REPORT SD-TR483-69

Modeling Study of a cw HF ResonanceTransfer Laser Medium

MUNSON A. KWOK and ROGER L. WILKINSAerophyuics LaboratoryLaboratory Operations

The Aerospace CorporationESegundo, CALf 90245

30 September 1983

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Kkrtlumd Air. Iorc Raset N. Mex. 87117

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. ;AL .1

This report was submitted by The Aerospace Corporation, El Segundo, CA

90245, under Contract No. F04701-82-C-0083 with the Space Division, Deputy for

Technology, P.O. Box 92960, Worldway Postal Center, Los Angeles, CA 90009. I.

was reviewed and approved for The Aeroepace Corporation by W. P. Thompson,

Director, Aerophysics Laboratory. 1st Lt Steven G. Webb, WCO, AFSTC, was the

project officer for Technology.

This report has been reviewed by the Public Affairs Office (PAS) and is

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This technical report has been reviewed and is approved for publication.

Publication of this report does not constitute Air Force approval of the

report's findings or conclusions. It is published only for the exchange and

stimulation of ideas.

teve bb, 1st Lt, USAF ess, GM-15, DirectorProject Officer West Coast Office, AF Space Technology

Center

A

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RuPNT wummeal 2. GOVT ACCESSION NO. 3. RECIPICNT*S CATALOG NUNSERI. TIL5edS010 . Type op REPORT 41 PERIOD COVERCD

K MODELING STUDY OF A CW HF RESONANCE

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Munson A. Kwo!k and Roger L. Wilkins F04701-82-C-0083

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IS. SUPPLEMENTARY NOTES

X IS. KEY WORDS (Co.nu.wo on revina side it neocsar and identify by hieck mmbar)

chemical lasers HF optical reso~nance transfer laser modelingcontinuous lasers HF optical. resonance transfer l.~sersHF chemical kinetic modeling hydrogen fluoride chemical kineticsHF chemical kinetics infrared lasersHF coutinuous chemical lasers lasers

noratieknciamoe j ofe fl n gaeu medium o a cv HF optical

resnane uanser ase (UTL)hasbee deeloed nd sedtoexavane theprouect ofthis type of laser for efficient performance. Model development

hsrequired the generation of HF(v1, J1) + HF(v2, J2 V-V, R-R,T, and V-Rcossecticns by classical trajectory calculations and by surprisal methods.

These cross section packages have been val-dated using non-ORTh, HF kineticsexperiments, and the entire ORTI. medium model has been validated by modeling

0040ACIIUILE) 1473 UNCLASSIFIEDSE9CURITY CLASSIPICATION OP 'TMIS PAGE (When Daom Ented)

-S . . . .. . . . . . . . . . .

UNCLASSIFIEDSCVuMT, CLAW PICATION OP T11s PAG(f bI DW. heft.

Is KEY IISCIDS (GOhked.)

optical resonance transfer lasersrotational-to-rotational processesvibrational-to-vibrational processes / .

" . AU5TWACT (C.wieud)

the reported experimental results of past ORTL experiments without anyadjustment of the kinetics packages.

The subsequent study observing the effect on small signal gain by varyingcontrollable paraetets, such as pumping laser radiative flux and fluxdistribution, flow velocity, flow density, and HF mole fractions, hassuggested a regim for most efficient ORTL operation, in which overallefficiency could reachs 0.50. For this regime, pumping laser fluxes shouldexceed 5000 W/42_with a spectral pattern in which most of the power is inPi(5), P1 (6), P2 (5), and P2 (6). The medium should be operated at slightlyelevated temperatures to enhance kinet.ic-pumping rates with characteristicvelocities allowing any ORTL fluid element to remain in the pump beam nolonger than 200 sec. At that point, V-R processes begin to degrade the gain.A potential protemn gas heating due to the absorption of pump radiationcan be nullifi by the add4ion of high specific heat diluents.

/,/

/

UNCLASSIFIED

SMCURITY CLASSMVICATION OF T1IS PAGIVIf" Dl Enruu.)

PREFACE

This study could not have been performed without the major assistance of

aren L. Foster in programing and computations. We thank George Judd for

adapting the NEST program to our problem needs. We appreciate the continuing

discussions with Dr. L. Wilson and Dr. D. Drumond of AFWL/ARAC. Finally, we

thank Lydia Hamond for typing the manuscript.

Aocession For

NTIS GRA&IDTIC TABUnanno-'ncedJust ification

ByDistribution/

Availability Codes

IAvail and/oriDist Special

. ~ ~~~ . . . . .. .

1 .

CONTENTS

PIU.AC. ............ 11, NTltDUCTION....... .............. ......... .................. 9

2. MODEL DEVELOPMNhT,,,.......,..... ..... .......... ,.,.. 11

A., Fundamntal Concepts............. 11........ . I

B. Collisional Energy Transfer State-to-StateCoefficients for HP 4 ...... ................................. 17

C. BF OIRTL Noe ........... ............ .. 23

3. MODEL VALIDATION AND SIMUJLATION OF HUGHES ORTL ............. ........ 31•A. Nmber Densiltes .. 31

B. Static Temperature............................................ 33

C. Smll Signal G.Ln........................................... 33

D. Sensitivity of ORTL to Collisional Processes......... . .•. • 37

4. OITL ODEL PARAMETRIC STUDIES.......... ............................ 41

A. Pump VeDistri...tio ............ Fw ................... ... 42B* Pump J-Distribution.. 42

C. Pump Flux Variations. ...... .. 8............ .................. 48

g. Best ea ....... . .. .... ,,..,,.. ...... 52

RRRZNiU seses................e............. ................ ........ees~s 59

APPENDICESA. Kinetics Kquatior L1sting.....s....... ................ 61

B. Gain and Absorption Cofficientse........................... 79

,I. -.,.....

7- .A' 70w -; T.- .-

4

FIGURES

1. HF energy level diagram showing an optical resonance pumpedtransfer laser syste.o°° ........ ....... ... ................ 13

2. R-R,T endothermic state-to-state rate coefficients forT.300 K predicted using surprisal analysis..°.....°...° ....... 19

3. ORTL model comparison to the rotational relaxation ofHinchen and Hobbs ............................ 21

4. Excitation of 97(v-1) and HF(v-2) .................................. 24

5. ORTL model schematic with double pass pump laser coupling.......... 27

6. Comparison of ORTL model and experiments of ORTL mediumHF(v) number densities as a function of HF mole fraction ....... .° 32

7. ORTL medium static temperature as a function of HF mole

8. Small signal gain coefficients as a function of flow distance Xor tie t. Initial conditions as shown in Table 6................ 35

9. Small signal gain coeffic- ents as a function of flow distance Xor tim t. For %H-0.01 .. ......... .............. 38

10. Case as in Fig. 8, but with V-V rate package removed............... 40

11. Small signal gain coefficients as a function of t or X atnearly four-fold slower flow velocity.......................... 43

12. The dependence of peak gain coefficient on pump flux Jdistributiou.. .. • ...... .. •.................... • ....... 45

13. The effect of gas heating on static temperature in the direction

of O1'L gas flow with pimp flux J distribution as a variable.°..... 46

14. The shift to higher J in the peak gain P (J) ORTL transitionas pump flux J distribution shifts to higner J ................ 47

15. The dependence of peak gain coefficient on total pumpingradiative flux .......... °...... ............................. 49

16. The effect of elevated initial static temperature, 700 K, onP2+1 (J) small signal gain cofficients......... 4.................... 51

5

-- -

i i - ' -' ' -- . , _- ;- - '- - - " "

TABLES

1. O TL Site... ...... .................... .................... 15

3. 11 + M4 Collision Processes v ( 2, J ( 15 ........................ 20

4. Comparison of Measured and Miodel Transfer ates.................... 22

5. Comparison of Quenching Coefficients at 'a300,K for theHF(v 1) + HF(v2-O) ys e . , . . . . . . ... . .. . . . . . .••••, 25

6. ORTL Input Paamte........ ....... . ............................ 30

7. Observed Lasing Compared to Model Gain Coeffic:ent................. 36

8. Increase in ORTL Mediuu Beat Capacity .......................... 52

7

1. INTRODUCTION

The cv Optic&l Resonance (pumped) (collisional) Transfer Laser (ORTL) has

been proposed as a device for improving high power lasers operating at HF or

DF? wavelengths. These lasers have been studied experimentally by Wang et

a1.1"5 In optical resonance transfer lasers, photon energy frcm a high flux

optical source is resonantly absorbed on vibrational-rotational transitions by

a passive, nonreacting, molecular gas. A ppulation in the upper state is

rapidly created. Collisional steps follow to access the part of the internal

NenerV manifold in the excited molecuie favorable to population inversions and

high gain.

The ORTL device is unique in that Wing at al. have concentrated on HF or

DF a the optical acceptor of pumping photon flux. They "rave introduced the

idea that the lasing molecular species need not be the same as that of the

* optical acceptor if rapid collisional transfer exists. They have conseqviently

invented many new lasor devices. They have also found that the HF (or DF)

ORTL, in whic the acceptor and lasing species are the same, has a potential

for high overall efficiency. Namely, a large fraction of the photon flux from

a pumping HF laser can be converted efficiently into BF ORTL power. This

potential high efficiency combines with features attractive to chemical laser

system. Properties conducive to better beam quality performance include pre-

mixed operation, laminar subsonic flow, and ORTL lasing oui viedominantly one

vibrational-rotational trancition under Wang's conditions of demonstration.

As one attractive feature, the ORTL medium is recyclable.

The object of this report is to examine the crucial iesue of RF ORTL

efficiency prospects under reasonable conditions of operation. These condi-

tions my differ markedly from those of the laboratory demonstrations. The

focus will be ,on the applicabilit4 if ORTn as a bean improvement device for an

BF high power laser system. It should be stressed that the results and

conclusions in this report will not necessarily apply to DF CRTLs, or to

sendius and low power applications of thv concept.

9

The performance of the ORTL medium depends on a detailed understanding ofthe individual collisional transfer mechanis involving H1(vl,jl) + IIP(v2 ,J 2 )

Cenergy transfer on a chual-by-channel basis. This is because the pump

radiation is quite state arecific on such an HJ(v, J) bam. In one sense,this current study is then an extension of the previous kinetic studies of

have been closely examined theoretically and experimentally and in which cod*

simulations of past experimental studies have been conducted using the appro-priate developed kinetic rate data. The objective of theme code studies has

always been the improvement of vital cross seztion data needed for laser

modeling.

In Section 2, the ORTL model code development TY1ill be described, includ-

ing validations of the listed rotational-rotational (R-R) and vibrational-

vibrational (V-V) kinetics packages by compariseons with selected non-ORTL ex-

perimental. results. In Section 3, the simulation of the reported2 ORTL medium

is presented an a further Illustration of our model validations. Successful

comparisons of HF number densities, static temperature, and zero-power gains

* are made. The important relative contributions of V-V and R-R transfer in the

production of inversions are also examined in Section 3. In Section 4, we

carry out parametric studies comparing various regims of UP pumping laser

flux distributions whiie varying medium initial conditions. For reasons of

code siqilitity and econoqy, our principal diagnostic in these sectious will

be the smll signal gain computat-4ons. Parametric regime suitable for ana O3TL medium as wall as the limiitations of the concept as a high power HP

device are discussed. The conclu*sions are summarized in Section 5.

10

2. 4ODRL DMVULOM4KNT

IP subeection A, we vill discuss some fundamental concepts needed for an

mderr tending of an EF (or DF) ORTL. Central to our studies is the

collisional energy transfer processes in the ORTL. The state-t,-state rate

co,,fften~ts computed by Wilkins for use in the modeling will be brieflyramartzed In subsection B. In subsection C we will provide a description of

the B ORTL mel.

A. FUNDAKINTIL CONC PTS

A cv EF ORTL system consists of the following elements:

a. Source of pumping laser radiation

b. fremixed medium (Be/F) In transverse flow

c. Mirror structure for coupling the pumped laser into the medium

d. ORYL resonator and beam extractor

a. ORTL gas handling systems

An important feature of an BF ORTL imdium with no chemical reaction in that

the same active F molecules can be used more than once (recycled) within the

mirror structure of the pumped laser. The effective umber of cycles has

significant influence on the overall ORTL efficiency. From a system view-

point, the reusability of the axhaust gases appears attractive.

This model describes aspects of the firs. three listed elements of an

ORTL system. The model predictions, which will be compared to experimental

results, are small signal gains of selected spectral lines, HF(v,J) number

densities, and medium static temperatures for appropriate spatial locations.

The advantage of a model, of course, is to enable us to make excursions eco-

nomically in chcices of parameters that are difficult to execute experimen-

tally in a short time.

The current version of the model will not fully assess the effects of

recycling. However, evidence for that behavior will be seen in our computa-

t tions and supporting analysis. To full7 simulate the effects on power

4". ,. . ,, .-- " , - . ,. ""-, , " ,

extraction from the mdium and from recycling, one needs, at least, a laser

model with Fabry-Perot mirrors.

1. THE ORTL CYCLE

An BY energy level diagram is shown in Fig. I describing the (v, J)

levels oc the molecules in the ground electronic state. HF molecules are

raised from the v a 0 state by the resonance absorption of P1 4 0(J) photons

from the pusping laser. The HF(v - 1, J) molecules can then be excited to the

v - 2 state by a second resonance absorption of Pi (W) laser photons from the

pump laser or by the following V-'V collisional energy transfer process:

HF(vI - 1,Jl) + HF(v2 - lJ 2 ) * HF(vl' - 0,Jl') + H.(v 2 ' - 2,J21) (R1)

Successful ORTL operation requires that lasii occurs at wavelengths

longer than those of the pumping transitions. A partial inversion with a sIg-

nificant gain must be developed. In the steady state under proper conditions,

the ORTL transitions being optically pumped shcmld be nearly saturated without

appreciable gain. The collisional dc-excitatiou of molecules to lower J

levels (or shorter wavelength regimes) leads to other HF transitions withabsorption. These transitions would tend to have populations in the lower

state larger than those in the upper state because of the Inclination of the

medium toward rotational equilibrium.. The collisional excitations of mole-

cules to high J states occur as a result of V-V processes [Eq. (I) I or rota-Iional-rotational, transitional (R-R,T) transfer processes [(!q. (W2)] or

combinations of both types:

HF(vl, Jl) + M + HF(v1, Jl') + M; (Jl' -Jl) - +1, +2, +3, +4 (R2)

At higher J, the partial inversion has the best chance to develop. The cross

sections for collision channels represented by Eqs. (UI) and (R2) should be

large for an efficient ORTL.

After ORTL stirnlated emission has occurred, the HF molecule must be

recycled to (v,J) states where optical or collisional pumping can again

12

I%

W- 7

E im ) ___12 18237

15,000 _____1

5___1 20 2

PUMPING R-RT _ 15W _VR10_ 2

J-5 -PJ-6 ___15_____

._ _-R_& 14- 20J=6 -&J*7 ______

10 1

SECONDARYF LASER___KINETICS

01

Fig. 1. H D eneRylvldagaOhvn a pia rsnnepmpdta e

'*01

y 13

Y . .. . .

occur. Important channels for this behavior are the backward reactions of Eq.

(R2) and perhaps the backward reactions of Eq. (RI) tf the v - I state is

involved after the ORTL lasing on the P2 (J) transition. The R-RT processes

are favored since they are exoLheric.

The backward processes of Eqs. (RI) and (R2) can also be construed to be

loss mechanisms affecting the efficiency of the ORTL lasing transitions if

they influence the populations of the upper states. Other secondary state-

scrambling or loss mechanisms might 'e V-V processes involving v1 - ! and v2 =

2 (or v1 - 2 and v2 - 2) and V-R,T ?rocesses:

:' 4,"F(vJ . ) + M + HF(v I Jj 1 ) + M (M)

where

M - HF(v2 ,J2 ), diluents

and

Vi-V 1 ' -+l,2,..,v 1

The V-RT processes will generally be too slow to be of great importance in an

ORTL cycle. In contrast, these mechanism would be quite noticeable in a

chemical laser description.

Ideally, pumping flux rates and collisional rates should be sufficiently

large so that one characteristic cycling time is considerably less than the

1'*1 time for an ORTL fluid element to pass through the flux fields of the pumping

laser.

2. DEFINITIONS OF EFFICIENCIES

Three efficiencies have been defined to describe ORTL performance.2 The

ORTL input efficiency is:

"1 . power absorbed by ORTL medium (HO

nt incident pump power

This quantity is highly dependent on the optical thickness of the transitions

in the medium absorbing the pump laser lines. The power conversion efficiency

is:

14

in coherent ORTL power (E2)c power absorbad by ORTL medium

and the outcoupling efficiency is

outcouple ORTL power

no co erent ORTL power

The overall efficiency is

nT n I x nc x no (M)

3. THE SIZE OF AN ORTL DEVICE

An estimate of the size of an ORTL device compared to that of a chemical

User device can be made by assuaing a steady state condition and an input

efficiency ni of unity. For a hypothetical chemical laser at 1000 W and

stated values of the laser power per unit area of the nozzle face, 8, and the

specific power, a, Table 1 presents estimates for the minimum required HF

Table 1. ORTL Size

Chemical Lase. (1 kW) Tm (80 Torr 0.05 HF Fraction)

__I I cycte 100 cycles

Photon flux (sec-1 ) 1.5 x 1022 HF flux(sec7-) 1.5 x 1022 1.5 x 1020

g (W/cm2) 50

a (kW sec/kg) 300

( S m/ls e ) 2 .5 at t o t al (g m ls e c ) 2 .5 0 .0 2 5

v(cM/sc) V(cu/sec) 1 3 10

A(cu2 ) 20 A(cm2) 125 1.3

15

.-- - - - - - - - - - - - - - - - - - ---..

.. ...

flowrate, total mass flowrates, velocities, and nozzle size for both the pump

chemical lascr Ani the ORTL. It is also assumed that the ORTL is operating at

80 To"- with a 0.05 HF mole fraction and a 0.95 He mole fraction.

Table 1 illustrates that for an average 100 recycles of ORTL HF molecules

within the pump laser fluT,, the ORTL nzzle will be about the same size as

that of a chemical. laser nozzle. By this thinkitg, an increase in the number

of effective cycles will corresroadingly reduce the ORTL nozzle size and the

flow requirements compared to the pump laser.

The overall efficiency nT of 0iRL will typically be less than 0.50 so

that in this situation, only about half the power will be produced. On the

other hand, the operation of ORTL at high prussures makes the exhaust recovery

problem much easier.

A similar ezauination of size of the ORTL system reported by Hughes

yields the data in Table 2.

Table 2. Hughes HF ORTL

Chemical Laser (0.8 kW) ORTL (80 Torr, 0.05 HF Fraction)

Photon flux (sec-I) 1.2 x 1022 HF flux (see-'1) <1.2 x 1021

(ga/sec) nom. 5 ;t (gm/mec) 0.2

V (cm/sec) -105 V 5 x 103

A (cm2 ) nominal 10 A (cm2 ) 1.8

It is apparent that a recycling chain on the order of 1-10 must be operating

when the fluxes are compared. Input efficiencies as high as 0.35 were report-

ed by the experimentalists; therefore, the number of cycles is around three at

best. For the approximate 0.38 cm width of the laser beam in the direction of

16

S' )

ORTL flor at this ORTL velocity V, the single cycle tim is on the order of

20 ucec. The comparison of the pump laser nozzle exit area with that of the

ORTL is somewhat misleading because the o of the pump laser is not high.

For Hughes' operating condition, estimates can be made of the character-

tstic time for radiative and collisional processes. These can then be co-

pared to the so-called cycle time. Typically, the pump laser flux ph on a

sin3le spectral line is 200 Wcrn2 and the radiative cross section arad On the

absorbing line Is 5 x 10-17 ca2. The characteristic time T rad (for radiative

pumping) is then

-1

rad e hT -( 7 x 10- 6 sec

Single channel V-V or R-R,T collision processes will have cross sections

ranging from one to five collisions in probability. At pressures of HF at 4

Torr,

coll -(coll NHF) - 1 0.25-1.2 x 10- 6 sec

Characteristic times for ORTL lasing would be on the order of cavity life-

times.-su-croseconds. It seem clear that the limiting process of an ORTL

cycle in this experiment was the radiative pumping process because the photon

fluxes were too low.

B. COLLISIONAL ENERGY TRANSFER STATE-TO-STATE RATE COEFFICIENTS FOR HF + M

The state-to-state rate coefficients used in the model have come from two

basic calculations: the classical trajectory studies by Wilkins 9 and recent

computations by Wilkins 10 using the surprisal analysis approach. To date,

there are no known measured absolute cross sections on single channel HF(v,J)

M *! M processes which include some knowledge of the product (v,J) states. Thic

17

44

-'...:--. I.- . . . . .

degree of refinement is necessary in the modeling of an optically pumped

medium in which the pumping fluxes excite very specific (v,J) states. To

validate the camputed state-to-state rate coefficients, the best available

experiments were modeled using versions of the ORTL model code. Some compari-

son with experiments is, of course, necessary to determine the surprisal parsr

meters when using the information theoretic technique.

A full listing of the kinetic equations used is given in Appendix A. The

details of state-to-state rate coefficients computed by the surprisal analyses

approach and their applications to modeling will be the subject of another

paper. 1 0

Sowi indicntions of the complexity of the kinetics are summarized in

Table 3 where the types of HY(v 1,J l ) + HF(v 2 ,J 2 ) processes are described. The

number of channels possible for each type of process is also given. For the

simple V-V energy transfer processes represented by HF(v-1) + HF(v-1) +

HF(v-2) + HF(v-0), an astonishing number of channels is possible when all pos-

sible initial and final J states less than 15 are considered for near-resonant

conditions IAKI C 400 ci - 1. To render the ORTL model manageable, we event-

ually limited the charnels listed to JIEI 4 100 c=7 1 . The subtleties of the

many channels of tbe V-V type of process would seem to be extremely important

in an ORTL medium model since the rate coefficient of each channel is typi-

cally quite large. There are fewer specific channels for the R-R,T processes,

but they are also extrenely important for particular ranges of J because therate coefficients are also quite large [order of (1014 cm3 /mol- 1 sec -1 )].

To properly write equations for V-K,T processes some product J values

greater than 15 were considered.

In Fig. 2, the t-R,T endothermic state-to-state rate coefficients are

plotted as a function of initial J for v - 1, J'-J - +1 through +5. The wide

range of values for the coefficients can be seen. Implicitly, one can see

that there Is a limitation to pumping very high J levels in an ORTL medium

because the rates become too slow.

a. 18

1014 T-300 K

-St 1013 AJ +2

< 1012A •+

--

"j -+4

10 11mAJ.+

100 1 34 569 10 11 12 13 14

14 Fig. 2. R-R,T endothermic state-to-state rate coefficients for T=300 K pre-, i dicted using surprisal analysis.

19

Table 3. HY + M Collision Processes v 4 2, J 4 15

Type Equation Type Channels Order k

R-i, T EF(VtJ 1 ) + HF(v 2,J2 ) + EF(v 1 JI') + HF(v2 tJ2 ) cm3/(mol sec)

JlI-Jl = *1,*2.1,3,*4 225 1014

V-V HF(vl-lJ 1 ) + D1(v 2-lJ 1)

+ SF(vI'-O,JI') + SF(v 2 -2,Jl1 ), I 1<500ci- 1 30000 1013 - 1014

V-V IElOAR<0oci 1 426

V-IT HF(vIJ 1 ) + HF(v 2 ,J2 ) + Wp(vI',JI') + Up(v2,J2 ) 340 1012

1 VALIDATION OF f-R,T STATE-TO-STATE RATE COEFFICIENTS

The validation of the R-R,T state-to-state coefficients is performed by

simulating the experimental results of Hinchen and Robbs, 1 1 ' 12 In which an

97(v-l, Jl) state was excited by photon pumping from a short pulse HF

laser. The cubsequent collisional excitation of neighboring HF(v 2-l,J 2 )

levels was carefully observed by the. Using the kinetic equations developed

for the ORTL model, we initially placed an amount of HF(v,J) population out of

Boltzmann equilibrium into an HF(v-I,J) state. The density was determined

with the aid of reported pulsed laser properties in a manner similar to that

to be discussed later. The results are shown in Fig. 3 for the case in which

the photolytically pumped state is HF(v-1, J-3). These results are further

summarised in Table 4. It can be seen that our kinetic simulation is qvAte

good for J'-J - *1, *2, and *3 over a range of photolytically pumped initial

states. The agreement for J'-J - 4 is not as successful. These slower rates,

however, are not as important in an ORTL simulation. Details of this work

will be given later in another paper.13

2. VALIDATION OF V-V STATE-TO-STATZ RATE COEFFICIENTS

The V-V state-to-state rate coefficients have been validated by simu-

lating the experimental techniques reported in the works of Osgood, Sackett,

and Javan1 4 and Bins and Jones. 15 Neither are really highly sensitive tests

20

I~~-' Z'

LOU01C Q~ 0-0

00 ~0

00

an

II 999.010 10000&

a a* 3A

LU0 000

a a

LU- 00000I00 cc

f0 0 o1.0 )-It10 3. 1- MONWKkI NI

a 9IFig.an 3.0 77lmdl cmaio-t h oainl rlaain o ce n

Dobbs. Phot lytic pumpi g of HF~ -, INKby H ul e la e s

Fig 3.~ -1 J-, mdlcari o td o theu1 rot)ateio n reaxatino fucio n ofnime

21

~~~*%w4. -' .- - l'

- - - - - -. ,-- =. - - -. ......... . - . *4~4

N

N

k.4

044

0 S S S S S S S 0 5 5 S S~

'tMC4"4

-4

a.4C..-Sine

U..

I*.4

.0

II! -I* 0'2

2 *~ - C S S 5 5 5 5 S ~ 5 5 5 SaU.. -

o*041~~~'

* -4

S.4.

*"4.0 4.'* .2 '~i.tir~O If~C?%~ 'Cr-. -I..

-.06A'-I

S

ILC.JC1(4(4 .q.~.4.4. 05U *6

* US

I S.C

22

x4.- ~

_ , . _ , .m i .. . I , , .. '.-. -. . . 7-7 .-- . . 7 -- r - .. 7, .7 - __7.7 7

p

of the rate scheme since the retults of the former study have already been

synthesized by us with a such loos dotailed scheme, and the latter work was

really preliminary. Nevertheless, the V-V kinetics are sufficiently succeses-ful in dupilcatingi all the reported quantiLtative features, as shown in Figs.

4 a and 4b for the two experimnts with quite different initial conditions.

Figure 4a show the growth end decay of HF(v-2) as reported In the Osgood et

al. work with the decay being twice that of HF(v-1). Bina and Jones reported

two decay regimes, as show in Fig. 4b, with the slovmr HF(v-2) decay beingtwice that of HF(v-1). A large number of experimental results can be compared

with our theoretical results in Table 5. In these experiments it was not

possible to separate the V-V and V-3.,T parts of the empirical quenching ]f(v)+ HY(v2-0).

C. BF ORTL W)DEL

The KF 0RTL model Is built upon the NEST code 1 6 , which handles nooaq".-

librium chemistry problms with one dependent variable, time t or distrtce x.The original code provided for photolytic excitation as a function of time by

selected spescee in a fixed optical voluma. The code accounted for the energyinput by the photon flux Into the gas volume, but It did not provide informe-tion on the spatial variation of the flux within that volume as a result of

optical thickness. The need to study individual HF(v,J) states required a

significant expansion of the NEST code and the photolytic excitation or

"fl^shlaup" option. Crucial to the ORTL simulation is a consistent expressionof the interaction of laser radiation with the gaseous H species within the

context of the code's flashlamp option. This development Is described below.

1, CODR EXPANSION

For this work an expanded version of NEST, designated NESTE, has beendeveloped. The version includes the capability to handle 1100 kinetic equa-

tions, 125 species, and the appearance of a species IM 250 equations. It alsocan handle eight flashlam s (or laser lines). Recently the code has been

further upgraded to 2000 equations and 16 flashlamps. This additionalcapability would provide an opportunity to study more complex ORTL systems,such as the cv DF ORTL. The flashlamp option has also been modified to accept

23

,¢,.,, ." .,,-€,.' .- . ... . ., ,,, \' ., .. ,- _..). .,.- -. -. • .. .. - . -.- . . . .- . . . .-. ... . .

-10

1071

10 0 2 4 6 8 10 12 14 16 18 20t I sec)

EV 10-1

t (psec) 106100

Fis. 4. (a) Excitation of RF(v-1) and )IF(vu.2) by the HF pulse laser pumpingof RF(v-1) and V-V transfer to HF(v-2). (b) Fxcitation of HF(v-2) bydirect pulse laser pumping.

24

0 C

*~ " a m W4 044 0 U a

a a a A10 a" u b

a"r 9% 6

U C Ca

4 C4

*~~ 00* 0

a'

C~~~ - N 40 a w*w A AjW w

916 a )3E

Sb.0V ~ %D. 0 00t0 0

PAP W4 S 0

0'a ~ ~ ~ ~ c 41 4 4' .N' % S

~b- a~ A5b~

£2

analytical functions as a function of t or x. Thole include linUmoidil

functions, square or rectangU.ax functions, the Gaussian function, Lnd steD

functions.

2. ORTL MODEL

The ORTL sdel describes the changes in the ORTL modium as a function of

x, the direction of subsonic flow. As a simple one-dimensional flow the trans-

formation between x and t involves U, a defined velocity of the flow,

t UI TnA t-.A.el Is scematically illustrated in Fig. 5. It has been assumed that

the ORTL medim is a cnnstant area, constant velocity flow. Necessarily in a

one-dimensional flow, this medium has a constant density as a function of x.

5Changes in the gasdynamic parameters of this flow are not great because of the

large anount of diluent employed.

The initial conditions of the medim are static pressure, p, static

temperature, T, average velocity, U, gas composition of the ith species (He

and HF) st, and dimensions d x W of the flow cross secticn. The initialconditions for photon excitation iticlude the spatial and spectral line distri-

butions of the pump laser fluxes as w.all as the absolute values of that power

distribution.

For the current work, the rectangular flux profile with dimensions a and

b will be used. The coupling of the pump laser into the ORTL medium includes,

in thee* cases, a double pass configuration, as shwn ir Fig. 5. The one-pass

interaction length is L.

The Important ORTL model outputs as a function of x include:

1. gain coefficient at the spectral line center of HF 2 + 1 and 1 * 0P-branch lines

2. HF(v,J) number densities

3. aJL.tic temperature

4. sta;.-:e pressure

5. Voigt line shape and parameters.

26

i "" I* "

b I . .. . , ' . ' .' 5 . . . . . . . .'" - . ........... .. ... -"" '-" "......

PoT, caI, U I

, a1

PHOTON _1FLUX b TOP VIEW

X ORTL MED I UM

IX-i

- P OTOX FROININ VIEW

Fig. 5. ORTL model schematic with double pass pump laser coupling.

27

There are conventional NEST code outputs of secondary importance to this prob-

lem. The formulation of the gain coefficient and line-shape expressions are

summarized in Appendix 2.

3. INTERACTION OF RADIATION WITH MATTER

Some discussion dealing with resonance absorption within the spectral

line is necessary in entering the proper initial conditions for the photolytic

excitation. It can be assumed that the pump laser is homogeneously broad-

ened;17 then the lasing mode of the pump laser has a high probability of being

near the spectral line center. It can be assumed that, on a given spectral

line, the lasing occurs on one mode at line center. Large Fresnel number

medium pressure flowing lasers, such as cw HF lasers with unstable resonators,

generally will fit this assumption quite well.11

In the cw pump laser used in the early reported work at Hughes, the cross

section of the lasing zone in the direction of the resonator is around

(1.2 x 2.3) cm2 and the stable resonator is far from confocal (300 cm radius

of curvature mirror and flat mirrcr 70 cm apart). The Fresnel number is

around 150 >>1. In this stable cavity, the chemical laser is operated on a

number of high order transverse modes and "geometri'c" modes, thus providing a

large number of modes within the spectral linewidth of a lasing transition

with fairly uniform spectral ard spatial distributions of radiant flux.

It is assumed that the ORTL medium is pressure broadened or homogeneously

broadened. The entire population of a specific PF(v,J) state is than avail-

able to participate in the resonance absorption or stimulated emission pro-

cess. There are no so-called hole burning effects.

From real rpqe computations using the linewidth formulae in Appendix B,

the pressure broadening width is found, in the Hughes work, to be about equal

to the linewidth for Doppler broadening. This calculation for pressure

broadening is conservative because the effects of elastic or inelastic long

% range or grazing collisions have not been included.

With these idealizations in mind, one can forulate the photon inter-

action as

28

-. *.*. 4-..-*

dN u I(V;U X)

U - AL - pL.-k(v x) Li}-x hVN A L tal

red (.for a differential interaction volume of area a V J (x), a4 lemth L

(cm), as defined in Fig. 5. The rate of chmg of1 *l(mle/), m upper

AF(vJ) state due to the photons, is given by this apresel.a. The fl x of

pumping laser photons for the trausitiou is I(x) in /cm2 at UM spictcrl

line center frequency val while h i1 PlanCk'S Constant sd N&A s Avogadro's

number. The absorption coefficiret at line center k(vu) (cm 1) is related to

the radiative cross section by

N PIk(v - (V ) ) o( i -(vUl red ul leA 1 SU

where gu and g are respectively the rotational statistical weights of upper

and lower states of the. transition. The derivation has assumed no st-n.

spatial dependances by N, or Nu in the propagation or L direction and very

narrow laser mode widths compared to ORTL medium line widths. An identical

interaction expression arises if I(x) versus frequency is nonzero across part

of the absorption line, and k(vui,x) is assumed constant within this range.

Then I(x) represents the total photon flux across the line. If I(x) lies

within the absorption linowidth, the error is not great; the average

absorption coefficient within a Gaussian linawidth is 0.79 k(v ul,X).

Table 6 presents a typical set of inputs for modeling the Hughes ORTL,

The double pass coupling of pump laser radiation into the ORTL mdium is

estimated by multiplying the incoming flm by factor M. The factor is

determined by estimating the flux after the first passage through the lengch L

of the medium. Although it is assumed that spatial dependences In that direc-

tion are weak, there art noticeable adjustmernts so M is not quite equal to 2.

The density N3 averaged in x is determined in an iterative process.

29

-- V w% 0 0% co C% C54

a0% %D -it en~ 4a 04 t -V

go0

kA- -A

koo

* 3P ' - - 0% 0% 0% C7%

I! P- -~ 4---Ul

.0 0 %4 C

'0a 9 C T- %0-4 u

i- 4 W4 -e e n P . % 1

-4.

P. . -0 LM N 4'

C- - 0 0 4 0 r4 0 0 0

03

3. MODEL VALIDATION AND SIMULATION OF HUGHES URTL

The experimental studies Gn the HF ORTL reported by Bailey et al. of the

Hughes Corp--, ation2 form the basis for uur simaulatioa v&liaation. In their

report a careful parametric study was made of a typicrl ORTL medium. Number

densities, static temperatores, and small signal gains were reported, The

principal variation was in the partial fraction of HF,. The objective of our

vlidation study is to 3ynthesize as many details as possible of the Bailey et

al. experiment- studies.

A. NURBER DENSITIES

Couparison of the ORTL model caa be made with the Hughes experf.mental

number densities. The pump laser conditions are summarized in Table 6. In

tars of Fig. 5, the dimensions of the flux beam are given by a - 2.3 cm and

b - 0.38 ca, while the dimensions of the ORTL flow are w - 0.3 cm and d - 6

ca. This geometry yields an effective L - 0.78. The initial temperature is

300 K and the centerline velocity is 7500 cm/sec (for a parabolic profile with

an average velocity of 5000 cm/sec). The model densities of the ORTL medium

are determined at the center of the pumping laser beam in the direction of

flow (i.e., x - 0.19 ca). Individual HF(vJ) populations were summed over J

for each level. The corresponding model results are shown in Fig. 6a along

with experimental results reported by Bailey et al. The independent variable

is the BF initial mole fracticn. It is apparent that the agreement is very

good. Similar agreement is achieved at XHF - 0.01 and for HF(2) at XHF - 0.03

in Fig. 6b, for the higher pressure (and higher HF density) ORTL medium

condition. It would appear that the most apparent reason for the disagreement

is a nominal BF loss (or a smaller than nominal HF flow) in the experiments at

78 Torr. A sumation of experimental HF densities for XHF - 0.03 yields

4.3 x 1016 particles/ca3 . A calculation using nominal pressure data gives 7.5

x 1016 particles/cm3 at 300 K or 400 K under the constant density assumption.

The latter temperacure is the value computed by the ORTL model during laser

pumping. The experimental density of HF Is 0.57 of nominal value, which was

used in the computer runs. If the experimental data were translated to X -

0.017, equivalent to 0.57 of nominal XHF, agreement would be greatly improved.

31

w

1017

I Iv 2

0 EXPERIMENTI - MODEL

10 0.01 102 0.03 0.04 0.05 0.06 00

HF MOLE FRACTION, .

32(2

In agreement with experimental results, rotational nonequilibrium ef facto arenot evident at these time scales on the centerline of the pumping bean.

B. STATIC TEMPERATURE

The model results are shown in Fig. 7 for static tamperature in the 41

Torr cases. The model static temperature data are likewise extracted from the

x - 0.19 ca position. The comparison with experimental results is also given.

Generally, the model temperatures are from 5 to 102 lower than observed rota-

tional temperatures* Unlike the vibrational number densities, which rise to a

nearly uniform condition, the static temperature steadily rises in the flow

direction throughout the pumping laser flux field due obviously to the absorp-

tion of laser power. The positioning of observation for comparison with model

calculations is therefore crucial. It is possible that this is the basis for

slight disagreement.

C. SMALL SIGNL GAINS

Model predictions are in general qualitative agreement with reported

observations of zero power gain coefficients. In Figs. 8a and 8b, plots are

shown of the gain coefficients go at spectral line center of positive gain BF

transitions as a function of flow direction through the pump laser beam. These

plots are for the flux of 660 W/cm2 of the pump laser with the pump line dis-

tribution tabulated in Table 6. The initial total pressure is 41 Torr, and

the initial static temperature is 300K with 0.03 BF in He. The largest gain

coefficients for our mode:' are in general agreement with the Hughes observa-

tions between 0.012 and 0.06 cm- 1 at the centerline of the pump beam. Since

the Hughes data are computed from chemiluminescence number densities on the

centerline of the pump beam, the comparable result with our model is 0.01 cm-I

on P2(8) at x - 0.19 cm(t - 36 usec). The model gain coefficients are seen to

rise virtually linearly with distance from a threshold. This behavior sug-

gests that the radiative pump flux levels are too low in these early exper-

imants. On this basis, one projects inefficient recycling of HF molecules

and extremely inefficient ORTL lasing. Indeed, the overall efficiency was

obe-ved to be around 2%. Alternatively, if the velocity were slowed so a

fluid element could spend more time within the beam and reach pumping

saturation, a recycling condition can occur, thereby improving greatly the

33

• ,% % ,.- .- , ",:i.:- - % '%, ', . ~% -, ._ %, ".*"",% -**-. .. -. *-. - ". ,. ". .- ' -. . . • . . .. ** .' ,-.

700-

650

600-

550

500-

450-

400

0 EXPER IMENT

- MODEL300

0 0.01 0.02 0.03 0.04 0.05 0.06IHF MOLE FRACTION, XHF

Fig. 7. ORTL medium I tatic temperature as a function of HF mole fraction.Flux-660 W/cm , P-41 Torr, T-300 X, Jp-5.

34

.1

~0.0

0.01 FLUX • 660 Wicm2

PI . 41 TorrXHF • O.I Pill'

0.m - T •M K

0.0 -"

0.01 -•

00 10v0tO 4 50 60 70,FWXI ON , I Pao OF

0 0.13 0.30 0.39. x ION) (U • M 520M-SK'!

qU

t*

0.06-

0.01

O.W pl19

0 10 20 30 40 50 60 70() FLUX:ON I t I g0) OFF

0 0.15 0. 3 0.38X (cm ) (U • 20 cm -SOc1 1

Fig. 8. Sia11 signal gain coefficients as a function of flow distance X ortaet. Initial conditions as shown in Table 6. (a) P2+I(J) "nag,and (b) PI ) lines.

100

35

. , , . . . --. . ... . , , .-

eff iciency of the ORTL. Later Hughes results showed that a factor-of-4

slowing in velocity leads to an order of magnitude improvenent in efficiency.

A further comparison of experimntal and model results is given in Table

7 where the lasing results are compared with model. mall signal gain

results. The normalization of results Is made to one of the better cases,

i.e., 440 W/cn2 case with Pi(4) and P2 (4) pumping at 78 Torr total pressure

and 31 HF. The model small signal gain coefficients for this table are taken

at the x - 0.38 cm position. The largest gain coefficient at this position

is used. This is because oem gain plots exhibit the triangular structure in

Figure 8 while others do not, depending on conditions. In reality, the 2xis

for the experimental lasing may be at some position equivalent to smaller x.

Table 7. Observed Lasing Compared to Model Gain Coeffcient

NormalizedLasing Normalized

Pump Laiers Pressure (From Fig. 4 ModelCase (W/cm' (Torr) XHF of Ref. 2) Gain Coefficient

1. 440 78 0.03 1.0 1.0

2. 440 78 0.01 1.0 0.9

3. 440 78 0.06 0.0 0.0

4. 660 78 0.01 0.5 0.2

5. 660 78 0.03 0.8 0.6

6. 660 78 0.06 0.0 0.0

7. 660 41 0.01 <0.05 0.2

8. 660 41 0.03 0.5 0.9

9. 660 41 0.06 0.75 2.2

36

'S ,r . 'C.., .: .y : :.,.. ,,.< ..:- -,- i -i:, - - ,-,- ::' :-: .S . : . - .- ? - : : . - : .- .-

The agreement is fairly good even on a quantitative basis. Casc 7 must

describe a case too close to experimental threshold where lasing output Is

quite sensitive to slight variations. In Case 9 the model gain coefficient,

at P2(10), to somewhat overpredicted. Since most relevant ORTL studies will

concentrate on the XVF regime less than 0.03, this deviation is not considered

serious for present applications.

The spatial behavior of the gain coeificients in the direction of flow

can be simarized using th conditions equivalent to Cases 7, 8, and 9 at 41

Twrr, variable ZEF at fixed laser pumping flux. As shown in Fig. 9, at X -

0.01, a steady state in gain is reached rather rapidly after the fluid ele2ent

enters the bean. Rowever, the steady state small signal gain coefficients are

quite low. The X[ - 0.03 condition exhibits triangular behavior beginning at

the upstream edge of the pump 'beam, x - 0, in Fig. 8. The X-F - 0.06 condi-

tion shows the same behavior, except the threshold of gain is halfway through

the beas, x - 0.19 ca, and the growth of gain is steeper to larger final

values. The condition is vary far from achieving final steady state. SimilarI model results are produed at 78 Torr. For a given radiative flux level of

pumping and for a given density of HF, it is apparent that there is an optimm

characteristic time for the gain on a given line to reach empirical steady

state. This is not &arpr±_sing. What is Important is that this characteristic

time way be unexpectedlv long although individual channel processes may have

time estimates shorter than 10 Usec, as noted in the previous section. Obvi-

4% ously, a fluid elemant should remain in the bean at least as long as this

characteristic time, and the effective tim for an ORTL "cycle" would be

greater than or equal to this characteristic time, which reflects the efficacy

of the radiative and collisional puping processes of the ORTL. The para-

mitric dependent of this characteristic time will be examined later.

D. SENSITIVITY OF ORTL TO COLLISIONAL PROCESSES

The simplest, global assessment of the relative importance of the R-R

and V-V processes is by directly removing those particular cross sections

in the modeling code -tud running a particular case. If one chooses the case

described in Fig. 8, also labeled No. 8 in Table 7, and removes the R-R cross

37

. -. ' '. . . . . . .

.M0.02-

0.0 )

0

0 02 Q40 50 60 70() FWX: ON tJc OFF

)0.15 0.50 0.38

0.04-X Icm)IU *5200 cm-sOC-1

0.04-

Is. 0.03 -

II(b) FLUX: ONI0 14wI F

0 0.15 0.30 0.38X (CM) (U - 520 cm-sec I

Fig. 9 Small signal gain coefficients as a function of flow distance X orItime t. For XHF -0.01. (a) P2,1(J) lines, and (b) P1 ~o(J) lines.

j 38

sections, one produces no positive gain greater than 0.001 cma- at x - 0.38 ca

in P(6) ad PI(7). This illustrate@ that the R-R collisional processes are

important In v-1 or v-2 in producing ORTL gain at higher J states than those

that are pumped by the laser. This observation is further supported by themodeling results In Fig. 10 for the sin- ORTL case (660 W/cm2 , 41 Torr, XHF -

0.03) when the V-V processes are removed. Gain coefficients on the P1 . 0 (J)

branch are unaffected (see Fig. 8). In fact, they are larger because the

HF(v-1) states have not been depleted by collisional V-V pumping to HF(v-2).

However, gain coefficients on the P2 - 1(J) branch are greatly affected by the

absence of the 1 + 1 * 0 + 2 V + V collisional mechanisms. Since one of the

potential benefits of ORTL is the conversion of multiline chemical laser

operation to near single-line ORTL lasing at an elevated v level, such as v-2,the V-V processes are likeise crucial in producing the relatively large gaiis

on important lines of the P2 o 1 J) branch of HF.

A limited sensitivity study of the R-R and V-V rate sets hats also been

attempted with an earlier version of the model in which the number of pumping

laser lines was five, and the number of kinetic channels available was one-

third. This limited us then to an incomplete expression of the V-V processes.

The general outcome of these early studies indicated that if the current R-K

cross sections were reduced a factor of 3, positive gain would be extinguished

on P2 (8). If the -t-R cross sections were increased arbitrarily tenfold, not

much change occurs to P2 (8) gain. Thus the ORTL provides a lower bound

experiment in establishing the sizes of R-R coefficients. The sensitivity of

P2 W (J) to the V-V processes was obseried even in this early work.

39

A&_ _. ',% ..,' "". -,L ."-. " .. . . % . . . . .,' . - . - - . + - - - . - - . - . - . - . . ..

.3--

0.01 2

0

0 10 20 30 40 50 60 70FLUX: ON ItI/.LSSC OFF

0 0.15 0.30 0.38NX

X(cm) (U -5200Ocm-sec-1

Fig. 10. Case as in Fig. 8, but with V-V rate package removed.

40

4. ORTL MODEL PARAMETRIC STUDIES

The objective of this section is to explore regimes of ORTL operation in

which good overall efficiencies might be expected and short "effective cy.-le"

times might be realized with regard to the sizing of ORTL. Accordingly we

will examine the effects of

a. Flow velocity variation (variation of the time that a fluid elementspends in pump beam)

b. Changes in the J-distribuitons of pump beam

c. Pump flux variation

d. Initial static temperature variation and temperature control.

Since our comparison will deal with small signal gain coefficients, we estab-lish as a baseline case that reported by Hughes as 20 W ORTL output at 78

Torr, XEF - 0.019, pumping input at 300 W or 440 W/cm2 with a P1(4)--Pl(7),

P2 (4)-P 2(7) pattern. The input coupling efficiency was 0.41, the conversion

efficiency was 0.18, and overall efficiency was 0.053. For that case our mod-

eling yielded a maximum gain coefficient [on P2(7) or P2 (8)] of 0.05 cm 1 on

the downstream edge of the beau. At the centerline of the beam, x - 0.19 cm,

the gain is around 0.020 c -1 .

If one assumes that ORTL is a homogeneously broadened laser in which the

spectral line with dominant gain will lase relatively independently of other

branch lines, the maximum extractable power P at optimized coupling is givenby 1 8

A

2WSAT (r- V 2 2WSATS T 0 0 T G0

where WSAT is the saturation energy inside the cavity, T is one round trip

time within the cavity, Go is the round trip zero power gain (obviously pro-portional to the gain coefficient), and 6

0 is the round trip internal cavity

loss. In HF lasers, Go is usually much greater than do. The parmeter WSATdepends on pumping and quenching parameters (such as cross sections) which are

41

"=-......

quite similar for the high J lasing lines of an HF P-branch. Therefore P isapproximately proportional to Go at high levels of gain, and we shall utilize

this dependence.

A. FLOW VELOCITY

One principal flow adjustment is the velocity of the flow. Basically

this variation adjusts the time that any fluid element spends within the pump

laser beam. In Fig. 11, the P2 (J) gain coefficients are ahown as a function

of . for a case in which the velocity is a factor of I slower than cases

previously discussed, i.e., 1300 cm/sec. The pump flux level is 440 W/cm2

with a P(4)-P(7) pattern, and the other flow parameters are an initial

pressure of 78 Torr, initial temperature 300 K, and XHF - 0.03. A concurrent

set of PI(J) gain coefficients at half the values shown is also generated.

It is quite clear that there is considerable improvement in peak gains

around 0.095 cm- I or a Go -1.2. This is a four-fold to five-fold improvement

on the original Hughes reported results on gain. Using the proportion one can

estimate that overall efficiency should improve from 20 to 26% with the sig-

nificant changes in the conversion efficiency. In fact, this advance has been

experimentally reported in unpublished Hughes results, in which overall

efficiencies between 25 and 302 were observed. The dominant P2(J) spectra,

according to the model, would shift to higher J states than P2 (8) under theseI conditions.

The results in Fig. 11 also serve to reinforce the previous remark that,

for a given pump flux level and HF density, there is a minimum characteristic

time for the fluid element to remain in the beam. In the depicted case, this

minimum time appears to be 30 usec and the number of possible HF molecular

"cycles* might be 5 or 6, out to 150 usec.

B. PUMP J-DISTRIBUTION

The pattern of pump HF chemical laser lines is crucial to the potential

success of the ORTL concept. Accordingly, a modeling study has been conducted

in which the flux input pattern has been varied in J in the following manner.

The input flux intensity pattern in Table 6 is maintained; however, the J

42

I

o00 P2 (Ill

0.08

0.06-

Cr 0.04 - P2 (8)

J2

0.02

010 50 100 150 200 250

FLUX: ON t (p.sec) OFFI I,,I

0 0.19 0.38X (cm) (U - 1950 cm-sec " )

Fig. 11. Small signal gain coefficients as a function of t or X at nearly. four-fo.d slowr flow v locity. Only P (J) branch lines are

presented. Flux-440 W/eea, P-78 Torr, XHF, 03, T-300 K, and Jp-4pump fluz distribution.

4

I1 43

- *-,*.*. L; '. /. ." ; . .-I -. . . - . .- .. - . - . -. . ,. - - 4-. . -. . ., . .. , . , . . .

4 -6

pattern on both the P 2 + I and P1 + 0 branches will be shifted. The lowest J

in the P(J) branch will be designated Jp as an identification of the pattern,i.e., J - 2 represents a P(2), P1 (3), PI(4), P1 (5), P2 (2), P2 (3), P2 (4),

P2 (5) pattern. For a total flux of 660 W/cm2 at 41 Torr, 3000K, the results

are exhibited in Fig. 12. The maximum achievable gain coefficient is plotted

as a function of Jp It can be seen, unsurprisingly, chat an ORTL medium can

work very well at low Jp pumping patterns and would probably approach very

high overall efficiencies. This is the result of high densities for resonance

absorption at the nearly-Boltzmanniied lower J HF states and also the result

of gery fast R-R,T rates at these low J patterns. At higher J, middle Jp

around 5 or 6, the peak gain coefficient appears to settle above 0.08 ci- I for

% F - 0.03 and 0.06. This is equivalent to possible overall efficiencies

above 20%, everything else held equal. The peak gain has been driven down

mainly by the steady increases in static temperature shown in Fig. 13. These

temperatures at the downstream side are large, and therefore with the given

positive gain, the inversiona (ratios of upper state density to lower state

density) are quite high. These great inversions must be partly due to the

match of pump spectra with the near-Boltzmann distribution in HF population at

the elevated temperatures above 1000'K.

Fig. 14 illustrates that the P2 (J) line of peak gain moves to higher J as

Jp, the lcwest pump line, increases. This peak gain line always occurs at J

greater than Jp. It reflects the fact that the inversions are found at higher

J where the lower state densities are Initially dropping. In this sense, the

peak P2 (J) lasing line in ORTL depends on the pump laser design.

It should be noted, as in Figs. 8 and 11, that significant gain coeffi-

cients are generated on lines that are simultaneously pumped by the chemical

laser at all patterns of J p This behavior would tend to lower the input cou-

pling efficiency as certain strong pump lines are effectively enhanced in pas-

sage through the ORTL medium and are not absorbed. Too thick an OTL medium

in the direction of the pump laser baam propagation will obviously convert the

ORTL medium to an inefficient amplifier for some lines. At low Jp, where the

gain coefficients are large, this problem will have a great influence in

lowering the coupling efficiency.

44

0.40-

FOXHF 0.06

- 0.010 0.03

0.30-

, 21

1= 0.20 -

LiJI'L

0.10

0[

o o_ . ,I It , t2 3 4 5 6 7

J, PUMP LASER LOWEST P (J LINE

Fig. 12. The dependence of peak gain coefficient on pump flux J distribution.Flux-660 W/cm - , P-41 Tort, T-300 K.

45

. .. . ," .- .' . "" ' ' ''.. . . . ' " - . . . .,'ie ':, , , ' ., - - -.-.-. , ,,-.,, -o. , / . ,,,.". " ". " ". . % ". . . ... '.', '.'. . .. . ...-.- '.. " . -- , ,

J~6

- 2000-

CL

~1000-

300

0 100 200 300ON t (psec) OFFI I I0 0.19 0.38

X (cm) (U - 1950 cm-sec-)

Fig. 13. The effect of gas heating on static temperature in the direction of

ORTL jas flow with pump flux J distribution as a variable. Flux=660W/cm, P-41 Torr, T-300 K.

46

11

10

9z

CD 8

i a.7

.6

.PUMPING PATTERN

P1 (Jp), P1 (Jp+l), P1 (Jp+2), P1 (Jp+3)

SP 2 (Jp ) P2 (p+ 1), P2 (Jp+2)p P2 (Jp+3)

0 1 2 3 4 5 6 7JP, PUMP LASER LOWEST P (Jp) LINE

Fig. 14. The shift to higher J in the peak gain P2+ (J) ORTL transition-ispump flux J distribution shifts to higher Flux - 660 W/cm - ,

P-41 Torr, T-300 K, XUJF.O.03.

47II

The steady temperature rise (Fig. 13) is due to the overall absorption of

large amounts of pump radiation. Needless to say, the overall efficiency of

ORTL is not unity, and the pump power which is not extractable as 0RTL lasing

will eventually heat the gas. As the size of the medium grows in larger

devices such that the characteristic times for a fluid element within a pump

beam become longer, heating mechanisms become more important. On these time

scales, this gas heating results from the R-T rates and may be a sensitive

indicator f or the correct rate scheme here. The gas heating problem is

aggravated at intermediate J patterns since the energy gaps in transferring

from J to (J-1) on a given vibrational level are increasing proportional to

J. From this model study, it seems clear that gas temperature control is an

important consideration in ORTL. At the elevated temperatures above 1000 K,

it must be noted that the kinetics scheme is no longer completely accurate

because literally tens of thousands of V-V channels with energy defects below

1000 cmn- have not been included. Some slight adjustments on V-R collision

partners ahould also have been made. Nevertheless, the model still reflects

the general qualitative behavior of the ORTL medium.

C. PUIMP FLUX VARIATIONS

As shown in Fi". 41, it is quite clear that the total pump fluxes of the

early Hughes studies were too low to be efficient. This limitation was also

discussed in Section 2. If the flux is raised to 50,000 W/cm 2 for the

case in Fig. 11, the peak gain coefficient is attained in 40 Usec rather

than 150 Usec. This should also improve the effective cycle time on a micro-

scopic basis since radiative pumping times are much faster. In Fig. 15, the

effect of flux increases or. -qak gain coefficient is shown. For an optimum

0RTL condition, -7, aro . -- the pumping flux should exceed 5000 W/cm2 or

600 W.ca 2 per pump lasing spectral line. At sufficiently elevated fluxes,

there is the additional advantage that the peak gain is attained before gas

heating becomes a serious prol- in the flow direction. Typically the static

temperature does not exceed . K at the peak gain in these cases. For the

cases with Jp- 4, Fig. 15 shows that an ORTL could operate with 50% overall

efficiency.

48

!-

1\ 5

01

0 1000 10,000 100,000-2FLUX IW-cm

* Fig. 15. The dependence of peak gain coefficient on total pumping radiativeflux. P-78 Torr, T-300 K, XHFO@O03 .

49

D. TZMRPVATURU

Temperature emerges as an important variable in any cw HF ORTL device.

Two aspects of temperature effects have been studied with this ORTL model.

The effect of initial temperature of the flow has beer. examined. Then the

possible control of gas heating by the pump laser beam is briefly discussed.

Setting the initial temperature can have two effects in an ORTL. The

temperature can be raised such that the initial distribution of HF(v=O, J)

densities better matches the pump laser spectral distribution. The obvious

practical limit is reached quickly, however. For J p - 6, nn initial ORTL

medium temperature around 2000 K would have to be produced for good match-

Ing. Even if the practical limit was not a factor, the gain coefficients

would generally be lower because of their adverse dependence on temperature.

Further, as Jp increases such that the pump laser spectral pattern 2oves to

higher J patterns, 3ne encounters slower R-R,T collisional cross sections, as

depicted in Fig. 2.

The second effect of initial temperature is more subtle. In Fig. 16,

small signal gain coefficients are plotted as a function of x or t for a case

in which the initial temperature is slightly elevated. The case is identical

to that shown in Fig. 8 except for the initial temperature. The temperature

dependence of the R-R and V-V rate coefficients is such that the coefficients

are faster at elevated temperatures. Steady state is apparently reached quite

quickly although the peak gain is about half that reported with the initial

temperature at 300 K. The temperature tise is under 100 K. The reaching of a

peak gain condition In 1 to 2 Usec at such low fluxes is important in estab-

lishing an effective "cycle time" for the kinetics, and this characteristic

time will determine the ultimate size of ORTL flows relative to pump chemical

laser flows. Thus the slight heating of the ORTL medium may be beneficial, at

the cost of some of the gain.

Control of gas heating by the pump beam can occur in two ways. If the

overall efficiency of the ORTL is unity, there will be no gas heating. Thus

power extraction from ORTL lasing is important in moderating the effects of

gas heating. The current model examines the worst case, in which no

50

I7 %

J

I P2 (91

2P s

0.0-': ., . 2 M,

0.0i-

010 20 30 40 50 60 To

FLUX: ON t Isec) OFF

0 0.15 0.30 0. i

X tcm) IU • 5200 cni-sac-1)

Fig. 16. The effect of elevated initial static temperature, 700 K, on P2.,1 (J)small signal gain coefficients. The cse illustrated is siitlar tothat shown in Fig. 8.

14

51

0-I r .." . ."-. ,"-" '. .'. ' '- -'- .'- .,.' .'- .'- -.- . --. ' .--" .' -" ." .''- "

... ,. .,.. ,- > :-,,. .,,._ .A . _, .. . . ... , .. .. .. . . ...A ; -.AL '.... .. . ., .,

.1

laser power is extracted. A manipulatiou of the specific heat C. of the gas

can be effected by adding a high Cp species, but poor IF quencher, such as SF6

in small quantities. For a 78 Torr case, some 15 Torr of SF6 has been

added. The results are presented in Table 8. One can obtain 70% of the peak

gain while temperature is nearly halved.

Table 8. Increase in ORTL adium Beat Capacity

Conditions Without SF6 With SF6

Initial total static pressure (Torr) 78 93

Initial static temperature (K) 300 300

)ole fraction of EI 0.03 0.03

SF6 pressure (Torr) 0 15

Pumping laser

flux (W/ca2 ) 660 660J-d1strlbtion PI(5)-PI(8) PI(5)-Pj(8)

P2(5)-P 2(8) P2(5)-P 2(8)

Final static temperature 1501 815

(at exiting pump bean) (K)P~eak gain (ca-1) 0.098 0.070

Pak gain line P2(I1) P2(1O)

. BEST REGUM

In evaluation of the ORTL medium as a gain generator, this modeling study

has established that the most attractive regime for a cw HF ORTL might be

total pup fluxes in excess of 5000 W/cu 2, pump spectral pattern with Jp c 4,

total pressures up to 78 Torr, XH betveen 0.01 and 0.03 (for a double pass

52

coupling mirror system), slightly elevated Initial tesperatures, high heat

Capacities In the flow, and fluid element times in the pump beam no longer

than 200 Usec. An attractive regime is defined 4s that with a peak gain

teeeding 0.2 cm' 1 equivalent to an overall efficiency of 0.5.

53

p.1

5. CONCLUSION

A model bas been developed to study the gas flow of an optically reso-

mntly pmed transfer laser as en efficient gain generator. A criterion of

0.20 cia1 for the peek gain coefficient has been used an equivalent to an

overall efficiency of 50 percent.* The equivalence was established in this

model of mll signal gain by simialating reported Rughes experimnts. This

evaluation has been conducted to determine if the OkTL device might effi-

ciently convert the beam of a high power cw HF chemical laser Into a laser

beam of the highest quality.

A regime has been found by the model In which the 0. 20 cs71 criterion Is

met and asceeded. This regime requires the pump) laser to produce:

a. Ceater than 5000 V/cu2 flux (1000 V/cia2 In one spectral line)

b. A pumpinug pattern with J p1C4 where the losig lines are

and over 80Z of the power is In the P(5) and P(6) lines of bothbranches.

The ORTL medium, He and 17, should operate at

a. Total pressures up to 80 Torr

b. Ilevctad initial temperatures up to 600 K for proper flow aizes

c. H1 sole fractiows between 0.01 and 0.03 f~or a double pass couplingmirror system for the pump laser.

For a indtiple-ass coupling mirror systes the sole fraction would be propor-

tionally reduced (10 passesb one-fifth the sole fra,.tion listed). The optical

depth for the pump laser beams total passage through the sedium should be

unity.

To achieve an attrac ;Ivo ORTL sizing relative to cv chemical laser flown,

the ORTL medim velocity should be around 10~ cu/seJ-1. Any fluid element

should be in the pp bean f or a period exceeding 100 lisec. In this way, the

55

time is, of course, determined by the flux level, concentrations, and the

effect of elevated static temperature on rate coefficients. In this identi-

fied regime, the ORTL flow at a higher velocity could be a fraction of the

size of the cw chemical laser nozzle area, as suggested in Table 1. it should

be noted that this discussion does not include system consider&tions such as

reservoir tanko and exhaust symtems.

The principal problems and limitations of .he ORTL medium have also been

observed with this simple model. The favorable spectral line distribution

required for high efficiency tends toward lower J P-branch lines at or below

P(5) and P(6). This distribution is not typical of mosi efficient cw HF

lasers, which tend toward higher J lines.

Elevated initial temperature operation appears to be not important in

achieving 0.2 cm - peak gain operation. However, this condition is important

in sizing the ORTL. It is an additional operational complication,

The ORTL medium is possibly limited in two of three dimensions by the

following considerations. In the direction of propagation of the pump laser,

the model has shown that in a multiple line pumping pattern in rotational non-

equilibrium, gain can be generated on transitions on which pumping laser lines

exist. For too large a dimension (or optical depth), significant amplifica-

tion will occur. This effectively lowers the input coupling efficiency (and

therefore the overall efficiency) and directs power way from improvement in

this bean quality. Therefore the shape of the ORTL medium has constraints

important to an ORTL resonator designer.

Significant gas heating by pump laser radiation is generated by the small

signal gain model at longer time scales in the flow direction. Practically,

this effect could limit the extent of the ORTL medium in the flow direction

(within the pump beam) to. characteristic times below 300 Usec. ORTL lasing

would moderate this effect. Additives such as SF6 augmenting the specific

heat of the flow are also helpful in controlling gas heating.

The ORTL coucept for improving beam quality could continue to merit

seriou- consideration if the pump laser line distributions ever reach the

appropriate medium-to-low J P-branch positions. It is also evident that a

56

proper evaluation of an actual device will require experiments at the proper

scale and size of pumping and ORTL devices. From our flux variation study, it

is apparent that a greater than 5000 W/cm2 pumping laser with an adequate pump

beam cross section (i.e., 10-20 cm2 ) is needed to evaluate simultaneously the

optim overall efficienc- and true ORTL size relative to the pump laser. The

p device should have a J ( 4 pattern; otherwise the benefits of such an

experiment may be limited. Current experiments at smaller scales are limited

in value in that they will have difficulty exhibiting satisfactory overall

efficiencies or sizes.

Our current model of an ORTL device can be further improved. Further

definitive paraetric studies should be made. The major model improvement

would be the conversion of the current code to a lasing model, at least at the

conventional level obtained by using Fabry-Perot mirrors. Then the defined

efficiencies of an actual ORTL can directly be estimated. Since parts of the

ORTL medium experience large elevated temperatures, a reexamination of R+ T

mechanisms and an expansion of the V-V manifold would seem useful. Modeling

of the pump laser coupling can be improved by converLtng factor M into a

density-dependent variable in the flow direction such that pump lines can

experience gain as well as absorption. In the current work, M - 2 because the

medium is thin, and any errors have not been large.

Finally, we note that an ORTL device seem an excellent, relevaut, empir-

ical test for HF(v,J) + M kinetics and laser modeling of c'- HF lasers because

of its basic simplicity.

57

REFERENCES

1. J. H. S. Wang, J. Finzi, and F. N. Mastrur, Appl. Phys. Lett. 31 35-37(1977).

2. P. K. Daily, J. Finzi, G. W. Hollemn, K. K. Hui, and J. H. S. Wang, HEnergy Optical Resonance Transfer Study-, Hughes Aircraft CorporationTechnical Report FR-79-73-538, Culver City, Calif. (Jan. 1979).

3. K. K. Hui, P. K. Baily, J. Finzi, J. U. S. Wang, and F. N. Mastrup, Appl.opt. 19 842-832 (1980).

4. J. Finai, J. H. S. Wang, K. K. Hui, P. K. Baily, G. W. Holleman, andF. N. Nastrup, IEZE J. Quantum Electron QE-16, 912-914 (1980).

5. J. H. S. Wang, J. Fiuzi, P. K. Baily, G. W. Holleman, K. K. Hui, andF. N. Hastrup, Appl. Phys. Lett. 3624-25 (1980).

6. G. W. Holleman and H. Inijyan, Hultivavelength 2-5 Micrometer Laser,

Hughes Aircraft Corporation Technical Report FR 80-72-653 (June 1980).

7. R. L. Wilkins and M. A. Rvok, J. Chem. Phys. 73, 3198-3204 (1980).

8. R. L. Wilkins and M. A. Kwok, J. Chem. Phys. 70, 1705-1710 (1979).

9. R. L. Wilkins, J. Chem. Phys. 67, 5838 (1977).

10. R. L. Wilkins, to be published.

11. Jo J. Hinchen and R. H. Hobbs, J. Chem. Phys. 65, 2732-2739 (1976).

12. J. J. Hinchen and Re H. Hobbs, J. Appl. Phys. 5 628-636 (1979).13. Re L. Wilkins and M. A. Kwok, to be published.

14. Re M. Osgood, Jr., P. B. Sackett, and A. Javan, J. Chem. Phys. 60 1464-1480 (1974)

15. M. J. Dina and C. Re Jonas, A22. Phys. Lett. 22, 44-6 (1973).

16. E. B. Turner, G. Emanuel, and R. L. Wilkins, The NEST Chemist~r CoputerProgEram TR-0059(6240-40)-l, The Aerospace Corporation, El Segurdo,Calif. (30 June 1970).

17,. Ho ire~s, A1AA J 17, 478-489 (1979).

18. A. E. Seigman, An Introduction to Lasers and Masers McGraw Hill Co., NewYork, (1971), p. 433.

59

19. M. A. Kvok and R. L. Wilkins, J. Chem. Phys. 63, 2453 (1975).

20. M. A. Kwok and N. Cohen, personal commnication.

21. P. R. Poole and J. W. M. Smith, J. Chem. Soc., Faraday Transactions II,73, 1434 (1977).

22. D. J. Douglas and Ci Bradley Moore, Chem. Phys. Lett. 57, 435 (1978).

23. J. Bott, J. Chem. Phys. 57 961 (1972).

24. J. 1. Airey and I. W. Me Smith, J. Chem. Phys. 57, 1669 (1973).

25. G. M. Jursich and F. F. Crim, J. Chem. Phys. 74,, 4455 (1981).

26. J. K. Lampert, G. M. Jursich, and F. F. Crim, Chem. Phys. Lett. 71, 258(1980).

27. G. D. Billing and L. L. Poulsen, J. Chem. Phys. 68, 5120 (1978).

28. H. K. Shin and V. H. Kim, J. Chem. Phys. 64 3634 (1976).

29. C. Clendening, J. I. Steinfeld, and L. E. Wilson, Information TheoryAnalysis of Daactivation Rates in Chemical Lasers, AFWL-TR-76-144 (Oct.1976).

60

APPENDIX A

KINETICS EQUATION LISTING(Photo Reduced)

IRte iEquatioa CM3 A n EcI(mole sec) cal/mole

1 HF(200), + MI - HF(201), + MI KF - .418B19 - .848 - 2565

k f AT" ezp (E/RT)

61

11 1%7 %- 'L Tk1R -

ve"Q*dre* t o94461O&oCN ZO *040%6o e .nfn D r)NC6WOa*= 0%a%40.%NV

a. W&Aa a. a a a.. a aJa. aSa a aJ. a asa a a** a.. a am... mjwwA. a min a *

q'b' 4, 4 4..

r4.4 cu49y^8W4 Neu 944 C.99444,1 r4oi Wougeut NeiN W N^Jq4 NN9 9499449 NWq NN4.4 Wq. Y q .9. 44

11111 11111111 m l$~ I** 4 l4 1*, 11I4 6 14 11 11 111fil o 11 o fIt$ 11 111 1 10 illto" It ol

aet f fa0-t w0 40 0M m s atm t fs 0 0 0m t

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* e~ e e e e o~ o e e e e e e e e e e e e.ee e e.u..e....* o eLe..g e e a g g Ue

cieN ggo g i S g, ga g ~ sc a g cgoug ae gn goa i o gagoeciggsc Sg *i cc 63ggicc

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.A

LABORATORY OPERATIONS

The Laboratory Operations of The Aerospace Corporation is conducting exper-

Iiental and theoretical investigations necessary for the evaluation and applica-

tion of scienttfic advances to new military space systems. Versatility and

flexibllty have been developed to a high degree by the laboratory personnel in

dealing vitt the many problems encountered in the nation's rapidly developing

space systems. Expertise in the latest scientific developments Is vital to the

accompliahment of tasks related to these problems. The laboratories that con-

tribute to this research art:

Aer2 hy*ic Latbor&tory: Launch vehicle and reentry aerodynamics and heattransT, pr;opul r rh'it try and fluid mechanics, structural mechanics, flightdynamic3; high-temperature thermosehanics, gas kineics and radiation; researchin environmental chemistry and contamination; cv and pulsed chemical laserdevelopment includin. chemical kinetics, spectroscopy, optical resonators andbeam- poict~ng, atmospheric propagation, laser effects and countermeasures.

Chemistry and Phvscs Laboratory: Atmospheric chemical reactions, atmo-spheric cptica, light scattering, statc-speciflc chemical reactions and radia-tion tranaport in rocket plumes, applied laser spectroscopy, laser chemistry.bhttery electro:hemistry, space vacuum and radiation effects on materials, lu-brication and surface phenomena, thermionic emssilon, photosensitive materials&nd detectorr, atomic frequency standards, ad bloenviroamental research andmonitoring.

Electronics Research Laboratery: Mticroelectronics, GaAs low-noise andpow r devices, semiconductor lasers, electromagnetic and optical propagationphenomena, quantum electtonics, laser communications, lidar, and electro-optics;

acommunication sciences, applied electronics, semiconductor crystal and devicephysics, radlometric lagting; millimaeter-wave and microwave technology.

Information Sciences Research Office: Program verification, program trans-lation, perjormane-sensitive system design, distributed architectures forepaceborne coautars, fault-tolerant computer systems, artificial Intelligence,and microelectronics applications.

Materials Science! .L rator : Development of new materials: metal matrixcomposites, polymers, sod i forms of carbon; component failure analysis andreliability; fracture mechanics and streati corrosion; evaluation of materials insace envirorment; materials performance in apace transportation systems; anal-yais of systems vulnerabirty and survivability in enemy-induced environments.

Space Sciences Laboratory: Atmospheric and fnospheric physics, radiationfrom iwh ituoiphi'. de:sity and coposition of the upper atmosphere, auroraeand airglow; magnetiapheric physics, cosmic rays, generation and propagation ofplasma waves In tbe agnetosphers; solar physics, infrared astronomy; theeffects of nuclear exclosions, iantic stcres. and solar activity on theearth's atmosphere, ionosphere, and wnecophsre; the affects of optical,electromsgnetic, ani particuldte radiations in space on space systems.

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