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ALANGMSCODENPAIA. At. SERTHEAIJDProject Engi neer Chief, EnergY Conversion Orench

Enery coverson BanchAerospace Power DivisionEnery Coverson BanchAero Propulsion Laboratory

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Chief, Aerospace Power DivisionAero Propulsion Laboratory

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UPST I UMWNTATIOM P=G

is. Argon and of Vibrattonal State.s of ftti

is. ~ A %j TASK

* Qnsntum PhysiLcs DivisionU.S. Butreau of Stamidaids 23018208Boulder. CO 80303 - I a P

ti. GOTOOLL6 OPPICGE WARE AND *AmOU IMPOR DpA? 01Amro Propulsion Laboratory (Al WAL/POOC) Agril 158Air Force Wright Aeronautical Laboratories (AlSO) is. wUusm@ o PAE~pWrigt-Patterson Air Force Base, Ohio 45433 32

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* Argon, Oxygen, lydrogga, flectroms, RAdiation, Excitatio Coefficient,Fraie-free Radiation, Vibration, Inftared

/1 40 -M4q POOdSL AS7NAGY (wlo ft &*I& ULsmn mE orU "I" now"m

Sisa , aein~ are reprted for tie prodeotias of free&-fre emissies by3., arq ilsr~ i I argee. Absolute Intensity tw ms at50o, m amd The electric filw to gS" dnstT rati Me varied ben0.25 to 10 to1Z mmrssdigtes eleatrom 1wie frm 1.2 to5. 4 *V. The e~sitlresUmt ierea well wItth d etoe wad*". V6 4 adasfrod aeas seetioss-for a atmtrmsfer ollwsioedtmm by tesq." N~su~mmtsof vibrattead smiatatim of di. xf a" 9; (sa'..

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,- fslemlce to a -- t.smaOWU molecul*, I'** .r for iad caj or C o

a" I SIuas wxe Obse"Wa usig & ad2

This work was perf ormed in the Quantum Physics Divisi.., U.S.

umreau of Standards, at the Joint Institute for Laboratory Astrophysics

under KIM FY1455-S 1-00626 and HIPR Fl1455-62-00604. This week ws

perf ormed dating the period October 1981 throuigh September 1962 unader

Project 2301 Task 52. "Plassa Research, Gas Discharge and Laser

Plasuma." The Air Force contract innager ws Dr. Alan Gsrscadden,

Energy Conversion Branch, Aero Propulsion Laboratory, VPA1I. ON 45433.

DTIc TAB

jAvail&billty (~3_

Dist Spca

iii

1.~~~A 0nAUMNA

IV OSILUSO * . . . * .. . . .** . . .I .. .

1. Calculated cross sections per fractional bandwidth

for the production of frea-f * pu* 0 at it.. a si

collisions of .lctrous withbAramd. , . . . .. 3

2. Tbeoretical cross section per fractional bandwidth for

the emission of 1.78 eV photons vs. electrom energy . . . 7

3. Schematic ofesuperient ......... a ..... . 14

4. Infrared emission transient near 1.3 pn from 0.05102 In At . . . . . . . . . .0is o a e. . . . .0 18 0 0 0 0 a i

5. Free-free emission cofficient per fractional

bandwidth for electron in argon vs. / .. e. g..... 20

6. Wavelength dependence of free-free emission

coefficient per fractional bandwidth for electrons

In AT .......................... 9 a aa a 21

• : o . .o .

[]I

SWUMP I . .

The aaueet described Iu this report are concerned with the

production of radiation snd of vibrationally excited molecules ubm

electron move through Woes under the Isf luence of aelectric field.

First, we describe our measurements of the production of photons as the

result of the collisions of electrons with argon stow In what ts known

as the free-free or bromstrahlung process. Second, we discos" progress

during this contract period toward the measurement of coefficients forthe vibrational excitation of the homonuclear molecules H12, D2 and 02.

The msurements of the coefficients for the production of free-

free radiation In the collisione of electrons with argon atoms were

completed said the results were submitted for publication daring this

contract period. Rather then rework this material for this report, we

have incorporated the anuscript of this paper as Sec. It. Iriefly, the,

results of this work are that we have verified to a mch higher degree

of accuracy -152 -then previously the utility of a simple theory for

predicting the magnitude of free-free radiation at smon electron suer-

Sias between 1 aid. OfeT As a result of this verification ona cam Con-

fideatly use free-free evissions a diegotic. for moderate energy

plasms, mebh as tose occurring I in b powes witching devices,

ehstged perticle beam propegatIon, ran w-U sshl ret, adIn the

Lemepher. We thsmse teosrettel wal is used toitepas

beten eeOu result (Bee,. I) and Uek sar ftbeera ei Sit

(Ref eraes 1),* the cross aectik for ti emssion of free-fre. radiation

at 500 m by electrons In arnon Is that shown In Fig. 1.* Figure 1

also shams the application of Wei tbeovp to helium; and to nitrogen

(Referenmces 1, 2).

Section III of this report describes the results of work daring

FT 82 on the development of techniques for the meurement of excitation

coefficients for the production of vibrationally excited H2, 1D2 and 02

by low energy electrons. Successful measurements of the vibrational

Kexcitation of D2 and B2 using these techniques were mae a few weeks

after the end of the FT 82 report period.

-. 7 .,. P

1.. s 1

LOW a EROy 33CTION COLLISIONS WITH Ar

I . INTRODUCTION

Interest In the Iemission of free-free radiation (bremsetrablung)

resulting from the collisious of low energy electrons with rare gas

atom has Increased with the demonstration by Pfau and Intscher (Ref-_

arenace 3) that free-free emission ts responsible for much of the visible

continuum emitted by rare gas discharges. Other emission measurements

using the discharge technique have been reported (References 4-6) along

with numerous measurements using the shock tube technique (References 6.

7)o The Inverse process of the absorption of radiation by free electrons

has been of even greater Interest because of the importance of this

energy absorption and electron heating mechanism In the laser Induced

breakdowa of pass (Reference 8). both of these topics have been It-

vestigated. in great detail theoretically (References 8-15). Finally.

there have been a tuaht -of recent epriviestal and theoretical Investi-

gations of narrw resonance structure In the free-free absorption cross

seaction (Rfeenffle.15). Becase of the narrow width and relatively

msxilotegrated L4 Ia V 1badveu of, time rosomme m to the Averaged free-

free crs seionsow' of ipiftieeoi In, far Valaftmtvy 'As energy to**-

lotion ezpeimenta, em wll not be conerned with tuns feature.

'toe prolsesot meueets of free-fre emission were catuled, cot

wsin the olootrm drift tabs teeholqus *Mdi e have sed -t.aVIome2Y

(Rf w...14-1S) lot Canneamta of exptati., asefftiete ftv

weakly radiating states of solecules. In these experiments a photo-

electrically produced electron current drifts throuA the gas Under the

action of a spatially uniform, time madulated electric field. About

one in 108 collisions of the electrons with the gas atom results in

the emission of a visible photon. A small fraction (-1 in 104) of these

photons is selected by wavelength and reaches the sensitive ares of the

detector. The absolute photon flux is comparod with that from a stand-

ard lamp and the ratio is used to calculate the excitation coefficient.

The principal advantage of the present technique over the discharge

technique used in previous experiments (References 3-6) is that the

electric field Z and gas density N can be easily varied end accurately

determined and that the theory of the experiment need not take into ac-

count electron-electron and electron-ion collisions (Reference 19). A

disadvantage of the drift tube technique in that the emitted intensities

are about 104 smller than in a typical discharge experiment.

2. TfhORY OF IXPEIKET

In this section we briefly review the results of theoretical cal-

culations of free-free radiation and of the excitation coefficients

which are relevant to this experiment. We then derive the equations

necessary to relate the observed signals to the excitation coefficients.

a. Free-free emission theory

For our purposes it is convenient to divide the free-free emission

continuum into a number of spectral beads of frequency width dv and to

regard the collision process loading to emission of radiation In this

3

band as an inelastic collision between the electrons and gas atoms. The

spectral Intensity Iv in units of photons per unit volume and per unit

frequency interval and per unit time is given by (Reference 3)

dI n nN f~ v f (C hV )e 11f (a)de kff (V )N AL * (1

Here ne and N are the electron and neutral atom or molecule densities, v

and c are the electron speed and energy, f(e) is the normalized electron

energy distribution and Qff(ehv) and kff are the cross section and rate

coefficient per fractional band width dv/v for emission of a photon of

energy bv by the free-free process. Figure 2 shows theoretical calcu-

lations of the cross section per fractional bandwidth Off(ehv) as ob-

tained by a variety of theoretical approaches for hv - 1.78 eV. The

dashed and solid curves are from the quantum mechanical calculations of

Ashkin (Reference 12) and of Geltuan (Reference 13). The solid circles

are our calculations using the very simple formula of Kas'yanov and

Starostin (Reference 10) for hv 0 e and momentum transfer cross sec-

tione used previously (Reference 17) for Ar. This formula is

4 a (c-hv/2)(e-hv)( 2 e- Qff(hv) ' 1 - a1

-6( liV 1 1/21.211 x (0 1 1 - 7-- %U(, (2)

where a is the fine structure constant (1/137), iy is the Rydbarg

(13.6 eV), c i in eV, and Q(s) is the cross section for momentum

transfer collisions of electrons with the atom or molecule. Calcula-

tions made using the formula of Holstein (Reference 11) and the total

and momentum transfer cross sections of Hayashi (Referencs 2) are shown

6 - :------,--

-25

,0

E o

26

Q<10

- Z -2?

0 z ASHKIN

C --

IL GELTMAN

1 1..

60

ELECTRON ENERGY (eV)

ligure 2. Theoretical cross section per fractional bandwidth for theeission of 1.78 *V photons vs. electron energy. The solidand dshed curves are from Geltumn (Refere.e 13) and A£skin(Reference 12), respectively. The circles and squares areour calculations based an the formalas of lA 'yafov wadSteroetin (Reference 10) end of Eolstein (Reference 11).respectively.

7,j

by the triangle& In Fig. 2. The differences among the various theoreti-

ca- cross sections shown in Fig. 2 are less than 30Z over most of the

electron energy range. Most of the difference between the cross section

calculated using Eq. (2) and those calculated using Holstein's formula

results from the fact that in Eq. (2) the Q is evaluated at , whereas

in'olstein's formula the cross sections are evaluated at e - hv/2.

The differences among the cross sections are larger near threshold,

e.g. a factor of 3 at 2 eV for Ashkin's results vs. our application of

Holstein's foruula shown in Fig. 2. The large differences between the

calculations at electron energies above 20 eV are caused by differences

in the momentum transfer cross sections used in Reference 17 and those

of Hayashi (Reference 2). As we shall see, our experiments are not

sensitive to cross sections at either of these extremes of energy. The

cross sections predicted using the older foruula of Firsov and Chiblsov

(Refe.rence 9) and the total scattering cross sections of Hayashi are

much larger than the values shown in Fig. 2.

Excitation coefficients for free-free emission were calculated from

the cross sections generated by Eq. (2), by Geltmsn (Reference 13) and

by the Holstein formula (Reference 11). The electron energy distribu-

tions for Eq. (1) are calculated using the numerical procedures of Frost

and Phelps (Reference 21) and the cross sections discussed by Tachibena

and Phelps (Reference 16). The calculated free-free emission coeffi-

cients will be presented with the experimental results in sec. 1.4.

Although not directly isefut in this pper because of the assumed

Vaweilian electron energy dtstribution, we note that hers is pod

agreement among a number of theoretical calculaloim (-e ee 6, 13,

Si

. ;- /', -, . . , . . , .' . . , . . -

14) of t ..- f me smisnon ad Abowrpto catfilciae tog electroms .is

Ai. The Maxwellian electron ema distributions am appropriate to

shock tube upei t (af erane 7) and to 4iashsmr ue , Ne ets at

high fractional loanis tio (Refereum 4).

It is important to keep In mind that thgoughout this paper we have

not followed the usual convention of expressing the f re-free emission

in term of a spectral intensity, i.e., cram section or excitation

coefficient per unit spectral bandwidth, but rather have defined cross

sections and rate coefficients per fractional bandwidth. This uncon-

ventional formulation has the advantages of yielding numbers which are

independent of units used to masure bandwidth and of yielding cross

sections and excitation coefficients which are readily compared with

cross sections and excitation coefficients for the production of ex-

cited states which emit lines or molecular bands. In our experiments

the fractional bandwidth of the detection system is typically 0.1.

b. Nodel of experiment

The si8al produced by the photon detector Sff is obtained by

integrating lq, (1) over the drift tube vola V and over frequency,, v

taking into account the optical system and detector characteristics,

i.e.,

dv 60€ff ;- dV k.(v)W)(v )D(v )fi(vW (3)

Aare fw(v) is the frctional tramemission 41 the Wtudowe beolsma the

collision cumber ad the detector, D(v) Is the k61spiniLvitW VW

aoton of the dstetor, mplifier and rnocAUS .etia a WtUaM 4*

9,

V.f icy) Is the fractional tresisation of tft interference rote

filter Inserted betwee thie collision di Ir ad the detector, 60 is

the solid ale of the detector as seew from the center of Ithe callision

chamber, and v1(r) is the efficiency of the detection syste at varies.

points in the collision der relative to dhot at the enater of 'the

chamber (Reference 16).

Equation (3) can he rristten as

-ff rO fvkfvD6fI~v V "~ (4)0 V

4 We define a geometrical factor Gff by the relation

I~ -! n uQWz/f a. dv 5

We note that Off Is equal to the C factor defined b~y Lawton and Phelps

(Reference 16) in the limit of no diffusion. Since Ionization and

attachment can he neglected in the present experiments at low E/V In

pure Ar, the electron density ne can be assumed to he Independent of

position In the electric field direction. If . sIn previouas papers

(References 16, 17), we neglect the effects of radial variations in

the electron density, then the expressionM for Off reduces to a constant

equal to the awarae of TI(yj over the active portion of the drift tuba.

This constant wee 0.97 for the Infrared detector and 0.60 for the photo-

multiplier detector.

tn doe usual me of a slow variation la two hjf(v) snd D(O) with

v compared to that of fi(v), the Integral over v In Eq. (4) am, to writ-

ten asf,(Vj)kff (4000(000~ AV. nor* OfI)V is the "ampe 1 tle

10

fMit. Arnemite cut Sod vi to the pbeas ftequegq. aast p~

the transmisson of the interference filter. 3quation (4) can aw bo.

approximaed by

where L Is the separation of the cathode and moode of the drift tawe,

lIet the current through the drift tube and e and we ar the electron

charge and drift velocity. Note that because of the absence of sigeif 1-

cast attachment or ionization, the q factor of Ref erence 16 to equal to

unity and so to omitted from Eq. (6). Masuremente at significantly

higher 3/3 would require that corrections be uade for Ionization. From

Eq. (6) we note that since the free-free emission signal increases with

the fractional bandwidth Lv /V of the detection system, one should use a

wide bend width Interference filter or a very low resolution monochrom-

tor for wavelength selection.

The reference signal S. reaching the detector from the reference.

I.e.,* the blackbody or the calibrated tungsten strip lamp, Is given by

where AD, I* the solid angle of the detector asseen from a limiting

aperture (Reference 16) of arm a,,, f,(v) Is the transmission of the

windows between the reference source sad the collision deder, * £()

is the emISsivity of the rifereace sOurce, 16W )~SMber of phAM pet

second emitted by a blacdW per usit 0f surface and Iper &it valid

angle. As discussed in Roferem s 1. t Mdats "are" ~2~

eu96 to spletaly fill their ausitgf apirtre asee ONO' doe

using sq$. (4), (5) ad (7) rather than sq. (6) for potter sew-,

racy, we find that the ratio of the free-free euissim signal to the

ref erence signal is

ma B r ,(kfv)vfi )41!ff.Mc 'ff I1L 0 ()

5r I"a 'e r f(V)t,(V)g~)()(~ivd0

If we define a free-free excitation coefficient off 41) by

off( Nd kff (Yu)/me(9

then

a ff Ot ) Cff Sff (0

where here X)L to taken to be the sma velenagth trasmitted by later-

ference filter and

Cff 1 k rear Q_ ~ '( 'f 0) H

0f I fj(CA1 )

Here

DO% D(v)Ihv md kbS~v)dv 21(%O)&

Eqmtatin (11) was se fee aulysinig the data preseted is this. paper..

Ve noe that the forma fee determiining afl~hi)/V from tineei~ee

data, I.e., 2q. (10), to very &m liM Eq. (1.7) of Laees sad 966104

(lefewesee 16) for dmteregig sb'3 Low the 02 (b1 ) utestebhs.

3. LDNTAL APFARATUS AND PRCDR

A schematic of the drift tube technique weed for determination of

the free-free excitation coefficients is shows in Its. 3. Ultraviolet

radiatios from a continuously operating 100 9 high pressure imercury lamp

to passed throu~gh, broad bend Interference filters with zmnim trawie-

sem at 1" an anid the through a quartz wIndar coated as the inside

with a si-transparest, cathode fila of evaporated Pd-Au alloy, The

resulting photoelectrons enter the parallel plate drift tube filled with

Ar at densIties from 3 to 15 X 1024 atom/a. The anode voltage is mdii-

lated so as to periodically apply a known electric field I and so pro-

duce electrons with a modulated soan enrgy. The photons emtted In the

froo-f ree transitions are detected with a photocsdctive detector for

the Infrared or with a photosultiplier for visible wavelengths. The

fre'free emission signal Is comared with the sixual. from a hollcor

cavity blackbody for the infrared and with a calibrated tungsten ribbon

lamp for the visible wavelengths.

The drift tube wsed In these experiments and ahoen in the schematic

of 7ig. 3 Is the eaus as the on used previously (References 16-16)

to masure excitation In molecular gases. The electrode spacing ws

36.4 am and the cathode diameter was 60 me. The accelerating volta&e

ranged from 60 to 3100. Y ad the total curreat In the os-period was 0. 02

to 0.09 pA. Ksrm anar reported at total Se densities of 3 to

15 X 10* m73. Argon of nominal ". 92 parity as fed Into the tube

directly from a bigh pressure cylinder.

13.

INTRINSIC Se COMPEN4SATED A TO a-

IR DETECTORAMLFECOVRR

ANODEINTERFERENCE FILTERS

STANDARD PHOTO- MULTICHANNEL MINICOMPUE

LAMPAM

Figure 3. Schematic of erperifat. Note that the asters Of the sen-transparent cathode, the anode, the drift tube and the UgLamp wxe a an wds perpendicular to the ples tite refer"snes sources and the detectors.

1Lm

The--- jknsmt -t13~ r i t~a Period at the set.-

beq4suaswar rnltsge qZ~ed to t" aoods of 25 oa p in the mes-

some",t of the 1.27 ons OWasiom from the 61,6 state of 0%. ThUS dst

raerding, period orn followe4 by a dead time of 15.9 fee cospter pro-,

ceasing of the, data. The U94id-5 2 "ld Intrinsic germialvis detector

had respospivity and 33? (noise equivalent power) of 7 x 10 V and

1 x 10-15 Vnx- 1 / 2, respectively. at 1.3 pm. The aiwia free the ode-

output of the detector for step function Infrared Input sigma consists

of rapidly and slowly rising cowmponets, the time constants of WhIch

were about 10 an and 3 a, respectively. A descr ibed in Reference 17.

this problem wa overcom by using an aplifier ontaining differentia-

tion and addition circuits which compensate for the 13 s response ad

partially compensate for the 10 soresponse. The copensaetion circuits

were adjusted for a square wave output signal using the choppied signa

f roe the blackbody as an input signa.

A inicomputer was used as a data acquisition and analysing syste.

The algnal from the copesaed lfier mes sampled every 0.1. u msn

an analog- to-digital converter. A set of data was stored In the comr-

puter and then analysed (3d soem.. 17) to rjet spikes Ass to cosmic

rays. Sixteen to thirty-two sets of data wers addItively accated

and averaged In the computer.

The msmentof the Sensitivity of the deteetiom sys"tf Re, I-

frayed ;ediatamt amkts4i Shre, eme of tbe os*ltar OW

tube, from thke detostor. A choppe Is fteft of tOR -eeMq =*SW144

blackbody emission wtth a period of 20 s. An apertur o tie~

ter s placed in frovnt of the orce .4 a from the detetar o as to

reduce the blackbody aigna. When the to"'raur of die sociuz 7

490 1 the Intensity at tihe detector wees *ON P4rable to' that observed It

the free-free, emission and v's large compared to' the thermal baekjrokled

signal. The spatial variation of the detectloo ef ficiency 11(r) wats

measured using a small diffuse light source which was scanned over the

drift region as described In Reference 17.

b.. Visible wavelength system

The detection system and reference light source for the measure-

meuts, of free-free emission at 500 and 650 am was a modification to

that described by Lawton and Pheips (Reference 16). An Improved photon

counting system was used to Integrate the photowiltip liar signals during

the on and off time for the high voltage applied to the drift tube.

The photsultiplier counts and the digitized average cathode current

were transferred to the minicomputer after a preset tie Interval. An

interference filter with 682 transmission and a band pass of 66 me 11M

was used for the measurements reported for 00 an. Mesreet at

65 nwere mede using an Interference filter with 652 peak transmission

and a bend pass of 33 am AM13. As pointed out previously (Reference

16), the final reaul ta are Insensitive to the magnitude of the inter-

forenee filter transmission. The f ilter characteristics mof ob murad

separately using a commrcial gsect-6p. omster., A mlft-alihall photom

multiplier ":'&' *traaeuitting emvlope vith a alawly wityln qh6mi

off teiemq betweent 20 add 60 M Vas WedWIh theee fiteft. g

princIpal diff iculty encountered in thae. usnsrnote was that of the

calibration of the neutre l density filters se to moduce the sign1al

from the standard lamp to values In the linear raspe of the photon.

counting systaft.

We estimate an uncertainty of t201 for the resltant mesured

excitation osefficients for both the Infrared an.d visiblea I*eemte

The significant changes In these estimates from those at Referwence 16

are the absence of a contribution to the uncertainty from a radiative

lifetim, a mnore accurate measurement of the aperture area (± 41),. and- a

sore accurate determination of the electron current (±51).

4. 113-1UX MaSSION DA

In this sect Ion we sumrize the results of masurements of the

free-f ree emission coefficients for electrons In Ar. Figure @bcow an

example of the Infrared emission signals 4hich led us to the conclusion

that the drift tube technique could he used to measure free-free emis-

eion coeff icients. This waveform, was obtained during masureents of

02 (sa1 ) production in a mixture of 0.051 02 In hr at a total gas density

Of 10 25 u73 and an 3/N of 3 x 1021 va2. The exponentially rising and

[. falling portions of this wavef ore ore Interpreted as emission from

02 4a16) molecules at 1.27 ps and yield excitation coefficients consis-

tent with those reported In Reference* .16 and 17. llhma the exponen-

tially varying portions are subtracted from the observed waveform wne Is

left. with a rectangular waveform which we Interpret as free-free

Smssion emitted In collisions between electrons and argon ato"*

1.7

diJ

V

0 2 6 202

TIE(SC

4iue4 nrrdsdoo rnintna . sfo .5 2I r

This interpretation is supported by the fact that In pure Ar only the

rectanular component of tbbwaveform was observed. Although one ox-

pects the free-free esissio Signal to follow the rapid changes in the

electron density, we mad no effort to observe he free-free emission

with 0 time resolution better than the 0.1 s value normally used in the

02 (alA) experiments. Vinkler, Nichel and Wilhelm (Refelemce 21) have

observed changes In the free-free emission from afterglows in e and Ar

on a microsecond time scale. The principal clues to the identity of

the signal were the slow variation of the signal with K/N and with wave-

length, as discussed in the remainder of this section.

The free-free emission coefficients for pure Ar at wavelengths near

1.3 pm are calculated from the observed magnitude of the infrared signal

using Eqs. (10) and (11). The averages of several runs are shown as a

function of I/U by the squares in Fig. 5. Similarly, the triangles and

the circles of Fig. 5 show the averages of results of measurements near

500 and 650 na, respectively. Plots of the free-free emission coeffi-

cient versus wavelength for /IN values of 3 x 10 "21 Vu2 (squares) and

2 x 10- 2 1 Vu2 (triangles) are shown in Fig. 6. Note that when appro-

priato corrections are made for the effects of attachment, the free-

free emission data of Fig. 4 and other data from 0 2 -Ar dxtures obtained

durin measurements at 1.3 pm are consistent with the 1.3 pm data shown

in Fig. 5.

The solid curves of ligs. 5 and 6 are the result of calculatioms of

free-free esiosiem eoefficests uti we hae made usin Eq. (2) for the

free-free miio drose seetion and the electron mrgy distributios

19

1624 I

-25

zU. Z

I.-3zZI-

w& 4,6-26

2z

_- _a 0 .50,&m

--IWl L. -027 _w -L

SI1.30±O.O7pm

0 0.6 5 ±O.02#amA 0.51O.03pm

io-22 i-2? 0o-20 io-19

E/N (V m2 )

ligure 5. OLdesioo iiet per frtonalssi beedsidctth forelectrons In arg vs. 11. The error bars show at low I/Mfor 500 and 400 m are the statistical usctitaimtl. mo-dlated with photon counting. The x and + are representativedata from leferences 4 ad 5, respectively. The solid rvescalculated values obtained using Eqs. (1) and (2). Thedashed curve ohms results calculated using 8olsteLn's fto-m (lefersece 11).

20

1.5

x 1.02 0

L.4

z zo 00.5-

0 0.5 1.0 1.5MEAN PHOTON WAVELENGTH, pm.

Pigor. 6. Wavelength dependence of fme-ftee emission coefficient perfractional bandwidth for electrons In Ar. The solid curvesare our calculated sles u hile the dashed carve is fromPfau, Itutacher and Winkler (Ref erence 22). The trianglee andsquares pre our eiiperimtal results for 313 values of 2 end3 x 10-2-L V42. respectively.

21

-7. which we have calculated. For this purpose, it Is convenient to write

Sq. (1) as

ff k 1 21j,N m- -- ( 3 ) JCO0 (e )f (e)dt (12)

We 'e liV

Here af is the umber of free-free photons emitted per unit distance of

electron drift and per fractional band width. According to Sq. (12) the

normalized excitation coefficient is expected to be independent of the

argon density. Our electron energy distributions were calculated using

the electron-Ar collision cross section data discussed In Sec. 11.3 ad

In Reference 17. The dashed curve for X. 650 -a of Fig. 5 was calcu-

lated using the Qff(e,hv) values for X. 650 em calculated using the

theory of Holstein. In this case the moment= transfer cross sections

of Hayashi (Reference 2) were used In the calculation of f(c), although

the Q,(0) values of References 17 and 2 agree for:e < 3 eV and differ by

less than 101 for e < 15 eV. The (ZfffW values calculated from the theo-

retical cross sections of Geltuan are not shown In Fig. 5 since they

differ from the results obtained with Sq. (1) by loes than about 52 for

E/I > 0.3 x 10-21 Vu2. The decrease In the calculated af1 values for

KIN greater than 4 x 10-21 VU2 is the result of an increase in the slope

of the drift velocity vs SIN data as wall as a decrease in the slope of

kff vs. 3,3 at Z/N whae Inelastic collisions ere Important (Ref greeces

16, 22). The calculated main electron energies vary from L.2 eV at

3/Ima2*5 x1O-22 I2to 5A eTat IMI x 10 2 0V62. The dashed

curve of Fig. 6 was obtained by Interpolation of graph* of calculatiome

by Pfau, Rutacher ad VIAkler (Reference 22). The lower smisiom oef-

fidgests obtained by these authors compared to those We ca]lVuaIte at the

22

ig4

III

sam 1/N appear to be the rsult of their use of so ht larger Q,(e)

values for electron-Ar collisions with a resultant lower mean electron

nergy and lower /

for I/N below 3 x 10-21 VU2, the agreement between xperiunt aad

the theory of as'yanov and Starostin (Reference 10) as shown by the

solid curves, Iswithin 1S%2 or the statistical uncertainty of the data

in spite of the fact that the bm values are comparable with the photos

energy. Although the theoretical curve calculated using the formula of

olsteain (Reference 11) lies well outside the statistical uncertainty of

our data, it is just within the confidence limits we have assigned to our

results. The relatively large experimental values and rapid increase of

the aff/N coefficients relative to theory for - 1.3 ipi at R/N values

above 4 x i0-21 Vs 2 are consistent with a/N values which we calculate

for the emission of line radiation by highly excited Ar atom. The ex-

cess of the measured signal at 650 - at 3/1 > 5 x 10-21 Vm2 varies much

less rapidly with 3/N than expected for highly excited states of Ar.

Although this discrepancy may indicate an error In the values of On(e)

at electron energies above about 10 eV, further measurements of the

spectral distribution of the radiation should be made so as to verify

that the emission at the higher 3/N Is free-free radiation.

Absolute measurements of free-fre emission signals from electri-

cal dseharge In Ar are reported for tmvelengthe from 300 to 500 -

by Vesileva, Zhdaneve, end Unateaksas Clefereuce 5) and for 480 -m by

_0ubsvski4, Kegsm and Ummaro (Peferences 4, 23). Their esult vere

aout (75 k 2OZ) sMd (100 t ,Z), respectively, *f their theoretical

,rlales, lepresenstive. eXpr stntal data obtained by these authors

23

- .1

at 500 = are shafn In 11g. 5. The 3,1 range of their low current

discharges sets the mm electron enerx In the roug of 4-5 *Y. The

agremntbetween experimnt and theory shown for these authors Is re-

merkably good when one consider, the problem of the determination of

the electron densIty and of the ef facts of gee heating on the analysis

of their experimental data (Reference 23). The resolts of Yaslleua, eL

al. (Reference 5) and of lutecher and Pfau (Reference 3) also provide

tests of the theoretical predictions of the wavelength dependence of

the free-free emission.

5. DISCUSSION

The results presented in this paper show the usefulness of the

electron drift tuthe tehnique for the measurement of free-f tee emission

coefficients for electrons In gaes. This technique makes possible mea-

surements of free-f ree emission coefficients under webh more accurately

known experimental conditions for a wide range of man electron esergies;

(1.*2 to 5.4 eV) than wom possible using the discharge technique. The

f ree-free emisono coef ficients for photon energies between 1 ad 2. 5 sV

and for was electron energies between 1.7 and 5.0e*V agree with theor-

retical predict ion to within t 152. At 650 m and men electron ener-

gies from 1. * s down to 102 OT the experimental and theoretical aree

Within the statistical Uncertainty .of lee tha * 252, ulile at mom

electron energies above 5.0 eY tie appareft deeeuybetween thesip

and experiment Increases with electron. emergy. Dmftormatolyo' theme

electron energies requi red to produce a omesrablas ignel eve toe lifte

24

-- w-..

to enable an to work in the threshold electron energy range where the

various theories are more easily distinguished. Measurements of free-

free emission at very high deainties of pure pas or absorption ma-

surements using low men energy electrons might sake possible a choice

from amog the theories. Free-fee emission measurements (Reference

24) at extremely high gas densities (-1029 m73) should provide data for

testing theories appropriate to conditions in which the time between

electron-atom collisions io comparable to the photon frequency, but

under such more accurately controlled conditions than in the laser

breakdown experiments (Reference 8) carried out at these densities.

Such high density emission experiments should provide a valuable com-

plemant to electron nobility measurements at high gas densities where

departures from the binary collision model of electron scattering my

occur (Reference 25).

On the basis of the success of the simple formula for calculating

free-free emission coefficients for argon, one Is encouraged to recom-

mand the use of this forwala for other gases for which the momentum

transfer cross section Is known. Obviously, it would be desirable to

test the formaa against experiment for other gseas, e.g., Be and KI.

25

VIBUTIOKAL UCITATIOIN OF UCKONUCIZaR NOLICMLI

Tb. objective of these experimnts .is to develop and apply tech-

niques, for the measuresent of coefficients of the production of vi bra-

tionally excited homonuclear soleculs by low energy electrons. The

molecules; of particular Interest are R2, 02- and 02. Reliable date for

the electron excitation of H2 and D2 molecules Is essential to the ac-

curate modeling of the role of these excited levels In negative Ion

sources and In hydrogen filled thyratrons and switches.* Thus, it is

known that the rate of negative Ion formation In 12 and D2 i6 a strong

function of the degree of vibrational excitation produced In an electri-

cal discharge (Reference 26). At the present tive there Is about a fec-

tor of two uncertainty In the slope of the cross section near threshold

f or vibrational excitation of 92 by electrons (References 27. 28). In

the case of D2, the only cross section data at energies of Interest for

discharges appear to be the result of an analysis of electron transport

data which, for the similar case of %,' are known to be significantly

In error at the higher energies (Reference 29). The Interest In vibra-

tional excitation of 02 a&rises from the fact that this process dominuates

tbe aeel lose by electrons In air with mean energies between 0.2 and

1 el, Ie., the amcgies of electrons predicted to be funid. Is plaalss

produced when high energ electron. beam propagte stably throug air.

At the present tim there Is a factor of two discrepsMc between t.

better of the two sets of aras section data obtained tolog eleetM

26

bem techniques (Rterence 30) and results w have derived from electron

transport data (Reference 16).

The experimutal arrangeu st ed in hee. mathsemu-ts is ideuti-

cal with that used for the infrared - u-re -ts described inSec. 11,

except for chages In the infrared detector and its associated ampli-

fiers. The basic approach to the measuremut of the densities of vi-

brationally excited homomuclear molecules is to uke use of excitation

transfer from the homonuclear molecule to a heteronuclear molecule which

radiates In the infrared. The theory of the experiment (Reference 31)

shows that the largest signals will be obtained when the vibrational

energies of the two molecules are in close resonance, as in the well-.

known case (Reference 31) of the 12(-1) and C02(001) levels and in the

less well-known cast (Reference 32) of 02 (v-1) and C82(001). In the

case of molecules in close resonance, our analysis suggests that an

optimum mixture typically contains 0.22 of the infrared emitter and

that most of the energy is stored in homonuclear molecules. Generally,

the collisional relaxation of the homonuelear molecule In the pure gas

is slow, as for N2 , H2 and 02, so that the added gas determines the rate

of collisional deexcitation and thereby the fraction of the energy ra-

diated before collisional deexcitatlon. Considerations such as these

lead to the prediction that the largest signals will be obtained for

D2-O mixtures. Smiller signals are expected for 2-00 and nf-Wo2 Utz-

tures with the signals from 22-02 and 02-052 significantly lower be-

cause of faster collisional deexcitation, an important factor in the

planning of our experimts is the availability, an a part-tim heals,

of a one-of-a-hMd, very larp arm lafh detector for easurm o of

the 002 and O emssion. Thea best detector we could purchase for the

C82 -02 measuemnts at 6.3 onu has a detectivity Which is a factor of 3O

smaller.

Ve have theref ore esphasited the D2 and" experimnts during the

closing montba of this contract period. The best way to summorie tOds

work is to no that during the two moths since the end of this am-~

tract period we have made an extensive series of mesento of the

vibrational excitation of D2 av %2 usn 00 en a2 8 te tarared

emitters. Analyses of the data to determine vibrational excitation

coefficients for 82 and D2 are now under way.

2t

SzCTION IV

VCCONCLUSIONS

The masurements of excitation coefficients for the production of

free-fres photons reported here serve to demonstrate the usefulness of

simple theories for the calculation of free-free emission In gases. On

the besi of this work and of theory and experiment at very high elec-

tron energies we have made predictions of free-free emission cross sec-

tions for several gases over a very wide range of electron energies. It

would, of course, be desirable to test these predictions experimentally.

particularly In the energy range of 20 to 100 eV where the poorly-known

effect of Inelastic collisions could result In increase of the cross

section which we estimate to be about 202. perivmntal measurements

at low electron energies in other gases would also be Important.

The development and application of techniques for the measurement

of rates of production of vibrationally excited hoonuclear molecules is

expected to provide important new information for use in the prediction

of the characteristics of gas discharge devices and atmospheric plasmas.

The work carried out during this contract period has recently led us to

successful measurements of the vibrational excitation of I 2 and D2 uole-

cules. The production of these excited states is of particular current

interest because of their importance in proposed negative ton sources

and in switching devices.

29

unmzs

1. C. X. Lee, L. Kissel, 1. I. Pratt, and I. L Tseng, Phys. Rev.A 13, 1714 (1976); L. Kissel, C. NecCullen, and . M. Pratt,"fremeetrahlung energy spectra from electrons of kinetic energy1 key 9 7 4 2000 keV on neutral atom 1 £ Z < 92," Sandia NationalLaboratories Report SAND81-1337, August 1981.

2. The somentum transfer cross sections used in Sq. (2) to obtain the

solid curves of Fig. 1 were taken from K. Iayashi, "tecommended

values of transport cross sections for elastic collision and totalcollision cross section for electrons In atomic and moleculargases," Report IPPJ-ME-19 InstItute of P1asms Physics, NagoyaUniversity, Nagoya, Japan.

3. S. Pfau and A. Rutscher, Z. Naturforech. 22&, 2129 (1967) adBeltr. Plasuaphys. 8, 73 (1968); A. lutcher and S. Pfau, Seitr.Plasuaphys. 8, 315 T1968) and Pbysica 8IC, 395 (1976).

4. Yu. K. Kagan and N. I. Kristov, Opt. Spektrok. 27 710 (1969)[Opt. Spectrose. 27, 388 (1969)1; Yu. B. Golubovskii, To. K.Kagan, and L. L. Iousrova, Opt. Spektrosk. 34 226 (1973) [Opt.Spectrosc. 34, 127 (1973)1; Tu. S. GelubovEfi, Tu.' I. Kagan. andL. L. ounova, Opt. Spektrosk. 33, 1185 (1972) [Opt. Spectrosc.33, 646 (1912)1.

5. I. A. Vasileva, Vu. Z. Zhdavona, and A. I. Knatskanyan, Opt.Spktrok. 29 664 (1970) [Opt. Spectrosc. 29, 345 (1970)1.

6. For a bibliography on free-free transitions in electron collisionswith atom and molecules see J. 1. Gallagher, JUIA InformationCenter Report No. 16, University of Colorado 1977 (unpublished).

7. IL L. Taylor and 0. Caledonia, J. Quant. Spectrosc. Radiat.Transfer 9, 657 (1969); 1. T. V. Kung and C. H. Chang, J. Quant.Spectrosc. Radiat. Transfer 16. 579 (1976).

S. C. 0. Morgan, Rapt. Ptrogr. Phys. 38, 621 (1975). Note that absorp-tion masuremnts have been made under the sch more controlledconditions of an electron bu sustained discharge In .1 and th [S. Alroy and W. U. Christiansn, Appl. Phys. Lett. 32 607 (1975).Also free-free transitions have been observed using1laser radiationand monoesergetic electrons by D. Andrick sad 1L. Leaghss, J, tby.3 1 IA59 (1976).

9. 0. 1. firsov and X. 1. ChIlisow, 3. atsp. Teor. ia. 39, 1770(1960) (Sov. Phys.-JII' 12 1235 (1961)1.

10. V. Eas'yanov and A. Starostin, 1h. ksp. Teor. Via 4. , 293 (1965)Ilov. Itys.-JT? 21 193 (195)1.

30

11. T. Holstein, private onmuaication end as quotediq R *fe 12.Equations (18) and (19) of Reference 12 are too lars by , factorof 2. lote that. Ae Vesteiw's forula is used with Ashkinstotal and momenutm transfer cross sections the agre withAshkin's Qff is very pod.

12. M. Asbkin, Phys. Rev. 141, 41 (1966).

13. S. Geitman, J. Quant. Spectroec. Radiet. Transfer 13, 01 (1973).We are indebted to S. Geltsn for tables of free-free transitioumtrix elements, which were interpolated to obtain the cross see-tion values shown.

14. T. L. John and A. R. William, J. Phys. I 6p L384 (1973); N. S.Pindsola and H. P. Kelly, Phys. Rev. A 14, 204 (1976). See, how-ever, J. 1. Stalicop, Astron. Astrophys,730. 293 (1974).

15. H. Gavrils and M. van der Wial, Comments Atom. Ml. Phys. 8, 1(1978); H. Krfger and M. Schulz, J. Phys. 8 9, 1899 (1976).Resonance structure In the free-free scattering of electrons hasbeen observed * L. Laughans, J. Whys. 11, 2361 (1978).

16. S. A. Lawton and A. V. Phelps, J. Cher. Phys. .9, 1055 (1978).

17. 1. Tachibana and A. V. Phelps, J. C bn. Phys. 75, 3315 (1981).

18. C. Ymbe and A. V. Phelps, J. Chen. Phys. (submitted).

19. L. K. Biberman and G. I. Norma, Usp. Piz. Nauk 91, 193 (1967)[Soy. Phys. Uspekii 10, 52 (1967)].

20. L. S. Frost and A. V. Phelps, Phys. Rev. 127, 1621 (1962); ibid.136, A153. (1964).

21. L Winkler, P. Michel, and J. Wilhelm, Bait. Plasmaphys. 18, 31(1978).

22. S. Pfau, A. latscher, nd L Winkler, Bait. Plasumphys. 16, 317(1976).

23. The data shown -i fig. 5 from Reference 4 are those for whichelectron-electron collisions effects are negligible, I.e., forthe largest value of p and the smallest wave of i/i u theirnotation.

24. Zvidenc, for free-free emiso n has been obtained from measurementsof electroluminesems f 'm efintllatom counters filled with Ieat dnitie war 6 1M eal and operated at 3/ of ls tbs x10"-2 V2. Sae Th. A. ftihow, 3. A. Pogoebein, V. 1. labe45*o.A. X. Rogoahin, ad B. T. Rediomo,, 1b. Omp. Tee. 712. ?, 41(1909) (Saw. Ph.-J- 30. 24 (1970)].

31

25. V. M. Atrashev and I. T. Yakubov, Teplofiz. Vys. Temp. 18,

1292 (1980) [High Temperature 18, 966 (1980)1; G. L. Bragliaand V. Dallacasa, in Electron and Ion Swarms, edited by L. G.Christophorou (Pergamon, New York, 1981), p. 83; G. R. Freeman,ibid., p. 93.

26. A. Garscadden and W. F. Bailey, International Symposium on RarefiedGas Dynamics, July 1980, Charlottesville, NC. To be published inProgress in Astronautics and Aeronautics (1981).

27. R. Ehrhardt, L. Laughans, F. Linder, and R. S. Taylor, Phys. Rev.173, 222 (1968).

28. R. W. Crompton, D. K. Gibson, and A. G. Robertson, Phys. Rev. A 2,1386 (1970).

29. A. G. Englehardt and A. V. Phelps, Phys. Rev. 131, 2115 (1964).

30. F. Linder and H. Schmidt, Z. Naturforech. A 26, 1617 (1971).

31. B. R. Bulos and A. V. Phelps, Phys. Rev. A 14, 615 (1976).

32. Few data are available regarding the kinetics of vibrationallyexcited CS2 . Our estimates are scaled from similar molecules, such88 02. CS2 deactivation Is discussed by J. K. Hancock, D. F.Starr, and W. H. Green, J. Chem. Phys. 61, 3017 (1974).

LV

32

T. -