AN ANALYSIS OF THE ROLE OF KINETIC MECHANISMS AFFECTING H2 + F2 LASER PERFORMANCE

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AN ANALYSIS OF THE ROLE OF KINETIC

MECHANISMS AFFECTING H2 + F2 LASER

PERFORMANCE

R. Kerber, R. Brown

To cite this version:

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JOURNAL DE PHYSIQUE CoZZoque C9, suppZLment a u n O 1 l , Tome 41, n o v e m b r e 1980, page C9-9

AN ANALYSIS OF THE ROLE OF KINETIC MECHANISMS AFFECTING Hz..+

F Z

LASER PERFORMANCE "'

R.L. Kerber and R.C. Brown.

M i c h i g a n S t a t e U n i v e r s i t y , E a s t L a n s i n g , M i e h i g a n 48824, U.S.A..

Abstract.- Computer simulations of pulsed H + F2 chemical laser performance have been made with a comprehensive model of VRT relaxation mechanisms in HF. The study includes an in-depth analysis of the role of vibrational to rotational, rotational to rotational, vibrational to vibrational and ro- tational and vibrational to translational relaxation mechanisms in HF lasers. The study also exami- nes the effect of rotational to rotational lasing on P-branch laser energy. The model is used to assess the strengths and weakness in our current understanding of HF relaxation kinetics through comparisons with experiment. Model predictions are found to be in good agreement with experiment.

'I. INTRODUCTION

Rotational nonequilibrium is an important kinetic mechanism in modeling the HF pulsed chemical laser, for e x a m ~ l e see 1-5. Its general effects are to increase the number of simultaneous vibrational lasing transitions, lower the intensity and in- .crease the duration of each transition and

shift laser energy to higher rotational levels. Early rotational nonequilibrium models assumed that rotational noneuuNib- rium arises from pumping of rotational levels and vibrational lasing transitions. These mechanisms alone are not able to explain all rotational nonequilibrium phenomena. Several researchers6-8 have observed P-branch lasing from J-levels higher than are known to be populated by pumping reactions. Early models also do not account for the occurrence of pure rotational lasing observed experimentally in rota- tionally excited HF gas, for example see 9-12. There is some evidence that rotational lasing could be a significant fraction of total laser power. 9

It is possible that these high rotational state phenomena are produced by"- vibrational to rotational (VR) energy transfer. Vibrational to rotational energy transfer assumes that part of the vibrational energy given up by a molecule during vibrational relaxation appears as an increase in rotational energy for the same molecp&e. . . If the product rotational _{. . -} %

This work ws: supported by AFOSR Grant No. AFOSR-

80-003.

state is chosen to minimize the energy defect, very high rotational states result with a very small contribution to the translational energy mode.

The three-dimensional classical trajectory calculations of wilkins13 pro- vide tho first multicruanta VP, TAT and rotational relaxation rates suggesting the importance of the V? mechanism in HF-HF interactions. Xotational relaxation by rotational to translational and rotational to rotational energy transfer may occur at rates slower than the VR

mechanism.

The importance of VR kinetics in understanding rotational nonequilibrium effects of the HF laser is investigated with two histinct laser' _{models. The first} model is a comprehensive formulation developed from the nonequilibrium model of Reference 2 and includes multiquanta VP, W , RP and 3T energy exchange mechanisms based on the trajectory calculations of

wilkins13

,

the experimental measurements of Hinchen and ~ o b b s l ~ , and the earlier

w

and VT kinetic recommendations of Cohen. l5 Rotational lasing was included in this model to assess the importance of the VR mechanism on this phenomena. ~lthough this model includes all kinetic .mechanisms suspected to be important to

the HF system, the model assumes spatially averaged fluxes and gains. For some ap- plications, this assumption is not

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C9- I 0 JOURNAL DE PHYSIQUE

properly satisfied. For single pass

amplifiers, the gain and radiation flux are critically dependent on the longitudinal position within the gain medium. Because it is important to be able to model systems which pre dependent on both position and time, a second model was developed.

This second model simulates a single pass, laser amplifier pumped by the Hz-F2 chain reaction and contains all reaction mechanisms included in the laser oscillator model. A spatially dependent model of a pulsed HF laser device has been developed by Moreno. Although 3oreno3 includes rotational nonequilibrium in his model, the model does not include VR energy transfer. The amplifier model is used to simulate the preliminary laser fluorescence experi- ments of Hinchen and sobbs16 designed to detect VR energy transfer.

The essential features of kinetic mechanisms incorporated in the models are shown in Figure 1. vibrational to

Energy Level Diagram

Energy

t

p-bronc Rotational L a s i n g 7 1 Lasing

Figure 1. schematic diagram of kinetic mechanisms included in computer simulation. The V-V and R-R mechanisms are included in the model but are not shown in the figure

.

translational transfer is replaced by the VR reaction

HF(v,J)

+

M

2

HF(vtrJ')

+

AE

where AE is the energy defect for the reaction. Instead of vibrational energy being lost to the translational energy mode, it may appear in part as an increase in rotational energy of the collision species. The product rotational state, J', takes on values ranging from Jmin-4 to Jmin+2 where Jmin is some specified fraction of the product rotational state which gives the minimum energy defect for VR relaxation (see Figure 1). If this

fraction is one, essentially all of the vibrational energy goes into rotation resulting in energy defects of only a few hundred inverse centimeters.

For the amplifier model, a simplifi- cation is obtained by choosing a

Lagrangian description for the system; hence, the flux equation reduces to the ordinary differential equation

df

dt

= caf (1)

where c and a are the speed of light and the gain, respectively and the input signal which is to be amplified by the medium is divided into incremental flux elements. Equation (1) is solved for each of these flux elements as it passes through the gain medium. Each integration time step, At, moves the flux element a distance AX = cAt through the gain medium, hence the space dependence of the flux element can be obtained in increments of cAt through the medium.

The amplifier model was developed from the laser oscillator model described previously and includes the same kinetic mechanisms, including VR energy transfer. The major revision to the oscillator model was the substitution of space averaged

fluxes with single pass fluxes in the flux equation (1). Optical losses are

neglected in the amplifier.

11. EFFECT OF VR MECHANISM

A. Comparison with V T Model

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equilibrium moc?e12 which simulated vibrational relaxation by the simpler vibrational to translational energy exchange

mechanism. Both models allowed rotational lasing to occur.

Several important results are note- worthy. The VR model predicts the occurrence of rotational lasing on all vibrational bands whereas no rotational transition reached threshold gain in any of the VT model computions. The failure of even the slow rotational relaxation times of wilkins13 to produce rotational lasing in the VT model indicates the strength of the rotational nonequilibrium effect of the VR mechanism and

suggests its importance in explaining rotational lasing. The effect of VR energy transfer on P-branch lasing from high J levels cannot be determined from this comparison. Although pulse lengths are similar for P-branch lasing, the VR model develops considerably less energy and peak power than the VT model. Subse- quent analysis will show this energy loss is not the result of rotational lasing.

B. Relative Contribution of VR and RRT Kinetics in Oscillator Model The effectiveness of the VR mechanism in populating high rotational states is dependent on its relative contribution to the total kinetic rates. Much of the in- terest in rotational lasing arises from its potential parasitic effect in com- peting for energy available for P-branch lasing. Computer simulations have been made to assess this effect. In particular, the phenomena of rotational lasing will only appear if rotational relaxation is not too fast compared to the VR rate. The effect of varying VR and RRT rates on both P-branch and rotational lasing energy are illustrated in Figure 2. wilkins13 recom- mended VR and RRT rates are taken as standard in these calculations. As VR rates are.increased, P-branch lasing rapidly de- creases, and rotational lasing increases. Vibrational energy is converted to rotational energy of high J states resulting in large rotational lasLng gains. The de-

IO-VO-~

lo0

101 10'

lo3

RATE/STANDARD RATE

10-61

10-2 10-1 100 101

lo2

103 RATE/STANDARD RATE

Figure 2. Effect of VR,T and RR,T rates on laser energy Gas Mixture: 0.02F:0.99F2:1H :20He; T.=300K1 Pi=20 Zorr 1 Cavity Conditions:

30% loss; 10 cm gain length (a) Total P-branch lasing energy (b) Total rotational lasing

energy

pletion of vibrational bands is illustrated by the shutting off of P-branch bands as VR deactivation dominates the kinetics. When VR rates are made so small that rotational relaxation can depopulate high J

states faster than they are populated, rotational lasing becomes negligible.

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JOURNAL DE PHYSIQUE

high rotational states. Increasing rotational relaxation rates by a factor of ten causes rotational lasing energy to decrease by three orders of magnitude. In fact, only one rotational transition ex- ceeds 'threshold gain in this case. In general, as rotational relaxation rates increase, P-branch lasing energy increased.

C. Translational. Contribution to the VR, T Mechanism

The postulation of vibrational to rotational energy tradfer occurring with a minimum energy defect has several con- sequences. The smaller energy defects result in population of very high rotational states and suggest faster vibrational deactivation rates than is expected for VT reactions. Because of the near resonant exchange of energy from vibrational to rotational modes, however, the excited HF

molecules only very slowly relax toward equilibrium with the translational tempera- ture through rotational to translational energy transfer. The translational contribution can be enhanced by allowing larger energy defects for the reaction. To test the effect of increasing the VT contribution, the product rotational state, Jminl predicted by the minimum energy defect assumption was decreased by 50% for all VR, T reactions in the laser oscillator model.

Rotational Lasing. Stanaad JMlN

&

z

J

Figure 3. Effect of increased VT contribution for VR,T reactions on relative lasing energy Gas Mixture:

0.02F:0.99F2:1H :20He; Ti=300KI Pi=ZO Zorr Cavity Conditions:

30% loss; 10 cm gain length

The effect on relative P-branch and rotational energy is shown in Figure 3. Be- cause the ability of the VR mechanism to populate high rotational states has been decreased by one-half, a change in spectral distribution is expected. Although rotational lasing above J-10 disappears and the relative contribution to P-branch lasing from high J levels slightly de- creases, very little other effect is predicted. To understand this behavior, the population distributions were examined. It is observed that the ability to pump very high rotational levels is markedly decreased in the enhanced VT computations, but for Jf12 the populations for the two cases are nearly identical. Since P-branch lasing is modeled only for rotational levels less than this, the absence of spectral differences is immediately understood.

There is little experimental or theoretical evidence to suggest what the proper partitioning between VR and VT reactions should be. Hinchen and Hobbs 16 recently performed laser fluorescence ex- periments designed to directly verify the qccurrence of VR by detecting the presence of nonequilibrium populations in high rotational states. The laser amplifier model is used to simulate their ex- ,periment

.

Hinchen and ~ o b b s ' ~ measured

the rotational distribution in v=O of HF by probing this manifold after pumping v=l with pulse laser radiation. The pump laser operated on the P1(4) transition. The cw probe laser could be tuned to resonance with P-branch transitions in the manifold. Although the uncertainties in their data were large, they found rotational populations exceeding equilibrium values for J>10.

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0.04 ysec square wave. No perturbation from a Boltzmann distribution was detected in the V=O manifold except for small dip at 5-4 where the pump laser removed population. The absence of a VR hump about J=8 is understood by estimating the expected rate of change of HF(v=OrJ=8). Even after 0.1 psec, the largest population to be expected in HF(v=O, J=8) is only 1% greater than the Boltzmann population. A second simulation was performed using a minimum energy defect VR reaction. The resulting rotational populations for v=O after 0.04 psec are plotted with the data of Hinchen and Hobbs in Figure 4.

0 Experiment A S~mulotion: Standard JMlN at 0.04~1sec Simulation: 80% of JMlN at 0.04usec 0 Simulotlon: 80% of JMlN at 0.5l~sec Rotational Level

Figure 4. Simulation of laser fluorescence experiment of Hinchen and Hobbs to detect VR

Gas Mixture: 0.1 torrZHF at 300X Input Pulse: 442 W/cm of

40 nsec duration

Both sets of data show clearly derined humps in the populations at high rotational numbers. It is evident that the use of a minimum energy defect VR reaction in the simulation causes the VR hump to occur at higher rotational levels than is suggested by the experimental data; the humps peak at 3=11 and J=14 for the experiment and simulation respectively. A

VR reaction for which the product rotational states are approximately 80% those of a minimum energy defect reaction is suggested by the experimental data. Such a choice of product rotational state was

_-

employed in the model and the results appear in Figure 4. Populations at both 0.04 usec and 0.5 ysec are illustrated. The VR hump is clearly discernible and has shifted to lower rotational levels as expected. The results compare favorably with the experimental results. Differences in relative magnitude between the simulation and experiment reflect differences in absorption lengths and time allowed for relaxation. There is also considerable uncertainty in the experimental values. The relative distribution over the product states is the important result shown by the model.

D. Comparison with Experiment Although a number of experimental studies of the pulsed HF chemical laher spectra have been reported in the litera- ture (for example see 8 r 9, 17-19) considerable discrepancy exists between their results. These differences reflect the extreme sensitivity of laser performance to initial gas composition and cavity conditions. Our model predictions are compared with the experimental results o# Parker and Stephens. l8 Rotational relaxation rates were based on the J-depenaence of wilkins13 and were adjusted so that for J=lOr the rate was 20% of the binary: collision frequency. The recommendations of Bartozek, et. a120 were used for th6' endo- thermic cold pumping reactions. The v- dependence of the VR reaction.and coeffi- cients are given by the most recent recommendations of C6hen. 21 Computations were performed for both the cases of the product rotational _state chosen as 50% and 80% of the value expected for a minimum energy defect reaction.

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C9- 14 JOURNAL DE PHYSIQUE

JMIN case, the predominate effect is on levels well above those involved in P- branch lasing. The experimental results of Parker and Stephens are compared with those assuming JMIN is 50% of that for minimum energy defect in Figure 5.

The model predicts smaller peak power than was experimentally observed; however, predicted energy was greater than the experimental value. Although the model com- pares favorably for the lower three bands, excessive P-branch lasing occurs for high J levels in the hot bands. Parker and Stephens results suggest that the hot bands shut-off before the cold bands. 18 This behavior was not predicted by the model.

Attempts to explain the discrepancies in terms of uncertainties in initial conditions were not successful. Taken to- gether, uncertainties in gas composition, F-atom dissociation and optical losses could explain the behavior, but it appears that uncertainty in a single initial con- dition cannot account for the discrepancy.

Parker 8. Stephens

0.10

Model Redictions Standard Case

5 10

We note that suchard17 and Sojka, et. a18 do observe hot band lasing late in the pulse.

IV. SUMMARY AND CONCLUSIONS

Vibrational to rotational energy exchange has the ability to populate high rotational states and has been used to qualitatively explain high 3 state phenomena in HF. Comparison of a VT model with a VR model suggests that VR energy exchange is necessary to produce rotational lasing. Existing rotational nonequilibrium mechanisms of rotational pumping and P-branch lasing do not significantly raise rotational gains above threshold. Rota- tional lasing has been shown to be strongly dependent on VR rates. The presence of even strong rotational relaxation did not appear to reduce P-branch lasing energy.

There is little experimental or theoretical evidence to suggest the proper translational contribution to VR,T energy transfer. The effect of different par- titions between VT and VR on predicted laser performance was considered. In- creasing the VT contribution produced lower product rotational populations and slower back reactions for VR,T resulting in smaller predicted pulse duration and laser power.

A VR reaction which populates rotational states that are approximately 80% of those with minimum energy defect best simulated the experimental results of Hinchen and Hobbs.

The oscillator model was compared with the experimental results of Parker and ,Stephens. l8 Although the model com- pares favorably for the lower three hands, excessive P-branch lasing occurs for high J levels in -the hot bands. Although changes in the nascent vibrational distribution of the hot pumping reaction could

J _{significantly decrease hot band lasing}

energy, Parker and Stephens' observation Figure 5. Comparison with experiment:

distribution of band energy of early quenching for the hot bands is Gas Mixture: not consistent with accepted rate data for

cavity Conditions :

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SAMSO-TR-