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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
Prepaed ftrAIR FORCE WEAPONS LABORATORY
Kkrtlumd Air. Iorc Raset N. Mex. 87117
L11 APPROVED FOR PUBLIC RELEASE;DISTRIBUTION UNLIMITED
SPACE DIVISION p 1M!R FORCE SYSTEMS COMMAND
Los Angeles Air Force Station al N" (aP.O. Box 92960, Wcoridway Postal Center
Los Angeles, Calif. 90009
All
. ;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
releasable to the National Technical Information Service (NTIS). At NTIS, it
will be available to the general public, including foreign nationals
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
hs
,4., ,.: :'-. i...:,i.. ,: > . - -,. ,?, , . .: ,.:" , . . i ? . ,i" ? . " ._ i: : . , ; i. .. . : . .
UN4CLASSIFIED-~~~~ ~SECURITV CLA411601ICATION Or THIS PA0E (000M. bfte EaMW4_________________
REPORT DOCUMENTATION PAGE EADR COMPTU G FORM
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
TRANFER ASE MEDUM . PERFORMiNG ORO. REPORT NUMSER
_____________________________ TR-0083(3603)-37. AUHOP4QS. CONTRACT OR GRANT HUMMis)
Munson A. Kwo!k and Roger L. Wilkins F04701-82-C-0083
. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -r PERoRIN ORAIAINNMOW'~0ES1~(RtM ELEMENT. PROJECT. TASK6. P"IrMMIN ORANIZTIO HAN AN AVOESSAP6A A WORK UNIT NUMUERS
The Aerospaca CorporationEl Segundo, California 90245
N ~ 1I. CRNTAOLLING OFF~ICE NAMC AND ADDRESS I . RK:vON1 DAT9
N ~Air Force Weapons Labcratory 3C Sepebr18Kirtland Air Force Base, N. Mex. 87117 tS. NUMerf14 C*? WAGES
S OITORING AGNCY NAME 6 ADDReSS~ildffeeo freg Cdatrelin Olfow. It. SCURITV CLASS. (*I this rwpet)
Spce Division_______ ______
Air Force Systems Connand UnclassifiedLos ngels, Clifonia 0009IS&. D8C_6ASSIFICATI"N/COWN3RADIKTLos ngeesCaliorna 9009SCHE~DULE
*1IS. DISTRIBUTIOK STATIEMENT (of Me.1 Aspew(
Approved for publ..c release; distribution unlimited
17. OISTRIGUTION STATEMIENT (of thm. abstrat entered in 35.4@k 0,It (9Mferst &00 fl.Ut)
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
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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).
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59
19. M. A. Kvok and R. L. Wilkins, J. Chem. Phys. 63, 2453 (1975).
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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
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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..
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aet f fa0-t w0 40 0M m s atm t fs 0 0 0m t
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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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