AD-763 716

EFFECT OF H2 PRESSURE ON PULSED H2^F2 LASER, EXPERIMENT AND THEORY

Steven N. Suchard, et al

Aerospace Corporation

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Space and Missile Systems Organization

30 March 1973

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Experime ts and Theory

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14 KEY WORDS

Cluiin-reaction laser Chcnical laser Chemical laser modeling Hydrogen fluoride laser Laser

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Air Force Report No. SAMSO-TR-73-207

Aerospace Report No. TR-0073(3540)-l

EFFECT OF H2 PRESSLTE ON PULSED n2 ♦ F2 LASER,

EXPERIMENT AND THEORY

Prepared by

MK3IANICS RESEARCH and CHEMICAL KINETICS DEPARTMENTS Acrophysics Laboratory

73 MAR 30

Laboratory Operations Tim AEROSPACE CORPORATION

^ETD^C

Prepared for

SPACE AND MISSILE SYSTBIS ORGANIZATION AIR FORCE SYSTEMS CtHiAND

LOS ANGELES AIR FORCE STATION Los Angeles, California

Approved for public release; distribution unlimited

its

This work reflects research supported hy the Defense Advanced

Researc,'l Projects Agency of the nepartmcnt of Defense Wlder u. s. Ail' Force Space and Missile Systems Organization (SAMSO) Contract No. F04701·72·C·0073.

This report \'laS prepared by S • ~. Suchard, n, L, Kerber, and -- . J. S. l'lhi ~tier of the t-1echanics Research. DcpartJOOnt and r,. Emanuel of

t.l",e Olemical Kinetics Department of the Aerophysics Laboratory.

The author!. gratefully acknowledge the assistance of N. Cohen for his help with the kineti=s, arul A, Chin~, I.. n. Bergerson, J, F. Bott, H. A. Kwok, and J. s. Lesser for their assistance in various phases of this '"ork.

This work, which docum.onts resesrch carried out fran September

1971 throuah February 1972, was submitted on 31 Jam\al")' 1973 for review and approval to Capt Robert C. Bower, DYX.

~~ w. ft. wa ;lr.' flirector Aeroz:hysics LabOJ:'atory

Publication of this report does not constitute Air r-orce approval of the report's findings or conclusions. It is puhlished only for the

exchanae and stbulation of ideas.

Robert C. Bower, Capt, USAF rroj ect Officer

·ii-

ABSTRACT

Stimulated emission predictions and measurements for an H- + F. laser

are conqpared for H. pressures from threshold to stoichiometric, a range of

several orders of magnitude. Slowly flowing, heliun-diluted, 50-Torr mixtures

are initiated photolytically. TVro dilution ratios and two output couplers are

considered, and good agreement is found for time to threshold and pulse dura-

tion vs H2 pressure. Spiking, relaxation oscillations, and possibly mode

beating, features not modeled, are observable in some pulses; however, pre-

dicted intensity vs time generally agrees in pulse shape with laser output.

Observed and predicted peak intensities nearly match for low H, pressure, and

the predicted increase of peak intensity with low I^ is followed fairly well.

For H2 in the vicinity of one-tenth stoichiometric, the peak intensity data

show an abrupt leveling off, while the calculations predict a continuing

increase. This disagreement most probably cannot be attributed to uncertain-

ties in the kinetic model. All rate modifications considered have pvoven

incapable of producing a change sufficiently large or abrupt to explain this

feature of the data. Experimental results are presented supporting the notion

that parasitic oscillations cause this change in laser output.

•ill«

\

ronEWORD ... ü

ADSTKACT iii

i. wmosjcrioN i

II. EXPLRIMNTAL PROOilXJIlLS 5

III. CCMPirrUR SIMJLATION 11

IV. RESULTS AND DISCUSSICN ig

A« Pulse Sliapc 29

U. Tine to Threshold 21

C. Pulse Duration 23

D. Peak Intensity 25

V. CnNCUUSIONS 35

VI. RliPERBICES 37

APPENDIX. TW-, REACTICN BtSOH A-l

Preceilnf pi|i blink -V-

- •

PIQJRI-S

Trace Concentrations of IIF in Various ll.,:r7:lle Mixtures Before Flash Initiation f , 9

2. Plashlanp Inteasity vs Time Ohservcd Tlirouph a 290 ♦ in nn Spectral Filter 7 16

3. Observed and Predicted Effect of 112 on Intensity and Pulse Shape for II-, ♦ IS Chain Reaction Laser 20

4. Observed and Predicted Time to Achieve Laser Threshold as a Function of Ih for Initial Composition Ratio IfotfyHB " 112:1:20 and for 25 and 65t Transmitting Outnut Mirrors 22

5. Observed and Predicted Pulse Duration vs Parts l^ . 24

6. Observed and Predicted Intensity vs IU 26

7. Predicted Values of Maximum Small Signal lain vs IL for Mixtures with Initial Composition Patio ll,:F:IIe - II2:1:20 and Il2:l:40 7 27

8. Effect of Laser Tube Length Exposed to Photolysis on Observations of Peak Intensity vs IL 33

TADIX;

A-I. ileactions and Pate Coefficients. * A-2

-VI-

y

■WWiMIWIiJli i »i—TIMT-

I. IT.KOmJCTION

Measurements and theoretical predictions of stimulated emission fox an

H- ♦ F- laser are compared in this report over a wide range of initial !!,, con-

centrations. While such comparisons were heretofore unavailable, several

earlier studies of pulsed H, + F- chemical lasers have been reported.

Experimental investigations have shown the existence of lasing for several

mixtures and initiation methods, and have presented the laser's spectrtm * » 7 8 12 or time-resolved spectrum. »0»" Most of this work, however, gives very

limited information about the effect on the laser pulse of changes in mixture 11 7 composition. Notable exceptions are the works of Hess and Dolgov-Savel'yev.

Hess investigated the effect of total pressure with a fixed composition ratio

H2:F?:He - 0.33:1:40 and the effect of varying the H^/^ ratio over a limited

range. Hess also presents results of simplified rate equation calculations

for the reacting mixture but without including the effect of stimulated

emission. He finds that his experimental laser pulses terminate at times, for

which his calculations indicate substantial cowpletion of the reaction.

A previous work that gives calculations of stimulated emission for the 17 H2 + F2 pulsed laser contains no comparisons with experiment. Tt neverthe-

less identifies the relative importance of the mechanisms in the theory and

shews the predicted effects of varying initial composition, teayerature, and

the optical, cavity.

V

nw» m ill mmm*** WBH

PioneerinR conqparisons of pulsed c)iemical laser experiments with theoret-

18 ital calculations are given by Airey for an HC1 laser pumped by the reaction

between hydrogen bromide and photolytically produced atomic chlorine. We ex-

tend Airey" s approach to the more complicated iL * F, system where vibration-

rotation bands cascade and where chain-react ion pumping can extend the laser

pulse well beyond the duration of the flashlamp used for photolytic initiation«

Moreover» the larger gain of HF as compared with HC1 gives rise to experimental

complications apparently not present in the work of Airey.

19 Emanuel and co-workers formulated a multilevel chemical laser theory

and computer simulation for prediction of laser perfomance from a rate model,

thermodynamic and spectroscopic properties, and parameters describing the

20 laser cavity. In addition, Cohen gives a critical assessment of rate coef-

ficients for reactions in the f^ ♦ F^ laser system, along with a recownended

set of "best" values for these rates. We incorporated the rate model suggested

by Cohen* into the theoretical model and present the first comparison of pulsed

H, ♦ F- laser experiments with complementary theoretical predictions.

The experiments measure output intensity vs time as a function of the

hydrogen-to-fluorine ratio. The reacting mixture has a fixed total pressure

of 50 Torr with varying initial composition, and the ^/F, mole ratio is

varied from 0,0008 to 1 with the He/F- mole ratio at 20 or 40. Tvo different

output coupling mirrors are used. Traces of HF in the reacting mixture before

initiation are measured by determining the attenuation of a probe beam fron a

*The rates used in our calculations reflect some new values obtained since the preparation of Ref. 20, Details are given in the Appendix,

-2-

line-selected HF laser. Our experiments are distinguished from earlier work

by their detailed study over a wide range of initial hydrogen concentrations

and by the measurement of initial HI-' concentrations, a precaution not included

in previous work.

Experimental and predicted pulse shapes are qualitatively very similar.

Measurements and predictions of time to laser threshold and pulse duration vs

hydrogen partial pressure are in good agreement. For H-ZF, ratir.» less than

0.1, modeling and experimental results have the same trend in peak intensity

vs hydrogen partial pressure. For H^/F, ratios greater than 0.1, our calcula-

tions predict a continuing increase of peak intensity with increasW hydrogen;

however, the experimental data for peak intensity in this region exhibit an

abrupt leveling off. With H^/F, - 1.0, the peak intensity is barely larger

than at H-ZF, "0.1. This behavior most probably cannot be attributed to un-

certainties in the kinetic model. All rate modifications considered have

proven to be incapable of introducing a sufficiently large or abrupt change

in the peak intensity vs H- curve to explain the data. Supplementary experi-

mental results are presented supporting the notion that parasitic oscillations

are the cause for this df crease in laser output. This indicates that previous

pulsed HF laser work may, in part, be misleading because of the presence of

parasitic oscillations.

ii. i-vn.mjMTAL nRnannmufi

12 Experiments were performed with a flash photolysis laser apparatus.

A quartz laser tube with a 1.27-ai i,d( and 53*3 en in lonptli was attached to

aluminum window holders machined to the Brewster angle for NaCl. The tube en-

closed a continually flowing reactant mixture. A laser cavity 100 on in length

was formed by a spherical mirror of 8.8-m radius and a dielectric-coated flat

of either 251 transmittance (sapphire substrate) or 65% transmittance (silicon

substrate). The spherical mirror was gold-coated to a nominal reflectivity of

98«.

Helium (Matheson, 99.99t) and fluorine fMatheson, 981) are premixed at a

mole ratio of 10 to 1 and a pressure of 7.1 atm in a passivatod stainless steel

bottle having a perforated sting to ensure complete mixing. The remainder of

the gas sample, H- (Matheson, UO.'.vin'L), nnd additional lie is flow nonitorcd an;',

mixed with the F^-He sample in an aluminun mixing block. The F.-He mixture is

injected through a calibrated sonic orifice into the FU-He flow. As a pre- 21 caution against preignition of the mixture, tubing from the mixer to the

laser tube and from the laser tube to a carbon trap is of Teflon and aluminum.

The carbon trap protects the vacuum pump from unreacted F,. Flame propagation

from the carbon trap back into the laser tube is discouraged by an aluminun

screen flame arrestor in this exhaust line. Gases from the laser tube are ex-

hausted by a 15 ft /min mechanical vacuum pump (Kinney KC-15). Pressures are

measured with gauges (Heise) having Cu-Be Bourdon tubes.

Preceding page link

-5-

—■'■ """■mmMnj&t.M

A 14.7 uF/20 kV capacitor CSangamo), it,nitron triggered, is discharged

through a xenon flashlamp (Kemlite) with an active length of 56 an to initiate

the laser reaction. The lamp and laser tube are 5 am apart and are optically

coupled by a closely wrapped aluminum foil reflector. Flashlamp output is

monitored by means of a 929 photodiode (RCA).

Laser radiation is monitored with a Au:Ge detector (Raytheon) placed

100 an from the output coupling mirror. The sensitive area of the detector,

which measures 2 im in diameter, acts as an aperture so that only radiation

very near the laser axis is monitored. Calibration against a black body source

indicates that, for the wavelengths of interest, the detector has a sensitivity

of 0.97 V/W with a 50-0 load. Total risetime of the detector and oscilloscope

is known from other experiments to be about 20 nsec.

Precise values for initial concentrations of the various reactants are

desired. Therefore, we measure the extent of the prereaction between the H,

and F- before flash initiation and the amount of HF initially present in the

Fy- Two independent techniques are employed: the first measures the change in

the fluorine concentration as H. is introduced, and the second measures the HF

pressure in the reactants prior to photolysis.

In the first method, uv radiation from a high pressure Jc mercury lamp

is split into two beams; one beam passes through the laser where it is partially

absorbed by the F,, while the other is used as a reference. By means of a

mechanical chopper, the beams are displayed alternately to a photomultiplier

22 covered \yy a band filter, 290 ♦ 10 nr», centered near the ^ absorption peak."

-6-

The phctomultiplier output (square wave) is displayed on an oscilloscope and is

interpreted by a differencing procedure." With this technique, we are able to

measure changes of a few percent in the F., partial pressure. Under the condi-

tions of the present experiments, the F- partial pressure was found to remain

constant, independent of the H- partial pressure.

The second method uses infrared absorption to measure directly the HF(O)

concentration in the laser tube, A transverse electrical discharge HF laser is

used for this purpose. In this laser, ninety 100-ft resistors in parallel act as

pin electrodes for discharge of a 1500-pF capacitor charged to 15 kV through an

H- + SF, mixture (mole ratio 1 to 10) at a total pressure of 50 Torr. The

optical cavity consists of a spherical mirror with a 3.15-m radius of curvature

and a 2-mm hole for output coupling, gold-coated to a nominal reflectivity of

981, and a plane reflectance grating (PTR) with 7200 lines/in. blazed at 2.6 urn.

With this arrangement, individual transitions in the v ■ 3^2, 1*1, or 1-K) bands

could be selected. The present measurements used the PjCS), P1(5)> and ?^p)

transitions.

Absorption coefficients associated with each of these laser lines are

determined, in place, by measuring the attenuation of each line with a known

pressure of HF(O) in the laser tube. A dual-beam experiment is used to avoid

error because of variability of the line-selected laser's pulse amplitude

(typically ^15%). The line-selected laser beam is split with a reference beam

sent directly to a detector and a probe beam sent through the photolysis laser

tube before detection. Nominally identical Au:Ge (Raytheon) detectors are used

for the two beams. The attenuation of the probe beam is calculated from

-7-

measurements of the ratio of the probe to the reference beam with and without

HF(O) in the laser tube. Values determined for absorption coefficients of the

probe transitions are: K^P^S)] - 6.50 * O.ZUcm-Torr)"1, ^[PjCS)] - 1.92 ±

O.lSCon-Torr)"1, and K [PjC?)] - 0.27 ± O.OZCon-Torr)"1.

After calibration, the dual-beam laser absorption apparatus is used to

determine the amount of HF(O) present in the F- or in the FL-^-He mixtures

before initiation. As shown in Fig, 1, the ?- sample contained approximately

1.6 ± 0.3 mTorr of HF(O) per Torr of F-. In addition, trace amounts of pre-

reaction of H« + F- are indicated by the rising portions of the curves in Fig. 1.

/

►2 10' E

g 10 CO CO Ui QC a.

10

H2 : tF2: 20 He

J I l—U I I l_L

H2: 1F2: 40 He

10 r2

10

H2

J I UJ I L_L_L .0 .x-2 .«-I ,«0

I0W 10 10

H.

10^

Piß. 1. Tr.-icc Concent rat ioas or l!T: in Various lu^rllc Mixtures Ueforc T:L'isli Initiation

III. CCMPUTF.R SMJLATION

The chemical laser computer similation used is described in Ref. 19, but

a resum£ of its features is presented in this section. Rate equations are used

to represent the chemical kinetic and stimulated emission processes occurring in

a representative unit volume within a Fabry-Perot cavity. All processes are

assumed uniform throughout the cavity. Rotational equilibrium at the transla-

tional temperature T is assumed. Only the transition with maxinun gain in each

band is assumed to läse; this is always in the P-branch. Combined Doppler and

collisional broadening (Voigt profile) is modeled. During lasing, the gain at

line center is held constant at the threshold value for the cavity; the gain

profile is assumed to saturate homogeneously.

Reaction of the H? * ^2 * ciiluent mixture is represented by:

1. Photodissociation of F-

F2 ♦ hw —► 2F

2. The H2 - F2 chain

F •■ F^^SäHFO) ♦ H

H + F25=iHFCv) ♦ F

3. Vibrational-translational (VT) deactivation

HF(v) + M 5^ HF(v-l) * M

H2(v) ♦ M 5=^H2(v-l) ♦ M

4. Vibrational-vibrational fW) quantum exchange

HF(v) ♦ HP(v') ^^ HF(v*l) ♦ HF(v'-l)

HF(v) ♦ H2(v') ÄHF(v*l) ♦ H2(v'-1)

Preceding pic« blank -ii-

5. Dissoc iat ion-recombinat ion

F2 + M^e-M + F ♦ F

H2+M^=tM + H + H

HF(v) +M^=iM*H + F

This reaction system is approximated by the 79 reactions and rate coefficients

listed in the Appendix. Except as noted, the rate coefficients are those sug-

20 gested by Cohen.

Photolytic initiation, i.e., dissociation of F, by the flashlamp, is

modeled by the F-atom production rate

-jl-ZZ^Ct) |l -expR^)) CD

where I(t) is the flash intensity normalized to have a maximum of unity, Z. is

the maximum output of the lamp in moles oT photons per unit laser volume per sec,

and Z7 is the product of a ncan absomtion coefficient and absorption length.

The chemical reactions are written as

L a .N n i L ß,;N. n i (2)

where N. is the molar concentration of species i. a . and ß . arc stoichionctric i ri ri

coefficients, and k, and k „ are forward and backward rate coefficients. r -r The rate of change of concentration N(v) for vibrational level v is given

by

^ - ^rad(v.J) - >rrad(v.l,JL) ♦ ^(v) (3)

•12.

/

where ^ ^(y,J) is the rate of change of concentration resulting from lasing

from v + 1 to v. Lower level rotational quantum numbers J and J. are selected

as those giving maximum gain for transitions v + 1 ■* v and v -► v - 1, respectively.

The rate of change of N(v) resulting from chemical reactions Af-uCv) is

*chM ■ E feri " »rl> Lr ^ r

where

^ - K y ^0rj ■ Bri

The laser cavity is assumed to have a uniform photon flux with active

i.-ridium length L and mirror reflectivities RQ and R.. Lasing initiates for any

v ♦ 1 -»• v band vhen the gain for the highest gain transition of that band is

equal to the threshold gain ath , where

1 a thr 21 inCR^) (5)

The gain is assumed constant over length L. As only P-branch transitions need

be considered, the gain of a transition with lower level v, J is

a(v.J) "^ uc(v.J) ♦(V,J) B(v,J)[|f4^ N(v + 1. J - 1) - N(v,J)l (6)

The wave number of the transition is w (v,J), BCv,J) is the Einstein Isotropie

absorption coefficient based on the intensity, and N. is Avogudro's number. Line-

broadening constants ana resonance constants used in the Voigt profile at line

center ♦(v,J) are those of Ref. 19.

•13-

The Boltzmaiin distribution of the rotational populations is given by

N(v,J) - N(v) 2J-li2 exp f-hcEVkrl (7) qf cn L

where values of the rotational partition function (/ (T) and rotational energy

lij are from the data of Mannf et al. Planck's constant, the speed of light,

and üoltzmann's constant are denoted as !i, c, and k, respectively. The

energy equation for a constant density gas is written in the form

picPi f" a? -" "L - ? ür "i (« where C is the specific heat at constant pressure and H. is the molar enthalpy

of species it p is the pressure, and P. is the output lasing power per unit

volume. The pjwer is

5 PL(t) ■ Eo hcNA »c (v.J) Xrad (v,J) (9)

Numerical integration of Eqs. (1), (3), (8), and the equation of state de-

termines the pressure, temperature, and species concentrations until, at some

time t. and for some value J • J0, the gain on a given vibration-rotation transi-

tion reaches athr. At this time, the laser pulse begins. Then Eqs. (1), (3),

(S), (8) and the equation of state are solved for the transient temperature,

pressure, concentrations, and, for each band that is lasing, output power and

active J. During lasing, this value of J shifts sequentially to larger values

because of HF concentration growth and temperature rise. Lasing terminates when

all o(v,J) become less than othr.

.14.

The laser power P. (t) in fiq. (8) is the sun from both mirrors of the

cavity. The power extracted from mirror lU is

prt . U - Bfl] ,-__ P, (t) 0 [1 MR0/V

i/ZH1 - (RoV1721 (10)

Initial conditions and model parameters are determined to reflect con-

ditions of the experiments. In these experiments, the laser has an active

medium length of 53.3 cm. The optical cavity is fonned by a gold-coated mirror,

with nominal reflectivity of 0.98, and one of two partially transmitting

mirrors — a 25% transmitting dielectric-coated sapphire flat or a 65% trans-

mitting ar-coated silicon flat. Other losses in the cavity were lumped with

the 981 reflecting gold mirror for an estimated value R. - 0.9. The output

mirrors were taken as RQ - 0.75 and 0.35, respectively. Initial concentrations

were matched to those of the experiment, including the effect of prereaction

(Fig. 1). The normalized flashlamp profile was determined (Fig. 2) and taken

as I(t), At these low concentrations, the mixture is optically thi.i, i.e.,

Z2NF ** 1' hence» &!• C1) beeves

dNp

ar^W^ (11) Therefore, only the product Z.Z- is necessary to model the flashlamp coupling.

Because an independent measure of Z.Z. was not available, we determine this

parameter to be 2.1 x 10 sec" by matching the computed time for the laser

■v

>-I-

(/)

z w 1-z

TIME- ~ l--1 0 fLSec Fig ,. 2. Hashlanp Intensity vs Time Observed

111rough a 290 .:!:.. 10 run Spectral r:iltcr

-16-

/

to reach threshold to the measured time for the case H-F-Iü: - 0.1:1:20 with

the 25t transmitting output mirror. This procedure seemed most satisfactory,

as time-to-threshold predictions for this case depend on only a few parameters

(Z.Z-, pumping rates, and 0^.-.).

•17-

\

<

IV. RESULTS AMP PISQISSION

In the sections that follow, the results of our experinental and theo-

retical investigations are compared. Interpretation of the character of the

laser pulse is given in regions where experiment and theory agree. In regions

of disagreement, the probable cause for deviation of experiment and theory is

isolated and additional experimental results are presented to enhance the inter-

pretation of the disagreement.

A. PULSE aiAPE

Experimental intensity vs time records are found to exhibit three types

of pulse shape. Pulses for vexy low H, have peak intensity at the beginning

and then an irregular decay to zero. Additionally, these records have pro-

nounced transients superposed on the basic pulse shape. Pulses for experi-

ments with somewhat larger H- rise from threshold to peak intensity in several

distincf steps. After peak intensity, there is a smooth decay to zero. Addi-

tional transients are less pronounced in these records. Finally, for R^ near

stoichicnetric, the pulses have small initial steps and a smooth rise to peak

intensity and decay to zero. Records of the observed pulse shapes with the 2SI

output coupler for F^/He - 1/20 and 1/40 are presented in Fig. 3. Also shown

in this figure are predicted intensity vs time pulse shapes. In order to facili-

tate comparison, the intensity scale for each computed pulse is selected so that

the peak intensity is approximately the same fraction of the ordinate as the

observed pulse; the time scales are identical. locccpt for the transients in the

experiment, tl« main features of these pulse shapes arc predicted quite well by

Preceding pue blink -19-

- — -

CO P ■ -

o L II \ \

HHHi CO - ^^^^^^^B o " - HH o 1" ^fl o _

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11 13 $1

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•20-

the theoretical mcx.lel. Tile tine location nf the ohscrvetl laser pulses is somewhat

arhitrary hccause, in sOI'le cases, rlashlamr triggering Has tlelaycd relative to

oscilloscope tri~erine. In the ne.·t sectj on.c; He find that, Nhen these trigger-

ing problems were averted, the observed ll.lK1 predicted tir:tc locationS '"ere in g•>Od

agreer.tent.

With the knowledge that observed and predicted pulse shapes are similar, we

selected three pulse characteristics for quantitative comparison. These are:

time from onset of the flashlamp until laser thresh.~.>ld, pulse duration measured

from laser threshold to the point in the tail of the pulse where the intensity

has fallen to one-tenth its peak value, and the peak intensity during the pulse.

For brevity, we refer to these parameters as: time to threshold, pulse duration,

and peak intensity.

B. TIME TO TIDmslkJLn

Observed and predicted values of time to threshold for F z!He = 1/20 and

for both output couplers are in good agreement as seen in Fig. 4. As expected,

the time required to reach thr~shold increases as the initial H2 decreases. For

small Hz• threshold is not achieved. Synchronization difficulties caused erratic time-to-threshold data for the F2/He = 1/40 mixtures; however, results similar to those in f-ig. 4 were fotmd for these mixtures in earlier experi.Jilents.

Chester and Hess26 compared theoTe~ical and experimental values of time t o

threshold for a pulsed HF laser based on flash photolysis of MoF6

+ H2 mixtures.

They found good agreement over a r:m~c of 1 tixturc pres sures. Detailed predictior. ,. \·

of other features of the laser pulses wns not included within the scope of their ~,

stwy.

-21-

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-22-

c. i'iiit:;i. iHii'Ano:.

In vii\. .1, observed and prc.lict.fvl rnUsp durations are cnnparcl as a func-

tion of II., for the four cases stiUlc', TIP overall ayrocnont is p.ocxl. Tor

H2:F2:He ■ Hj'.l'AO and the 25% output mirror, there is excellent agreement.

The main trends are the same for the other cases, but there are some deviations

between theory and experiment. For example, the theoretical point in Fig. 5d

that is quite high stems from a condition that produced an output with a double

spike; the small second spike results when, in the calculation, the gain on

another vibrational transition achieves threshold. The pulse duration of the

first spike at this same concentration is in good agreement with experiment.

An upper limit on the laser pulse duration is imposed by the time required

to consume the FL, i.e., the reaction duration. The reaction duration is nearly

constant for small H- where the heat release is negligible. For increasing H-

above ^/F- "0.1, however, there is a decreasing trend to the reaction duration

caused by thermal acceleration of the pumping rates. This decreasing trend

appears for both experiment and theory in all four cases of Fig. 5.

The laser pulse is actually shorter than the reaction duration. A finite

time interval of pumping occurs before lasing begins, and deactivation processes

quench the laser before the reaction is complete. In the model, the dominant

deactivators are F (Reacts. 44-50), H (Reacts. 23-29), and HF (Reacts. 37-43);

their relative importance depends on the initial HL/F- ratio. For H-ZF, 0.01, deactivation by HF and H is more

important.

As H2 is increased, a "knee" is found in the theoretical prediction of

pulse duration and is most evident for the F2/He ■ 1/40 mixture with the 651

CD CO

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•24-

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output, coupler, 'lliis "l.nco" occurr i.licrc tlic conputation changes abruptly

fron prcdonination of losing on \mls associated witli the pumninp. reactions

F + IL (Reacts. 11-13) to lasing on all bands associated with the chain and,

hence, a much higher degree of cascading. This abrupt behavior was not ob-

served experijncntally.

The following section presents evidence that leads us to the conclusion

that parasitic oscillations rob power from the observed laser beam, especially

in the regime ^/F- > 0.1. Based on the good agreement shown in Figs. 4 and

5, it appears that time to threshold and pulse duration are little affe:ted by

these parasitics. This is in marked contrast to the behavior of some ruby

lasers where the onset of parasitic oscillations causes premature quenching of

27 the observed laser beam or of some glass lasers where parasitics reach thres-

28 hold first and quench the observed beam altogether.

D. PliAK L'.TIINSITY

In Fig. 6 are presented the theoretical curves and experimental data for

peak intensity vs parts H- for the four cases studied. In interpreting the

experimental records, an average is used when transients occur in the vicinity

of the peak intensity. These plots show that, below one-tenth part H-, theory

and experiment have the same trends. Above this H. pressure, the agreement

vanishes; theoretical peak intensity continues to increase with JU, while the

experiments exhibit an abrupt leveling off. The best agreement is observed

in Figs. 6c and 6d and the poorest agreement in Figs. 6a and 6b. For a fixed

H^/F, ratio, the small-signal gain is lower for mixtures represented in Figs.

6c and 6d than those in Figs. 6a and 6b as shown in Fig. 7. The influence of

gain on these observations will be discussed again shortly.

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Fig. 7, ProJlctod VAIUM of Maxlrun Sruill Signal Gain v$ H, for Mixtures with Initial Conposition Ratio H;JF!HO - H-iliM anJ H,:l:4n mm —

-27-

A similar, but nore severe, experimental trend is reported by Hess for

cases witb a conposition ratio lL:F_:Ile ■ 11^:1:40, pressures near 160 Torr,

and a 99-cm laser tube. His data show that, on incrcasinc the IL/F-, ratio from

0,33 to 1.0, the observed peal; power decreases by nearly a factor of three.

The discrepancy shown in Tig, ö is investigated by an evaluation of the

effect of uncertainties in rate coefficients for the deactivation mechanisms.

As a limiting case, we examine the effect of an extreme change in the rate for

VT deactivation of HF by H- (Reacts, 30-36). In place of the rate coefficient

given in the Appendix, which is based on experimental data, we hypothesized

a largest plausible rate. This rate was chosen as three times the HF - IIP VT

rate (see Reacts. 37-43). As shown by the dashed curve in Fig, 6e, this

hypothetical fast deactivation causes a moderate reduction in the predicted

peak intensities for the larger values of IL. The fast deactivation effect

is not large enough to account for the experimental results. Moreover, it

occurs gradually; whereas, the experiments show an abrupt leveling off of

the peak intensity,

17 Other variations in rate coefficients were considered. It was known

that variations in the pumping reaction rates, pumping reaction distribution,

or in the HF - HF and HF - IL W rates within reasonable bounds were not

capable of predicting the behavior indicated by the experimental results

in Fig, 0, The effect of variations in the IIF - F and IfF - II VT rate

coefficients was also examined. Multiquantui deactivation l

mixtures for F2/lle ■ 1/40 and 1/20 reach temperatures as high as 870oK

and 1230oK, respectively, at pulse termination, the uncertainty in

the temperature dependence of the major mechanisms is not sufficient to

explain the experimental results. » These uncertainties in the

kinetics showed less pronounced effects than that illustrated by the

dashed curve in Fig. 6c. We therefore conclude that it is improbable

that a purely kinetic explanation exists for the leveling off of

experimental peak intensity shown in Pig. 6,

Explanations for the sharp level in}, off of peak intensity may also

l>e sought in the area of undesired optical phenomena. The actual laser

is more complicated than assumed in the theory ml is subject to

several problems. Spatial nonuniformity of the reaction and concomitant

gradients of refractive index may increase cavity losses, as well as

steer the beam away from the detector. A host of parasitic lasing modes

is also conceivable because of the high gain of the medium and because

the reaction occurs within a tube whose wall and windows are not

perfectly transmitting. Because parasitic oscillations are known to

occur in solid-state lasers under high-gain conditions, we have

given them first attention.

Parasitic modes are thos^ that reflect off the tube's wall and are

regenerative. We will limit our discussion to two possible types:

circumferential or whispering modes and axial modes. Nonparasitic modes

are referred to as fundamental (either longitudinal or transverse)

modes.

.20.

The likelihood of parasitic modes is shown in Vig, 7 by an order of

magnitude comparison between the largest small-signaj. gain of the medium

and the gains required for threshold for several nodes of oscillation in

our apparatus. Threshold gains for wall grazing nodes with either near-

axial or Circumferential paths are obtained by use of expressions including

Presnel law estimates of losses suffered in near-grazing reflections at the

laser tube wall (Fig. 7). In making these threshold estimates, we neglect

gain saturation due to carpeting modes. Likewise, we do not account for

mode-coupling effects that could cause a lowering of the threshold gain for

31 32 certain parasitic modes. •

Figure 7 shows that variation of the IL pressure serves as a convenient

way of varying the peak small-signal gain over several orders of magnitude.

As expected, peak gains are larger for the less dilute mixture. As IL

increases, the small-signal gain for either mixture becomes nearly as

large as the threshold for circumferential modes and much larger than

the threshold values for either fundamental or near-axial grazing modes.

The fundamental modes of lowest loss saturate the gain down the center of

the laser tube but not near its walls. A competition for this outer

annulus of high gain exists between fundamental modes with greater losses

(i.e., high-order transverse modes) and near-axial grazing modes, either

of which can degrade the intensity along the laser axis. Grazing modes,

once oscillating, are particularly detrimental to our comparison (Fig. 6),

because they extract energy when passing near the tube center that might

otherwise be emitted in a longitudinal mode that contributes to the

28 29 measured intensity. •

-30-

Measurenents of the output intcasity of flash pliotolysis IJF- ♦ H-

and MoF, ♦ 1L lasers as a function of the total sample pressure by 7

Dolgov-Savel'yev have shown a similar behavior. As the sample pressure

was increased, the laser output intensity for the MoF, ♦ 11. mixture

was found to first increase with pressure, then decrease with further

increasing sample pressure. Similar results were found in the UP, ♦ H.

system. These observations can also he explained in terms of parasitic

oscillations. Tliis is because an increase in sample pressure corresponds l

to an increase in the gain of tV system if wc assume that their samples

are optically thin to the flas'il.'tip radiation and tliat 'Vrppler broadening

is controlling the gain. Once the system gain has reached a critical

value, a further increase in sample pressure will lead to the onset of

parasitic oscillations and a decrease in the fundamental mode laser

intensity.

Supplementary experimental results arc given that serve to isolate

further the nature of the discrepancies in Fig. 6. In one set of

experiments, total small-signal gain is varied by a change in the length

of the active medium. In another, the effect on laser spot size of gain

coefficient variation is studied. Both experiments lend credence to the

idea that nonideal optical behavior is present.

Previous studies indicate that parasitic oscillations are difficult

to avoid when the total snail-signal gain exceeds a critical value. Thus,

experiments that vary this gain by changing the length of active medium

are expected to be informative. Such experiments are performed by the

•31-

I

use of masks outside the laser tube to diange the length of the photolyzed

rnediun. Measurements are made of peak intensity as a function of the IL

pressure with illuminated lengths of 10, 5, and 2.5 on, with a laser mixture

of Is/"0 ' ^Z20 an^ 251 output coupling. Hie results of these measurements

are shown in Fig. 8, In the lO-on case, the trends are much the same as with

the 53.3-an length. With the 5-cm active length, intensity leveled off at

1/10 part iL, hut no decrease in power vas observed on further increasing

the lU. Data for the 2.5-cm active length agree more closely with the theoret'

ical trend, because they exhibit a nonotonic increase. Also displayed in

11* Pig. 8 are the results of l!ess. The trend observed in this laser peak in-

tensity agrees well with the pattern of trends we observed, ■

The effect of decreasing the length is reflected in the theoretical

model through Cqs. (5) and (10). For mixtures capable of attaining gains well

above threshold, the variation of peak intensity with length is dominated by

VJC[, (10). Therefore, the model implies that the peak intensity should vary l

proportional to L for II- > 1/100 part. This trend is shown by the data in

Fig. 8.

With an active laser length of 2.5 en, a moderate leveling off of the

peak I IF power was observed. A possible explanation for this effect, the t i

threshold estimates of Fig. 7 notwithstanding, may be the existence of cir-

cunfcrential modes. These modes can oscillate independent of the laser

length, as they are dependent only on the gain and the reflection angle from

1 *We have converted the power data of lief. 15 to intensity by dividing by a detector area of 0.0314 an2.34

•32-

/

I04 1 1—IT

CM E o

10'

>-

^102

=3 O

a. 10'

1 1 TT

o PRESENT RESULTS • HESS F2/He • 1/40

P-160 Torr FLASH ENERGY 630J

- o

10° 0.001

i V—r-r s \

L = 99cm\ -

Ls 53.3 cm o o -^

o 0

L=l0cm o 0 0 oo

L = 5cm o o o o o 0

Ls2.5cm 0J) rs OOO -

J LJ. I I I L-L J I L-L Q0I 0.1

PARTS H2 1.0

Fig, 8, liffect of I^iscr Tul)C Ungth Exposed to Photolysis on Ohscrvations of Toal; Intensity vs H,

•33-

the inner surface oT the laser tube, fMnperinj» laser ncxles have previously

been observed in a Sm liopoJ CaP7 ^.n!ler(, of radius I ntn nnd solid-state

. , 35,36 toroids. *

In a second set of experiments, the offect of j*ain variation on laser

spot size was studied. V.'e define the lasor snot size as the largest diameter

of an iris, external to the laser cavity, throuph "hich the laser beam passes

with uniform intensity, i.e., beam power varies as the square of the radius.

As the flashlamp energy increases, the fraction of r. molecules dissociated

to F atoms increases. Consequently, incrrnsing flnshlanp energy increases the

rate at which the 1L + P,, chain runs, anil this increases the small-signal gain.

It was found that, as the flash energy incmased from zero, the laser spot

size increased in diameter. A further increase in energy did not effect the

spot size, and finally, at high flash energies, the spot size vas found to

vary inversely with flash energy. Tie incrrnsr in spot size at low flash

energie3 can be explained by an increase in the number of fundamental laser

modes that reach threshold as the flash energy increases. V.'e expect parasitic

oscillations to compete with these modes, however, and ultimately cause the

spot to decrease.

•34-

v, crruir-ioNS

Stimulated emission from an HF chemical laser is shown to be well pre-

dicted by a theoretical model that is based on chemical rate equations and

that assumes constant gain and rotational equilibrium. For an FL ♦ F- chain

reaction laser initiated by flash photolysis, comparisons of pulse shape, time

to threshold, pulse duration, and peak intensity show excellent agreement con-

sidering the approximations of the model. Where cavity transients are observ-

able, the constant gain predictions agree with a smoothed curve through the

average of the transients.

Detailed study of the effect of li? partial pressure on laser performance

is a useful diagnostic technique for identifying the presence of undesired

optical behavior. With this technique, we have shown the regime H./F- > 0.1

as one where parasitic oscillations are believed to occur and to dominate the

interpretation of the experiment. Supplementary calculations and experiments

tend to confirm this. Spatially-resolved laser output measurements are needed

to delineate further the character of parasiti:s. On the basis of these re-

sults, we are led to the conclusion that previous pulsed H- ♦ F. laser inves-

tigations may, in part, show misleadingly small laser outputs because of para-

sitic oscillations.

n. REFERENCES

1. N. G. Basov, L. V. Kulokov, Ye. P. Markin, A. I. Nikitin, and A. N.

Oraevsky, JETP Lett. 9, 375 (1969).

2. 0. M. Batovskii, G. K. Vasil'ev, E. F. Makarov, and V. L. Tal'rose,

JETP Lett. 9f 200 (1969).

3. 0, M. Batovskii, G. K. Vasil'ev, and V. L. Tal'rose, International

Symposium on Chemical Lasers, Sept. 1969, Moscow.

4. V. S. Burmas'"/, G. G. Dolgov-Savel'yev, V. A, Polyakov, and G. M. Churaak,

JETP Lett. 10^ 28 (1969),

5. G. M. Chumak, G. G. Dolgov-Savel'yev, and V. A. Polyakov, International

Symposiun on Chemical Lasers, Sept. 1969, Moscow.

6. N, G. Basov, E. P. Markin, A. I. Nikitin, and A. N. Oraevsky, IEEE J.

Quant. Elect. QE-6. 183 (1970)..

7. G. G. Dolgov-Savel'yev, V. A. Polyakov, and G. M. Chumak, JETP 31, 643

(1970).

8. N. G. Basov, V. T. Galochkin, V. I. Igoshin, L. V. Kulakov, E. P. Markin,

A. I. Nikitin, and A. N. Oraevsky, Appl. Opt. 10, 1814 (1971).

9. N. C. Basov, V. I. Igoshin, E. P. Markin, and A. N. Oraevsky, Kvantovaja

Electronika 2. 3 (1971).

10. L. D. Hess, Appl. Phys. Letters 19, 1 (1971).

Preceding page blank •37-

11. I,. :>. Hess, .1. C'icn. Pliys. 55, 24^ (IP?!).

12. S, N, Sucluml, P.. W, r. ^ross, and \ "■, '.Mttior, Arnl. P'iys. Letters 10, 411 (1071).

1^, G. c. IJolgov-Savel'yev, v. r. Zharov, Yu, S. .'.'opianov, and r>, M. Diimak, JLTP, 34 34(1972).

14. .T. Wilson and .1. Stcnhenson, Apnl. !'!.r-;. Letter-, 2M, f.1(in72).

15. L. P. Hess, .T. Aprü. Phy... 43, UrStV?.).

16. J, l.'ilson, M. 'iorthan, and P. Lcvis, "i^rr nrennnte! at Tliird Conference

on Chemical and Molecular Lasers, St. Louis, Mr>,fMay 1P72.

17. R. L. Korl>cr, G. Lmanuel, and T. '*>, : ittier, "Cmputer ^:odolinß antl Paranetric Study for a Pulsed H? * r-> Lisor," Applied Optics 11, 1112 (1072).

18. J. R. Airey, .T. Chen. Pliys. 52, ]r.r. (1070),

10. C. Ijuuuiel, W. I>. Ad;ins, and I.. I>, Turner, rL.SALii - 1; \ flicnical Laser

Computer Pngrim, Toclmical Report TK- '172(2776)-1, Tlie Aerospace Corpora- tion, LI Se^untlo, California (15 Mar l''"2).

20. N. Cohen, A Review o( Rate Coefficients for Reactions in the H, - F» Laser ■System, Technical Report TR-oi72(277n)-:, Die Aerospace Corporation, El r.c£undo, California (3 Sept 1071).

21. A. V. Grosse and A. 1). Kirshenhaun, T. Mtys. Soc. Tapan 77. 5012, (1955).

•38-

22. P.. K. Stoimcnbors and R. C. "oftol, .T. ,\n. Cliom. .Soc. 78, 001 (1956).

23. S. N. Sucliard and L. D, !Jernorr.on (to I'O published in Rev. Sei. Instr.).

24. M, C, Lin and IV. H. Creen, .T. f'en. Phys. 53, 33S3 (1070).

25. D. Ii. Mann, U, A. Thrush, '). R. Lide, ..t, .7, Ball, and N, A. Acquista,

J. Chom. Phys. 54, 420 (1061).

26. A. Chester and L. n. Hess, 1133: .T. Quantum Electronics. QD-S, 1 (1072).

27. A. C. Siegnan and .1. W. Allen, Il.lii: T. Quantun Ulectronics, 'f.'l, 386 (1965).

28. I)„ I'üss and P. Mockcl, Z. ^.,,■lt^^rrorsch ."n.-i, 40 (1065).

29. I). Ross, Z. .'Jaturforsch 2na, 264 (1065).

30. I/, R. Sooy, R. S, Conijlcton, H, K. Dohratz, and 17. K. NR, Proc. Third Intl.

Connress on Cjiicint, riectronics. vnl. 2, ed. P. Crivet and N. Rloemljergen, Coliinl)ia University ^rcss, NCT-; Yorl: (]%4),

31. R. J, Collins and J. A, 'liord-ialno, Proc. Tln'rd Intl. Concrrss on Qgant.

lilcctronics. ed. P. Hrivot and :.'. Bloenhergcn, Colunhia 1'nivcrsity Press, New York (1964), pp. 1239-12 to.

32. C, M, Varma, IliLIi J. Quantum Electronics. QE-5. 78 (1060),

33. P. A. Miles ami J. VI, Lotus, II11 T. Quantun Electronics. QIM. 811 (1968).

34. L, l), Itoss, private comnunication (1071),

•30-

35. C. r,, j;. rHirrctt, I/, Kaiser, an.! W, L, Uotvl, l'!iys. Pev. 124, 1807

(1%1).

3(). H. I'oss anJ r„ Cchrcr, IVoc. of inET, S2, 13.r.:: (1064).

37. P.. V/ilKins, ^ntc Tarlo Cnlculntions of "cnction Rates and linergy DistriNutions Among Reaction Products, I. F ♦ 11^—IIP + H, Technical Ilcport TO-ni72C277f))-4, The Aerospace Corporation, El Segundo, Calif. (April 11)72).

38. J. F, Itott and N, Co!?cn, .T. Oww, Pliys. S5, 3698 (1071).

30. B. A. Pidley and I. IV. ». Smith, Chen. n'iys. Letters 0, 4S7 (1071).

40. I). Rapp anJ P. Unglandor-Goldcn, T. f^m. PMys. 40, .r.73 (1064).

-40-

\

APPIINDIX. T^. PIACTTO?: SYSTT-»'

The chemical kinetic model and corresponding rate coefficients used in

this study are listed in Table A-1. The rate coefficients are mostly from a 20 compilation prepared by N. Cohen." Several additional studies have appeared

recently, however, and the present rates reflect the new data. Implications of

the difference in rates between the table and Ref. 20 are not serious and are

covered in the footnotes of Table A-I.

Some of the catalytic species listed at the end of Table A-I are multiplied

by a constant. This is equivalent to using a rate coefficient whose value is

larger by this factor, 'lac tlicmodynanic data were token fron the JANAP (Joint

Army, Navy, Air Porcc) pidillcatirn (Ustributcd by the Dow Chcnical Corporation.

The themodynamic data of excited «pecios, ''ovovcr, v.'crc generated at this

laboratory.

A-]

Table A-1. Reactions and Rate Coefficients

Reaction No. RMCtlon*

1 F^Mj^F.F.:^

Z HjCO) ♦ Mj^^H ♦ H ♦ Kj

V .,10S HFCvj ♦ MjssiH • F ♦ Mj

n6 F ♦ HjWssiHFd) ♦ H

u F * l!2(0)^±HF(2) * H

13 F • HjOD^HF») * H

u F ♦ H2(0)5=*HF(4) ♦ H

15,16 F ♦ HjWmMWi ♦ H

17ü H ♦ F^=fe HF(1) • F

18 H * I-2:=±1{K(2) * F

19 H ♦ Fi»=*PO(3) ♦ F

20 H ♦ Pj5sSHF(4) ♦ F

21 H ♦ F2^tHF(5) • F

22 H • F2s=±HF(6) • F

Zi, ...207 HF{v) » MjjstHFCv • 1) ♦ Mj

X.. .,,3(.S HF(v) ♦ M45^HF(v - 1) » M,

J7, ..,4J» *(v) ♦ MjS^IIHv - I) ♦ Mj

44° HF(1) »^»-«=(0) »^

45,, HF(2) ♦ ^5=*HF(1) ♦ H^

46,. ...»» HF(v) ♦ ^5=*HF(v - I) ♦ ^

51,. ..,57ln tff(v) * ^«r'-KKv - 1) ♦ H,

5«,. ..,63 2HF(v)«a&HF(v • 1) * W(v * 1)

64,. ...6« HP(v) ♦ WCv * DjriHFCv - 1) ♦ HP(v ♦ 2)

69,. ...72 »(v) ♦ »(v • 2)^=tHF(v • I) ♦ W(v ♦ 3)

731, HF(1) • HjtOj^iHFCO) ♦ Hjll)

T41 fffC) ♦ HjCOlssiWCl) ♦ KjU)

7511 WC3) • HjCOj^ilKl) • HjO)

761, HF(1) ♦ HjCDssi*») ♦ ^(2)

7711 HF(2) • ^(Da^HFd) ♦ Hj(2)

»,1 9 HjW ♦ t^s^HjCv • n • ^

Rate Coefficient*" k(3noT

k, . 1.0 . lo".35-" 9.64 « in*13

k., - iolV1-0 3,33 X 10"15

k^ - 1.5 . lO1«!-1-0.»»-«-^» v.0 7 5,93 X 10'M

fcy - 2.7 . lo",1-* 1,«4 XIO12

hi • »•»*« 6,01 xIf12

fc,, ■ 1.63^

k.l4 - 4.0 . lO12^-".3«

k.jo-v " »•* " «l11^-15 v - S.6

^ - 6.3 • lO12.2-48

3,01 xin12

6.14 xin>n

2.82 XIO13

1.12 xm11

^ ■ l-Slk17 H, - 2.7k17

40 - S-3Jk17

^1 * 5-S6k17

1.70 xm11

i.

k.T4 • 2.0 . wV*5

1,30 x in12

1,04 x 1012

k 7$ -1,3. io¥-s

k.77 • 1.4 . loV,s

k,^ - 2.5 - 10-V-5 v - 1,2

o.rs x lo11

6.24 x 1012

7.27 x 1012

1.12 x 107

/

Mnrr-s "nn TABI,H A-F

Catalytic species:

H, ■ all species 7 2

M? - L "F(v), 2.5 £ H7(v), 20H, F, F-, He v-0 v-0 ^ ^

KL - H 3 2

v-0 7

"4 " K "2^

a v-0

l^ - F2, l.SHe 7 2

Mo - E "W. 4 L H7(v), H. He, F, F. 8 v-0 v-0 Z i

'Rate coefficients k+ aiK? k_ designate forward and backward rates, respectively,

with units in terns of moles, cm , and sec. For each rej

coefficient is determined from the equilibrium constant.

3 with units in terms of moles, cm , and sec. For each reaction, the missing rate

The quantity 6 - - (10 /RT), where the temperature T is in 0K and R is

1.987 cal/mole-0K.

4 For reactions with more than one value or v, the into coefficient at SOO'K

is given for the smallest v.

A-5

-**•« x

vibrational energy above the gronnl state is denoted as F, .

'Overall punping or Heactioas (11) throun'1 O7') «V«' (17) t'iroiiRh (22), ami

tlieir distribution './it!i v(v>l) are tbo s.-ino as Pof, 20; however, based on

calail.ations by lulKinsv these reactions do not populate v - 0.

7 ^O Hie SSIIT rate calculated by Cohen" is used. Tils rate is so large that it

was assumed independent of v.

8 Rates of Reactions (37) through (dii) arr r^scntinlly the sane as Pef, 20 at

3nn0K; hoi-zcver, we have used a slightly different tonporaturr variation that

reflects an earlier interpretation of the data of Rof, 38, Hie efficiency of

FL in deactivating !IF(v) is assuned to lr tho snno as ÜF-IIF at high temperatures,

TJe ratio of kjjjk.prk,,- is .assuned to be t'io sane as the rates for deactivation 44 45 4f)

of IICl(v) by Cl, v ■ 1, 2, 3, in Ref. 39. V\c rate k4. is suggested by Cohen"0

for all v; we use k., for v>3.

"Die efficiency of T7, in deactivating IF(v) is assned the same as Ar, and the

3S I IF (v)-He rate is taken as 1.5 tines tho \r rate.

1L_ ""i ihe alternate rate suggested by Cohen" based on t'ie Harr» ami linglander-rolden

40 theory is used after a roevaluation of fio cxr