One-dimensional modelling of TEA CO2 lasers

Optics & Laser Technology,

Vol. 28, No. 3, pp. 183-186,

Copyright Printed

ELSEVIER ADVANCED

in Great

Cm 1996 Elsevier Britain.

1996

Science Ltd

All rights reserved

0030-3992/96

$15.00+0.00

0030-3992(95)00082-S

TECHNOLOGY

One-dimensional TEA CO2 lasers

modelling

of

T. Y. TOU, K. W. BEAK, Y. H. CHEN One-dimensional modelling was applied to a TEA Cop laser whose discharge volume was divided into multiple narrow channels. Each of these channels was regarded as a separate laser channel in which a circuit-coupled kinetic model was employed to compute its discharge formation, and a rate-equation model was used to predict its laser output. Such a one-dimensional model could be employed to study the spatial variation in the transverse discharge-due mainly to a one-sided ultraviolet-preionization and the electrode contour-and its effects on the laser output. Reasonably good agreement was obtained between the one-dimensional model and the experiment, which employed a pair of Ernst profile electrodes. Copyright @ 1996 Elsevier Science Ltd. KEYWORDS: one-dimensional

modelling, preionization, laser profiles

Introduction

On the other hand, the discharge behaviour of the TEA COZ laser has been described by a number of circuitcoupled kinetic models 14-16.The discharge kinetics and hence the laser excitation were all taken to be homogeneous in the entire discharge volume, in particular, laterally towards the edges of the laser electrodes. These models may be regarded as zerodimensional as their discharge gap and width were usually predetermined by two fixed values. As such, these models could not possibly be used to investigate any spatial variation in the transverse discharge, which may be caused by, for example, a non-uniform distribution of the ultraviolet-preionization and the electrode contour. To this end, one-dimensional modelling was considered in which the discharge volume was divided into multiple narrow channels. Each of these channels was considered as a laser channel in which its temporal discharge formation was described by the circuit-coupled kinetic model15 and the laser excitation was by the rate-equation mode19.

Profiled electrodes, such as those designed by Chang’ and Ernst2 have been commonly used to create a volumetric glow discharge in the transversely excited atmospheric-pressure (TEA) CO2 laser because of the highly uniform field they could produce. In practice, the calculated field at these electrode surfaces could be changed by a number of factors, for example (i) spatial distribution of the preionization394; (ii) the dielectric support structures, misalignment, imperfect machining et& and (iii) the effect of the current return path6. Effects due to a non-uniform distribution of the ultraviolet preionization have been reported to change the discharge formation3 and laser gain profile4. Dyer7 derived a relationship for the field uniformity requirement for a stated electron-density distribution in the Chang’ profile electrode. The output characteristics from a TEA CO2 laser have been predicted by various models which may be classified into three different types: (i) rate-equation819; (ii) multi-temperaturelO~l ‘; and (iii) comprehensive kinetic12. A rate-equation model is relatively simple, yet is able to provide some basic guidelines for designing and optimizing the multiparameter TEA CO2 laser. Such effects as the gas heating and gain saturation13, however, could only be investigated by the multitemperature model. Reasonably good agreements were obtained between the calculated and measured laser pulse shapes by using the rate-equation and multitemperature models.

Model The basic idea of one-dimensional modelling has been previously applied to the discharge-pumped excimer17 and mercury-bromide ‘* lasers. Geometrically, the discharge volume was divided into multiple narrow laser channels. The laser output was summed over the entire discharge cross-section. We have adopted this idea for the TEA C02-laser discharge for the purpose of studying the effect of a one-sided ultravioletpreionization on the laser output, for which a pair of Ernst profile electrodes (k = 0.03) were used. Figure 1 shows the cross-sectional area of the transverse discharge which was equally divided into narrow channels, labelled as i = 5 1, f 2, f . . . etc. Each

The authors are in the Laser and Electra-Optics Laboratory, Institute of Advanced Studies, University of Malaya, 59100 Kuala Lumpur. Malaysia. Received 15 March 1995. Revised 29 June 1995.

183

184

One-dimensional

modeling

of TEA COP lasers: T. Y. Tou et al. total laser output energy was summed over all these narrow channels. This model was chosen for its simplicity and a much shorter computer run time. However, we have used E/N-dependent values20 for the electron-impact excitation rates of the: (i) CO? molecule to the upper laser level; and (ii) nitrogen molecule to the first vibrational level, where N2 (v = l), rather than constants. This minor modification was found to improve the predicted laser output.

Laser electrode

Experiment I

I

I

I -I

-2

I

I 0

I

I I

I

I

I

*

2

X (cm) Fig. 1 volume

Multiple between

laser channels, each 2 mm wide, for the discharge Ernst profile electrodes (k = 0.03)

channel has a discharge width of 2 mm. The discharge gap at the centre was designed to be 2 cm. This gap gradually increases for outer channels, as defined by the Ernst profile of k = 0.03. The gap was taken to be the average value in all these channels. In each of these channels, the circuit-coupled kinetic modeli of the TEA CO2 laser was employed to describe the temporal development of the discharge. Its electron density n,(i) was governed by dn,(i)/dt

= (a - u)ne(i) W - -yn,2(i)

where 01, a and y are the electron ionization, attachment and recombination coefficients. These are time-varying coefficients which are dependent on the E/N values, where E is the electric field and N the total ambient particle number. The discharge channels were coupled to the external driving circuit by an average discharge resistance R, which was given by’7s’x R, = 1

l/R,(i)

c i

1

where R,,(.i) is the discharge resistance of the ith channel. The individual value of Rp(i) was calculated from

A TEA CO2 laser system was designed with two Ernst profile electrodes2 (k = 0.03) which were 5 cm wide and 38 cm long. A sliding spark array2’ was used to provide the ultraviolet-preionization from one side of the laser chamber. Both circuits for driving the ultravioletpreionizer and the laser discharge were controlled by a novel two-stage cascade spark gap21. This spark gap could easily delay the laser discharge from the ultraviolet-preionization for 50-500 ns; the optimal time delay was about 150 ns. The main discharge circuit consisted of a storage capacitor (C,) and a peaking capacitor (C,). The peaking capacitor was used to enhance the discharge uniformity. Although the laser output energy was not significantly increased by having this peaking capacitor, it was rendered more reproducible mainly as a result of a more uniform discharge formed at its early stages. The laser gas was a mixture of CO2 : N2 : He = 1 : 1 : 8 and the laser optics consisted of a lOO%-reflectivity back mirror and a 70% output coupler. The transverse laser beam profile was measured by using a vertical split of 2 mm width. As this laser was operated with a one-sided ultravioletpreionization, a non-uniform spatial distribution of photoelectrons in the discharge volume was expected when the laser discharge was launched about 150 ns later. The photoelectron density, neo was calculated using the measured results of Babcock et a1.22. Figure 2 shows the transverse distribution of neo in the laser channel. The preionization capacitor, C,,, was usually 2 nF, which was estimated to provide at least lo6 photoelectrons cm P3 in the centre of the discharge volume. IOR

I

Rp(i) = V/ [en,(i) wd(i) Ai] where e is the electronic charge; n,(i) the electron density; wd(i) the electron drift velocity and Ai the crosssectional area of the ith channel. The discharge voltage V was essentially the same for all the channels at any time but since their discharge gaps were different in +x-directions, their E(i)/N values were expected to be different. It should be noted that the measured voltage is different from the discharge voltage V across the laser channel. This is mainly due to the geometrical constraint at the laser chamber such that an inductive component, L,(dZ,/dt), is always added to the measured voltage waveform. The term, L,, represents the inductance and Ii, is the discharge current in the laser channel.

-2

-I

0

I

2

X (cm)

After obtaining values of ni(i) and E(i)/N, both as functions of time, the rate-equation model of Andrews et al.9 was applied to each of the laser channels. The

Fig. 2 Spatial distribution of photoelectron density, neo as a function of distance, +Xfrom the centre of the discharge volume (based on the results i Ref. 22)

One-dimensional modelling of TEA CO2 lasers: T. Y. Tou et al.

-

185

Calculated Measured

---

Time (ns) I

I

-I

-0.5

I

I

I

0

0.5

I

I

1.5

X (cm) (‘4

---

4

Calculated Measured

Fig. 4 A comparison between the calculated and measured transverse beam profiles (fluence) for a charging voltage of about 24 kV (C, = 37.6 nF)

t

1200 + Measured loo0 -

I

I

,

I

I

I

I

100

200

300

400

500

600

Time (IN) Fig. 3 Comparisons between the (a) calculated and (b) measured discharge voltages and currents

Results and comparison Figures 3(a) and (b) show, respectively, the measured and computed voltages and currents for the above TEA COZ laser. Reasonably good agreements were obtained between these two sets of discharge waveforms. However, two discrepancies between the measured and computed discharge waveforms were usually observed: (i) the computed breakdown voltage is usually higher at time t = 85 ns; and (ii) the computed current swing is larger at t ‘v 105 ns. These discrepancies were found to be mainly due to the coupling between the main discharge and the preionization circuits via the twostage spark gap. The measured discharge waveforms at the two points, (i) and (ii), could change if the preionization time delay and capacitance, C,,, were varied. For time t > 105 ns, the computed voltage, with the exception of the first and second peaks, was generally slightly lower than that measured. The reverse was true for the current. Figure 4 shows both the calculated and the measured transverse beam profiles of the laser output at a charging voltage of about 24 kV (C, = 37.6 nF and C, = 1.76 nF). Both of these transverse beam profiles show that their peak fluence shifted to the right (+x-direction) by a few millimetres. The shift was predicted to be 2-3 mm as compared with the measured value of 3-4 mm. This predicted right-shift substantiates the early report4 on the laser gain profile, which was shifted closer to the ultraviolet-preionizer. The measured transverse beam profile also shows increasingly large error bars in its right wing. These were probably due to the discharge instability as the discharge was shifted to regions with an electric field that was increasingly non-uniform.

2 B 5 5 5 ,a 5 j

800-

600

400-

200 -

I

I

I

I

I

20

30

40

50

C, (nn Fig. 5 A comparison between the calculated and measured laser output energies as functions of the storage capacitor, C,. The charging voltage was about 20 kV. 1 -D and O-D: one- and zerodimensional models respectively

Both the measured and computed laser output energies are presented in Fig. 5, as a function of the storage capacitor, C, . These two energy-curves show reasonably good agreement between them; also, both were essentially not linear functions of C, . The dotted line is the predicted laser-output energy by a zero-dimensional kinetic model, which assumed a discharge width of 2 cm. This discharge width was estimated from the thermal paper used for detecting the laser output. It should be mentioned that a zero-dimensional kinetic model could also produce fairly good agreement for discharge waveforms of voltage and current but not the laser output by the rate-equation model, as shown in Fig. 5 by the dotted line. If we were to increase the discharge width arbitrarily, for example to 2.2 cm, and tolerate some mismatch between the computed and measured discharge waveforms, the predicted laser output would still fall onto a linear line. This new line might agree with the measured energy-curve at some

One-dimensional modeling of TEA CO2 lasers: T. Y. Tou et al.

lower C,-values but it would suffer an increasing deviation at the higher end. Discussions

3

4

and conclusions

A one-dimensional model for the TEA CO2 laser was developed which enabled the effect of a non-uniform spatial distribution of ultraviolet-preionization on the transverse beam profile to be investigated. For simplicity, the laser oscillation in each of the ith channels was assumed to be single-mode and the spreading of laser energy from one channel to another was not taken into consideration. A right-shift in the peak laser fluence was predicted but not the left-right asymmetry in the transverse beam profile. This may imply that there could be other factors involved that were not considered in this exercise. For example, the electric field lines were all taken to be vertically straight within each laser channel, which for the outer regions becomes an increasingly poor approximation. Electrode misalignment as well as machining errors were also not taken into consideration. Although the computed voltage was slightly lower than that measured, and the reverse was true for the discharge current, these discrepancies were not found to shift significantly the agreement between the predicted and measured laser profiles and energies. This might be explained by the fact that, in the rate-equation model, electron excitation of CO2 and N2 depends on both the E/N value and electron density. A lower computed voltage might mean a reduced E/N value and hence electron excitation rates for CO* and NZ; however, these were compensated by a higher electron density or discharge current. Thus, the voltage and current could have compensated each other in the rate-equation model.

5 6

10 11

12

13 14

19

20

References 21 1

2

Chang, T.Y. Improved uniform-field laser and high-voltage applications, 405-407 Ernst, G.J. Uniform field electrodes Commum. 49 (1984) 275-277

electrode profiles for TEA Rev Sci Instrum, 44 (1973) 22 with minimum

width,

Opr

Denes, L.J., Kline, L.E. Electrode- and preioniser-geometry effects on TEA laser discharge formation, Appl Phys Left, 30 (1977) 197-199 Denes, L.J., Weaver, L.A. Laser gain characterisation of nearatmospheric CO2 : N2 : He glows in a planar electrode geometry, J Appl Phys, 44 (1973) 4125-4136 La&~ C.A., Ruth, H.N. Field uniformity in a Chang electrode svstem Ovt Laser Technol, 21 (1989) 99-104 cazzaro,‘P.Di., Giordano; G., ‘Mezi, L., Zheng, C.E. Field uniformity of discharge lasers: electrode profiles and current return path effects, Opt Laser Technol, 26 (1994) 15- 19 Dyer, P.E. Field uniformity requirements in TEA CO2 lasers, J Phys E: Sci Znstrum, 11 (1978) 1099%1101 Vl&es, G.C., Moeny, W.M. Numerical modelling of pulsed electric CO, lasers. J Avvl Phvs. 43 (1972) 1840-1844 Andrews, KJ., Dyer, PII!,., James, d.J. A’rate equation model for the design of TEA CO* oscillators, J Phys E: Sci Instrum, 8 (1975) 493-497 Manes, K.R., Segiun, H.J. Analysis of the COz TEA laser, J Appl Phys, 43 (1972) 5073-5078 Davies, A.R., Smith, K., Thomson, R.M. Calculations on output pulse shapes, gain pulse profiles, and gain limitations in the CO2 TEA laser, J Appl Phys, 47 (1976) 2037-2043 Hokazono, H., Ohara, M., Midorikawa, K., Tashiro, H. Theoretical operational life study of the closed-cycle transversely excited atmosnheric CO? laser. J Ad Phvs, 69 (1991) 6850-6867 Smith, A.L.S.; Meltis, JI Operating efficiencies‘in pulsed carbon dioxide lasers, Appl Phys Left, 41 (1982) 1037-1039 Kline, L.E., Denes, L.J. Investigations of glow discharge formation with volume preionisation, J Appl Phys, 46 (1975) 1567-1574 Ernst, G.J., Boer, A.G. Kinetic modelling of a self-sustained TEA CO, laser. Ovt Commum. 35 (1980) 249-254 Beverly Iii, R.E. P’ulsed power modeling of very-large-aperture, transverse-discharge CO2 lasers, Appl Phys B, 53 (1991) 187-193 Krause, U., Kleinschmidt, J. One-dimensional model of discharge pumped excimer lasers, J Appl Phys, 72 (1992) 1237-1243 Kushner, M.J., Pindroh, A.L., Fisher, C.H., Znotins, T.A., Ewing, J.J. Multidimensional modeling of transverse avalanche laser discharges: Applications to the HgBr laser, J Appl Phys, 57 (I 985) 2406-2422 Nighan, W.L. Electron energy distributions and collision rates in electrically excited N2, CO and COz, Phys Rev A, 2 (1970) 1989-2000 Norris, B., Smith, A.L.S. Operation of sliding-spark arrays for laser preionisation, J Phys E: Sci Instrum, 10 (1977) 55 l-554 Tou, T.Y., Low, K.S., Tan, B.C. A simple two-stage cascading spark gap for ultraviolet-preionised transversely excited atmospheric CO* laser, Rev Sci Instrum, 62 (1991) 2584-2587 Babcock, R.V., Liberman, I., Partlow, W.D. Volume ultraviolet preionisation from bare sparks, IEEE J Quantum Electron, 12 (1976) 29-34