A critical evaluation of the metastable time-of-flight technique for obtaining molecular velocity distributions

"A CRITICAL EVALUATION Of THE MErr'MjTABLE TlME-OF-FLIGfiT TECHNIQUE FOR OBTAINING MO~CULAE VELOCITY DISTRIBlJrIONS"

by

"A CRITICAL EVALUATION OF THE METASTABLE TlME-OF-FLIGHI'

TECHNIQ,UE FOR OBTAINING MOLECULAR VELOCITY DISTRIBUTIOm"

by

J.

w.

Locke

..

ACKNOWLEDGEMENT

I wish to thank the Director and staff of UTIAS for the opp-ortuni ty of pursuing this research. I am particularly grateful to Dr. J. B. French for suggesting the subj ec·t and for his enthusiastic supervision of the project.

The assistance of W. R. Jones and E. Zaremba in constructing some of the apparatus is acknowledged with pleasure. H. Winter's skill as a machinist also contributed great;y.

No words here could adequately express my gratitude to my wife, Mary, for her unflagging support throughout this work •

Financial support for this work was provided by the U.S. Navy Office of Naval Research under Contract Nonr 4073(00) and by the Canadian Defence Research Board, and is gratefully acknowledged.

SUMMARY

This paper describes how a fUndamentally new method for measuring the distribution of molecular velocities, the Metastable Time-of-Flight (MTF) method, was taken from the concept stage to a point where it may be used with a considerable degree of confidence by workers in such fields as rarefied gas dynamics, surface physics, and gas-phase chemistry.

The sensitivity of the MTF method has been measured in absolute terms and as a function of impact voltage for ten common gases - He, Ne,

Ar,

Kr,

_{Xe, N2 , H2'} 02' _{CO and CO2 . On the basis of the cross section values} obtained, the MTF method might seem to be less sensitive than methods employ-ing rotatemploy-ing mechanical systems with ionization detectors. However, other considerations such as the extremely narrow entrance slits required to achieve good speed resolution by mechanical methods mean that the two approaches are comparable in sensi ti vi ty in practice. In addi tion, noise due to statistical fluctuations in the signal due to background gas is a problem with these other methods and is not present in the MTF approach. It is shown that MTF does work well in the case of the first seven of these gases with the detector used and with a different detector would likely work with 02 and CO. There does not s_{eem to be any hope of using MTF with CO2 as it lacks} a suitable state. There is every reason to believe that the method will work in stillother gases, however.

All second order effects associated with this method have been in-vestigated and shown to be generally small. Operating conditions to ensure that accurate velocity distributions are obtained are discussed and demon-strated.

The hardware requirements for implementing the MTF technique are discussed at length including the design of the electronic instrumentation required.

The result of this work is the existence of a new, well-character-ized method for velocity analysis. The hardware that is inserted into the flow is simple, rugged, reliable, compact and completely compatible with ultrahigh vacuum. Using MTF one is also able to analyze fast flows (>10,000 m/sec) and one component of a gas mixture.

1.

2.

3.

TABLE OF CONTENTS

ACKNOWLEDG EMENT SUMMARY

NOTATION

INTRODUCTION 1

1.1

Introductory Remarks

1

1.2 Previous Methods 2

1.

2

.1

Rotating Mechanical Systems

2

1.

2.

2

Doppler Shift Methods

2

1.

2

.

3

Methods Using Deflection by Gravity

3

or Inhomogeneous Magnetic Fields

1.

3

A Search for a Better Velocity Analyzer

3

THE METASTABLE TIME OF FLIGHT TEX::HNIQUE FOR VELCCITY ANALYSIS

4

2

.1

Performance Analysis with Delta Function Modu-

4

lation

2.2 Other Modulation Schemes Possible

6

2

.

3

Conditions Necessary for MTF to Work

7

2

.

4

Recoil Effects

7

2

.5

Errors Due to Collisions and Decay in Flight

10

2

.6

A Suitable Detector 11

.AN EXPERIMENT TO VERIFY THE MTF MEl'HOD

3

.1

Basic Considerations

3

.

2

An Initial Test

3.2

.1

The Geometry

3.2

.

2

The Detector

3

.2

.

3

The Electron Gun

3

.2.

4

Initial Results

3

.

3

The Improved Apparatus

3.3.1

The Geometry

3.3.2

The Electron Gun

3.3.3

The Detector

3.3.4

The Vacuum System

3.3.5

The Gas Delivery System

3.3.6

Ionization Gauge Calibration

3.3.7

In Summary

11

I I 12 12

13

13

14

15

15

17

17

18

19

19

20

4.

5.

6.

INSTRUMENTATION FOR MErASTABLE TIME OF FLIGHT VELOCITY

ANALYZERS

4.1 Basic Requirements

4.2 A Preliminary Single Channel System

4.3 A Multichannel MrF Instrumentation Package

4.3.1 Design Philosophy

4.3.2 The Buffer Principle

4.3.3 The Digital Time of Flight Unit

4.3.4 The Performance of the Multichannel

Instrumentation Package

ElCPERIMENrAL RE3ULTS

5.1 Introduction

5.2 The Velocity Analysis Tests

5.2.1 The Inert Gases

5.2.2 Nitrogen

5.2.3 Hydrogen

5.2.4 Carbon Monoxide

5.2.5 C02

and

02

5.2.6 A Gas Mixture Example - He/Ar

5.3 Sensi ti vi ty Data

C ONCLUS I ONS

REFmENCES

APPENDIX A:

A Survey of Metastable States in COJnmon Atoms and

Molecules

APPENDIX B: Analysis of the Losses of a Buffered Counter

21

21

24

25

25

27

28

32

34

34

34

34

36

37 37 37

38

38

41

43

NOTATION

Some locally-defined symbols appearing only in a single section are not listed below.

A d e f(y) h i

r

J k L m m e Nt

P

_l

,P

₂

AP

Radius of the first Bohr orbit of a hydrogen atom with a nuclear of infinite mass

(5.2917

x

10-9

cm)

Detector entrance area

Characteristic length of the electron beam

The charge on the electron

(1.602

x

10-19

coulomb)

The velocity distribution function (the density of molecules in velocity space)

Width of the source slit

Planck's constant divided by

2w (1.0544

x

10-34

joule sec) Instantaneous electron beam current

Electron beam current averaged over a complete cycle of the experiment

Current density

Boltzmann's constant

(1.380

x

10-23

joules oK-I)

Distance from the electron beam to the detector (the length of the flight path)

Distance from the source slit to the detector Maas of an atom or molecule

Maas of the electron

(9.109

x

10-31

kg) Number density of all molecules in a gaa

Initial and final magnitudes of the momentum of an electron in a collision with an atom or molecule

Magnitude of the momentum exchanged between an electron and atom or molecule in a colli sion

q t t e.b. t m.p.

'l'

u v v

v

w

y Tl

e

a-( e) or

cr

(AP)

Collision cross section describing the probability of exciting sn atom or molecule to a metastable state by electron impact Time, usually the time for a metastable atom or molecule to travel the distance

l

Duration of the electron beam pulse

The most probable time taken by an atom or molecule to travel the distance

t

Absolute temperature Velocity of sn electron

Velocity of an atom or molecule

~8':

,mean velocity in a Maxwellian gas

Volume element in velocity space Voltage

Energy required to excite sn atom or molecule

Secondary electron yield of a metastable atom or molecule in a collision with asolid surface

Base of natural logari thms

Detector qusntum efficiency (the average number of detectable output pulses per metastable atom or molecule incident on its entrsnce area)

Angle through which the path of an electron is deflected in exciting an atom or molecule

The differential cross-section describing the probability of an electron exciting an atom or molecule and having its path deflected angle eor transferring a qusntity AP of momentum to that atom or molecule

I, ;I::N~ODUCTION

This paper is concerned with the conception and experiment al verifi-cation of a new method to'r measur:i.ng th.e d.i~t!l'ibution

ot

molecular veloeities at any point in a rarefied gas flow, The introduction ot any new method to measure such a fundamental characterlstic

ot

low density gas tlows should be most significant. as so tew methods have been available up until now, The rarefied gasdynamdcist needs a velocity analyzer as much. as his colleague werking with ordinary continuum flows needs a Pitot probe. Moreover, as this paper will demonstrate, the Metastable-Time-of-Flight (MTF) method has a number of unique advantages that viII permit certatn types ot experiments not previously possible using existing methods, (TO be tair, the MTF method also has certain limitations whlch will be discussed later),

This is perhaps an opportune time tor the introduction of a new velocity analysis technique as many major areas where it can have significant utility are coming into prominenee, Workers in surtace physics and chemistry for instanee, should find the MTF technique usetul for studying distributions of veloeities of partieles leaving surfaces, MTF was conceived with the requirements of the gas~urface interaction and the molecular beam fields in mind where the recent availability of techniques for generating high energy

(nearly 10 eV) gas beams and scattering them off solid surfaces makes new deinands of the detection system, particular.ly in regard to resolving details' in the velocity distributions in the fast flows leaving the surfaces. MTF is particularly suited to this problem. Applications may also exist in measurements of kinetic temperature and composition in the upper atmosphere of the earth and the other planets by MTF instrumentation on board satellites and planetary probes • Since i t has 00 rotating parts, no large angular

momentum, an MTF instrument is a velocity analyzer well-suited to flight applications, and it can also be expected to be very reliable.

The author believes that the present paper describes the first development and testing of a method using electronically excited neutral molecules for velocity analysis. This work was initiated in

1963

at the Institute for Aerospace Studies, University of Toronto. A paper describing this technique and showing a velocity analysis of a helium tlow was given at the Fifth Srnposium on Rarefied Gas Dynamies in

1966

and was published in the proceedings, There has been independent contemporary work involving time of flight measurements on excited atoms and molecules ~03 the somewhat different purpose of ~eas~ing excited state lifetimes' and fo'r observing dissociation products 4 •5,6. In addition two recent papers describe appli-cations of the MTF method (crediting our earlie'r pa~er) to a gas~surface interaction problem

7

and to a residual gas analyzerÖ , Dtstortion in a velo ... city distribution in N2 shown in Ref. 7 is explained in th1s paper.

A brief review of previous techni~ues would help to put the present development in perspective9~ An extensive discussion of the history of velo-city analysis is available so that only the techni~ues themselves will be discussed here. Available techni~ues are as follows.

1.2.1 Rotating Mechanical Bi':stems

These systems usually employ one or more discs with peripheral slots through which gas may pass and re ach a detector, of ten an electron bombard-ment ionizer. There are two basic ways of using these arrangebombard-ments - as a velocity filter with multiple discs such that only molecules with the correct velocity pass through the assembly to the detector and aS a time-of-flight system in which a single rotating disc gates the flow so that the time history of

in-flight density downstream ~om the disc may be measured to obtain velocity information. Most velocity distribution measurements have been made with equipment of this type and Ref.9 describes the use of a single-disc time-of-flight arrangement.

This type of equipment is limited in resolution in high speed flows because the peripheral velocity of a rotating mechanical s~stem is constrained by material strength considerations to be less than 1 x 103 m/seclO,ll with

the best available materiaIs. Practical systems have a maximum speed of the order of five times slower than this. Let us consider how long a flight path would be necessary if we were to use such a practical rotor to analyze the flow near an earth satelli te in a circular orbi t at 100 km alti tude, whi ch has a speed of

7.9

x 103 m/sec. If the slots in the chopper disc are 1 mm wide and we require 1% resolution from the analysis, then the flight base must be about 100 times as long as the distance that a

7.9

x 103 m/sec parti-cle moves in the time the disc periphery moves 1 mmo That is

Flight base

=

100 x

7.9

x 103 x -"-'--;:..;..;...~ 1

x

10-3

=

3

.95

meters 2 x 102

Thus a mechanical velocity analyzer must be very large if it is to an.alyze fast flows with good resolution. It can only be made more compact by trading off sensitivity (by making the slots narrower) and/or resolution. 1.2.2 DOppler Shift Methóds

Observations of the broadening of spectral lines due to the DoppIer effect date back more than fifty years. It is only in the past three years that this principle has been applied to the gasdynamics field. E. P. Muntz12 has derived molecular velocity distributions from the profiles of spectral lines excited in gas flows by electron beams, The technique is successful in flows at relatively high pressures (typically 100 microns) where a rotating mechanical system could not possibly werk because of molecular mean free path considerations. However. the sensitivity of this technique is low and it has never been applied to very low density floWS. Tt is not likely to become a

1.2.3 Methods Usirig Dè:f'lèction bl Gtayitl or InhOn'l.ögeneous Ma.gnetic :Fields

; -. .

Unfortunately these two forces are so weak that only-small de-flections are possible even with massive electro magnets in the case of the latter method. However, in specialized circumstances these effects can be useful, The well-known experiment of Estermann, Simpson and Stern13 did show that gravitational deflection could De used to achieve velocity analysis of a molecular beam, The famous Stern-Gerlach experiment14 , the first to measure the magnetic moment of an at om , also indirectly confirmed the Max-wellian distribution of velocities by a method involving the deflection of atoms in a st rong inhomogeneous magnetic field. As important as these demon-strations have been for physics, it does not seem possible to utilize these effects in a practical velocity analyzer of general utility.

1,3 A Search for a Better Velocity Analyzer

We have th us noted that if we seek a convenient method for making velocity distribution measurements in low density flows (say < 10-5 torr) in practical circumstances, we have only the rotating mechanical systems to choose from. Furthermore, even these methods fail us if we seek a compact instrument capable of measuring distributions in fast flows, such as are necessary for simulating the conditions near an earth satellite or a plane-tary probe. For surface physics or chemistry experiments we would also be wary of putting the rotor of such a system near an atomically clean surface for fear of contaminating the surface with materials outgassed from the rotor, its bearings and their lubricant.

The motivation for developing the MTF method came from the desire to avoid these difficulties. What the mechanical methods do in essence is modulate the flow at one station (by physicallyblocking it) and then detect the resultant disturbance at a station downstream. Are there not other means of modulating gas flows? Another agent for affecting a gas flow used in this laboratory was the electron beam. Could ions created by electron im-pact be used in some way?

A quick calculation showed that electric fields due to space charge are sizeable in electron beams typically used in ionizers. Since ions are charged they would be accelerated by these fields and the information about their original velocity might be_lost. For instance, in a cylindrical 100-volt electron beam with a total current of 1

mA,

the potentialof the axis is 1.52 volts lower than the electron beam surface (independent of the size of the beam). By comparison, the average energy of a molecule in a gas at

300~ is 0.0259 eV. We could reduce the beam curr&nt (and the potential differences in direct proportion) to solve this problem at the expense of sensi ti vi ty, However, for less than 1% velocity perturbation of a 0.0259 eV molecule we would have to reduce the beam current by

100

2

1.52

0.0259

=

29301

as might be caused by contact potential differences in the apparatus,

A

potent;i..al dit't'erence ot' m.ore than 0,5 m.illivol t would be serious. Thus

~easure~ents of the yelocities of the ions would seem to oe a poor w~ to

obtain the velocity distribution of the origina.l flcw except in yery high energy flows where these effects are not so seriol1s. Intensity modulation of the

gas beam by producing a high degree of ionization and sweeping the ions aside with an electric field was investigated but it did not seem possible to ionize more than about 3% of the gas with the highest perveance electron gun thought practical.

Fortunately, there is another interesting type of particle created by the electron beam that survives for a long time - a metastable atom or molecule. The reader should refer to Appendix A for an extensive discussion of the nature and properties of these interesting particles. Briefly, an atom and molecule is said to be in a metastable state of electronic excitation if its radiative lifetime is greater than I microsecondl5. Moreover, most gases possess metastable states whose lifetime is of the order of a second. These metastables can be distinguished from ordinary molecules by their ability to eject electrons from metal surfaces due to their potential energy. Also, as will presently be argued, a metastable has substantially the same velocity as the molecule in the ground state from which it was created by electron im-pact. The electron impact event that excites a molecule or atom to a meta-stabIe state can be regarded as a tagging of that molecule as it passed through the electron beam. If a way of measuring how long it takes for each of many metastable molecules to travel some known distance can be devised, then a new velocity analysis technique will be available. This is the basis of the

Metastable-Time-of-Flight Velocity Analyzer. The potential advantages for high speedjhigh resolution measurements in clean experiments seem very attractive, but many tests wererequired and many questions had to be considered before one

could expect this new idea to work.

2. THE METASTABLE TIME Or FLIGHT TECHNIQUE FOR VELO CITY ANALYSIS 2.1 Performance Analysis with Delta Function Modulation

Basically, the electron beam current is modulated and the resultant modulation in the population of metastable particles at a station some di stance from the electron beam can be interpreted to obtain the velocity distribution in the gas at the location of the electron beam.

What type of modulation is best? The simplest modulation scheme to interpret is one that might be called delta-function modulation. In this scheme the electron beam is pulsed to tuIl intensity for a sufficiently short time that all of the metastables it creates are still in the immediate vicinity of the beam at the end of the pulse. Thus we know that all metastable

arrive at a small detector a distance

".t"

from the axis of the electron beam were in the electron beam at the time of the pulse. Thus if each metastable

arriving at the detector creates a signal pulse at the detector output, then by measuring the time of occurrence of each of many signal pulses with respect to the time of the electronbeam pulse we can plot the velocity distribution by noting that -the speed of a metastable,

"v",

is simply related to i ts flight time in this situation by

;I:n practice. we. )l1ight require tha.t the width of: the electron beam ;pulse, t b ' be less than 1/100 01' the most proQa,ble night time

ot

a,

parti-cle in

o~der

to ensure

t~t

all metastables are

ade~uatel~

close tothe electron beam at the end of the pulse. When ~

=

15.~1 cm as ~t was in ouT tests then this criterion requires t b to be less than

0.7

~

5.4

~seconds (depending on the molecular weight of tliè gas) assuming a Maxwellian distribution at 3150K. For faster flows, say

7.9

x 103 meters/sec (earth satellite velocity), we would like to have te.b. < 0,19 ~second with this same flight base. Pulses

of these lengths are easily within the electronic state of the art. Of ten it is convenient to increase t b above these values to gain sensitivity (be-cause more metastables are

~reáted

by a longer pulse) at the cost of reso-lution.

How will the distribution of arrival times of the metastables be related to the velocity distribution of the flow? Let us make several assumptions which we will shortly justify. Let us assume that the impact process that excites a molecule to a metastable state does not disturb its velocity appreciably, that the detector has a probability ,~, of producing an output pulse for each metastable incident on its entrance area,

'A',

independent of the velocity of the metastable, and finally that the lifetimes of the metastable states involves are all long compared with the fiight time of the slowest molecule.

In general one cau define a velocity distribution function, f(~),

that denotes the density of molecules in a gas in velocity space by writing that the number density of the gas in phase space (the six~dimensional space having three position coordinates and three velocity coordinates) is given by

From the definition of a collision cross section,

'q',

(Ref.

16,

Section

1-4)

the rate at which an electron beam of total current 'i' travelling a distance 'd' through a gas generates metastable molecules in the volume

element of velocity space 'd3v' about the velocity

'v'

is given py

However, only those metastables with velocities directed into the solid angle subtended at the electron beam position by the detector entrance area will be recorded. That is, the

MTF

instrument measures the portion of the velocity distribution function contained in this solid angle. If this solid angle is small enough we are justified in approximating it by

A/t2

and if we interpret f(v) as being f(v) evaluated along a vector parallel to the mean line joining the electron impact volume and the detector entrance, then the rate at which detectable metastables with speeds between v and v + dv are generated is given by

Nt qdiA 2

- - - v f(v) dv e~2

1;1' we obse;rye th.e :p;reyiously' noted ;J;'e~t:rict~.on~ on electron bee.n\ pulse width and repeat the ;pulses at a, sui.ta,bJ.e ;ra,te such. that the slowest ~etastable molecules of interest generated b~ one pulse ~ye arr~yed at the detector before the next pulse is initiated~ then by including the detector quantum efficieno~

tn.

and putting in a tjme-ayer~ged value

ot

electron beam current

'rl

:ror

ti t the mean ra.te at which cou.rrts are initiated in the de .... tector b~ metastables of speed between 'V' and

v

+ dv is

Flnall~. it is convenient in a time of flight instrument te generate a display in which a histogram of numbers of counts versus the flight time increment in which they were detected, We can then convert the above count rate into a form with flight time 't' as a parameter by means of

'V'

=

"

t and t dv

=--t 2 dt

Ignoring the sign, we obtain for the mean rate at which counts occur at the detector from metastables with flight times between t and t + dt,

~

fU/t) dt t

Thus, if instrumentation is provided to sort and accumulate the detector counts in increments of the flight time, then a close approximation to the above distribution will be generated which can easily be converted into a velocity distribution ff desired. In practice the flight time distribution which the MTF system naturally generates is oftèn as useful as the velocity distribution itself,

For later reference we shall note that for the Maxwellian

distri-.... ( v) = (;-kT

)3/2

( m v 2

)

.I. exp .. 2kT

(2-1)

and hence the mean count rate from particles with fllght times between t and t + dt is

( )

3/2

~rlkT

2,2 Other Modulation Schemes rossible

1

0"

ex-{

mt

2 2 )dt

I\::

2kTt (2-2)

What has just be discussed is the performance of the system with the e~ectron beam current modulated b~ an approximation to a delta function. This form of modulatien was chosen and used in the present work largely because

it rields a si~le ~nverse of the yelocity distriQution , tue fligut ti~e distribution, Since what is being dete~ned is the impulse ~esponse of a linear Systelll. other vtdeoe,nd W'aveforll1s l'dght De usef'ul,

A

no1se-like wavetorm lSuch as a re,ndom. square wa.'V'e W'Ould seem I'!,ll attr~ctive alternative for f'uture lnvestigation. Th.e ~pulse response we se ek c0uld be 0btained by cross~correlating the detector output with the random electron beam current waveform. Such a method could improve the system sensi tivity appreciably as the electron beam can be on

50%

of the time (as compared with <

1%

in the delta fUnction modulation approach).

2.3

Conditions Necessary for

MTF

to Wórk

In order tor

MTF

to W'Ork properly as a velocity analyzer, several important conditions must be satisfied:

1) The velocity distribution of the métastab1és must be êssentially the

same as that of the flow in which they are created. That is, recoil v~locities from the electron impact must be small compared with the flow velocities.

2) All metastables must survive the flight to the detector, or failing this, the decay rate tor each metastable species being detected must

be accurately known.

3) The detector must have a quantum efficiency,

n,

for metastables that does not depend on the velocity of the metastable.

Let us examine these requirements in turn.

2.4

Recóil Effects

Recoil trom the impact of the electron on an atom or molecule in

exciting it to a metastable state certainly occurs. We must calculate how serious an effect this might be in practice. We first examine the constraints imposed by conservation of momentum and energy in such a collision.

For an inelastic collision between an electron with mass

'me'

and an atom with mass 'm' moving initially with velocities ~l and 0, respectively, we can write the conservation of momentum equation in the Laboratory frame

of reference

m~l - m~2 = ~

where ~,

1Q

are the velocities of the electron and atom af ter the collision. Conservation of energy requires that

2 2 2

meu_l ~ m_eu2

=

2W

+

_mV2

where W is the energy required for the excitation of the at om , From the momentum conservation equation

Jll.

e

<

4

m

Since we are normally interested in collisions in which W > 5 eV (which exceeds the work function of tungsten and can thus produce Auger ejection of electrons for detection)~ me/m ~ me/mH

=

111837

(where ~ is the mass of a hydrogen at om) , and 1/2 mUl < 100 eV then we can show that

m~ ~ W/ll.5 and ~ence neglect mv~ compared to 2W in the energy conservation

equation. We can then write

2 2

meul - meu2

=

2W

'I'hus for a given incident electron energy, the energy and hence the speeds of the electrons leaving the collision regionare independent of the recoil angle. Figure 1, showing the conservation of momentum equation in graphical form, uses this fact to illustrate that the end of the momentum

transfer vector lies on a sphere whose radius depends on the inéident energy of the electron. Figure 1 is drawn to scale for a typical situation in helium (a gas in which recoil effects are particularly pronounced) and adds the momentum transfer vector to a typical value of the velocity of the atom,

v

at 20oC, at right angles to the initial direction of the electron. It thus is useful in showing the typical errors that might be introduced in a velocity analysis of room temperature helium by MTF.

Since Fig. 1 shows conservation limitations only, we do not know what events with these limitations are likely without further information.

In general, one can only say what is likely in two limiting cases.

The simplest limiting case is that of threshold where m u2

=

2W. Then the scattering sphere collapses to a point. We can see

thatet~is

is simply the case where the electron has just enough energy to excite the state, does so and leaves the impact region with a momentum negligible com-pared to the momentum it carried initially. All of the initial momentum of the electron is transferred to the atom in this case. Table 1 shows how the momentum transferred at threshold compares with

v

at room temperature for a number of gases. (The energy of the lowest metastable state for each gas has been used) •

Thus, at threshold, for the light gases (He, H

2) an appreciable veloc1ty component, up to 31.8% of v at 150C,is added at right angles to the f11ght path in a MTF instrument. No error in determining the velocity dis-tribut10n results, because the component of velocity parallel to the flight path, which is what determines the t'light time of apartiele to a detector plane normal to the flight path, is not changed. However, one must clearly be very cautious about applying MTF to a narrow collimated berum with a narrow detector where the change in direction of the atoms by the collisons could cause atoms corresponding to some porti on of the velocity distribution to miss the detec~or.

The other limiting case where samething of the relative likelihood of various events permitted by the conservation equations is known is the

,.

ca~e of large incident energy, Lassettre in a long and continuing series of p~pers in tQe Journal of G.Qemical rhy~ics hA~ re~o~ted tQe results of electron scattering experiments in wTIjch a colli~ated elect~0n be~ ~s pas~ed through a gas in a cell and the angular dist:t"ibution of elect:t"ons that have excited speeifie electronic transitions in the gas is measured, Such data can tell us where on a seattering sphere in Fig. 1 a collision is likely to be,

Figure 2 shows data fo:t" the direct excitation of the 21s metastable

s~ate of helium from three of the papers of Lassettre and his colleagues17,18, 1 replotted in a form useful in our problem. The ordinate

~AP

is thepro-duet of the differential cross section1ó , ~, times the magnitude of the

momentum given by the electron to the atom in a collision, AP.

(a

has the 2 dimension of area and is expressed in the atomie unit na~~

=

8.806 x 10 .. 17cm AP is in the atomie units ofmomentum.,1'l./a

o = 1.993 x 10" gm-cm/sec). The curve can be expected to be valid for all impact energies for which the Born approximation holds. This follows directly from the discussion in Ref. 20 concerning this same voltage .. independence property of the generalized osci~­ lator strength, (W/2) (P

l /P2) ~Ap2, by assuming that the voltage is also

high enough that P

l/P2 ~l. Pl and P2 are the initial and final magnitudes of the momentum vector of the electron. To the accuracy required by the present argument, say ~ 20%, the plot of aAP versus AP for a particular excitation in a particular gas should be correct for any electron impact energy of 100 eV or higher. To the same order of accuracy we may replace AP by P1S where S is the angle, assumed small, through which the electron is

deflected. We can then interpret a ~AP versus AP plot as being proportional to a plot of OB versus S or AP. Finally since o'S for small

a

is proportional to the total number of electrons that are deflected into a small increment of e, de, centered at

e

(directly from the definition of different cross-section), we can interpret the o6P versus AP curve as a plot of the number of collisions versus the magnitude of the momentum transferred from the electron to the atom. Since the curve in Fig. 2 peaks at 0.5 A.U. and tails off rapidly towards 2.0 A.U. wi can then say that when high energy electrons (>100 èV excite He to the 2 S metastable state the most probable momentum transfer is 0.5 A.U. (150 meters/second recoil) and that transfer is rarely greater than 2 A.U.

Looking back at Fig. 1 the reader will notice two sets of arcs

marked '0.5 A.U.' and '2.0 A.U.'. They represent spheres formed by AP vectors of these lengths. Their intersection with the scattering spheres for energies of 100 eV or greater show the most probable events and the largest expected momentum transfer events. Thus one can see that at high impact energy the momentum transfer is always nearly in the plane perpendicular to the electron beam, and furthermore has a most probable value more than two times smaller than the threshold value (150 m/sec versus 362 m/sec from Table 1),

The author has also made a aAP versus AP plot forlthe only other data available for a transition to a metastable state,the a

ng

_{state of N22l.} It is very similar in shape to Fig. 2, peaking at 0.5 A.U. as did the helIum curve, but the nitrogen curve tails off faster at the larger AP's and seems to indicate a negligible PTobability of a momentum transfer larger than 1.5A.U. In N

2 a reeoi1of 0.5 A.U. of momentum corresponds to a recoil velocity of 21.5 m/sec (again much less than the threshold value, 29.1 m/sec !rom Table

IJ)

One would like to have data for other gases as well. Since exci-tat_{ion in two very different gases, He and N2 , are charac}terized by quite similar momentum transfers at high energy, one is tempted to think that all gases would have similar behaviour. If further data supports this surmise

then we can say that the values for the most probable recoil velocity in the various gases at high energy will be somewhat lower than those listed for the threshold case in Table 1.

Neither theory nor experimental data is available for the region from threshold up to 100 eV and one can only suggest that inasmuch as 6P is not grossly different above 100 eV from 6P at threshold it is not likely to be far above or below the threshold value at intermediate energies. Lack-ing more concrete knowledge of this energy range, it would seem best to estimate 6P at the threshold value.

Thus for the lightest gases at room temperature (He, H2)~momentum

transfer can be a serious source of error at any impact energy. For the other gases the effect is not likely to be serious in using MTF provided that one avoids situations in which a small deflection can cause appreciable numbers of molecules to miss the detector.

2.5 Errors Due to Collisions and Decay in Flight

Failure to meet the requirement that all metastables that are created by the electron beam must reach the detector could come from two sources (other than the recoil effect discussed above). The metastables could collide with gas particles along the flight pa th or they could decay (radiate) in flight.

T0 avoid the colli sion problem one must simply ensure that the mean free path along the flight base be much greater than

'l'.

This condition sets an upper limit to the gas density in which one can use MTF for accurate velo-city distribution analysis, of the order of 10-

4

torr.

To ensure that no distortion occurs in the flight time curve due to decay in flight, one must ensure that ene excites only states with lifetimes much longer than the flight time of the slowest particles of interest and

states with lifetimes much shorter than the flight time of the fastest particles of interest. It may seem unlikely that this requirement could be easily satis-fied. An examination of the lifetime data collected in Appendix A will reveal that nature has been kind in this regard. All of the inert gases plus Hg,

H,

H2,

N, 0, NO, have easily detectable states that have lifetimes long compared with typical flight times. All other states in these gases are very

shQrt-lived, 0(10-

8

sec). In the important exception,

N2~the

lowest state,

Aj E+,

is fortunately long lived. Hence, one can use an electron beam energy ne~ the threshold for this state and not excite any of the other short-lived states, thus avoiding distortion problems. The same trick may work in CO, 02 may

also be a suitable gas provided a low work fUnction detector is used. Thus decay in flight is not usually a problem. Exceptions to this, in a sense, are C02 and ~20 which simply do not seem to have any metastable states at all.

2.6

A Suitable Detector

The need for a detector whose sensitivity is not a function of the

velocity of a metastable is fortunately met by the convenient Auger-ejection

detector. Metastable atoms and molecules are capable of ejecting electrons from

the metal surface by virtue of their internal potential energy provided this

energy exceeds the work function of the surface. These electrons can then be

detected with an electron multiplier. Hagstrum

22

has shown that, for rare-gas

metastable atoms at least, the secondary electron yield should be the same as

for the corresponding ion. Experiments with noble gas ions

23

and theory for

He+

24

show that the secondary yield is independent of ion energy up to about

100 eV. Thus for the inert gas metastable (and likely all others) the

assump-tion of the velocity-independence of the detector sensitivity seems entirely

justified over the entire gas particle velocity range that MTF would be likely

to be used.

Thus, in summary, by combining an electron gun pulsed briefly at

intervals to excite the gas molecules flowing through a compact region, an electron ejection detector for the resultant metastables some distance, $,

away and suitable pulse sorting instrumentation, it appeared th at a velocity

analysis system with many attractive features could be developed, providing

the overall system sensitivity could be made adequate. The following sections

discuss the system design, construction, and validátion experiments required

to achieve this goal.

3.

AN EXPERIMENT TC VERIFY THE MTF METHOD

3.1 Basic Considerations

Because MTF is an entirely new approach to velocity analysis it would

seem wise to thoroughly evaluate this technique with regard to sensitivity and

second order effects before using it extensively. The remainder of this paper is thus concerned with the development of the hardware needed to implement the MTF method and the design and execution of an experiment using this equipment to evaluate the method when used upon ten common gases.

An

experiment to evaluate the method should be sensitive to the three

types of second order effects which were anticipated in Sections

2.3-2.6.

Ideally

such an experiment would unambiguously indicate the presence of small errors due to recoil, decay in flight and the rather unlikely possibility of velocity de-pendence of the detector sensitivity. The type of experiment chosen for practical reasons is sensitive to all of these effects simultaneously. However, the

effects can usually be readily separated by the distinctly different way each depends upon electron impact voltage. For instance decay in flight occurs only when the impact voltage is in excess of the threshold for a short-lived state.

The experiment decided upon was to measure the velocity distribution

of a free-molecule flow of gas effUsing from a small aperture in a large source

cavi ty at known temperature . Previous experiments such as are described in

Ref. 25 have verified (using a rotating mechanical velocity analyzer) that the velocity distribution in such a flow is Maxwellian provided that the source Knudsen number (mean free path in the source divided by the characteristic dimension of the aperture) is sufficiently high. With a Knudsen number of 4.0

the distribution is virtually indistinguishable from the Maxwellian distri-bution. (See Ref. 25, Figure 6). In the present tests the Knudsen number was always larger than 5.0. Thus, by comparing the velocity distributions indi-cated by the MTF method with the Maxwellian distribution one could then see any errors that could be attributed to the method itself.

This type of test was chosen not only

to

obtain a known velocity distribution but also to obtain a broad, highly-nondirectional flow with a

directionality described by a eosine law dependenee of the intensity off axis. I! MTF were used to analyze a highly collimated gas beam with a narrow entrance detector, a very small recoil (say 1% of v) directed transverse to the flow axis could cause almost all metastable molecules to miss the detector entrance, thereby grossly distorting the apparent velocity distribution (due to the re-coil preferentially removing slow partieles from the beam) and also reducing the apparent sensitivity of the method. Recoil effects are expected to be reasonably small even in room temperature Maxwellian flows, in terms of the ratio of the magnitude of the velocity perturbation due to recoil to typical molecular velocity magnitudes. For the present purposes at least, there would be no point in exaggerating. recoil effect by choosing a configuration in which the directional recoil effects was noticeable. Hence, a broad eosine law molecular beam effusing from an aperture was chosen and the electron beam was located adjacent to the apperture. In this situation almost as many

molecules are scattered into the detector as are scattered away from it. For our geometry and the lightest gases used, the effect of recoil on the measured sensitivity of the technique would be less than

3%.

The effect of the compo-nent of recoil parallel to the flow axis and to the flight base remains, of course. This type of experiment thus allows us to see recoil effects in proper perspective. That is, the effects seen in this experiment will be of the same order as those in a properly designed practical application of the technique. (The source temperature was approximately 3150K in our tests and most

applica-tions would involve flows at least as hot or fast. The recoil effects seen in our tests are then typical of, or greater than, those that will usually be found in practice).

In choosing a detector for this work it was decided that the sensi-tivity data would be most useful if it applied to a suitable comm~rcially­

available device. A Bendix Model M306 Magnetic Electron Multiplier was selected as it provided aplanar cathode, desirable in a time-of-flight experiment, of large area (0.62 x 0.72 inChes), made of any material. Tungsten was selected because more is known of the secondary electron yield of this material for metastables and ions than any other.

3.2 All Initial Test 3.2.1 The Geometry

Figure 3 shows the configuration of the apparatus used in some early tests of MTF. The geometry suggested by the arguments in Section 3.1 is in use here. The gas effuses through a very small orifice (0.25

mm)

in a rela-tively large cavity, the stagnation volume, drilled into a block of stainless steel. The gas came from a commercial bottIe and was controlled by means of a standard regulator followed by a fine needle valve. It was introduced into

the source cavity by means of a small tube in its side. The near-cosine-law molecular beam issuing from the orifice immediately passed through a pulsed electron beam and then out into a large glass chamber pumped by a 100 litrej second General Electric triode ion pump. That small portion af the flow that was directed toward the small entrance of the detector (0.29 x 0.95 cm) 15.2 cm downstream constituted the gas flow being velocity ana~zed.

3.2.2 The Detector

In these early tests a different type of detector from that mentioned at the end of Section 3.1 was being used.

An

electrostatic 14-stage electron multiplier of the form designed by Allen26 and manufactured by National Radio Company Inc. was used with the metastables being allowed to impinge upon the cathode. The cathode and other dynodes were 98.3% Agjl.7% Mg alloy. This type of nrultiplier is very sensitive to contamination when expos~d to the atmos-phere and was later replaced by the Bendix M306 type which is claimed by its manufacturer not to have this disadvantage. (Our experi:enoe supports this claim). The Allen-type multiplier was satisfactory for these initial tests, however.

3.2.3 The Electron Gun

The electron gun was the author's own design and was intended to provide relatively large curregts at the low voltages

«

100 eV) of interest for MTF. As is well known27 ,2 Aan upper limit, the space-charge limit, to the current in a low voltage electron beam is provided by the nrutual repulsion of the electrons in the beam. With a given geometry,space charge limits the beam current to a value proportional to the accelerating voltage raised to the 3/2 power. A low voltage electron gun may then be characterized by the value of the ratio, called the perveance, of the current in the electron beam it generates to the voltage raised to the 3/2 power.

The gun designed by the author is intended to have a high perveance. One way to achieve high perveance is to minimize the distance over which the electrons are accelerated thereby providing astrong electric field to overcome the nrutual repulsion effect. Tbis is suggested by the equation for the space cqarge limit in aplanar diode 28 • In units of amperes per unit area per volt 3/2 , the perveance of a planar diode with a cathode/anode spacing, 'x', is

-6

2.335 x 10 2 x

Thus, reducing the spacing increases the current density rapidly.

(3-1)

In the author's gun a closely-spaced planar diode has been formed between a stainless steel anode and a small, 3 mm diameter, oxide-coated cathode

of a type normally used in a television picture tube gun. The precision and the mechanical stability of the oxide-coated cathode permitted the relatively close

spacing of 0.5 mmo A 1 mmo diameter hole was drilled in the anode plate and by means of two small permanent magnets the entire diode was immersed in a uniform magnetic field directed normal to the plane of the anode, as cao be seen in the inset in Fig.4. One expects the assembly to operate as a planar diode with that

portion of the current that would normally be collected by the missing portion of the anode plate proceeding through the hole /orming an electron beam on the other side. The magnetic field serves to confine this beam and prevents it from spreading due to space charge repulsion and due to the divergent-electrostatic-lens action at the exit from the anode plate. The field strength is adequate

(670

G) to do this as the radius of the path of an electron moving at right

angles to such a field at the design energy

(50

volts) is

0.36

mm compared with

the nominal electron beam radius of

0.5

mmo The confinement of the beam was

verified visually by looking at the fluorescence with nitrogen issuing from the source. The fluorescence in the gas was very neatly confined to a 1 mm diameter column as expected.

The perveance of this gun can be fairly closely estimated by observing that the acceleration distance for the beam is roughly the cathode/anode spacing

plus the radius of the hole in the anode,

0.5

mm., to allow for the penetration

of the electric field into the hole. If this total distance

(1.0

mm) is put in

the R.H.S. of

(3-1)

in place of 'x' and we multiply the resulting current

den-sity by the area of the hole we get an estimati for the perveance of the re sult-ing elect~on beam of

1.835

x

10-

6 (amps./volt

3 2).

The measured value was

1.4

x

10-

0 . Figure

4

shows the voltage/beam current characteristic of this gun.

The curve follows an approximately

3/2

power law up to about

60

volts. (The

experimental curve is closer to a square law than

3/2

power.) Above

60

volts

the emission limit of the cathode is being approached and the rate of increase of current with voltage decreases appreciably.

The perveance achieved with this design is high both in an absolute sense and relative to other types of guns that produce small diameter beams. It is known that an upper limit exists for the perveance of any cylindrical

electron beam regardless of diameter, even if confined wi~h astrong magnetic

field, and that this is

32.4

x

10-6

amperes per volt

3/ 2

7.

We are thus

with-in a factor of

23

of this absolute upper limit. Practical guns normally fall

much further short of this limit. For instance, a Pierce geometry (see Section

3.3.2)

welding gun rated

1.5

amperes at

25

kV is considered a very high

perv-eance gun29 but is in fact

3.7

times lower than the present design.

A high perveance electron gun is essential to a sensitive MTF instru-ment.

This electron gun can be seen in Fig.

3.

The cathode is held in a

cavity machined into the same stainless steel blQck that contains the source cavity. The block itself is the anode of the gun and the electron beam passes through a 1 mm hole in it and then passes through the gas effusing out of the orifice. The beam is then stopped by an electrode by meana of which the beam current may be monitored. The magnetic field from t:re permanent magnets (not

shown) and hence the electron beam is inclfuned

70

0 _{from the gas beam centre}

line rather than

90

0

so that no gas from the orifice can enter the gun directly.

(The oxide cathode deteriorates if exposed to certain gases~

3.2.4

Initial Results

The apparatus just described,together with a simple form of MTF

instrumentation which we will describe separately (see Section 4) ,was used in

..

the results of these tests with helium. The 'simple theory' curve is a plot of equation (2-2), the expected result if the velocity distribution in the flow fram the source is Maxwellian. The vertical scale was adjusted to match the peak

heights of the two curves. The harizontal scale was left unchanged from that which resulted from substituting the actual measured values for the length of the flight base and the source temperature in the exponential term. The good agreement with theory in this initial test was certainly encouraging. The streng signal at short flight times (

<

75

~sec) was believed to be due to a fluorescence on the portion of the orifice plug that was adjacent to the electron beam. (Apparently a black material that plated out on this surface af ter several hours of operation was being struck and excited by electron~ This signal was present even when the gas flow was turned off and if subtracted from the experi-mental curve with gas present left aresult agreeing well with the Maxwellian curve throughout.

The source pressure could only be estimated roughly in these tests as it was obtained very indirectly from a measurement of the discharge current in the nominally 100 litre/second ion pump due to the flow from the source. The speed of this pump was also rather low 60r the purpose in that the back-ground pressure, while only about 1.0 x 10- torr, initiated a discharge in the electron multiplier a few minutes af ter the gas flow was started. (The Allen type of multiplier may be prone to this type of difficu

5

t y as the problem never

arose in later work at even higher pressures, up to 10- torr, with the Bendix magnetic type of multlplierJ This discharge in the multiplier manifested itself as a large background count rate at the detector which masked the metastable signals. The end result was that, because the discharge initiated much mare slowly when helium was f10wing in the system than with the ot~er gases that were tried at the time

(Ar,

N2), it was posaible to get a number of flight-time curves with helium but only an indication of the presence of a signal from the metas-table states in Ax, N

2•

It was decided that a different electron gun/ source geometry was re-quired to eliminate the "early" signal problem and that a pressure gauge should be provided to measure the source pressure directly to permit accurate sensi-ti vi ty measurement s • A bigger vacuum chamber wi th larger pumping speed ( ... 2000

l./sec) also became available at this time. These changes were incorporated in an apparatus that is described in the next section.

This initial success in applying MTF to a helium flow1despite these

annoying experimental problems .. was encouraging and no insurmountable difficulty had presented itself. It seemed reasonable at this point to think that the MT1 method could be made to work with many more gases. These initial results were reported in the P'ifth S~osiu.m on Rarefled Gas Dynamics in

1966

and were pub-lished in the Proceedings •

3.3

Th€! lseroved AEEaratus

3.3.1

The Geometry

still keeping in mind the gener al requirements arrived at in Section

3.1

and incorporating the changes required to avoid the above-noted difficulties with the earlier setup, the arrangement shown to scale in Fig.

6

was designed.

A much larger source cavity (5.3 cm. inside diameter) was provided so that it could be fitted with an ionization gauge (Balzers Model IMR3) to measure source density directly. The electron beam was moved somewhat down-stream of the source exit to avoid having the electron beam adjacent to any surface that might fluoresce as had previously been the problem. A mask was provided as further insurance in this regard so that the detector could not directly "see" any of the surfaces anywhere near the exit of the electron gun

or the entrance to the Faraday cup. Because the previously used

magnetically-confined electron gun was replaced by an electrostatically-focussed design, a grid was added in the flight path to prevent ions created in the flow by the electron beam from reaching the detector and masking the metastable signals.

With the magnetically-confined gun used previously, the ions were trapped in

the magnetic field that had been provided primarily for guiding the electrons. It was now also found necessary to provide a biased metal cover enclosing the detector to prevent ions from entering the detector by indirect routes (such as reflecting off the walls of the vacuum chamber). To stop the ions a small

positive voltage (+ 10 volts) was applied to the grid and detector cover.

In order to ensure that q~, the collision cross section for metastable

excitation times the detector quantum efficiency, could be accurately calcu-lated from measurements of the count rate, source density, electron beam

current, and the characteristic dimensions of the apparatus, the source

aper-ture was made in the form of a slit with its length transverse to the electron

beam axis as viewed from the detector. Figure 7 shows this arrangement as i f

viewed from the centre of the sensitive area of the detector. The slit is nearly rectangular and it is somewhat longer than the apparent diameter of the

electron beam where it intersects the molecular beam. The geometry is not

sen-sitive to small errors in the position of the electron beam in the plane nor mal to the molecular beam axis because small displacements fr om the nominal position of the electron beam do not change the characteristic distance the electrons travel through the gas.( The slit was also long enough that the same

characteris-tic distanee applied to all parts of the detector) Similarly, angular errors

are well tolerated as the electron beam would have to cross the slit more than

8

0

from the normal to the slit edges before the resultant eosine correction would

exceed 1%. Similarly, the flight base is sufficiently long (15.21 cm.) that the

small positional error of the beam parallel to the flight base due to mechanical tolerances could be neglected. Also the eosine correction for the particles that could reach the detector travelling at the largest possible angle from the nominal molecular beam axis was negligible in this geometry. When the source aperture is in the form of a long slit of width, 'h', one can easily show that equation (2-2)

relates the cond1tions in the source and q~ to the observed count rate provided

that~for the characteristic distance an electron travels through the gas, 'd',

one substitutes the quantity 'hijL'.

,t,

and 'L' are the distances fr om the

detector to the electron beam and to the source slit respectively. The quantity

'hljL' is very nearly equal to 'h' in this apparatus as

,t,

and 'L' are similar

(15.21 and 17.11 cm. resp.) 'h' was known to be 0.381 cm + 1% from a measurement

made with an optical comparator.

Figure 8 is a photograph showing the apparatus near the electron beamj molecular beam intersection.

3.3.2 The Electron Gun

In redesigning the apparatus it was thought best to use an electro-statically-focussed electron gun in place of the high-perveance magneti. cally-focussed design described earlier (Section 3.2.3). It would then be unnecessary to correct the electron path length for electron spiralling. Furthermore it was thought that in the previous design appreciable numbers of secondary elec-trons from the simple current monitoring electrode that acted as a beam stop might be trapped in the magnetic field making it difficult to estimate what the effective electron current actually was. With an electrostatic gun a Faraday cup could be used to accurately monitor the beam current without re-flecting appreciable numbers of secondary electrons back across the molecular beam. It was necessary to accept a lower perveance to obtain the advantage of

the electrostatic design. In practical applications of MTF these effects could be calibrated out and a magnetically-confined gun would of ten be very attractive.

The design of the new gun was based on the parallel-flow Pierce-geometry type described on page 452 of Ref.28 and was scaled to provide a 2 mm diameter beam. Figure 9 shows a cross section of this gun. The internal elec-tron flow in this design is parallel but the beam external to the gun can be calculated from information in Ref.28 to diverge slightlyas shown in Figs. 6, 7, 9 due to an electrostatic lens effect at the exit hole in the anode and due to space change effects. This was allowed for in designing the geometry of intersection of the molecular beam and the electron beam and does not cause any difficulty or error.

-6

3/2 This gun was expected to have a perveance of 9.130 x

èO

(amps. per volt ) from data in Ref.28 and actually achieved 0.091 x 10-. For com-parison,the perveance for the magnetic design was .15.4 times higher than this.

At first, difficulties were encountered a~ the lowest electron ener-gies used in this work (5 eV) due to the deflection of the electron beam inside and outside of the gun by the magnetic field of the Bendix magnetic electron multiplier and by stray fields created by other nearby equipment. The effect was to grossly reduce the beam current leaving the gun with most of it reaching Electrode

A

(Fig.7). Orienting the multiplier with its far field parallel to the electron gun axis and providing additional small compensating magnets solved the problem.

Electrode A (Fig.7) and the Faraday cup were used to measure the beam current and to estimate how well the electron beam was focussed. Less than 10% of the beam current was observed to be picked up by Electrode A under normal circumstances and thus a 10% error could possibly exist in our electron-beam-current measurements. This factor is included in the error analysis in Section

5.

3.3.3 The Detector

As discussed in Section 3.1~a Bendix M306 Magnetic Electron Multiplier with a tungsten cathode was used. The condition of its cathode was not controlled in any special way.