Diagnostics of the active medium of a waveguide CO2 laser: Vibrational distributions and plasma-chemical processes

Pergamon

J. Quanr. Specrrosc. Radial. Transfer Vol. 52, No. 5, pp. 621-630, 1994 Copyright 0 1994 Elmier Science Ltd 00224073(!M)fMtO!57-3 Printed in GreatBritain. All rightsreserved 0022-4073/94 $7.00+ 0.00

DIAGNOSTICS OF THE ACTIVE MEDIUM OF A WAVEGUIDE CO, LASER: VIBRATIONAL DISTRIBUTIONS AND PLASMA-CHEMICAL PROCESSES MAXIM V. SPIRIDONOV,~ SUSAN MCKENNA-LAWLOR,$ 11and SERGUEY Y. SAVINOV$ tGenera1 Physics Institute, 38 Vavilov Street, Box 117942, Moscow, Russia, @pace Technology Ireland, St. Patrick’s College, Maynooth, Co. Kildare, Ireland, and QP.N. Lebedev Physical Institute, 53 Leninsky Ave., Box 117924, Moscow, Russia (Received

23 November 1993)

Abstract-High-resolution diode laser spectroscopy has been used to study the active medium of a waveguide COz laser. Detailed rotational and vibrational distributions of the CO, molecules in a capillary glow discharge plasma have been obtained over a wide range of

experimental conditions. Influences exerted by plasma-chemical processes on the rates of excitation and deactivation of the molecular vibrations in the discharge plasma have been investigated. The results of this study make it possible to construct a satisfactory kinetic model of the active medium of the waveguide CO2 laser.

1. INTRODUCTION In view of the various applications of compact CO2 lasers of the waveguide type, having high specific energy parameters and unique spectral characteristics, investigations of their active media are of great interest. The active element of such a laser is a discharge in a narrow tube of radius R - 1 mm, and the electric power density input exceeds by about two orders of magnitude the corresponding power in the wider (R - 1 cm) discharge tubes of open-cavity CO2 lasers. First order approximations to CO, waveguide laser active medium parameters are frequently obtained from the results of various investigations of the active media in wide tubes, using the premise of gas discharge similarity theory. However, this premise is deemed to be only an approximate one.’ More reliable predictions of CO2 waveguide laser parameters require special simulation techniques. During the first stage of the work it seemed quite natural to use known CO2 laser design methods that have been adequately developed for traditional systems, where the agreement between the experimental and theoretical values, say for the population inversion, does not exceed lO-50% over a wide range of conditions. Attempts along these lines, however, were not successful since the energy parameters calculated for CO2 waveguide lasers by this procedure turned out to be appreciably larger (by up to an order of magnitude) than was found by experiment. Of particular interest, from the standpoint of assessing the possibility of simulating the processes in an active medium, is a comparison of the calculated and experimental distributions of the working molecules over their rotational and vibrational levels. The determination of these distributions under waveguide conditions meets, however, with considerable difficulties. The methods of emission spectroscopy have no clear cut physical justification at pressures higher than 30 torr, while a method based on measuring the gain for a group of rovibrational transitions is not accurate enough under waveguide conditions.‘s3 (ITo whom all correspondence

should be addressed. 621

MAXIMV. SPIRIWNOVet al

622

In this paper we present detailed investigations technique of diode laser spectroscopy. 2. EXPERIMENTAL

of CO2 molecular distributions

CONDITIONS

using the

AND TECHNIQUE

In this study, the active medium of a CO2 waveguide laser operating on the mixture CO,-N,He (1: 1: 8) was investigated using a water-cooled discharge BeO-ceramic capillary, with inside and outside diameters 2R = 2 mm and 6 mm respectively. The total length of the discharge tube was 60 mm, and the length of the discharge region along the capillary axis was 50 mm. The gas pressure wasp = 30-100 torr, and the discharge current was i = 1-12 mA d.c. Kovar electrodes were led out through side stubs. The rate of gas flow through the discharge gap was 5 m *set-‘. A diagram of the experimental arrangement is presented in Fig. 1. The emission from the diode laser was shaped by BaF, lenses, passed through the discharge capillary, and then entered the monochromator. The grating monochromator, which had a spectral resolution of about 0.5 cm-‘, served both for coarse absolute frequency calibration and for laser mode selection. The frequency references were set by the Fabry-Perot etalon. The signal on the InSb photodetector was fed via an amplifier to an oscilloscope, from thence to a boxcar averager (PAR, Model 162) and subsequently recorded using a plotter. The PbSSe diode laser operated in a pulse-periodic mode and was excited by rectangular current pulses of amplitude - 1 A, duration up to 500 msec and repetition frequency about 100 Hz. These pulses were suitably shaped by an oscillator and amplified by a current amplifier. The laser output power was - 100 ,uW. The lasing frequency was tuned during the time of the current pulse due to the unsteady heating of a p-n junction. The position of the tuning band was changed by varying the temperature (in the range 40-80 K) of the cooling duct on which the laser was mounted. A long-time temperature stability of 1O-3 K was achieved with the aid of a feedback temperature controller. To compensate for temperature fluctuations < low3 K, leading to frequency fluctuations of - 10m3cm-‘, an optical triggering system was used. The joint action of the feedback temperature controller and the optical triggering system made it possible to maintain the laser frequency stable at a level of 10m4cm-‘. The diode laser spectrometer described provided the following characteristics: region of wavelength tuning 2 160-2330 cm-‘, ranges of continuous frequency tuning up to 12 cm- ’ , spectral resolution 10e4 cm-‘, response time of the recording system lo-' sec. The small diameter of the waveguide capillary channel leads to severe difficulties with regard to the localization of the radial zone of the measurements. In those cases where the diameter of the probing laser beam (B 1 mm) is comparable with the capillary diameter (2 mm), it is necessary to

9 GJllent amp.

Photodetector

Fig. 1. Diagram

of experimental

configuration.

Diagnostics of a waveguide CO2 laser

0 01

0.5

1.0

1.5

2.0 ER ,

623

2.5

103cm”

Fig. 2. Rotational distributions of CO, molecules for various vibrational states. i = 9 mA; p = 60 torr; TR = 530 K.

reduce the measured averaged quantities to those on the discharge axis. A reduction procedure was developed, and associated numerical calculations4 carried out within the range of the investigated conditions showed that, at a probing beam diameter of 1 mm, the corrections needed to reduce the values of the rotational temperature to the centre from the average measurements, amount to 5-7%. A complementary correction for the vibrational temperature does not exceed 10%. Since the real measurement accuracy for both rotational and vibrational temperatures was reliably of the order of 2%, control measurements were made in which the beam was collimated to 0.3 mm in the axis discharge zone. Experimental measurements have fully confirmed the correctness of this procedure. 3.

EXPERIMENTAL

RESULTS

For all fixed values of the gas pressure and the discharge current, we recorded in the frequency interval 2160-2330 cm-’ about 1500 vibrational-rotational absorption lines that coupled more than 30 pairs of vibrational levels of ‘2C’60, and 5 pairs of vibrational levels of ‘3C’60, from all four vibrational modes of the molecules. The corresponding vibrational transitions pertain to the sequence vlu:03+ ul 0: (z++ 1). The range of observed rotational levels in low-lying vibrational states reached a value of J = 100. These detailed investigations have guaranteed a high accuracy and reliability for the results obtained. Figure 2 shows examples of the COz molecular distributions over rotational levels for the four vibrational levels 01’0,00°2,01 ‘2, and 01’3 at a total gas pressurep = 60 torr, and current i = 9 mA. The rotational temperature for all vibrational levels was 530 + 10 K. The rotational temperature was, from general physical considerations, identified as the gas temperature, T, = T. A typical example of the CO* molecular distribution over the vibrational levels at p = 60 torr and i = 9 mA is shown in Fig. 3. In this case, the data relate to the population of the 31 vibrational levels. Knowing the molecular distribution and the gas temperature, we can determine also the total density of the CO, molecules.’ This yields, in particular, information on the degree of dissociation of the working molecules in the plasma discharge. The corresponding data, in the form of the dependencies of the quantities N,o,/N go-o, on the discharge conditions at various pressures, are given in Fig. 4 (Nzoz is the density of the CO2 molecules in the initial gas mixture at the real gas temperature). This technique can be used to determine the densities of the molecules CO, and CO. It will be useful in what follows to present data concerning the density of the oxygen atoms determined, under similar conditions, by mass spectrometriP and optical actinometry’ methods. Figure 5 shows the ratio of the density of the oxygen atoms to the density of the CO* molecules in the initial mixture at the real gas temperature in the discharge.

MAXIM V. SPIRIWNOVet al

624

Fig. 3. Distribution

of CO, molecules

4.

over the vibrational T,=T,=560f15K.

DISCUSSION

levels. i = 9 mA; p = 60 torr; T, = 2410 + 40 K;

OF

RESULTS

4.1. Comparison of calculation with experiment To calculate the vibrational level populations of the molecules, we used both the level-by-level approach and the vibrational-temperatures approach.4 The high electric power density input typical of CO, waveguide lasers calls for analysis of the validity of the theoretical approach based on the (known) vibrational-temperatures approximation. We have therefore carried out a level-by-level examination and comparison of the calculated and experimental results on the discharge axis. The values of E/N, gas temperatures, and dissociation degree used in the calculations were taken from experiment. A comparison shows that calculation leads to a substantially higher degree of excitation of the asymmetric stretch CO, mode than is found experimentally. The character of the divergence is illustrated in Fig. 6 for p = 60 torr and i = 9 mA. Nevertheless, as the deviation of the vibrational level populations from a Boltzmann distribution is small, this justifies the use of the vibrational-temperatures approach. Furthermore, comparison of the experimental and calculated data was carried out under a wide range of experimental conditions using a vibrationaltemperatures approach.

i,mA

0

i

Fig. 4. Density

4

i;

of CO1 molecules

i

io

as a result of dissociation.

i2

Diagnostics of a waveguide CO, laser

0.0 4 0

2

6

4

8

625

10

12

Fig. 5. Density of the oxygen atoms in a capillary discharge (see Ref. -I\,,.

Table 1 shows the experimental and calculated results for 11 different conditions in the pressure range 30-100 torr, for currents l-12 mA. All the results pertain to the axis of a discharge capillary. In the first three columns are listed the pressure, discharge current, and the relative axial/field strength E/N. These are followed by the excitation power density on the tube axis (column 4); measurements of the CO, dissociation degree in the discharge (column _5),and the gas temperature (column 6). In columns 7 and 8 are given the values of the vibrational temperatures T, of the bending mode (the experimental values of T, in all the investigated cases were equal to the vibrational temperature T, of the symmetric stretch mode) and T3 of the antisymmetric mode. Both experimental and calculated values of T2 and T3 are listed. In columns 9 and 10 are shown the values of the rate constants K, and K3 of VT-relaxation of the bending and antisymmetric stretch modes. Each lower value has been obtained by using the procedure described in Ref. 4, which gives good agreement between experimental and calculated results in the wide discharge channels of open-cavity CO, lasers. These constants yield those calculated values of T, and T, which are indicated in the lower lines in columns 7 and 8. The upper lines contain K2 and K3, which are fit parameters chosen to give the best agreement between the calculated and measured vibrational temperatures. It can be seen from Table 1 that in order to attribute the measured results to relaxation of the vibrational modes over the entire range of conditions, it is necessary to increase the VT-relaxation rate constants by 1.5-5 times. It is deemed that the causes of such strong discrepancies may lie in failure to take into account the influence of the specific plasma-chemical transformation on the rates of the excitation processes and on the deactivation of the molecular vibrations in the discharge plasma. 0

2

4

6

8

10

12

14

EV , 103cm”

Fig. 6. Distribution of CO, molecules over the vibrational levels of the antisymmetric stretch mode. l-experiment; 2
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et al

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4.2.Influence of chemical-transformation products on the relaxation rates The real chemical composition of the plasma of a CO, waveguide laser with d.c. excitation was investigated in a number of studies and is already adequately well known. The change of composition from the initial is due mainly to CO* dissociation. The supplementary components are CO, OS, and 0. Both CO and O2 insignificantly influence the VT-relaxation constants K2 and K3.On the contrary, it is known that oxygen atoms are quite active in the quenching of asymmetric vibrations of CO,. The corresponding rate constant is (6.7 + 1.2) . lo3 set-’ torr-‘.* At a 1% concentration in the mixture, the contribution of the oxygen atoms to the relaxation is approximately equal to the contribution of all the remaining components. The pressure of noticeable amounts of oxygen atoms is a distinctive feature of CO, waveguide lasers compared with traditional COz lasers with wide tubes, owing to the substantially higher current density. This circumstance was pointed out already in Ref. 6. It appears in Ref. 9 that the rate of CO relaxation on 0 atoms is approximately the same (measurements were however made only at temperatures higher than 1500 K). The relaxation rate of N, on 0 atoms is slower by about one order.’ The dependence of the 0 atoms density on the discharge conditions is shown in Fig. 5. These data expanded as a percentage of the total particle density are also presented for convenience in Table 2, which shows also the values of AK i. These values should be added to the calculated constant K y'to take into account the action of the oxygen atoms. Comparison of Tables 1 and 2 shows that, by making allowance for the influence of oxygen atoms on the acceleration of the VT-relaxation, it is possible to bring the calculated and the experimental results closer to each other, although the difference between them still remains significant.

Diagnostics of a waveguide CO2 laser

4.3. Influence of plasma-chemical density

processes

621

on the spatial distribution of the excitation power

As is always the case with respect to calculations for traditional CO, lasers with wide tubes, the rate of excitation of the molecular oscillations was determined from the measured total discharge current and field intensity, under the assumption of Bessel radial distributions of the current and electron densities. It is common knowledge that the Bessel distribution follows from Shottky theory of the positive column of a glow discharge. This theory is based on the assumption that ambipolar diffusion prevails over bulk recombination and that the charged component of the plasma consists of electrons and positive ions. If, however, the plasma contains electronegative particles, it is possible to have a level of formation of negative ions such that they accumulate in amounts that exceed the electron density. The theory of the positive column in electronegative gases was considered in many papers (as in Ref. 10, for example). The main result is that the electron density can be distributed under certain conditions over the radius more uniformly than over a Bessel function. In this case the excitation power density on the discharge axis will be lower than that for a Bessel distribution. We now discuss, in this connection, the ionic composition of the plasma of interest to this study and the formation, therein, of a radial profile of charged particles. The three component positive column plasma model used in the theory takes into account impact ionization, processes of attachment and detachment of electrons and dissociative ion-ion recombination.‘O The characteristic values of the rate constants of dissociation and ion-ion recombination amounts to lo-*-lo-’ cm3 set-‘. At a charged-particle density of 10’“-lO” cmm3 the recombination frequency does not exceed lo4 set-‘. In the investigated mixture, the rate constant of the dissociative attachment E/N = (2.5-3) 9 lo-l6 V . cm* amounts to k 2’2 = (2-3) * lo-l2 cm3 set-’ for CO,, see Ref. 11, and to k? = (6-10). lo-‘*cm3 set-’ for 02, see Ref. 12. At densities N x 5. 10’6cm-3 and for N o2 E (l-2) . lOI6cm-3, the attachment frequency, even only for these tw60’molecules, is v, = k 2’2 . NCo, + k ? . No, x 2 . 10’ set-‘. Therefore, in the electron balance, recombination can be ignored. As shown by analysis of the published data,13.14an important role in the formation of the ion content of the plasma should be played by reactions in which the O- ions take part. The O- ions are produced in dissociative attachment processes e+CO,+CO+Oe+O,-+O+Owith rate constants k $‘2 and k 2 as given above. The O- ions then enter into rapid processes of associative detachment.14 O- + CO + CO2 + e,

k z” = 7.3 . lo-‘O cm3 set-‘. kj=2.

O-+O-+O,+e,

10-‘0cm3sec~‘.

The total frequency of the detachment in these processes is v,, = k 2’ . NC0 + k y . No, where

Table 2. Influence of oxygen atoms on the values of VT-relaxation rate constants K,.

3 NO/N,

%

0.3

0.5

0.8

1.3

2.5

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0.8

1.0

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0.4

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184

255

40

87

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44

108

124

152

190

278

380

157

187

248

145

187

N,,

MAXIM V. SPIRIDONOV et al

628

and No are the densities of the CO molecules and the 0 atoms respectively. can be formed in very rapid three-particle reactions’3,‘4 O-+CO,+CO,-+CO;

+CO,,

O-+CO,+He-+CO;+He,

In addition,

cluster ions

k, = 1.1; 10-27cm6sec-‘. k,=2.8.10-**cm6sec-‘.

The clustering frequency is v,, = (k, . Y $o, + k2 . Y,,, . Y,,) . N 2, where Yc,, and YHeare the relative fractions of COZ and He in the mixture, and N is the total density of the particles. Since the degree of CO2 dissociation under the considered conditions is 0.2-0.5 (Table l), the frequency v, of the dissociative attachment turns out to be about two orders lower than the detachment frequency in collisions of O- with CO and 0. The density of the O- ions is therefore low N, = v,n,(v,, + v,‘))‘. The rate of CO;

ion formation

is V,I W

=

v, nev,,

/(vc, +

V,I 1.

Destruction of the CO; ions is a complicated process that includes direct and associative detachment, exchange, and further clustering. If it is characterised by an effective detachment constant, it can depend on the conditions in the discharge. The results of Ref. 14 lead to the conclusion that CO; is the principle negative ion in the discharges in working mixtures of CO, lasers. At low pressures, when the frequency of negative ion formation turns out to be low compared with the detachment frequency, the number of negative ions is smaller than that of electrons and the usual Shottky regime with a Bessel electron-density profile is realized. With increase of pressure, negative ions will accumulate in the discharge and non-Bessel electron density distributions can be obtained. Arguments and estimates of this kind are confirmed by results” which concern an open microwave cavity used to investigate a discharge in a capillary of 2 mm diameter under conditions close to those discussed here. It was found that, at 20-60 torr, the fraction of the ion current is 15% and the radial profile of the electron density deviates noticeably from a Bessel profile. An estimate, based on the experimental data, of the effective detachment constant leads to a value kd = 1.5 . 10 -I4 cm3 set ’ If this and the other rate constants given above are assumed, the transition to the regime of negative ion accumulation should take place for the relevant composition of gaseous components at a pressure > 20 torr. Using the experimental results of Ref. 15 we calculate that the excitation power on the capillary axis is smaller by a factor of 1.S than it would be for a Bessel profile in the absence of an ion current. Figure 7 compares the experimental and calculated dependencies of the temperature T, on the discharge current at pressures 30, 60, and 100 torr at the discharge capillary axis. In the final calculation variant (dashed lines), the quenching of the molecular oscillations by the oxygen atoms and the deviation of the electron density radial profile from a Bessel profile were taken into account. A satisfactory agreement between prediction and experiment is apparent (the discrepancy between them is from 30 to 150 K over the entire range of conditions). For the sake of clarity, the results of the initial calculation where the two factors mentioned above are not taken into account, are shown in the same figure. We have noted (see Table 1) considerable discrepancies between the calculated VT-relaxation constants of a block of bending and symmetric stretch modes of CO?, on the one hand, and the constants needed for fitting to the experiment, on the other. Here the strongest relaxator in the mixture is helium, which constitutes 80% of the mixture, and the presence of small amounts of oxygen atoms can not influence substantially the relaxation rate. Allowance for the influence of the negative ions on the electron component (decrease of the excitation power on the axis) makes it possible to reconcile, almost completely, the predicted and experimental values of T2 when the calculated values of the relaxation constants are used. It must be noted that the attainment of this agreement is not as instructive as for T,. The point is that the kinetic calculations make it possible to determine only the difference between the gas and vibrational temperatures, which is large for T3 and small for T2. By experiment, on the other hand, the gas and vibrational temperatures are measured separately with an error of 2-3%. Since, in our range of conditions, the deviation of the vibrational temperature in the bending and symmetric stretch modes from the gas temperature is

Diagnostics

of a waveguide

CO, laser

629

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.

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l 60 Torr n 100 Torr 1.0

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I 2

I 4

I 6

I 8

temperature T3 vs the discharge current. Solid curves-xperiment; of calculation; dashed curves-final calculation.

I 10

i,mA

I 12

dots-initial

variant

5-15%, the error in the experimental determination of this discrepancy can exceed 50%. We note at the same time that these errors do not influence greatly the results of laser parameter calculation.

5.

CONCLUSION

The experimental investigations carried out, and the associated simulation of kinetic processes, allow us to reveal circumstances that are substantial for understanding the difference between the descriptions of the active media of traditional cw CO* lasers with wide tubes, and CO, waveguide lasers. The main cause of the difference is the higher specific energy input and gas density in the case of waveguide lasers with capillary discharges, where plasma-chemical processes assume a larger role. This results in an increased density of oxygen atoms which influence the relaxation of the antisymmetric stretch mode of CO,, the presence of noticeable amounts of negative ions, the redistribution of the electron density over the radius, and the presence of an ion component of the current. Formation of negative cluster ions takes place in three-particle reactions, and the effect of increasing their concentration is proportional to the square of the gas density. This, and a number of other factors, impose restrictions on the prediction of laser parameters through using for the gas discharges similarity relations that assume dominance of bimolecular reactions, thereby ensuring invariance of the Boltzmann and Pauli equations under scale transformations. Nevertheless, the results of the present study show that the use of numerical calculations based on traditional schemes, but supplemented by notions concerning the specifics of plasma-chemical processes, makes it possible to construct an adequate kinetic model of the waveguide CO, laser active medium.

REFERENCES 1. R. L. Abrams, Laser Handbook Vol. 8, p. 41, North-Holland, Amsterdam (1979). 2. V. P. Avtonomov, V. N. Beltyugov, A. A. Kuznetsov, V. N. Ochkin, N. N. Sobolev, M. V. Spiridonov, Y. V. Troitsky, and Y. B. Udalov, Soviet J. Quantum Electron. 12, 1400 (1982). 3. K. V. Vereschagin, A. Y. Volkov, A. G. Sviridov, and S. N. Tskhai, “ A Study of the Active Medium of a Waveguide CO2 Laser,” Preprint No. 189 P. N. Lebedev Physical Institute, Moscow (1983) (in Russian).

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MAXIM V. SPIRIDONOVet al

4. I. I. Zasavitsky, R. S. Islamov, M. A. Kerimkulov, Y. B. Konev, V. N. Ochkin, S. Y. Savinov, N. N. Sobolev, M. V. Spiridonov, and A. P. Shotov, “Investigation of the Active Media of a Waveguide CO, Laser,” Preprint No. 18 P. N. Lebedev Physical Institute, Moscow (1988) (in Russian). 5. A. V. Demianenko, I. I. Zasavitsky, V. N. Ochkin, S. Y. Savinov, N. N. Sobolev, M. V. Spiridonov, and A. P. Shotov, Soviet J. Quantum Electron. 17, 536 (1982). 6. V. I. Volchenok, V. N. Komarov, and V. N. Ochkin, Soviet J. them. Phys. 8, 1061 (1982). 7. N. Z. Zhenbaev, M. Mamytbekov, and D. K. Otorbaev, Soviet J. appl. Spectrosc. 51,12 (1989). 8. W. I. Buchwald and G. I. Wolga, J. them. Phys. 62, 2828 (1975). 9. Y. M. Gershenzon, E. E. Nikitin, V. B. Rozenshtein, and S. Y. Umansky, “Interaction Between Vibrational Excited Molecules and Chemical Active Atoms,” Plasma Chemistry 5(3), Moscow (1978) (in Russian). 10. C. M. Ferreira, G. Gousset, and M. Touzeau, J. Phys. D D21, 1403 (1988). 11. W. L. Nighan, Phys. Rev. A A2, 1989 (1970). 12. R. S. Islamov, I. V. Kochetov, and V. G. Pevgov, “Analysis of Interactions Between Electrons and Oxygen Molecules,” Preprint No. 169 P. N. Lebedev Physical Institute, Moscow (1988) (in Russian). 13. H. S. W. Massey, Negative Zons, Cambridge University Press (1977). 14. W. L. Nighan and W. J. Wiegand, Phys. Rev. A 10, 922 (1974). 15. A. S. Smirnov and K. S. Frolov, Soviet J. tech. Phys. 58, 1878 (1988).