current density at 
the grids of about 1.0 mA/cm 2 . This may appear to be in the desired range but there 
are several loss mechanisms. At typical discharge chamber operating conditions 
(discharge voltage of 45 V), atomic oxygen will account for about 20% of the beam 

27 



ions [14]. Since at least half of the atomic and all of the diatomic ions would be 
stopped with the filtering grid, over 90% of the beam will be lost. Further, some 
ions might be lost on divergent trajectories when ions are decelerated by the filtering 
grid. Loses during the charge-exchange process will further reduce the oxygen atom 
flux. Therefore, it is desirable to extract more current from the system. 

Figure 9 shows time-averaged impingement currents to the grids and the 
extracted current as well as the total current supplied to the single-stage Bennett mass 
spectrometer when the current supplied is increased to 3.1 mA. Again the currents 
are measured as a function of radio frequency with an RF voltage of 0.06 applied. 
The impingement current to grid 1 of the single-stage Bennett mass spectrometer is 
negligible. Grid 2 is seen to collect about 15% of the total impingement current 
while grid 3 collects about 85% of this current. In this case, less than half of the 
current supplied is extracted from the 19-hole grid set and detected by the Faraday 
probe. The proportion of current extracted in this case is similar to the fraction 
extracted from the single-aperture grid set. 

It is noteworthy that although the current supplied to the single-stage Bennett 
mass spectrometer tripled from the conditions in Fig. 8, the amount of current 
extracted increased by at most 50%. The rest of the current impinged on the 
downstream grids (i.e. grids 2 and 3). To eliminate the impingement currents to 
these grids, the system was modified by removing the two downstream grids. The 
resulting system accomplishes the ion extraction and RF mass discrimination 
processes in one system called the three-grid optics/RF mass discriminator. 



28 



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29 



IV. THREE-GRID OPTTCS/RF MASS DISCRIMINATOR 

The preliminary experiments described in the preceding chapter demonstrated 
that an RF signal could be used to induce a spread in the energies of ions extracted 
from a broad-beam source. However, to be effective the three-grid optics/RF mass 
discriminator must not only induce an energy spread, it must also accomplish two 
additional processes. The system must extract ions from the discharge chamber and 
the difference in energies induced by the RF signal must be exploited to remove the 
more massive species from the beam. 

Figure 10 shows a schematic of the apparatus used to accomplish these 
processes. Shown downstream of the discharge chamber is the three-grid optics/RF 
mass discriminator which will be discussed briefly. The three grids combine the 
functions of an ion optics system and a single-stage Bennett mass spectrometer. As 
an optics system component, the screen grid acts to confine the plasma in the 
discharge chamber. Here it also serves the function of grid 1 of the single-stage 
Bennett mass spectrometer by providing a boundary which limits the spatial extent of 
the time-varying electric field. As part of an optics system, the accel grid is biased 
negative to create an electric field which draws ions from the discharge chamber. 
The accel grid also serves the function of grid 2 of the single-stage Bennett mass 
spectrometer by having a sinusoidal RF signal superposed on this mean negative 
potential. The decel grid serves the function of grid 3 of a single-stage Bennett mass 
spectrometer by providing a boundary to confine the electric field. In an optics 
system, the decel grid serves to decelerate but not stop ions. However, in the 

30 



DC 



DECEL GRID 



DECEL GRID 
SUPPLY 



RF SUPPLIES 



DC 



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ACCEL GRID 



ACCEL SIGNAL AMPLIFIER 
GRID GENERATOR 
SUPPLY 



ANODE 
POWER 
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DISCHARGE 

CHAMBER 

BIAS SUPPLY 



SCREEN GRID 



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CATHODE 
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THREE-GRID 
OPTICS/RF MASS 
DISCRIMINATOR 



DISCHARGE 
CHAMBER 



Fig. 10 Experimental Apparatus for Three-Grid Optics/RF Mass Discriminator 



31 



three-grid optics/RF mass discriminator, the decel grid is used to stop all of the 
unwanted ions and it, therefore, serves the function of the filtering grid described 
previously. 

Most of the non-dimensional variables used to describe the single-stage Bennett 
mass spectrometer operating conditions are also applicable to the three-grid optics/RF 
mass discriminator. However, non-dimensional kinetic energy, which was an 
important parameter for the single-stage Bennett mass spectrometer, is not used here. 
Instead, for the three-grid optics/RF mass discriminator the important non- 
dimensional parameter is the non-dimensional retarding potential. This is the 
potential applied to the decel grid to slow or stop ions. The other non-dimensional 
variables-mass, charge, potential, time, frequency and effective frequency-are all 
used and defined in the same way as for the single-stage Bennett mass spectrometer. 
Experimental Apparatus 

Figure 10 shows the experimental apparatus used to study the three-grid 
optics/RF mass discriminator. The same discharge chamber that was used in the 
preliminary experiments with the single-stage Bennett mass spectrometer was also 
used during this testing. In addition, the 0.25 mm thick, 19-hole, graphite grids that 
were described for the preliminary experiments were used for the three-grid optics/RF 
mass discriminator. To provide a uniform potential at the decel grid a nickel wire 
mesh with a transparency of 0.85 and 0.4 mm wire-to-wire spacing was attached to 
the downstream side of the decel grid. This wire mesh provided a nearly uniform 
potential plane at the location of the decel grid. 

The need for a uniform potential surface at the decel grid can be demonstrated 
with the following argument. The RF signal applied to the accel grid causes the 
kinetic energies of some of the less massive ions to be about 5 eV greater than those 

of the more massive species. The decel grid functions to stop the more massive ions 

32 



while slowing the less massive ones to about 5 eV. Because the decel grid 
surroundings are at lower potentials than the decel grid, the potential at the center of 
the decel grid hole is also at a lower potential than the grid webbing. Since all of the 
more massive ions must be stopped, the retarding potential applied to the decel grid 
must be increased until the potential is high enough to stop the more massive ions at 
the center of the hole. If the potential varies more than about 5 V between the center 
of the holes and the decel grid webbing, the potential will be high enough to stop the 
less massive ions in addition to the more massive ones in the region near the grid 
webbing. However, with a uniform potential the unwanted species can be stopped 
while allowing the less massive ions to be extracted over the entire area of the decel 
hole. Initial experiments suggested that the retarding potential needed to stop ions at 
the center of the decel hole was up to 50 V higher without the wire mesh than it was 
with the mesh in place; therefore, the nickel mesh was used during all subsequent 
experiments. Of course some potential difference between the center of the holes in 
the wire mesh and the mesh surface still existed. However, because the holes in the 
mesh were not as large as the decel hole the potential variation was smaller. 
Experimental results, which follow, demonstrate that the potentials provided by the 
nickel mesh were adequate to achieve reasonable performance. 

In some of the testing it was desirable to use only a single hole to eliminate 
any effects associated with overlapping beamlets. In those tests all but the center hole 
of both the screen and decel grids were blocked by attaching a 0.25 mm thick piece 
of graphite to cover the holes on the downstream face of each of these grids. In other 
testing, where it was desired to show that diatomic oxygen could be removed in a 
broad-beam optics system, all 19 holes were used. Although, for the 5 eV atomic 
oxygen source to provide a beam to a large sample area, it may be necessary to use a 
system with considerably more holes, the 19-hole grid system is considered to be 



33 



adequate to model a broad-beam system. The diagnostic equipment used to study the 
beams extracted from the three-grid optics/RF mass discriminator included a retarding 
potential analyzer (RPA) and a Faraday probe. Additionally, an ExB probe was used 
to differentiate between the two species of ions. 

The RPA, shown in Fig. 11, was used in a different manner than that 
described for testing the single-stage Bennett mass spectrometer. Unlike those 
preliminary tests, the RPA collector was not biased to stop ions; instead, ions were 
stopped by applying the retarding potential to the decel grid. Therefore, the RPA 
served to measure total, time-averaged beam current density as a function of the 
retarding potential applied to the decel grid. As this figure suggests, some of the ions 
extracted through the decel grid passed through the 2 mm dia aperture and struck a 
molybdenum collector held at ground potential. As in the preliminary experiments, 
the current of these ions was determined by measuring the current of electrons 
through the ammeter required to neutralize them. The Faraday cage was biased 
sufficiently far below ground potential to stop electrons from passing through the 
aperture and reaching the collector. Under these conditions no electron currents were 
observed when the decel grid was biased to high enough potential to stop all the ions. 

The Faraday probe shown in Fig. 12 was used to measure time-averaged beam 
current density profiles. As with the RPA, beam ions passed through the 2 mm dia 
aperture and impinged on the collector held at ground potential. The Faraday probe 
was mounted on a structure which allowed it to pivot radially over the grids as 
suggested by the arc and centerlines in Fig. 12. The current arriving at the collector 
was measured as a function of angular position using a position sensing potentiometer 
mounted to the pivot which the probe support structure swung on. The Faraday cage 
was biased negative to stop electrons from entering the aperture; therefore, current 

measurement errors due to electron collection were negligible. 

34 



FARADAY 
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GRID GENERATOR 
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DISCRIMINATOR 



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DISCHARGE 

CHAMBER 

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Fig. 11 Retarding Potential Analyzer (for Three-Grid Optics/RF Mass 

Discriminator) 



35 



FARADAY 
CAGE 
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ACCEL SIGNAL AMPLIFIER' ' 

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Fig. 12 Faraday Probe (for Three-Grid Optics/RF Mass Discriminator) 



36 



The ExB probe, shown schematically in Fig. 13, was used to determine the 
ion composition of the beam extracted from the three-grid optics/RF mass 
discriminator system. This was accomplished by first collimating a small diameter 
section of the incident ion beam. This beamlet was then directed into the plate region 
at normal incidence to both the mutually perpendicular electric (E) and magnetic (B) 
fields shown in Fig. 13. The permanent magnet-induced B field was fixed but the E 
field could be varied by changing the potential difference between the plates shown. 
Changes in the E field caused the trajectories of the ions to change through the range 
suggested by the dashed curves. The drift section shown in Fig. 13 increased the 
velocity resolution of the probe by allowing ions that were deflected only slightly in 
the ExB section to diverge away from the collector. Hence at a given plate potential 
difference, all ions travelling through the crossed-field region except those within a 
specific velocity range were deflect away from the collector. Because the probe 
distinguished on the basis of ion velocity, ions with different masses but nearly the 
same kinetic energy were sensed at different plate potential differences. By sweeping 
the plate potential difference, a plot of the current reaching the collector as a function 
of this difference could be generated; the various species of ions could be identified 
from such a plot. As with the RPA and Faraday probes, the ExB collector was 
shielded with a Faraday cage (not shown in Fig. 13) which was biased negative to 
repel stray electrons. More detail on this ExB probe can be found in the literature 
[24]. 
Experimental Procedure 

Single-species testing was conducted using either argon or krypton. This 
testing was done with the RPA to determine the minimum retarding potential applied 
to the decel grid required to stop all ions in the beam as a function of RF voltage and 
effective frequency. During this testing the three-grid optics/RF mass discriminator 

37 



DRIFT 
SECTION 



ExB 

SECTION 



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COLLECTOR 



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Fig. 13 ExB Probe Schematic Diagram 

38 



was used in the single-hole configuration and the RPA was aligned coaxially along the 
grid aperture centerline. 

Two-species testing was done using mixtures of argon and krypton to 
demonstrate that appropriate application of the retarding potential to the decel grid 
with the system operating at an appropriate frequency, resulted in extraction of one 
ion species while the other one was filtered out of the beam. This testing was done 
with the single-hole grid configuration and the ExB probe was used to differentiate 
between two species of ions being extracted from the three-grid optics/RF mass 
discriminator. During these experiments, ions were typically decelerated to less than 
30 eV at the decel grid. At these energies it would have been impossible to 
differentiate between two species because the difference in their speeds would have 
been smaller than the ExB probe could resolve. In order to obtain speed differences 
large enough to resolve the two species easily, kinetic energies on the order of a few 
hundred eV were needed. In order to accelerate the ions into this energy range 
before they reached the probe, the ExB probe was held at ground potential and the 
discharge chamber was biased to a few hundred volts above ground potential. 

Once species separation was demonstrated with argon and krypton, testing was 
performed using oxygen. Since extraction of atomic oxygen from a broad-beam 
source was desired, this testing was conducted with current being extracted through 
all 19 holes of the grid system. The ExB probe was used to verify that atomic ions 
could be extracted while diatomic ions were stopped. 

Once demonstration that diatomic oxygen could be removed from the beam 
while atomic oxygen was being extracted from the three-grid optics/RF mass 
discriminator, the Faraday probe was used to measure atomic oxygen current density 
profiles. Testing was conducted using the 19-hole grid system configuration. Due to 
the configuration of the probe support structure, only one probe could be placed 

39 



inside the vacuum system at a time; therefore, the current density measurements were 
made without determining that atomic oxygen was the only species being extracted. 
However, the point at which diatomic oxygen was removed from the beam could be 
estimated from ExB probe data. The stopping potentials for both diatomic and atomic 
oxygen ions were measured with the ExB probe. Due to slight variations in operating 
conditions, these potentials could vary from one experiment to the next; however, the 
difference between these potentials was observed to be constant. Therefore, 
experiments that involved current density measurements were conducted by raising the 
retarding potential to the point where the Faraday probe did not sense any current 
(i.e. the stopping potential for atomic oxygen ions). Then the potential was decreased 
by the difference in stopping potentials for diatomic and atomic ions determined from 
ExB probe data. At this condition, where the probe should have sensed only atomic 
oxygen ions, current density profiles were measured. 
Experimental Results (Argon and/or Krypton) 

As with the preliminary experiments, experimental results are presented in 
terms of non-dimensional frequency and potential. Again, dimensional values are 
listed to enable identification of the actual operating conditions. As with the single- 
stage Bennett mass spectrometer, the source gas and grid spacing are listed. 
However, the dimensional values associated with system potentials are different for 
the three-grid optics/RF mass discriminator. Instead of listing the mean ion energy, 
the difference between discharge chamber anode potential and the mean potential 
applied to the decel grid, called the mean-total-accelerating voltage, is used. In 
addition, the mean potential applied to the accel grid is also listed. Given these 
dimensional values the actual operating conditions can be determined using the 
definitions in Appendix A. 

As noted above, systematic stopping potential offsets are observed when 

40 



experiments are repeated. Variations in discharge chamber plasma potential (the 
potential at which ions are created) and variations in the RF voltage applied to the 
accel grid contribute to the observed shifts in stopping potentials. The amplitude of 
the RF voltage can be measured within ±2 V. The actual plasma potential is not 
measured during experiments. However, the discharge chamber plasma potential is 
usually within a few volts of the potential of the most positive surface in the discharge 
chamber, which is the anode (Fig. 10). Therefore, it is assumed that the discharge 
chamber plasma potential is equal to the anode potential. The anode potential can 
vary from one experiment to the next due to the resolution of the voltmeters used to 
measure the potentials. The discharge chamber bias supply potential can be measured 
within ±3 V and the anode power supply voltage can be measured within ±1 V. 
Additionally, variations in discharge currents during different experiments also can 
cause some variation in discharge chamber plasma potential. It is also noted that the 
potential applied to the decel grid can be measured within ±1 V. The systematic 
stopping potential offsets from different experiments varied as much as 7 V. 

One additional note about non-dimensional potentials is given here. For the 
experimental data presented below, the potential is non-dimensionalized using the 
mean-total-accelerating voltage which is 500 V. Therefore, in the data presented 
below, 1 V corresponds to a non-dimensional potential of 0.002. 

To determine the retarding potential required to stop all ions during single 
species testing, RPA traces like the one in Fig. 14 were obtained. Two traces, 
obtained at typical operating conditions, are shown; one (solid line) is obtained at an 
effective frequency of zero (no RF signal applied) and the other (dashed line) is 
obtained with an RF voltage of 0.08 and an effective frequency for argon of 0.5. 
Two phenomenon cause the observed shape of these traces; beam focusing varies as 
the decel potential varies (i.e. the current directed toward the RPA depends on the 



41 



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42 



electric field in the grid system and the field changes as the decel potential changes) 
and at high enough decel potentials the current decreases because ions are being 
stopped. The minimum retarding potential required to stop all ions is the potential at 
which the collector current goes to zero. This potential is called the stopping 
potential and is identified for each of the RPA traces. When the effective frequency 
is zero the stopping potential is 1.01. For the case where the RF signal is applied, 
the stopping potential is substantially greater (about 1.11), indicating that a significant 
energy spread can be induced with the three-grid optics/RF mass discriminator. 

As noted, at the zero effective-frequency (no RF signal applied), the stopping 
potential is slightly greater than unity. Theoretically these ions would be stopped at a 
retarding potential of unity because the ions have negligible kinetic energy when they 
are produced in the discharge chamber plasma which is assumed to be at a potential 
of unity. Three possibilities, which have been previously discussed, could contribute 
to this shift. The potential applied to the decel grid may have to be slightly higher 
than unity to stop ions from passing through the center of the holes in the nickel wire 
mesh attached to the decel grid. It is also possible that the potential of the discharge 
chamber plasma is slightly different than the anode potential which is used in 
computing the stopping potential. In addition, systematic errors in reading potentials 
due to volt meter resolution could also contribute to this shift. Regardless of the 
reason for the shift, it is noted that in general, the stopping potential measured during 
experiments is between 1 to 5% higher than the theoretical predictions. 

The stopping potential for a given species can be calculated using the first- 
order model derived in Appendix A. The first-order solution for the stopping 
potential is 



43 



"s = l + *RF*(F') ■ (3) 

where #, the stopping potential parameter, is a function of effective frequency (Ft). 
The equation for $ is given in Appendix A. Figure 15 shows a comparison of 
theoretically and experimentally obtained stopping potentials for RF voltages of 0.04, 
0.06 and 0.08 at effective frequencies for argon ranging from to about 1.4. The 
solid curves are the theoretical values for stopping potential and they are seen to 
increase from unity as the effective frequency increases from to about 0.5 where 
they go through a maximum. The traces then decrease to a relatively constant value 
at an effective frequency of about 1.2. The experimental traces exhibit the same 
trend; however, the whole trace is shifted to a slightly higher potential. Aside from 
the shift, the experimental maxima appear to be somewhat broader and to be shifted 
to a slightly higher effective frequency than predicted theoretically. Nevertheless, the 
theoretical and experimental results correlate fairly well. 

Similar data were obtained for krypton at similar operating conditions and 
some of them are shown in Fig. 16. Here the stopping potentials shifted to even 
higher values than were observed with argon. Slight variations in power supply 
settings and changes in discharge chamber operating conditions caused by switching 
form argon to krypton could easily have caused the observed shift. Aside from the 
shift to higher energies, the comparison of experimental and theoretical results for 
krypton is similar to that obtained with argon. 

The single species testing is useful because it gives a guide to the frequency 
and retarding potential ranges over which separation of the two species might be 
achieved. This information is shown in the direct comparison of the stopping 
potential data for argon and krypton made in Fig. 17 for the 0.06 RF voltage data 
from Figs. 15 and 16. A few words about the comparison are in order. First it is 

44 



1.12 

z z 

2 s 1.08 

zo 

So- 1.06 



SOURCE GAS = ARGON 

MEAN ACCEL POTENTIAL = -200 V 

MEAN TOTAL ACCELERATING VOLTAGE = 500 V 

GRID SPACING - 4.1 mm 



NON-DIMENSIONAL RF VOLTAGE = 0.04 

.— B , 




1.12 r 

i 



So 

911.04 

£ °- 

i 2 1.02 



NON-DIMENSIONAL RF VOLTAGE = 0.06 




NON-DIMENSIONAL RF VOLTAGE = 0.08 

V 




0.2 0.4 0.6 0.8 1.0 1.2 1.4 
EFFECTIVE FREQUENCY FOR ARGON [Fr] 



Fig. 15 Comparison of Theoretical and Experimental Stopping Potentials for 

Argon 



45 



SOURCE GAS = KRYPTON 

MEAN ACCEL POTENTIAL = -200 V 

MEAN TOTAL ACCELERATING VOLTAGE = 500 V 

GRID SPACING =4.1 mm 



NON-DIMENSIONAL RF VOLTAGE = 0.04 




NON-DIMENSIONAL RF VOLTAGE = 0.06 




1 .1 2 r- 



-s NON-DIMENSIONAL RF VOLTAGE = 0.08 




0.4 0.6 0.8 1.0 1.2 1.4 1.6 
EFFECTIVE FREQUENCY FOR KRYPTON [Ft] 



1.8 2.0 



Fig. 16 Comparison of Theoretical and Experimental Stopping Potentials for 

Krypton 



46 



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47 



noted that frequency and not effective frequency is used in this comparison. Recall 
that frequency is held fixed during system operation. Since ions travel at different 
speeds due to their mass difference each species has a different effective frequency 
resulting in different stopping potentials at a given operating condition. By examining 
the stopping potentials for each species, the frequency range over which one species 
can be stopped while the other is extracted can be determined. Second, comparing 
the data of Figs. 15 and 16 a systematic shift in the krypton and argon stopping 
potential data is observed. However, if both species are simultaneously produced and 
extracted from the discharge chamber plasma, the stopping potential should be the 
same for both species at a frequency of zero (corresponds to steady-state operation). 
Therefore, to compare these data the krypton curve is shifted so that the argon and 
krypton stopping potentials match at zero. When the argon curve lies above (below) 
the krypton curve, argon (krypton) can be extracted from the three-grid optics/RF 
mass discriminator. These curves suggests that it is possible to extract krypton at 
frequencies between and about 0.4 and that argon can be extracted at frequencies 
greater than 0.4. 

To verify this, two species testing was conducted using argon and krypton 
mixtures. Figure 17 suggests that the difference in stopping potentials for krypton 
and argon is greatest (about 0.028) near a frequency of 0.6. Figure 18 shows ExB 
probe traces taken at this frequency and an RF voltage of 0.06. The top trace is 
obtained with a retarding potential of 1.060 applied to the decel grid and the krypton 
and argon peaks are clearly evident. When the retarding potential is increased to 
1.070, the middle trace of Fig. 18 is obtained. It is evident that most of the krypton 
has been removed from the beam while a significant portion of the argon is still being 
extracted. At a retarding potential of 1.074, all the krypton is stopped while argon is 

still being extracted as seen in the bottom trace of Fig. 18. Figure 19 shows ExB 

48 



.-12 



SOURCE GASES = ARGON AND KRYPTON 
MEAN ACCEL POTENTIAL = -200 V 
MEAN-TOTAL-ACCELERATING VOLTAGE = 500 V 
GRID SPACING = 4.1 mm 
NON-DIMENSIONAL RF VOLTAGE = 0.06 
NON-DIMENSIONAL FREQUENCY = 0.6 



KRYPTON PEAK 



ARGON PEAK 




NON-DIMENSIONAL 
RETARDING POTENTIAL = 1 



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ARGON PEAK 




KRYPTON PEAK 



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NON-DIMENSIONAL 
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ARGON PEAK 




5 10 15 

PLATE POTENTIAL DIFFERENCE (V) 



20 



Fig. 18 ExB Data Demonstrating Krypton Filtering for Krypton- Argon Ion 

Beam 

49 



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cc 

<J 

CC 

o 

t- 
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x10 
10i- 

8- 

6- 

4- 
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SOURCE GASES = ARGON AND KRYPTON 
MEAN ACCEL POTENTIAL = -200 V 
MEAN-TOTAL-ACCELERATING VOLTAGE = 500 V 
GRID SPACING =4.1 mm 
NON-DIMENSIONAL RF VOLTAGE = 0.06 
NON-DIMENSIONAL FREQUENCY = 0.6 



ARGON PEAK 




NON-DIMENSIONAL 
RETARDING POTENTIAL = 1 .080 



LU 
CC 
CC 

D 

o 

CC 

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x10 

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6- 
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NON-DIMENSIONAL 
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1.094 



LU 
CC 

CC 

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CC 

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I- 

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LU 



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x10 



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8- 
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NON-DIMENSIONAL 
RETARDING POTENTIAL = 1.100 



± 



5 10 15 

PLATE POTENTIAL DIFFERENCE (V) 



20 



Fig. 19 ExB Data for Argon After Krypton is Stopped 

50 



probe traces obtained as the retarding potentials are increased to 1.080, 1.094 and 
1.100 (top, middle and bottom traces, respectively). Comparing the bottom trace in 
Fig. 18 with the top trace in Fig. 19, it is seen that the amount of argon being 
extracted decreases slightly as the retarding potential changes from 1.074 to 1.080. 
At 1.094 the argon peak has almost disappeared and at 1.100 there is no trace of 
argon. These data show that the difference in the stopping potential for krypton and 
argon is greater than 0.02 but less than 0.03, in agreement with the single species 



data 5 . 



Although the goal of this study is to demonstrate extraction of the less massive 
species while stopping the more massive one, it is interesting to note that Fig. 17 
suggests that it should be possible to extract krypton while stopping argon at 
frequencies between and about 0.4. Figure 20 shows ExB probe traces taken at a 
frequency of 0.3. The top trace in Fig. 20 is obtained at a retarding potential of 
1.080; at this condition, the krypton peak is evident and the argon peak is small 
indicating that most of the argon ions are being stopped. At a retarding potential of 
1.090 the argon peak has disappeared and krypton, albeit less than at a retarding 
potential of 1.080, is still being extracted as seen in the middle trace of Fig. 20. 
When the retarding potential increases to 1.100, the krypton peak also disappears as 
seen in the bottom trace of Fig. 20. Because this particular test was not considered 
essential, finer resolution of the retarding potentials required to stop each species was 
not obtained. Nonetheless, these data show that the range of retarding potentials over 
which argon in stopped but krypton is still being extracted is smaller than 0.02, which 
is in agreement with the data of Fig. 17. 



5 At the particular operating conditions of Figs. 18 and 19, 0.02 to 0.03 amounts to 
argon ions being slowed to kinetic energies between 10 and 15 eV at the decel grid when 
it is biased to the stopping potential for krypton. 

51 



x10 



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1.2 


z 


1.0 


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cc 


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LU 




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SOURCE GASES = ARGON AND KRYPTON 
MEAN ACCEL POTENTIAL * -200 V 
MEAN-TOTAL-ACCELERATING VOLTAGE - 500 V 
GRID SPACING = 4.1 mm 
NON-DIMENSIONAL RF VOLTAGE = 0.06 
NON-DIMENSIONAL FREQUENCY = 0.3 
KRYPTON PEAK 



NON-DIMENSIONAL 
RETARDING POTENTIAL = 1.080 




x10 



-11 



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— 




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cc 


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/\ 


UJ 






J \ 


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/ \ 


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1 




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NON-DIMENSIONAL 

RETARDING POTENTIAL = 1 .090 



~JL 



x10 



-11 



< 


1.2 


z 


1.0 


UJ 




DC 




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_L 



NON-DIMENSIONAL 
RETARDING POTENTIAL = 1.100 



± 



5 10 15 

PLATE POTENTIAL DIFFERENCE (V) 



20 



Fig. 20 ExB Data Demonstrating Argon Filtering for Krypton-Argon Ion Beam 

52 



Experimental Results (Oxygen) 

Since testing with argon and krypton verified that the more massive species 
can be removed while the less massive species is being extracted, testing was 
conducted to demonstrate that separation of atomic and diatomic oxygen can also be 
achieved using the three-grid optics/RF mass discriminator. To obtain a guide for the 
range of frequencies over which atomic oxygen ions can be separated from diatomic 
oxygen ions, theoretical curves of stopping potential v. frequency were generated for 
both species. Figure 21 shows the theoretical curves at an RF voltage of 0.06 which 
suggest that diatomic oxygen can be stopped at a lower potential than atomic oxygen 
for frequencies greater than 0.6. The curves suggest that, for the given RF voltage, 
the largest difference is about 0.02 and that this difference should be observed at 
frequencies between about 0.75 and 1.2. 

Figure 22 shows ExB traces obtained with the RF discriminator operating at a 
frequency of 1.2 at various retarding potentials. The top trace is obtained with a 
retarding potential of 1.040 applied to the decel grid and both the atomic and diatomic 
oxygen peaks are evident. When the retarding potential is increased to 1.050, most of 
the diatomic oxygen is stopped while most of the atomic oxygen is still being 
extracted as shown in the middle trace of Fig. 22. When the retarding potential is 
increased further to 1.056 the diatomic oxygen is completely removed from the beam 
and the trace at the bottom of Fig. 22 is obtained. Another trace (not shown) 
indicates that all the atomic ions are stopped when the retarding potential is raised to 
1.070. Considering the actual dimensional conditions at which these oxygen data are 
collected, it is evident that the difference between the stopping potential for diatomic 
and atomic oxygen is about 7 V. This demonstrates that the three-grid optics/RF 
mass discriminator can be used to extract an atomic oxygen beam with ions being 
decelerated to near 5 eV kinetic energy at the decel grid. 

53 






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cc 
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cc 
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.-11 



DIATOMIC 
OXYGEN PEAK 




SOURCE GAS « OXYGEN 

MEAN ACCEL POTENTIAL = -200 V 

MEAN-TOTAL-ACCELERATING VOLTAGE = 500 V 

GRID SPACING = 4.1 mm 

NON-DIMENSIONAL RF VOLTAGE = 0.06 

NON-DIMENSIONAL FREQUENCY = 1.2 



NON-DIMENSIONAL 

RETARDING POTENTIAL - 1.040 



ATOMIC 
OXYGEN PEAK 



LU 

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OXYGEN PEAK 



NON-DIMENSIONAL 
RETARDING POTENTIAL 



ATOMIC 
OXYGEN PEAK 



1.050 



z 

LU 
CC 

cc 

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RETARDING POTENTIAL = 1 .056 



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OXYGEN PEAK 



10 20 

PLATE POTENTIAL DIFFERENCE (V) 



30 



Fig. 22 ExB Data Demonstrating Filtering of Diatomic Oxygen 

55 



Since demonstration that atomic oxygen with about 5 eV kinetic energy can be 
extracted from the three-grid optics/RF mass discriminator, testing to determine the 
atomic oxygen current density was conducted. Figure 23 shows a typical Faraday 
probe trace obtained with the 19-hole grid system configuration. Shown is the current 
density measured on an arc 4.5 cm downstream of the decel grid. This trace is 
obtained at operating conditions that maximize the current density at an angle of 0°. 
Although it is possible to extract more current from the system, the beam becomes 
more divergent and, therefore, the current density decreases. The current density is 
largest at an angle of about -10° because the probe passes near the center of a grid 
hole at this angular location. At 0° the probe passes near the edge of a hole and at 
about 10° the probe passed near the webbing between grid holes. The current density 
in the central portion of the beam varies between 2.5X10" 4 to 4.5x1c 4 mA/cm 2 and 
the mean value is about 3X10" 4 mA/cm 2 . This is 0.3% of the current density needed 
to simulate the low-Earth-orbit environment (0.1 mAeq/cm 2 ). However, by 
decreasing the grid spacing and increasing the radio frequency (as discussed in the 
Future Work section) it might be possible to obtain current densities on the order of 
0.1 mA/cm 2 . 



56 



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57 



V. CONCLUSIONS 

Discrimination of ions having about a 2-to-l mass ratio in a three-grid 
optics/RF mass discriminator based on a modified single-stage Bennett mass 
spectrometer has been demonstrated. To gain an understanding of how mass 
discrimination is accomplished, physical insight into the intra-grid acceleration process 
was sought through a simple first-order, one-dimensional model. Application of this 
model to a single-stage Bennett mass spectrometer suggests that if the frequency of 
the applied RF voltage is selected so that ions of one species experiences two full RF 
cycles while travelling through the system, they will emerge with the same kinetic 
energy that they had when they entered the spectrometer. Due to the difference in 
mass, ions of the other species travel at a different speed and do not experience an 
integer number of cycles while travelling through the single-stage Bennett mass 
spectrometer. As a result, they have a significant spread induced in their energies 
when they emerge from the system. Ion energies measured during preliminary 
experiments conducted with the single-stage Bennett mass spectrometer show good 
agreement with these theoretical predictions. 

The simple model can also be used to predict the stopping potential for a given 
species in the three-grid optics/RF mass discriminator. Examination of the model 
shows that the stopping potential is different for different species of ions at a given 
frequency. This suggests that it should be possible to stop all ion of one species 
while still extracting ions of the other species. Further investigation suggests that 
below a certain frequency the more massive species can be extracted and above this 
frequency the less massive species can be extracted. Experiments conducted using 

58 



mixtures of argon and krypton ions demonstrate that either krypton or argon can be 
extracted from the three-grid optics/RF mass discriminator, while the other species is 
stopped, in the frequency ranges predicted by theory. 

Experiments demonstrating that the three-grid optics/RF mass discriminator 
can be used in a 5 eV atomic oxygen source were also conducted. Using the model 
predictions as a guide in choosing system operating conditions, experiments showed 
that the three-grid optics/RF mass discriminator can be used to filter out diatomic 
oxygen ions while extracting an atomic oxygen ion beam with kinetic energies near 
5 eV. Extraction of these atomic oxygen ions has been demonstrated using a 19-hole 
grid system representative of a broad-beam ion source. Although higher current 
densities of atomic oxygen than those demonstrated during experiments are desired to 
simulate the low-Earth-orbit environment, it is anticipated that the desired current 
densities can be achieved by scaling down the system dimensions and increasing the 
frequency of the applied RF signal to values suggested by the simple model. 



59 



VI. FUTURE WORK 

The work presented in this dissertation demonstrates that the three-grid 
optics/RF mass discriminator can separate diatomic and atomic oxygen ions and 
produce a beam of atomic oxygen ions with about 5 eV kinetic energy. However, if 
a 5 eV atomic oxygen source is to be constructed, two additional concerns must be 
addressed. First a system which charge neutralizes the atomic oxygen ions must be 
incorporated into the system and secondly the atomic oxygen current density should 
be increased to low-Earth-orbit flux levels. 

Figure 24 shows a system configuration incorporating a charge neutralization 
system along with the three-grid optics/RF mass discriminator which could be used to 
produce a 5 eV atomic oxygen beam. Shown is the screen grid attached to one end of 
the discharge chamber within which atomic and diatomic oxygen ions are produced. 
The accel grid has a sinusoidal RF voltage superposed on a negative mean potential 
applied to it. The decel grid serves two functions; it stops the diatomic oxygen ions 
and also charge neutralizes ions that impinge on the glancing incidence charge- 
exchange surface. An array of charge-exchange surfaces might be arranged on the 
decel grid as shown in Fig. 24. Since about half of the atomic oxygen ions are not 
charge neutralized, an electric field-set up between a pair of metal deflection plates 
located downstream of the decel grid-is used to deflect atomic oxygen ions out of the 
oxygen atom beam. Hence, all the functions required to deliver the low energy 
atomic oxygen are accomplished within a very compact grid system located 
immediately adjacent to the ion source. Because the atomic oxygen does not travel 

long distances between the ion source and the target, this system should minimize 

60 



GLANCING INCIDENCE 

CHARGE EXCHANGE 

PLATES 



DEFLECTION PLATE 



DEFLECTION PLATE 



DC 



A \ \ \ \ V£ECEL_GRID 




DECEL GRID 
SUPPLY 



RF SUPPLIES 



ACCEL GRID 



ACCEL SIGNAL AMPLIFIER 

GRID GENERATOR 
SUPPLY 



DC 



DISCHARGE 

CHAMBER 

BIAS SUPPLY 



THREE-GRID 
OPTICS/RF MASS 
DISCRIMINATOR 



SCREEN GRID 



DISCHARGE 
CHAMBER 



Fig. 24 Envisioned Configuration for a 5 eV Atomic Oxygen Source 



61 



loses of atoms on divergent trajectories. 

Increasing the atomic oxygen flux could be accomplished by increasing the 
fraction of atomic oxygen ions produced in the discharge chamber and by scaling the 
dimensions of the grid system to increase the current density obtained from the 
discharge chamber. A microwave discharge can be used to increase the fraction of 
atomic oxygen over that produced in an arc discharge [25] with atomic oxygen ion 
fractions as high as 0.85 having been reported. A more than 4-fold increase in 
atomic oxygen current density should be obtained from such a source. (Recall that 
the atomic oxygen ion fraction was about 0.2 in the arc discharge used during the 
experiments reported in this dissertation.) Since only about half of these ions would 
be charge neutralized, the atomic oxygen flux downstream of the glancing incidence 
plate would be about double that shown in Fig. 23 (about 
6X10" 4 mAeq/cm 2 ). 

In order to obtain fluxes of 0.1 mAeq/cm 2 , needed to simulate the low-Earth- 
orbit environment, the grid system must be scaled. The atomic oxygen current 
density extracted at the decel grid is proportional to the current density extracted from 
the discharge chamber. The current density drawn from the discharge chamber 
depends on the electric field between the screen and accel grids. In turn, the electric 
field depends on the grid spacing and the mean-total-accelerating voltage (i.e. the 
difference between the discharge chamber plasma potential and the mean potential 
applied to the accel grid). The RF voltage is a small perturbation, typically less than 
0.1 times the mean-total-accelerating voltage, and it therefore should not significantly 
affect the current density being extracted from the discharge chamber. Thus, scaling 
laws which are applicable to systems operated at steady-state conditions also should be 
applicable for this system. For a system operated at steady-state operating conditions, 
it is known that keeping the hole-diameter-to-grid-spacing ratio and the 

62 



total-accelerating voltage constant while reducing the size of the grid system will 
result in increase current density [26]. Specifically, the current density increases as 
the inverse square of the grid spacing. Thus, to obtain current densities on the order 
of 0.1 mA/cm 2 , the grid spacings must be reduced from 4.1 mm, used while 
obtaining the data of Fig. 23, to 0.3 mm and the hole diameter must be decreased 
from 2 mm dia to 0.15 mm dia. Ion optics systems have been operated at grid 
spacings as small as 0.22 mm with the total-accelerating voltages as high as 900 V 
[27]. Therefore, it is feasible to scale the system to 0.3 mm grid spacings while 
operating at a 500 V mean-total-accelerating voltage (used while obtaining the current 
density data shown in Fig. 23). 

In addition to scaling the grid system dimensions, the frequency of the RF 
signal applied to the accel grid also must be scaled. The frequency scales as the 
inverse of the grid spacing. The oxygen data presented in this dissertation were 
obtained at a frequency of 8 MHz. Scaling the grid spacing down to 0.3 mm requires 
that the frequency be increased to about 110 MHz. The RF amplifier, used during 
the experiments reported above, has a bandwidth of 15 MHz and , therefore, it could 
not be operated at 110 MHz. Because of this equipment limitation, experiments could 
not be conducted on a scaled-down system. 



63 



REFERENCES 

1. Leger, L. J. and Visentine, J. T., "Protecting Spacecraft from Atomic Oxygen", 
Aerospace America . July 1986, pp. 32-35. 

2. Zimcik, D. G. and Maag, C. R., "Results of Apparent Atomic Oxygen 
Reactions with Spacecraft Materials During Shuttle Flight STS-41G", L. 
of Spacecraft and Rockets. V. 25, March-April 1988, pp. 162-168. 

3. Vaughn, J. A., Linton, R. C, Carruth, M. R., Jr., Whitaker, A. F., 
Cuthbertson, J. W., Langer, W. D., and Motley, R. W., "Characterization of a 
5-eV Neutral Atomic Oxygen Beam Facility", Fourth Annual Workshop on Space 
Operations Applications and Research (SOAR '90), Albuquerque, New Mexico, 
June 26-28, 1990, NASA Conference Publication 3101, Vol. II, R. T. Savely, 
ed., pp. 764-771. 

4. Banks, B. A. , Rutledge, S. K. , Paulsen, P. E. , Steuber, T. J. , "Simulation of the 
Low Earth Orbital Atomic Oxygen Interaction With Materials by Means of an 
Oxygen Ion Beam", NASA TM-101971, Feb. 1989. 

5. Vaughn, J. A., NASA Marshall Space Flight Center, Private Communication, 
Feb. 1992. 

6. Cole, R. K., Albridge, R. G., Dean D. J., Harlund, R. F., Jr, Johnson, C. L., 
Pois, H., Savundararaj, P. M., Tolk, N. H., Ye, J., Daech, A. F., "Atomic 
Oxygen Simulation and Analysis", Acta Astronautica . Vol. 15, No. 11, 1987, pp. 
887-891. 

7. A. A. Lucas, "Self-image excitation mechanism for fast ions scattered by metal 
surfaces at grazing incidence", Physical Review B . Vol. 20, No. 12, 15 
December 1979, pp. 4990-5001. 

8. Cuthbertson, J. W., Langer, W. D., Motley, R. W., Vaughn, J. A., "Atomic 
Oxygen Beam Source for Erosion Simulation", Fourth Annual Workshop on 
Space Operations Applications and Research (SOAR '90), Albuquerque, New 
Mexico, June 26-28, 1990, NASA Conference Publication 3103, Vol. II, R. T. 
Savely, ed., pp. 734-741. 

9. Holmes, A. J. T., The Physics and Technology of Ion Sources . John Wiley and 
Sons, New York, 1989, I. G. Brown, ed., pp. 66-69. 

64 



10. Enge, H. A., Focusing of Charged Particles . Academic Press, New York, 1967, 
A. Septier, ed., Vol. II, pp. 203-264. 

1 1 . Wilson, R. G. , Brewer, G. R. , Ton Beams W ith Applications to Ion Implantation. 
John Wiley and Sons, New York, 1973, pp. 431-444. 

12. Bennett, W. H., "Radiofrequency Mass Discriminator," J. Appl. Phvs.. 
V. 21, February 1950, pp. 143-149. 

13. Aston, G. and Kaufman, H. R., "Ion Beam Divergence Characteristics of Three- 
Grid Accelerator Systems", AIAA Journal . Vol. 17, No. 1, January 1979, pp. 
64-70. 

14. Rapp D., Englander-Golden P., and Briglia D. D., "Cross Sections for 
Dissociative Ionization of Molecules by Electron Impact", The Journal of 
Chemical Phvsics . Volume 42, Number 12, 15 June 1965, pp. 4081-4084. 

15. Kaufman H. R., and Reader, P. D., "Experimental Performance of Ion Rockets 
Employing Electron-Bombardment Ion Sources", presented at the ARS 
Electrostatic Propulsion Conference, U. S. Naval Postgraduate School, Monterey, 
California, November 3-4, 1960. 

16. Reader, P. D., "Investigation of a 10-Centimeter-Diameter Electron- 
Bombardment Ion Rocket", NASA Tech. Note TN D-1163, Jan. 1962. 

17. Reader, P. D., "Experimental Effects of Scaling on the Performance of Ion 
Rockets Employing Electron-Bombardment Ion Sources", presented at the 
National IAS-ARS Joint Meeting, Los Angeles, California, June 13-16, 1961. 

18. Kaufman, H. R., "An Ion Rocket with an Electron-Bombardment Ion Source", 
NASA Tech. Note TN-585, Jan. 1961. 

19. Wilbur, P. J. and Han, J. Z., "Constrained-Sheath Optics for High 
Thrust-Density, Low Specific-Impulse Ion Thrusters," AIAA Paper No. 
87-1073, May 1987. 

20. Chen, F. F., Introduction to Plasma Phvsics and Controlled Fusion . Plenum 
Press, New York, 1984, pp. 8-11. 

21. Rapp, D. , Englander-Golden, P. "Total Cross Sections for Ionization and 
Attachment in Gases by Electron Tmpact". The Journal of Chemical 
Physics . Volume 43, Number 5, 1 September 1965, pp. 1464-1479. 



65 



22. Friedly, V. J., "Hollow Cathode Operation at High Discharge Currents", NASA 
CR-185238, April 1990, pp. 83-87. 

23. Anderson, J. R., Wilbur, P. J., Carruth, M. R., Jr., "An Ion Optics System 
Incorporating Radio Frequency Mass Separation", AIAA Paper No. 90-2567, July 
1990. 

24. Vahrenkamp, R. P., "Measurements of Double Charged Ions in the Beam of a 
30-cm Mercury Bombardment Thruster",AIAA Paper No. 73-1057, October 
1973. 

25. Sakudo, N., The Physics and Technology of Ion Sources . John Wiley and Sons, 
New York, 1989, 1. G. Brown, ed., p. 240. 

26. Jahn, R. G., Physics of Electric Propulsion . McGraw-Hill Book Company, New 
York, 1968, pp. 164-165. 

27. Rovang, D. C, "Ion Extraction Capabilities of Two-Grid Accelerator Systems", 
NASA CR-174621, Feb. 1984, p. 90. 

28. Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., Numerical 
Recipes The Art of Sci entific Computing (FORTRAN Version^ . Cambridge 
University Press, Cambridge, 1989, pp. 147-151. 

29. Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., Numerical 
Recipes The Art of Sc ientific Computing (FORTRAN Version V Cambridge 
University Press, Cambridge, 1989, pp. 498-515. 



30. 



Lanczos, C, Applied Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 
1964, pp. 219-221. 



3 1 . Haberman , R. , Elementary Applied Partial Differential Equations. 2 nd Edition . 
Prentice-Hall, Englewood Cliffs, New Jersey, 1987, pp. 75-78. 

32. Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., Numerical 
Recipes The Art of Sci entific Computing (FORTRAN Version V Cambridge 
University Press, Cambridge, 1989, pp. 401-407. 

33. Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., Numerical 
Re cipes The Art of Scientific Computing (FORTRAN Version) r Cambridge 
University Press, Cambridge, 1989, pp. 386-387. 



66 



APPENDIX A 
A One-Dimensional Model of the Intra-Grid Acceleration Process 

The important parameters for both the single-stage Bennett mass spectrometer 
and the three-grid optics/RF mass discriminator are the terminal ion energy and the 
stopping potential, respectively. In order to predict the values of these parameters, a 
simple one-dimensional model of the intra-grid acceleration process for both systems 
has been developed. Since the model does not account for three-dimensional effects, 
such as ion divergence due to radial electric fields, it can be used only as a guide to 
predict general trends. Therefore, other effects which are even less significant are 

also neglected. 

The magnitude of the magnetic fields set up by the discharge chamber 
electromagnet were typically less than 5xl0" 3 Tesla during experiments; therefore, 
magnetic effects are neglected. At typical operating conditions background pressures 
and temperatures in the bell jar were in the 10' 5 to 10" 4 Torr range and about 300 K, 
respectively. In addition, the entire grid system extended less than 10 cm in all 
experiments; therefore, it is assumed that the ions have no collisions as they pass 
through the grid system. In order to minimize the divergence of the extracted ion 
beam, the system was operated at less than 20% of the space-charge limited current 
density; therefore, space-charge effects are also neglected. 

As previously mentioned, the model uses only one spatial variable (x) in 
addition to the temporal one (t). Because of this and the fact that the grid thickness is 
much less than the intra-grid spacing, the grids are modelled as evenly-spaced, 
equipotential planes. Figure Al shows the planar geometry and boundary conditions 



67 



>" 



w 

CM 



q 

QC 



C 
'in 



01 
> 



10 



CM 

g 

GC 



> 

II 
> 




o 

QC 
CD 



bfi 



68 



associated with both the single-stage Bennett mass spectrometer and the three-grid 
optics/RF mass discriminator. The two systems differ because of the boundary 
conditions imposed on each. For both systems, ions are generated and have 
negligible kinetic energy in a discharge chamber plasma which is at potential V p . 
Ions extracted from the plasma approach grid 1, located at x=0 and held at a constant 
potential V 1? at a speed v t . The equation for the speed at which ions approach grid 1 
(v^ can be obtained from conservation of kinetic and electric potential energy and is 



v i = 



2q(V.-V 1 ) (Al) 



m 



where q and m are the charge per ion and mass per ion, respectively, of the ionic 
species being considered. In the single-stage Bennett mass spectrometer, ions are 
extracted from the discharge chamber through an optics system and approach grid 1 
with a substantial kinetic energy obtained by falling through the potential difference 
between the discharge chamber plasma and grid 1. In the three-grid optics/RF mass 
discriminator, ions are extracted directly from the discharge chamber plasma through 
a sheath which develops near the screen grid (corresponds to grid 1 in Fig. Al). In 
general, the exact location of the sheath is not known. However, for the modelling 
done here, it is assumed that ions enter the system with negligible speed from a 
surface at plasma potential at the location of the screen grid. Therefore, although the 
screen grid was held at a potential slightly negative of plasma potential during 
experiments, for this modelling it is assumed to be at plasma potential (i.e. V^Vp). 

Grid 2 is located at x=s and is maintained at a voltage with a constant 
component V 2 and a superimposed sinusoidal RF component characterized by an 
amplitude \^p and a frequency f. For the single-stage Bennett mass spectrometer, 
the same mean potential is applied to each grid; therefore, V 2 =V 1 . In the three-grid 

69 



optics/RF mass discriminator, however, the mean potential (V^) applied to the accel 
grid (corresponds to grid 2 in Fig. Al) is substantially lower than the screen grid 
voltage (Vj) to facilitate ion extraction from the discharge chamber. 

Grid 3 is located at x=2s and is held at a constant voltage V 3 . Again the 
same mean potential is applied to each of the grids in the single-stage Bennett mass 
spectrometer so V 3 =V 1 . The three-grid optics/RF mass discriminator uses the decel 
grid (corresponds to grid 3 in Fig. Al) to slow or stop ions and the value of V 3 can 
be set to any desired value. 

Since magnetic and space-charge effects are neglected, the equation governing 
the potential variation in the intra-grid region is 



d 2 V(x,t) _ Q 
dx 2 



(A2) 



Using this differential equation and the boundary conditions shown in Fig. Al, the 
potential between grids 1 and 2 (V 12 ) is found to be 



V 12 (x,t) = 



s -x 



Vi + 



[ V 2 +V RF sin ( 27rf 0] 



(A3) 



and the potential between grid 2 and 3 (V23) is 



V 23 (x,t) = 



2s-x 



[V 2+ V RF sin(2 1 rft)] + 



X -s 



(A4) 



The equation describing ion acceleration in the intra-grid region is obtained by 
combining the Lorentz force law with Newton's second law. When magnetic fields 
are neglected, the Lorentz force acting on a charged particle is equal to the charge 
multiplied by the electric field. The electric field is the gradient of the potential; 
therefore, the ion acceleration between grids 1 and 2 is given by 



70 



dv 
dt 



m 



Vi-V 2 



'RF 



sin(2xft) 



(A5) 



and between grids 2 and 3 it is 



dv _ q 
dt m 



V2-V3 



r RF 



sin(2xft) 



(A6) 



Before solving for the acceleration of the ions in the intra-grid region, the 
preceding equations will be non-dimensionalized using important system parameters as 
shown in the following table. 



Mass per ion 


M = - m - 


Charge per ion 


Q = S 

e 


Length 


s 


Time 






- 






T =i 

s 

1 


<=(V V 2> 
2m 02 


1 + 

m y 


v p- v i 

v p -v 2 _ 


Frequency 


F = fs 








- 




-1 


_ > 


e ( V p" V 2) 
2m 02 


1 + 


Vp-v, 

V P" V 2 J 


Speed 


t?=v 

1 


m 02 




2e(V p -V 2 ) 




Potentials 


V-V 2 Vgp 

"v p -v 2 ' *" v p -v 2 


Energy 


t mv 2 
2q(V p -V 3 ) 



Table Al. Definition of Non-Dimensional Variables 

71 



Figure A2 shows the geometry and boundary conditions associated with the 
non-dimensional model. Grid 1 is located at © =0 and is held at a constant potential 
v±. Ions extracted from the discharge chamber plasma at a potential v v = l, approach 
grid 1 at a speed d l . Grid 2, located at © = 1, has a sinusoidal RF voltage with an 
amplitude prj? and a frequency F applied to it. Note that the mean potential applied 
to grid 2 is used as the non-dimensional reference potential. Grid 3 is located at 
© =2 and it is held at a constant potential p 3 . 

Recasting the dimensional equations in terms of non-dimensional variables, Eq. 
Al becomes 



^(Q/MMl-^) 



(A7) 



Eqs. A5 and A6 become 







^RF 


sin(2irFT) 


di? _ Q 


1-^/1-*!- 


dT M 


1 + ^ 1 - v x 



(A8) 



and 



dT M 



1 +^1 -v x 1 +^1 -v i 

respectively. Also, the non-dimensional kinetic energy is 



"RF 



sin(2irFT) 



(A9) 



£ 



Mi? 2 



Q(i-" 3 ) 

In addition, the relationship between non-dimensional speed, position and time is 



(A10) 



72 



II 

a, 



(0 



II S 



to 

a 
cc 
o 



c 






II 



O 

cc 



II 




a 
cc 






73 



t? = 



1+jl-pi 



d© 
dT 



(All) 



In order to determine the speed of an ion, which enters the system at time T 2 
with speed i? x (given by Eq. AT), in the region between grids 1 and 2, Eq. A8 is 
solved to give 



t?(T) = 



Q(l-„ l)+ §(l-/T^)(T-T 1 ) 



"RF 



M 



2tF(i+^1 -pJ 



[cos(2tFT) - 008(2x^)1 . ( A12 ) 



Using the relationship in Eq. All in Eq. A12, and solving for the time- 
dependent position of an ion that passes grid 1 at time T l yields 



©(T) = 



Q 

M 



f 



l+^l-^i 



M 



"RF 



xf(i + ^1-^) 



cos(2?rFT 1 ) 



(T-Ti) 



M 



i-/^~ 
i+/i-^ 



(T-T x ) 2 



M 



"RF 



2* 2 F 2 (l+^l -irj j 



[sin(2TFT) - s^TFTi)] . (A13) 



In order to determine the speed of an ion, which passes grid 2 at time T 2 with a speed 
d 2 , in the region between grids 2 and 3, Eq. A9 is solved to obtain 



74 



*(T) = » 2 - ± 



"3 



i + sl l - "1 



(T - T 2 ) 



Q 

M 



Vrf [cos(27rFT)-cos(2irFT 2 )] . 

2tf(i +\jl-vi) (A14) 



To obtain the time-dependent position of an ion travelling between grids 2 and 3, Eqs. 
All and A14 are used to find 



(T) = 1 + 



2t>, 



"RF 



(l+^l-J'l) tf(i+^1-i' 1 ) 



cos(2tFT 2 ) 



(T-T 2 ) 



Q 


"3 


M 


(l + ^l-Fl) 


Q "RF 


M 





(T - T 2 ) 2 



[sin(2xFT)-sin(2TFT 2 )] . (A i 5 ) 



Equations A12-A15 can be solved numerically to obtain the terminal ion 
energy for the single-stage Bennett mass spectrometer and to determine the stopping 
potential for the three-grid optics/RF mass discriminator. However, because the RF 
voltage is a small perturbation to the steady-state solution, a first-order (in p w ) 
solution for both the terminal ion energy and the stopping potential are derived. This 
analytical approximation will show the functional dependence of both parameters on 

effective frequency (Ft). 

To solve for both the terminal ion energy and the stopping potential, the 

conditions at grid 3 are needed and these are found using Eqs. A14 and A15. In 

75 



order to solve these equations, however, the speed of ions at grid 2 is needed. 
Therefore, a first-order solution for the speed of the ions at grid 2 is found from Eqs. 
A12 and A13. To obtain the first-order solution, speed, position and time are 
linearized as a steady-state term plus a perturbation term as follows. 

d =y + vjz F d' (A16) 

© =W + Vrf ©' (A17) 

T = Tj + ~K + p RF A' (A18) 

In Eq. A18, A is the time it takes an ion to travel from grid 1 to a given location 
under steady-state conditions and A' is the first-order perturbation in this travel time. 

Plugging Eqs. A16 and A18 into Eq A 12 and keeping terms through first 
order in v^p yields the steady-state equation 



3 = 



and the equation due to the first-order perturbation 



Sc-'i) +%[ i -fi^h (A19 > 



■■Sf(l-^A- 



M 



1 

+ 



2tf(i + ^/1- J ; 1 ) 



[( 1 - cos (2tF2) ) cos (2xFT) 



- (sin (2tF2) ) sin (2tFT)]} (A20) 

Plugging Eqs. A17 and A18 into Eq. A13 and keeping terms through first order in 

76 



j/rp yields the steady-state equation 



W = 2 



Q 

M 



f 1 ^ 



M 



and the equation due to the first-order perturbation 



1-/1-^ 



1+/!^ 



(A21) 



>' = 2 



M 



_Q 

M 



/i^T 



l+^/l-I'l 



tf(i +^1 -"i ) 



M 



1-/1^7 



i + /r^7 



A' 



.cos(2tF(T-S)) 



M 



2tt 2 F 2 (i +\Jl-v 1 



sinfexFT) - sin(2TF(T -S))J (A22 ) 



The first-order solution for the ion speed is desired at © = 1; therefore, Eqs. A21 
and A22 are evaluated at ©(© = 1) = 1 and ©'(© = 1) = 0. Eq. A21 is evaluated 
to find the steady-state time which it takes an ion to travel between grids 1 and 2, 
namely A(© =1) = r, which is found to be 



M 
Q 



(A23) 



Equation A22 is then evaluated to determine the first-order perturbation in the ion 
travel time at grid 2, namely A'(© = 1) = r', which is found to be 



77 



r =. 



M 
Q 



(i + /T^7) L 



cos[2irF(T 2 -r)] 
2ttFt 



(sin(2irFT 2 ) - sin[2irF(T 2 - r)]) 
(2tFt) 2 



(A24) 



These expressions for r and r' are used in Eqs. A19 and A20 to find d 2 and t? 2 \ 
respectively. Combining these speeds as shown in Eq. A 16 yields the speed of the 
ions at the second grid, to first order, which is found to be 



t?,= 



Q 

M 



1 + 



"RF 



1 + / 1 - v Y 



1 -^\-v l cos(2xFr) 
(2xFr) 



(l -y'l -p l jsm(2r'FT) 



(2tFt) 2 



cos(2ttFT 2 ) 



sin(2xFT 2 ) 



^1 -v x sin(2irFT) 
(2xFr) 



(l -/l -j/Jfl -cos(2ttFt)) 
(2irFr) 2 

This expression for i? 2 is valid for both the single-stage Bennett mass spectrometer 
and the three-grid optics/RF mass discriminator. At this point the problem will be 
specialized to solve either for the terminal ion energy for the single-stage Bennett 

mass spectrometer or for the stopping potential for the three-grid optics/RF mass 

78 



(A25) 



discriminator. 

To begin the derivation of the first-order solution for the terminal ion energy, 
recall that the same mean potential is applied to all three single-stage Bennett mass 
spectrometer grids and that the mean potential applied to grid 2 is used as the 
reference potential in the non-dimensional model. Therefore, the non-dimensional 
boundary conditions for the single-stage Bennett mass spectrometer are 1^=1/3=0. As 
was done between grids 1 and 2, speed and distance are linearized as shown in Eqs. 
A16 and A17 and time is linearized to first order in v^ between grids 2 and 3 as 
follows. 

T = T 2 +S + »' RF A' ( A26 > 

Here A is the steady-state time that an ion takes to travel from grid 2 to a given 
location and A' is the first-order perturbation in this time. 

Using the boundary conditions for the single-stage Bennett mass spectrometer, 
plugging Eqs. A16, A25 and A26 into Eq. A14 and keeping terms to first order in 
v^p yields the following steady-state equation for the ion speed between grids 2 and 3 



3 = 



Q 

M 



(A27) 



and the equation due to the first-order perturbation is 



"i 



Q 

M 



1 -cos(2xFr) 
2tFt 



cos(2tF(T -3)) 



sin(2xFr) 
2xFt 



sin(2xF(T-2)) 



Q l 

M 4tF 



cos(2tFT) - cos(2xF(T-S)). 



(A28) 



79 



Note that r' does not appear in the first-order perturbation of the ion speed; therefore, 
when Eqs. A17, A25 and A26 are plugged into Eq. A15, only the steady-state 
equation is needed. It is found to be 



"©"=1 + 



M 



(A29) 



Since the first-order solution for the speed of an ion arriving at the third grid is 
desired, Eq. A29 is evaluated at ©(©=2) = 2, where it is found that A(©=2) = 
JM/Q = r. Plugging this back into Eq. A28, the speed, to first order, of the ions 
when they reach grid 3 is determined to be 









, ,. 






#3 = 

> 


Q ■ 

M 


1 + 


"RF 
2 







2sin(2xFT) -sin(47rFr) 
2xFr 



sin(2TFT 3 ) 



1 -2cos(2tFt) +cos(4tFt) 
27tFt 



cos(2tFT 3 ) 
The ion kinetic energy at grid 3 can also be linearized as 



) 



(A30) 



e =f + "RF£' 



(A31) 



Using Eqs. A30 and A31 in Eq. A10 and keeping terms to first order in p^ yield the 
following first-order expression for the terminal ion energy from a single-stage 
Bennett mass spectrometer 



£ = 1 + v 



RF 



2sin(2TrFT)-sin(4TFT) 
2tFt 



shi(2tFT) 



1 - 2cqs(2tFt) + cos(4ttFt) 
2tFt 

Using trigonometric identities this can be rewritten as 

80 



cos (2 



tFT) 1 



(A32) 



I = 1 +j> RF ^sin(2TFT + 5) 



(A33) 



where 



* = 



and 



2sin(2xFT) - sin(4xFT) 
2tFt 



1 -2cos(2xFt) + cos(4ttFt) 
2tFt 



(A34) 



5 = tan 



-l 



-1 +2cos(2ttFt) -cos(4tFt) 



(A35) 



2sin(2xFT) -sin(4xFr) 

Here the product of \p (the energy spread parameter) and the RF voltage gives the 
magnitude of the maximum perturbation of the ion energy to first order. Thus Eqs. 
A33-A35 give the first-order solution for the terminal ion energy from the single-stage 
Bennett mass spectrometer. 

Now that the first-order solution for the terminal ion energy has been derived 
for the single-stage Bennett mass spectrometer, a first-order solution for the stopping 
potential in the three-grid optics/RF mass discriminator will be derived. The first- 
order solution for the terminal ion energy can be derived by linearizing the speed, 
position and time using Eqs. A16, A17 and A26, respectively. In addition, the 
potential applied to grid 3 is linearized as follows. 

"3 = ^ + v kf v 3 ( A36 ^ 

Recall that for the three-grid optics/RF mass discriminator v x = 1. Using this 
boundary condition, plugging Eqs. A16, A25, A26, A36 into Eq. A14 and expanding 
to first order yields the steady-state equation 



81 



3 = 



M M 3 



(A37) 



The equation due to the first-order perturbation of the ion speed is not needed to solve 
for the stopping potential; therefore, it is not listed here. To determine the first-order 
solution for the stopping potential, however, the position equation must expanded 
through first order in v^. To find these equations, plug Eqs. A17, A25, A26 and 
A36 into Eq. A15 and keep terms through first order in i^p. This yields the 
steady-state equation 



W = 1 +2 



2 - H Trf 



M M 
and the equation due to the first-order perturbation 



(A38) 



©' = 2 



Q Q— r 

M M 3 



A' 



M 



"3' 



+ 22 



Q 

M 



1 _ sin(2xFT) 
(2ttFt) 2 



2ttFt 



cos(2ttF(T-2)) 



1 - cos(2xFt) 
(2irFr) 2 



sin(2xF(T-S)) 



+ §Aoos(2tFCT-S)) 
M xF 



" % —5-5 I sin ( 2TFr ) " sin(2xF(T -2))] 
M 2 , r 2 F 2 



(A39) 



The potential required to stop an ion at grid 3 is found be setting d = and © = 2. 

82 



Simultaneous evaluation of Eqs. A37 and A38 at t?(t5=0, © =2) = and at 
©(i?=0, ©=2) = 2, respectively, yields the steady-state stopping potential 
v 3 (d=0, © =2) = Pm = 1 and the steady-state time for an ion to travel between grids 
2 and 3 A(i?=0, ©=2) = t* = \ M/Q = t. To find the first-order perturbation of 
the potential required to stop an ion arriving at grid 3, Eq. A39 is evaluated at 
©'(#=0, © =2) = 0. Note that when t is plugged into Eq. A39 the term 
multiplying the A' term is zero; therefore, the first-order perturbation in the potential 
required to stop an ion arriving at grid 3, v 3 '(d=0, © =2) = v* , can be found 
directly from Eq. A39 and it is 



*•' =2 



2cos(2tFt) sin(4irFT) 



27rFr 



(2TFr) : 



cos(2irFT 3 ) 



2 sin(2irFT) 1 - cos(4tFt) 



2ttFt 



(2xFt) 2 



sin(27rFT 3 ) 



(A40) 



Using trigonometric identities this can be rewritten as 



j// =$sin(2irFT + 5) 



(A41) 



where 



$=2 



2cos(2xFr) sin(4xFr) 



2tFt 



(2 it Ft) 2 



2sin(2xFr) 1-cos(4tFt) 



2ttFt 



(2tFt) 2 



(A42) 



and 



83 



5 = tan" 



2cos(2tFt) _ sin(4xFT) 



2tFt 



(2xFr) 2 



2sin(2-irFT) _ 1 -cos(4ttFt) 
2xFr 



(A43) 



(2tFt) 2 

The stopping potential is the potential which must be applied to grid 3 to stop the 
most energetic ions at the third grid, which is equal to the steady-state stopping 
potential plus the maximum value of the first-order perturbation. Since the maximum 
value of v* occurs, in Eq. A41, when the sine factor is 1, the product of $ (the 
stopping potential parameter) and the RF voltage gives the first-order perturbation on 
the stopping potential. Thus, to first-order the stopping potential v 8 is given by 



" s = l + "rf # 



(A44) 



Thus, the stopping potential is determined, to first order using Eqs. A44 and A42. 

Finally, a brief discussion about the use of the non-dimensional values to 
present experimental data are in order. Experimental results are given in terms of 
appropriate non-dimensional variables; however, experiments are always carried out 
at specific conditions which have dimensional values. The equations in Table Al are 
used to define the non-dimensional variables. From these equations it is seen that the 
actual operating conditions can be identified if the ion species as well as dimensional 
values for three variables is given along with the non-dimensional conditions. To 
identify the ion species the gas which is fed into the discharge chamber is given and 
referred to as the source gas. The three variables chosen to identify dimensional 
operating conditions are the grid spacing (s), a potential difference (V - V^ and the 
mean potential applied to grid 2 (V^. These values are listed when experimental data 
are presented. 



84 



Discussion of the potentials is warranted because the potentials are identified 
with different parameters in the single-stage Bennett mass spectrometer and the three- 
grid optics/RF mass discriminator. In the single-stage Bennett mass spectrometer 
V 2 = 0; since this is implicitly understood, it is not listed with data. The potential 
difference (V p - V?) multiplied by the charge on an ion corresponds to the energy that 
such an ion would have while travelling through the spectrometer in the steady-state 
case and is termed the mean ion energy. Thus in addition to the source gas, the 
dimensional values which are listed for the single-stage Bennett mass spectrometer are 
the grid spacing and the mean ion energy. 

For the three-grid optic-RF mass discriminator, the potential difference 
(V -V 2 ) corresponds to the total-accelerating voltage in the steady-state case; here it is 
referred to as the mean-total-accelerating voltage. The mean potential applied to the 
accel grid (V2) is always below ground potential in the three-grid optics/RF mass 
discriminator and is referred to as the mean accel potential. Thus for the three-grid 
optics/RF mass discriminator, the dimensional values that are listed along with the 
source gas are the grid spacing, the mean-total-accelerating voltage and the mean 
accel potential. 



85 



APPENDIX B 
Electron-Induced Errors in Probe Data 

The retarding potential analyzer (RPA), Faraday probe and ExB probe each 
have a Faraday cages surrounding the sensor (collector) plate used to measure ions. 
The Faraday cage of both the RPA and Faraday probe have a 2 mm dia aperture 
which ions can pass through and the cage is biased negative to keep electrons from 
passing through the aperture and reaching the collector. Although electrons should 
not have been able to reach the collector, negative currents were observed in RPA 
probe data under certain operating conditions. 

Before discussing the cases where negative currents were observed, it is 
worthwhile to describe the conditions at which the RPA works properly. Figure 14 
shows raw RPA data obtained from the three-grid optics/RF mass discriminator. 
These data are obtained with the RPA collector held at ground potential and the decel 
grid is used to stop ions. Also, the Faraday cage is biased negative enough to stop 
electrons from entering the aperture. This is observed to be the case because the 
current density 6 is observed to go to zero and remain zero at high retarding 
potentials. Thus, the RPA is operating in the desired manner; namely, the only 
species being detected are positive ions. 

Since the RPA functions correctly when data are obtained from the three-grid 
optics/RF mass discriminator, it might be anticipated that there would be no errors 



6 The RPA actually measures the current to the collector and the current density (such 
as that shown in Fig. 14) is determined by dividing this current by the area of the 2 mm 
dia aperture. 



86 



due to electron collection when the RPA is used to measure ion energies for the 
single-stage Bennett mass spectrometer. However, this is not the case. Fig. Bl 
shows the raw RPA data of the "corrected" trace shown in Fig. 7. In Fig. Bl it is 
observed that the current density arriving at the collector is relatively constant at low 
retarding potentials and its magnitude is denoted J + . It is observed that the current 
density goes negative at a retarding potential near 1.17 and the curve levels out at a 
relatively constant value at a retarding potential near 1.21. The magnitude of this 
negative current density is denoted J. and it is less than 20% of the ion current density 
measured at low retarding potentials. This is typical for RPA traces obtained while 
using the single-stage Bennett mass spectrometer. This negative current density 
represents an error in RPA measurements and a simple equation has been developed 
to account for these electrons and correct raw RPA data. 

In order to determine why the RPA works properly for the three-grid 
optics/RF mass discriminator but not for the single-stage Bennett mass spectrometer, 
the difference in modes of operation between the two cases must be examined. In the 
three-grid optics/RF mass discriminator the retarding potential is applied to the decel 
grid which stops ions before they reach the Faraday cage. In the single-stage Bennett 
mass spectrometer the retarding potential is applied to the collector which stops ions 
after they enter the Faraday cage. To see how ions stopped after they have entered 
the Faraday cage might cause the observed negative current density, Fig. B2 shows 
several current associated with RPA data collection. The ion current passing through 
the 2 mm aperture, denoted I + , is assumed to remain constant as the retarding 
potential changes. This current is equal to the maximum positive current density J + 
multiplied by the area of the 2 mm dia aperture. After this current enters the Faraday 
cage a fraction of it goes to the collector and the rest of the current is repelled away 
from the collector. The ion current to the collector is denoted I; and the current 

87 




B 

OS 

Q 

I 






( 2 .uio yuj) A1ISN3Q !N3UdnO 



88 



RETARDING 
POTENTIAL 

1-0-1 



JT 



FARADAY 
CAGE 
BIAS 



f~ 






COLLECTOR 
RPA SUPPORT 

FARADAY 
CAGE 




n 



COLLECTOR 
CURRENT 



-0-1 



■RPA 



I l I I fca 



2 mm DIA 
APERTURE 



Fig. B2 RPA Currents Flowing During Single-Stage Bennett Mass Spectrometer 

Testing 



89 



repelled by the collector is denoted I R . The fraction of I + going into ^ and I R 
depends on the retarding potential applied to the collector. At low retarding potentials 
all ions strike the collector so I + = \ and at high retarding potentials all ions are 
repelled and I + = I R . The ions which are repelled by the collector can either leave 
the Faraday cage through the aperture or they can impinge on the inside surfaces of 
the cage. Ions which are repelled onto the inside surfaces of the Faraday cage can 
cause secondary electron emission. Since the Faraday cage is always at a more 
negative potential than the collector these electrons will travel to the collector and be 
sensed as a negative current. In Fig. B2 the magnitude of this secondary electron 
current is denoted I e . The last current to be described is denoted I RPA and it is the 
current measured with the collector current ammeter shown in Fig. B2. I. is the 
magnitude of the secondary electron current going to the collector when all of the ions 
are repelled. In Fig. Bl the negative current density J. is equal to I. divided by the 
area of the aperture. 

The current measured by the ammeter, I RPA , is due to both ions and secondary 
electrons and is given by 

The magnitude of the current due to repelled ions, I R , is the total ion current passing 
through the 2 mm dia aperture minus the ion current arriving at the collector and is 
given by 

I R =I + -Ii (B2) 

It is assumed that the fraction f of repelled ions which strike the inside surfaces of the 

90 



Faraday cage remains constant over the range of retarding potentials at which ions are 
repelled (the fraction of repelled ions escaping through the 2 mm dia aperture is 1-f). 
The magnitude of the secondary electron current I e is equal to the product of the 
secondary electron emission coefficient g and the repelled ion current striking the 
inside surfaces of the Faraday cage and is given by 

When the retarding potential is high enough to repel all ions, I R = I + and I e = I.. 
Using these relations and also assuming that the secondary electron coefficient is 
constant over the range of energies at which repelled ions strike the inside surfaces of 
the Faraday cage, Eq. B3 can be solved for the constant product gf to obtain 

gf=- <B4) 

Using Eqs. Bl, B2, B3 and B4, the following expression for the ion current Ii is 
obtained 

t _ X RPA +I - 

lj 7-T (B5) 



1 + 



This is the formula used to correct raw RPA traces, such as the one in Fig. Bl, for 
secondary electron errors. For this trace the corrected current l { is divided by the 
aperture area and is plotted as a function of retarding potential in Fig. 7. It is noted 
that if I. = 0, Ii=lRp A - In words, the current which is measured is the actual ion 

91 

a ■$- 



current and no correction is necessary. This is the case in RPA traces like those of 
Fig. 14. 

During both three-grid optics/RF mass discriminator and single-stage Bennett 
mass spectrometer experiments, the Faraday probe was operated with the collector at 
ground potential. In addition, the Faraday cage was always biased to a potential that 
was sufficiently negative to keep electrons from passing through the aperture. The 
probe was operated at conditions where all ions passing through the aperture should 
have reached the collector and none of the ions should have impinged on the inside 
surfaces of the Faraday cage. This and the fact that the current to the collector is 
observed to decrease to zero when the Faraday probe is out of the beam indicate that 
errors due to electron collection are negligible. 

The Faraday cage surrounding the ExB probe collector was also biased 
negative to stop stray electron which might approach it. Although it was anticipated 
that negative currents would not be observed, a 0.8 pico-amp negative offset was 
measured in all ExB data. The exact cause of this offset has not been determined; 
however, calibration of the ammeter used to make the measurements indicated that it 
was zeroed correctly. The negative current is probably a small leakage current in the 
probe because it is also observed in ExB probe traces taken when the ion source is 
not being operated. Because the negative current appears to be a constant leakage 
current, it is subtracted off the ExB probe data. 

It is also noted that the current signal to the ExB probe collector tended to be 
noisy. Therefore, averaging procedure was used to filter out the noise. To obtain the 
ExB probe traces, the plate potential difference was varied between and 30 V in 
0. 1 V increments. At each plate potential difference, three current measurements 
were obtained and the average and standard deviation of these measurements were 
computed. The average and the standard deviation were needed to fit the data with a 

92 



Chebyshev polynomial series [28] using the general linear least squares fit 
technique described in the literature [29]. Once the coefficients of the Chebyshev 
polynomial series had been computed, the series was summed to obtain ExB traces 
like those shown in Figs. 18-20 and 22. 



93 



A ppendix C 
A Fourier-Series Technique for Differentiating Experimental Data 

A general procedure for applying Fourier sine series to obtain derivatives of 
experimental data is developed in this appendix. The mathematics described can be 
used in any application requiring differentiation of experimental data; however, 
analytical functions and Retarding Potential Analyzer (RPA) data will be used to 
demonstrate the usefulness of the technique. 

In experimental work one often obtains discrete data pairs of the form [e, 1(e)] 
over some range e = e to e = e + E. For example, Retarding Potential Analyzer 
(RPA) data are collected in the form of a plot of positive ion current to a probe (I) as 
a function of retarding potential applied to the probe (e). Numerically the value of 
applied retarding potential in volts is equal to the kinetic energy of the ions in eV, 
assuming singly charged ions are collected and that ions have this kinetic energy at 
the reference potential (i.e. at V). For RPA traces the ion energy distribution 
function is obtained using 



d?j 
de" 



_m J_ dl (ci) 

2e eA de 



where rj is the ion number density (in m" 3 ), m is the ion mass (in kg), e is the ion 
energy (in J), e is the electronic charge (in Coulombs) and A is the area (in m 2 ) 
through which current flows to the plate. Obviously, the function 1(e) must be 
differentiated to determine the energy distribution function. The method being 
proposed here to obtain this derivative, is to use a finite Fourier sine series to fit the 

original data and to then differentiate this series term by term. In order to ensure that 

94 



this differentiated series converges, the Lanczos [30] convergence factor should be 
used. Before discussing this factor, it is appropriate to discuss some of the drawbacks 
of Fourier series techniques. The Lanczos convergence factor will then be presented 
and examples (using data pairs obtained from analytical functions and experimental 
RPA data) demonstrating how this factor improves the convergence of Fourier sine 
series will be given. These examples will also illustrate some of the problems that 
can still arise when using this technique. 

A standard finite Fourier series [31] representation can be used to represent 
a function 1(e) on the open interval (e , e + E). This Fourier series is periodic with 
period E and converges to 1(e) in the open interval (e , e + E), but the series 
converges to the average value l/2[I(e ) + I(e + E)] at the interval endpoints e and 
e + E. Therefore, unless I(e ) = I(e + E), the Fourier series will not converge to 
1(e) at the interval endpoints. If the Fourier series is discontinuous at any point 
including the interval endpoints, the Gibbs phenomenon is observed when a finite 
number of terms is used to approximate 1(e). The Gibbs phenomenon is manifest as 
an overshoot of the finite Fourier series which makes it difficult to estimate 1(e) near 
points of discontinuity. Another problem that arises if 1(e) has discontinuities, is that 
the derivative of the Fourier series does not converge. Because of these problems, 
the standard Fourier series has limited usefulness in many applications. However, the 
convergence problems can be overcome by using the Lanczos convergence factor. It 
is also possible to eliminate the discontinuity at the interval end points for both the 
function and its first derivative. This involves subtracting off the straight line 
connecting the data at the interval end points and using a Fourier sine series to 
approximate the remainder. The appropriate math for obtaining the Fourier sine 
series and the Lanczos convergence factor is described below. 

The standard Fourier sine series representation of a function G(u) on the open 

95 



interval (0, 2x) is given by 



N 



G(u) = 53 a n sin 



nu 

T 



(C2) 



where 



2t 

a n = I| G(u)sin 



nu 

T 



du 



(C3) 



Since the Fourier sine series is defined on the interval (0, 2t) and the data is 
given on the interval (e , e + E), a method of mapping between the intervals is 
needed. The simplest mapping is the linear mapping 



u = 



2r 



(«"0 



(C4) 



Also, for numerical stability, the dependent variable can be mapped from the interval 
(I min , Imax), where 1^ and I max are the minimum and maximum values of 1(e) in the 
interval (e , e + E), into the interval (-1, 1) using 



H = 



21-Imin-Im; 



ax 



(C5) 



Tnax min 

Thus the data pairs [e, 1(e)] are mapped into [u, H(u)] data pairs. 

The function H(u) will now be approximated analytically. As mentioned 
above, the discontinuity at the interval end points can be eliminated if the straight line 
connecting these points is subtracted from H(u). This yields a new function G(u) 
defined by 



96 



G(u)=H(u)- rfH(2x^-H(0) 



u + H(0) 



(C6) 



Using the Fourier sine series representation (obtained from Eqs. 2 and 3), both G(u) 
and its first derivative will be continuous at the interval end points. 

Although the discontinuity at the interval end points has been eliminated for 
the function and its first derivative, the Gibbs phenomenon can still be encountered if 
the function has a discontinuity within the interval. To remedy this problem, the 
standard Fourier sine series in Eq. 2 can be modified with the Lanczos convergence 
factor. The main idea behind this factor is to modify the standard Fourier sine series 
so that the derivative will converge by applying a finite difference operator D N to the 
finite Fourier series. D N is defined by 



( _ F(u + 7 /N) - F(u - 7 /N) 
N v ' 2 7 /N 

where 7 is a finite constant. From this definition it is seen that, 



(C7) 



lim D N F(u) = -^ 
du 



N-00 



(C8) 



therefore, 



lim D N = _ 

N-00 du 



(C9) 



Thus, it is seen that for large N, Dn provides a reasonable approximation of the 
derivative operator d/du. Applying D N to G(u) gives 



D N G(u) = * 
2 7 



N 
E a n sin 



n=l 



N]]-JM*["-s 



1 (CIO) 



Using trigonometric identities, the fundamental theorem of calculus and performing 

97 



straight forward algebra, the following is obtained 



D N G(u) = " 



d_ 
du 



N 
E*» 

11 = 1 


sin 




n7 
2N 




sin 


nu 

2 








n7 

2N 







(Cll) 



The value of the factor 7 in Eqs. 10 and 11 must still be chosen. If 7 = is used, 
the standard Fourier sine series is obtained and the Gibbs phenomenon is observed at 
discontinuities. As 7 increases, the Gibbs overshoot decreases but the Fourier sine 
series representation broadens at the discontinuity. (That is, the sine series 
representation accomplishes the jump over an increasingly broader range.) Lanczos 
does not appear to have addressed the issue of what value of 7 gives the optimal 
trade-off between reducing the Gibbs overshoot and the broadening at a discontinuity; 
he simply used the length of the interval, 7 = 2x. Although no theoretical work has 
been done to determine the best value, 7 = 2x is deemed to be a reasonable choice 
and will be used here. Thus, Eq. 11 becomes 



D N G(u) = " 



d_ 
du 



N-l 

E>» 

n=l 


sin 




nx 

N 




sin 


- 

nu 

2 






1 


[IX 

N 







(C12) 



(Note that this series is summed from n = 1 to N-l because sin(nx/N) = when n 
= N.) From this it is evident that the finite Fourier sine series should be written as 



G(u) = 



N-l 
n=l 



sin 




nx 

N 




sin 


nu 

2 




i 


nx 
N 







(C13) 



The factor sin(nx/N)/(nx/N) is called the Lanczos convergence factor; it causes the 

98 



finite Fourier sine series to converge to G(u) faster because it attenuates the high 
frequency terms which cause the Gibbs phenomenon. Consequently, the derivative of 
G(u) will converge even if G(u) has discontinuities. The derivative of G(u) will 
converge, if the first power of the Lanczos convergence factor is inserted into the 
standard Fourier sine series before differentiation; however, better convergence is 
achieved if the square of this factor is inserted before differentiation. In general, the 
best convergence is achieved if the Lanczos convergence factor is raised to the m+1 
power before the m* derivative of the Fourier sine series is taken. 

Including the Lanczos factor, the analytical approximation of H(u) is found by 
combining Eqs. 6 and 13 to obtain, 



H(u) = 



H(2t)-H(0) 
2t 



N-l 

u + H(0) + £ a n 

n=l 



sin 



n?r 

IT 



nx 
"N 



sin 



nu 

T 



(C14) 



Although an analytical approximation to H(u) has been obtained, it is the 
representation of 1(e) that is desired. This is obtained from the inverse linear mapping 



1(e) 



*max *min 



H(u) + 



*max + A min 



(C15) 



where H(u) is defined by Eq. 14 and u is related to e by Eq. 4. Eq. 1 requires that 
the first derivative of I with respect to e be determined. Differentiating both sides of 
Eq. 4, it is evident that du and de are related by 



du = 

Thus using Eqs. 15 and 16 it is found that 

99 



2x 
E 



de 



(C16) 



dl(e) _ T 
de 



max 



"Imi 



in 



dH(u) 
du 



(C17) 



where, with the square of the Lanczos convergence factor applied, dH(u)/du is 



dH(u) _ 
du 



H(2x)-H(0) 

2x 



N-l 

+ E a n 
n=l 



sin 



nx 
If 



nx 

If 



2 


n 

2 


cos 


nu 

2 



(C18) 



Thus, dl(e)/de is found using Eqs. 4, 17 and 18. The formulas for higher order 
derivatives are given below; however, problems can be encountered with these higher 
order derivatives. Because of the properties of the Fourier sine series, the second 
derivative will be zero at the interval end points. This is not a problem if the second 
derivative of the function is zero; if it is not, the second derivative will not be reliably 
estimated near the interval end points. The latter case will also result in unreliable 
estimates of third and higher order derivatives. Although indiscriminate use of the 
formulas for higher order derivatives is cautioned against, the formula for the m* 
derivative of I with respect to e, when m is greater than or equal to 2, is given by 



d m I(e) 
de m 



1 
2 



-» v'max Tnin / 



2x 



m jm 



d m H(u) 
du m 



(C19) 



Again u is related to e by Eq. 4 and the m* derivative (for m greater than 1) of H 
with respect to u is, with the m+1 power of the Lanczos convergence factor applied, 



d m H(u) _ d 1 



du' 



du 1 



N-l 

E a n 

n=l 



sin 



nx 
"N 



nx 

"N 



m+1 



sin 



nu 

T 



(C20) 



100 



When this technique is to be applied to data pairs, Fourier sine series 
coefficients must be computed. This can be accomplished using the integral 
expression for the coefficients given in Eq. 3. Any standard numerical integration 
technique, such as the trapezoidal rule can be used to do this. The coefficients can 
also be computed using the least squares method [33] or if there are 2 L evenly spaced 
data points, where L is an integer, a fast sine transform [32] can be used. 

A further practical concern is the number of Fourier sine coefficients needed 
to achieve a reasonable approximation to the function 1(e). A fast sine transform will 
return the same number of coefficients as the number of data points. The Nyquist 
criterion [33], which states that the sampling frequency must be at least twice as 
high as the highest frequency to be measured, would seem to indicate that only the 
first half of the coefficients should be used; however, the Lanczos convergence factor 
damps the high frequency terms and errors in estimating the high frequency 
coefficients do not significantly affect the results. This is the case through the second 
derivative; however, an example is given below using the third derivative which 
shows that using only half the coefficients can result in substantial improvement over 
using all the coefficients. In the examples below, unless stated otherwise, 128 data 
pairs are used to obtain the Fourier sine approximation and 128 coefficients are used 
when the series is summed. 

Now that the pertinent mathematics has been discussed, examples illustrating 
the improved convergence achieved by using the Lanczos convergence factor and 
some of the possible problems with the Fourier sine series approximation will be 
given. The first example uses the Heavyside step function to demonstrate the 
improvement to the approximation due to the Lanczos convergence factor. The step 
function was chosen because a discontinuous function is more difficult to approximate 
with a Fourier sine series than a continuous function. Fig. CI shows the step 

101 



1.2 
1.0 
0.8 
0.6 
0.4 
0.2 
.0 











- 








- 






— STEP FUNCTION 




1 1 1 1 


1 


1 1 1 1 



1.2 
1.0 
0.8 
0.6 
0.4 
0.2 
.0 



t 



J l I !l 



"*** *^M 



I^WWMMM 



STEP FUNCTION 

FOURIER SINE SERIES APPROXIMATION 

WITH LANCZOS CONVERGENCE FACTORS 



J I I I 



1.2 
1.0 
0.8 

0.6 
0.4 
0.2 



J 1 I L 



STEP FUNCTION 

FOURIER SINE SERIES APPROXIMATION 

WITH 1 LANCZOS CONVERGENCE FACTORS 



J 1 I I 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



Fig. CI Step Function and Fourier Sine Series Approximation 



102 



function (top), the Fourier sine approximation without (middle) and with (bottom) the 
Lanczos convergence factor applied. The Gibbs phenomenon is clearly seen in the 
middle trace where no Lanczos factor is used. In the bottom trace where one 
Lanczos convergence factor has been applied, the Gibbs phenomenon has nearly 
disappeared but there is some broadening at the discontinuity. Thus, it is evident that 
the Lanczos convergence factor ameliorates some of the problems associated with the 
Gibbs phenomenon and allows a reasonable approximation to the step function to be 
obtained. 

To illustrate how the Lanczos convergence factor can be used to obtain 
derivatives, the first derivative of the step function was taken. Fig. C2 shows the 
Fourier sine series approximation of the first derivative of the step function. The top, 
middle and bottom traces show the approximation using 0, 1 and 2 Lanczos 
convergence factors, respectively. The first derivative of the step function is the 
Dirac delta function which is zero everywhere except at 0.5 where it spikes to 
infinity. Clearly none of the approximations shown in Fig. C2, exactly represent the 
delta function. This is the result of using a finite number of coefficients in the 
Fourier sine series. Considerable ringing is observed when no Lanczos factor is used 
(top). One Lanczos convergence factor substantially reduces the ringing (middle). 
Two Lanczos convergence factors virtually eliminate the ringing and therefore this is 
considered to produce the best approximation even though the height of the spike is 
reduced over those obtained using or 1 Lanczos convergence factor. For the rest of 
the examples m+1 Lanczos convergence factors will be used to obtain the m * 
derivative. 

The next example illustrates some of the problems that can be encountered 
when using Fourier sine series to obtain second or higher order derivatives. The 
function to be approximated is the exponential function on the interval to 1. All 

103 



160 

120 

80 

40 





LANCZOS CONVERGENCE FACTORS 



I l I I IlL I I I I I 



160 

120 

80 

40 





1 LANCZOS CONVERGENCE FACTORS 



J I I I I I L 



160 

120 

80 

40 





2 LANCZOS CONVERGENCE FACTORS 



A 



J I I I I I I I I 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



Fig. C2 Fourier Sine Series Approximation to Step Function Derivative 



104 



derivatives will again be the exponential function. Fig. C3 shows the exponential 
function along with the Fourier sine series representation of the function (top), as well 
as the first (middle) and second (bottom) derivatives. The Fourier sine series 
representation of the function and its first derivative are in excellent agreement. 
Actually, there is a slight discrepancy for the first derivative near the interval end 
points but it is not discernable at the scale of Fig. C3. The second derivative 
obtained from the Fourier sine series gives a good approximation to the function on 
the middle 90% of the interval but drops to zero at the interval end points. The 
series representation is zero at 0. The reason the series representation is not zero at 1 
is that the fast sine transform used to obtain the coefficients uses one additional data 
spacing interval. Since 128 evenly spaced data points were used, the interval to 1 is 
divided into 127 equal intervals. The fast sine transform uses 128 spacings, so the 
second derivative goes to zero at 1 + 1/127. Nonetheless, it is evident that the 
Fourier sine series gives a poor estimate of the second derivative near the interval end 
points. Therefore, in general, the second derivative should only be used on the 
middle 90% of the interval. 

Fortunately, in most applications, third or higher order derivatives are not 
needed; however, an example showing some of the problems associated with 
obtaining a good estimate of these derivatives will be given. Fig. C4 shows the third 
derivative of the exponential function and the series representation obtained using 128 
coefficients. The series representation spikes to a large positive value near and to a 
large negative value near 1. This occurs because the second derivative of the series 
decreases to zero at the interval end points. The third derivative of the Fourier sine 
series is also very noisy on the interior of the interval, resulting in a poor 
approximation to the third derivative. As mentioned above, the Nyquist criterion 

suggests that better results might be obtained by using the first 64 coefficients instead 

105 




EXPONENTIAL FUNCTION 

FOURIER SINE SERIES APPROXIMATION 

J L 




FIRST DERIVATIVE OF EXPONENTIAL FUNCTION 

FOURIER SINE SERIES APPROXIMATION 




SECOND DERIVATIVE OF EXPONENTIAL FUNCTION 

FOURIER SINE SERIES APPROXIMATION 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



Fig. C3 Fourier Series Approximation to Exponential Function and its First 

Two Derivatives 



106 




i 

I 

16 

8 

oo 
«s 

u> 

•§? 

P 

{ 

! 

i 



3 



107 



of all 128. Fig. C5 shows the approximation to the third derivative using 64 
coefficients. Again the derivatives spike at the interval end points, but the 
approximation is much less noisy away from the end points. Some ripple is still 
evident but it is a better approximation than that obtained using 128 coefficients. 

The problems with the second and higher derivatives do not arise if these 
derivatives are equal to zero at the interval end points. For example, all derivatives 
of the step function are zero at the interval end points. Fig. C6 shows the second 
(top), third (middle) and fourth (bottom) derivatives of the step function using 128 
coefficients. These curves are not noisy; all are seen to be reasonable approximations 
to the derivatives of the step function. This suggests that it might be possible to 
eliminate noise by artificially adding data beyond the ends of the interval in such a 
way that the higher order derivatives are zero at the end points of this extended data 
set. This has not been attempted but if good approximations to higher order 
derivatives are needed, it might be worth investigating. 

The final example shows the result obtained when the Fourier sine series 
technique is applied to experimental data. A retarding potential analyzer trace is 
shown at the top of Fig. C7. A set of 128 raw data pairs describing this RPA trace 
were obtained by measuring the singly ionized (assumed) argon ion current flowing 
through a SxW 6 m 2 hole onto a current sensing plate as a function of the voltage 
applied to the plate. The bottom plot on Fig. C7 shows the energy distribution 
function (dn/de) obtained using Eq. 1, The derivative dl/de was obtained using a 128 
term Fourier sine series with a squared Lanczos convergence factor. The resulting 
distribution function shown in the bottom curve is seen to be reasonable. 

From these examples it is evident that use of the Fourier sine series in 
conjunction with the correctly applied Lanczos convergence factor does provide a 
useful technique for analyzing experimental data. 

108 




d 



oq 

O 



d 



d 



d 



d 



to 
d 



CM 

d 



I 

3 
I 

I 



•a 

| 



c 

&b 



109 



4000 
3000 
2000 
1000 


■1000 

■2000 

■3000 - 



J I I L 



FOURIER SINE SERIES APPROXIMATION TO THE 
SECOND DERIVATIVE OF THE STEP FUNCTION 



J I 



X10 
30 

20 

10 

-10 
-20 
-30- 
-40- 



J I L 



FOURIER SINE SERIES APPROXIMATION TO THE 
THIRD DERIVATIVE OF THE STEP FUNCTION 



J I 



50 

40 

30 

20 

10 



-10 

-20 

-30 

-40 



x10 



J L 



Jl 



FOURIER SINE SERIES APPROXIMATION TO THE 
FOURTH DERIVATIVE OF THE STEP FUNCTION 



V 



J I 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



Fig. C6 Fourier Sine Series Approximation to Higher Order Derivatives of the 

Step Function 



no 



!> 

0) 



Z 

g 

H 

m 

£ 

H 



> 

a 

CC 

ai 

Z 

HI 



x10 

6r 



-6 



z 

LLI 

a. 
cc 

U 

LU 

2 2 
a. 



I 



I 



_L 




220 240 260 280 300 320 340 360 380 400 
RETARDING POTENTIAL |V) 




220 240 260 280 300 320 340 360 380 400 
ION ENERGY (eV) 



Fig. C7 RPA Trace and Corresponding Ion Energy Distribution Function 



ill 



Appendix D 
Nomenclature 

F Non-dimensional frequency 

M Non-dimensional mass 

Q Non-dimensional charge 

T Non-dimensional time 

5 Phase shift between sinusoidal RF signal and terminal ion energy 

v Non-dimensional potential 

pri? Non-dimensional RF voltage amplitude 

£ Non-dimensional kinetic energy 

r Non-dimensional steady-state transit time for an ion to travel between grids 1 

and 2 

¥ Energy spread parameter 

Appendix A 

e Electronic charge (C) 

f Frequency of sinusoidal RF voltage signal (Hz) 

F Non-dimensional frequency 

m Mass per ion (kg) 

m ^ Mass of diatomic oxygen (kg) 

M Non-dimensional mass per ion 

q Charge per ion (C) 

Q Non-dimensional charge per ion 

s Spacing between adjacent grids (m) 

112 



t Time (s) 

T Non-dimensional time 

T x Non-dimensional time at which an ion passes grid 1 

T 2 Non-dimensional time at which an ion passes grid 2 

T 3 Non-dimensional time at which an ion passes grid 3 

v Ion speed (m s" 1 ) 

v : Ion speed at grid 1 (m s" 1 ) 

V_ Discharge chamber plasma potential (V) 

Vrp RF voltage amplitude (V) 

W l Potential applied to grid 1 (V) 

V 2 Potential applied to grid 2 (V) 

V 3 Potential applied to grid 3 (V) 

V 12 Potential variation between grids 1 and 2 (V) 

V23 Potential variation between grids 2 and 3 (V) 

x Length (m) 

A Non-dimensional steady-state time for an ion to travel from a specified grid to 
a given point 

A' Non-dimensional first-order perturbation of time for an ion to travel from a 
specified grid to a given point 

5 Phase shift between sinusoidal RF signal and output at grid 3 

v Non-dimensional voltage 

v p Non-dimensional discharge chamber plasma potential 

j/RP Non-dimensional RF voltage amplitude 

v s Non-dimensional stopping potential 

v l Non-dimensional potential applied to grid 1 

j> 3 Non-dimensional potential applied to grid 3 

1> 3 Non-dimensional steady-state potential applied to grid 3 

113 



v' Non-dimensional first-order perturbation of potential applied to grid 3 

v* Non-dimensional steady-state potential required to stop ions arriving at grid 3 

v* Non-dimensional first-order perturbation of potential required to stop ions 
arriving at grid 3 

f Non-dimensional kinetic energy 

t Non-dimensional steady-state transit time for an ion to travel between grids 1 

and 2 

t' Non-dimensional first-order perturbation of time for an ion to travel between 
two grids 

t* Non-dimensional steady-state transit time for an ion to travel between grids 2 
and 3 

$ Stopping potential parameter 

^ Energy spread parameter 

t? Non-dimensional ion speed 

d l Non-dimensional ion speed at grid 1 

$ Non-dimensional steady-state ion speed 

#' Non-dimensional first-order perturbation of ion speed 

© Non-dimensional length 

© Non-dimensional steady-state ion position 

© ' Non-dimensional first-order perturbation of ion position 

Appendix B 

f Fraction of repelled ions that strike inner surfaces of the Faraday cage 

g Secondary electron emission coefficient 

Magnitude of secondary electron current emitted by the Faraday cage 

Ion current to the RPA collector 

Ion current repelled by the collector 
RPA Collector current measured by the RPA ammeter 
+ Ion current arriving at RPA collector at low retarding potentials 

114 



I. Magnitude of secondary electron current arriving at collector when all ions are 
repelled 

J + Current density measured at low retarding potentials 

J. Magnitude of current density measured at high retarding potentials 

Appendix C 

A Area through which current flows to the RPA collector (m 2 ) 

e Electronic charge (C) 

I Current flowing to the collector (A) 

m Ion mass (kg) 

e Ion energy (J) 

77 Ion number density (m" 3 ) 



115 



REPORT DOCUMENTATION PAGE 



Form Approved 
OMB No 0704 0188 



^•r-en^j and Aai^T»>rv 



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a r , rtnpr asce.r o-r trvs 

7'C ?D5CJ 



1. AGENCY USE ONLY (Leave blank) 



2. REPORT DATE 

January 1993 



3. REPORT TYPE AND DATES COVERED 

Contractor Report 



4. TITLE AND SUBTITLE 

Discrimination of Ionic Species From Broad-Beam Ion Sources 



6. AUTHOR(S) 



J.R. Anderson 



7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 

Department of Mechanical Engineering 
Colorado State University 
Fort Collins, CO 80523 



9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) 

National Aeronautics and Space Administration 
George C. Marshall Space Flight Center 
Marshall Space Flight Center, AL 35812 



S. FUNDING NUMBERS 



G NGT-50370 



8. PERFORMING ORGANIZATION 
REPORT NUMBER 



M-708 



10. SPONSORING 'MONITORING 
AGENCY REPORT NUMBER 



NASA CR-4483 



1U SUPPLEMENTARY NOTES 

Grant Monitor— M.R. Carruth 

Materials and Processess Laboratory, Science and Engineering Directorate. 

NASA-Marshall Space Flight Center, AL 35812 



12a. DISTRIBUTION /AVAILABILITY STATEMENT 



Subject Category: 72 
Unclassified' — Unlimited 



12b. DISTRIBUTION CODE 



13. ABSTRACT (Maximum 200 words) 

The performance of a broad-beam, three-grid, ion extraction system incorporating radio 
frequency (RF) mass discrimination was investigated experimentally. This testing demonstrated that 
the system— based on a modified single-stage Bennett mass spectrometer— can discriminate between 
ionic species having about a 2-to-l mass ratio while producing a broad-beam of ions with low kinetic 
energy (<15 eV). Testing was conducted using either argon and krypton ions or atomic and diatomic 
oxygen ions. A simple one-dimensional model, which ignores magnetic field and space-charge 
effects, was developed to predict the specie separation capabilities as well as the kinetic energies of 
the extracted ions. The experimental results correlated well with the model predictions. This RF mass 
discrimination system can be used in applications where both atomic and diatomic ions are produced, 
but a beam of only one of the species is desired. An example of such an application is a 5 eV atomic 
oxygen source. This source would produce a beam of atomic oxygen with 5 eV kinetic energy, which 
would be directed onto a material specimen, to simulate the interaction between the surface of a 
satellite and the rarefied atmosphere encountered in low-Earth orbit. 



14. SUBJECT TERMS 

Atomic Oxygen, Broad-Beam Ion Source, Mass Discrimination 



15. NUMBER OF PAGES 

124 



16. PRICE CODE 
A06 



17. 



SECURITY CLASSIFICATION 
OF REPORT 



Unclassified 



18. SECURITY CLASSIFICATION 
OF THIS PAGE 

Unclassified 



19. 



SECURITY CLASSIFICATION 
OF ABSTRACT 



Unclassified 



20. LIMITATION OF ABSTRACT 

Unlimited 



NSN 7540-01-280-5500 



Standard Form 298 (Rev 2-89) 

Present** bv ANSi Sid £39-18 
298-102 

NASA-Langley, 1993