1927 I t ~ I . 1 . J O U R K A L OF QLANTL'LI EL-tCTKONICS. VOL 24. KO 9. SEPTEMBER 198X

Parametric Study of the CuBr Laser with Hydrogen Additives

DIM0 N. ASTADJOV, NIKOLAY K. VUCHKOV. AND NIKOLA V. SABOTINOV

Abstracr-A systematic investigation of the electric parameters of the CuBr laser plasma during the excitation pulse in their correlation to the laser output characteristics is presented. Based on the electric pa- rameters we have calculated the temporal course of the electron den- sity during the discharge. We offer a simple mechanism which gener- ally explains the hydrogen occurred in copper vapor laser. The mechanim conrists of shielding copper ionization bj the process of electron detachment from negative hydrogen ions.

I. INTRODUCTION HE average output power of CuBr laser as well as the T lifetime of the sealed version [ 11, [2] associated with

some of its inherent advantages determine the attention to this promising modification of the copper vapor laser.

The processes in the discharge plasma of copper and copper halide lasers have been a subject of investigation in a great number of experimental and theoretical works. However in almost none of them (excluding a very few, e.g. , recently [28]) the occurrence and the strong effect of .hydrogen on their performance have been taken into account. As it was first established in [3] and [4] small amounts of hydrogen added to the neon buffer gas lead to doubling of CuBr laser power and efficiency. It has been also revealed that hydrogen changes the decay rates and the radial distribution of the copper metastables in CuBr laser [ 5 ] . The approach applied in [4] for an evaluation of some electric pulse parameters of the laser plasma is lack- ing because of poor precision and requires an improve- ment of their adequate measurement and processing. It is an explicable attempt to associate them with the micro- scopic parameters of the laser plasma (gas and electron temperature, electron density, plasma composition, etc.) which might help us to come closer to the explanation of the hydrogen effect.

This paper presents a systematic investigation of the electric parameters of the CuBr laser plasma during the excitation pulse in their correlation to the laser output characteristics. The electric parameters of the plasma have been studied as functions of the pressure of the buffer gas, the pressure of the CuBr vapor and the repetition rate of the excitation pulses. A calculation of the radial profile of the gas temperature with and without hydrogen has been done as well. On the basis of the electric parameters the

Manuscript received March 13, 1988; revised April 15, 1988. The authors are with the Institute of Solid State Physics, Bulgarian

IEEE Log Number 8822226. Academy of Sciences, Sofia, Bulgaria.

temporal course of the electron density during the dis- charge has been computed. In the conclusion we offer a simple mechanism which explains the hydrogen effect in copper (and possibly gold) vapor laser.

11. EXPERIMENTAL Either of two 50 cm electrode-separated fused silica

tubes of 4 cm (tube A ) and 4.6 cm i.d. (tube B ) was em- ployed in the experiments. Four quartz diaphragms of 2 cm i.d. were mounted in the discharge region. CuBr was put in three reservoirs. A thyratron pulser incorporated a 1.1 nF storage capacitor and a 0.5 nF peaking capacitor was used for discharge initiation. Average input power from HV rectifier of 1.2 kW ( f 5 percent) was main- tained for all experiments.

The discharge current and the tube voltage were mea- sured, respectively, by a Rogowski-coil probe and a low inductance HV probe. The laser pulse was detected by a p-i-n diode optical detector (Linconix Model 40 D). Then the optical pulse was integrated to eliminate its complex structure. For that a 20 MHz cutoff filter incorporated in the oscilloscope (Tektronix 2445) was used. The integra- tion caused a certain error (about 10 ns) in the time char- acteristics of the optical pulse, but this was within the accuracy of our data processing. All pulses (voltage, cur- rent, and emission) were photographed on the oscillo- scope display. Afterwards they were mathematically pro- cessed in order to eliminate the inductive component of the voltage and to calculate the active voltage U,, the pulsed power P , the plasma resistance R , and the pulsed energy E( t , ). The following well-known equations were used:

U, = U - L d I / d t ( 1 )

P = U,I ( 2 )

R = U,/I ( 3 )

E ( t , ) = P d t (4)

where U and I are the voltage and the current from the oscillograms, L is the inductance of the discharge circuit, to is the time of the start of the gas discharge (conditioned to be at I = 10 A), and t , is a certain moment during the excitation pulse. The inductance L was calculated from the oscillograms and it was about 0.7 pH.

0018-9197/88/0900-1927$01 .OO O 1988 IEEE

1928 IEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. 24, NO. 9. SEPTEMBER 19x8

The total average output power was measured by a ca-

The pressure of the buffer gases was measured by a hy- lorimetric powermeter (Scientech 362).

drostatic gauge.

A. Hydrogen Pressure Scanning The scanning was carried out in the range 10-'-1 torr

H2. The neon pressure was optimum-15 torr. The repe- tition rate (RR) during the hydrogen pressure scanning was 15.5 kHz.

In general the experiments confirmed the results of our previous paper [4]. Using a better technique for hydrogen dosing we succeeded to correct the dependence of the out- put power and the efficiency on the hydrogen pressure at pressures higher than 0.3-0.4 torr (Fig. 1). It was found that when the hydrogen pressure pH > 0.4 torr the laser power starts to drop and when pH = 1 torr it is as much as in pure neon (i.e., when pH < lop2 torr). Meanwhile the difference in the cross-sectional pattern of the laser emission was preserved. When p H < 0.1 torr the pattern was annular, but when pH > 0.4 torr the central area of the laser beam was brighter than its periphery (we called such a pattern Gaussian-like). This aspect of the behavior of the laser emission was observed with a cavity as well as without it.

As the electric plasma parameters varied during the ex- citation pulse it was necessary to fix some typical instants of time correlated wjth the laser emission. We selected three moments of the integrated laser pulse and indexed them, respectively, by 1 the beginning, 2 the maximum, and 3 the end of it. The electric parameters which are given below had good reproducibility.

Fig. 2 depicts the electric parameters corresponding to the beginning of the laser pulse. The following inferences could be made whenp, was increased from to 1 torr.

1) U,, and RI increased. 2) ZI abruptly decreased maintaining nearly constant

3) P , and E, degraded. The appearance of local extrema about 0.3 torr H2 is

not sure because the experimental error involved them. Besides the parameters described in Fig. 2, when pH

was increased from lop2 to 1 torr, the following param- eters had a typical behavior too:

4) The breakdown voltage (conditioned to be U, at I = 10 A ) increased 3-5 times (from 2-3 to 10-11 kV).

5) U,, doubled (from 3-4 to 7-8 kV) and U,, increased 10 times (from 0.2-0.4 to 2-4 kV).

6) R2 increased 2-3 times (from 15-20 to 40-60 Q ) and R 3 increased more than 10 times (from 1 to 10-20 Q ) .

7) P2 (which is almost the peak power) appeared max- imum near 0.3 torr H2.

All of these facts ascertain the rough estimations re- ported in [4]. Moreover the detailed study of the electric parameters has revealed that there is no peculiarity in their behavior (excepting P 2 ) around the optimum value P H = 0.3 torr.

from 0.1 to 1 torr H2.

1 '

0 0.5 PH .To r r 1

Fig. 1. The average output power P and the efficiency of CuBr laser versus the hydrogen pressure p H . The solid curve is for tube B and the dashed curve is for tube A. The neon pressure is 15 torr and the repetition rate is 15.5 kHz.

11 200

I 7

0 0.5 PH.Torr 1

Fig. 2. The behavior of the plasma parameters (resistance R I , active volt- age U,,, discharge current I,, pulsed power P I , and energy E, at the beginning of the laser pulse) and the laser power P as functions of the hydrogen pressure p H . The solid curve is for tube B and the dashed curve is for tube A. The neon pressure is 15 torr and the repetition rate is 15.5 kHz.

Fig. 3 gives an idea of the typical waveforms of the voltage, the current, and the integrated laser pulse, as well as the calculated U,, R, and P during the discharge in two cases. Fig. 3(a) is for 15 torr Ne buffer and Fig. 3(b) for 15 torr Ne and 0.3 torr H2. The addition of 0.3 torr H2 caused the following changes.

1) U, and R increased, and I decreased up to the end of the laser pulse.

2) The rate of the current rise did not change. 3) The delay between the beginning of the voltage and

the beginning of the current increased from 25 to 40-50 ns .

4) The laser pulse became about 20 ns longer (from 60-65 to 80-85 ns at base).

5 ) The variation of the whole energy E, of the excita- tion pulse (calculated from (4) for t l corresponding to the end of the positive halfwave of the current) was within the experimental error of 20 percent.

It is important to note some other concomitants. First,

ASTADJOV et d.: CuBr LASER WITH HYDROGEN ADDITIVES 1929

U W

10

5

UwV

5

IO P,MW

0.5

U , K V

10

5

10 U a,KV

5

10

P,M W

0.5

I

100 200 t . n s

(a)

11.4 n- 1200 . z o o

- 500

(b)

Fig. 3 . The voltage (shown inverted), the current, and the laser emission pulses, as well as the time-dependent active voltage (shown inverted) U,,, plasma resistance R , and the pulsed power P; (a) 15 torr Ne and (b) 15 torr Ne and 0.3 torr HZ. The repetition rate is 15.5 kHz.

the width of the laser pulse (measured at the base) in- creased peaking 80-85 ns when p H = 0.3 torr. Afterwards it shortened and when p H = 1 torr it became 60-65 ns long as it was in pure neon. So the laser emission with 0.3 torr H2 was about 30 percent longer than in pure neon. But the energy of the laser pulse increased not less than twice. This way the energy increase was a result of the sharper increase of the pulsed power. Second, when p H was increased the delay between the beginning of the cur- rent and the beginning of the voltage increased as well. Without hydrogen it was about 25 ns and when 1 torr H2 was added the delay mounted to 70 ns. Third, when p H was increased the current rise decreased, and fourth, the whole-energy variations were within the 20 percent ex- perimental error; hence hydrogen was considered not to change the excitation pulse energy E,.

In order to eliminate the influence of CuBr and the products forming in the plasma from it on the electric pa- rameters we had examined them before the reservoirs of tube A were filled with CuBr. Under operating conditions (e.g., average input power, repetition rate, insulation,

etc.), which were optimum for the laser performance we studied the electric parameters of the neon-hydrogen plasma varying p H at constant neon pressure of 15 torr. In summary, the main results are the following, namely when p H was increased from to 1 torr.

1) U, and R increased. 2) E, changed within the 20 percent experimental er-

3 ) The delay between the beginning of the current and

4) The current rise decreased. The observed similarity in the behavior of the electric

parameters of the plasma with and without CuBr indicates that it is most likely the essential process responsible for the more efficient oscillation of the CuBr laser to occur in the buffer neon-hydrogen plasma.

In this connection we held experiments in which helium substituted for hydrogen. Concerning some properties (i.e., atomic mass, elastic cross section, heat conductiv- ity, etc.) helium is the closest element to hydrogen. The pressure of helium was varied from 0.5 to 5 torr and the neon pressure was 15 torr.

In all cases the addition of helium to the neon buffer resulted in a deterioration of the laser performance-the output power decreased and strong discharge instabilities appeared. The laser emission remained annular. But like hydrogen, when the helium pressure was increased it caused an increase of the resistance and the active voltage of the plasma.

These experiments have shown that the effect of hydro- gen is probably attributed to the specific properties of hy- drogen as an atomic particle, i.e., in the energetic struc- ture of the hydrogen atom and the hydrogen molecule (the latter is very stable) and/or the occurrence of specific atomic (or molecular) formations (e.g., ions, complexes, etc.) in the neon-hydrogen plasma.

Special attention was paid to a very possible reason for the more powerful laser emission with hydrogen-whether the addition of hydrogen raises the optimum temperature of the CuBr reservoirs (the optimum reservoir temperature is when the average output power peaks). The experimen- tal evidence of this fact would mean that hydrogen causes an increase of the copper density (e.g., by initiat- ing plasmo-chemical reactions) which might result in more powerful laser emission.

For measuring of the reservoir temperature T, we used chromel-alumel thermocouples. In the strong RF field near the laser tube the measurements were not very ac- curate. Apart from that RF disturbance the great number of experimental findings showed that hydrogen does not change the optimum reservoir temperature which main- tains T, = 490 + 10°C. The pressure of the saturated CuBr vapor at this T, is 0.33 ?::$ torr [6].

Fig. 4 shows the dependence of the average output power on the reservoir temperature with 15 torr Ne (curve 1) and with an additional 0.3 torr H2 to neon (curve 2). In pure neon the lasing began at T, = 370 10°C. With 0.3 torr H2 it started at T, = 400 + 10°C and increased

ror.

the beginning of the voltage increased.

IEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. 24. NO. 9. SEPTEMBER I Y X X 1930

11

P .W

7

3

J .J . LOO 500 T,.’C 600

Fig. 4. The dependence of the average laser power P on the reservoir tem- perature T, in 15 torr Ne (1) and in 15 torr Ne and 0.3 torr HZ ( 2 ) . The repetition rate is 15.5 kHz.

very sharply to several watts of average power. In pure neon the laser emission was annular. With 0.3 torr H2 it had no “black hole.” When T, was raised the center be- came brighter than the periphery. With the rise of T, the diameter of the laser beam reduced and in the optimum it was between $ and 3 of the initial size. When T, went beyond the optimum the laser power degraded. Often (but not every time) a discharge contraction appeared leading to either removing of the laser beam off the cavity axis or laser beam twisting.

B. Neon Pressure Scanning The neon pressure scanning experiments were done in

tube B . The preliminary tests showed that the optimum hydrogen pressure is a constant of 0.3 torr and it does not depend on the neon pressure. Thus the experiments were carried out with a constant 0.3 torr H2 additive. The same scanning experiments were repeated in pure neon.

Fig. 5 depicts the average output power and the electric energy El (i.e., until the beginning of laser pulse) as func- tions of the neon pressure pNe. In summary the main re- sults are as follows.

1) The optimum neon pressure ( 15-20 torr) remained the same in both cases.

2) With 0.3 torr H2 the operating range of pNe became less than in pure neon. The upper limit of pNe decreased from 250 to 100 torr.

3) At p N e - 80 torr the output power in pure neon was as much as with 0.3 torr HZ. WhenpNe > 80 torr hydro- gen caused the output power to decrease.

4) When pNe was above 80-90 torr the electric energy El in pure neon tended to be less than 0.3 torr H2.

The neon pressure scanning was accompanied by some characteristic phenomena on which we will comment be- low. First, we observe the behavior of the cross-sectional pattern of the laser emission. In pure neon the cross sec- tion of the laser beam was annular in the whole operating range of pNe except when p N e < 10 torr. Then it had a tendency to be uniform. Unfortunately, we did not suc- ceed in examining laser performance at lower pNe for technical problems. It should be mentioned that the an-

10

P ,W

6

2

20

E,.mJ

10

50 150 PNe, Torr

Fig. 5 . The average output power P and the energy E , versus the neon pressurep,,. Curves 1 are in neon and curves 2 are in neon with 0 .3 torr H,. The repetition rate is 125.5 kHz.

nulus diameter decreased when pNe was increased. At op- timum reservoir temperature with 0.3 torr H2 the laser emission was Gaussian-like irrespective of pNe. When the CuBr vapor pressure was low (i.e., at low T,) somewhere about the generation threshold the laser emission was uni- form or annular, respectively, for pNe < 50 torr and p N e

> 50 torr. Second is the observation that the laser operation was

stablest in the optimum pNe range ( 15-20 torr) and the moving of pNe away from this range caused the discharge contractions and near-electrode instabilities to become more frequent which were detrimental to the laser oscil- lation.

Third, we would note that based on the dependence of the output power and the electric energy deposited in the discharge until the beginning of the laser emission (Fig. 2 and Fig. 5) hydrogen increases the excitation efficiency of the copper laser levels.

C. Repetition Rate Scanning

The examination was performed in both tubes A and B . The experimental results in both cases were in good agreement to each other. Two series of experiments were carried out.

The first series was a repetition rate (RR) scanning from 11 to 20 kHz with constant storage ( 1.1 nF) and peaking (0.5 nF) capacitances. The RR range was limited for technical reasons-the impossibility of maintaining an in- put power of 1.2 kW from the HV rectifier without any capacitance change.

The output power dependence on the RR is plotted in Fig. 6: Curve 2 is for 15 torr Ne and curve 3 is for 15 torr Ne with 0.3 torr H2 additive. In that series the reservoir temperature was kept constant-T,. = 485 f 5°C. As could be seen the output power dependence on RR was not uniform; there were sags and peaks which generally coincided for curves 2 and 3. The sharp sags of power were featured by a discharge contraction and unstable laser oscillation. The optimum RR range from 14.5 to 16.5 kHz was not affected by the hydrogen addition. It is important to note that in the whole tested RR range the average laser

ASTADJOV et al.: CuBr LASER WITH HYDROGEN ADDITIVES 1931

e. I

,I' ~ \ J

10 RR,kHz 20

Fig. 6. The dependence of average output power P on the repetition rate R R . Curves 1 and 2 are in 15 torr Ne and curve 3 is in 15 torr Ne and 0 .3 torr H,. The solid curves are without any capacitance changes.

output with 0.3 torr H, was higher than in pure 15 torr Ne.

The second series of RR scanning was carried out in pure 15 torr Ne. In order to maintain an input power of 1.2 kW from the HV rectifier the respective capacitances were increased-the storage one from 1.1 to 4 nF and the peaking from 0.5 to 1.65 nF.

The output power dependence on the RR in that series is shown in Fig. 6 by the dashed curve 1. Noteworthy is the fact that the average laser power was nearly propor- tional to the RR. Meanwhile, the optimum reservoir tem- perature decreased slowly from 480°C (at 15.6 kHz) to 410" (at 3.3 kHz). The most likely reason for that might be the more intensive reconstitution of CuBr molecules during the longer interpulse interval. The only exception was about 6.7 kHz where the laser output and the opti- mum reservoir temperature abruptly dropped to a magni- tude typical for 3.3 kHz.

During the experiments of the second series an inter- esting behavior pattern of the radial distribution of the laser emission was observed. When the RR > 9-10 kHz the laser beam was annular and with an RR increase it became more distinct. The annulus diameter increased too. Between 6 and 9 kHz the radial profile was uniform (plateau-like) with the exception of 6.7 lcHz when the laser emission was concentrated in a small area around the op- tical axis and looked like a tiny annulus with very bright contours. When the RR < 6 kHz the laser beam was Gaussian-like.

The analysis of the plasma electric parameters of the second series showed that the laser intensity in the central area of the beam was proportional to the plasma resistance in the moment of the beginning of the laser pulse.

Generalizing the study of the electric parameters of the CuBr laser plasma we reveal the following correlation be- tween the cross-sectional pattern of the laser emission and the ratio El / E 3 (E, and E3 are, respectively, the electric energy deposited in the discharge until the beginning and the end of the laser pulse). When E, / E 3 < 0.1 the pat- tern was Gaussian-like, when 0.1 < E, / E 3 < 0.13 it was plateau-like and when El / E 3 > 0.13 it became annular.

The above energetic relations might reflect the fact that in certain conditions the spatial (especially radial) electric energy input in the discharge was not uniform and/or a considerable part of it was lost in nonlasing channels (e.g., ionization of copper atoms).

D. Radial Projile of Plasma Gas Temperature One of the possible mechanisms of hydrogen on the

CuBr laser performance is to change the gas temperature of the plasma due to the very high heat conductivity of hydrogen. In order to estimate to what extent hydrogen changes it, we have simulated the thermal mode of oper- ation of our CuBr laser.

The axial section schematic of a part of an experimental tube is given in Fig. 7 . One of the features of our design was the confining diaphragms which separated the tube interior in two zones. The electric discharge was located in zone Z with radius RI. The power input was considered to be uniform. In zone I1 (within RI I r I R2 where R2 is the tube radius) there was no power deposition. For simplifying the heat modeling we assumed that the dia- phragms are very thin and they do not disturb the gas tem- perature. The tube wall thickness was also not consid- ered. (The factual discrepancy was less than 50 K.)

The steady-state heat conduction equation is

div ( k grad T) + q8 = 0 ( 5 )

where k is the thermal conductivity, T i s the gas temper- ature, and q8 is the power deposited in zone I per unit volume.

Assuming that the gas temperature varies only in the radius direction, ( 5 ) transforms to

l d ( r k z ) + qv = 0. r dr

The dependence of the thermal conductivity of gases and gas mixtures has the form [7]

k = BTU

where a and B are constants (within a certain temperature range) which are specific for each gas or gas mixture.

(7)

Equation (6 ) is solved considering that

and

= k(R, + 0) (8) dr R I + O

where T, is the temperature of the tube wall.

the form for zone 11: Taking into account (7 ) and (8) the solution of (6) has

111 + a

l + a 2B quR:lnR,) r (9)

and for zone I

where 111 f a

q,R: In "> l + a TI = (T;' + -

2B RI

1932 IEEE

diaphragms

Fig. 7. The axial section schematic of a part of an experimental tube. Zone I has radius R , and zone I1 is confined between R , and R , .

The average gas temperature in zone I is found by av- eraging (10) over the radius of zone I:

where To = TI,=,. The constants a and B were computed by the least

squares method using experimental data. The thermal conductivity of the neon-hydrogen mixture was calcu- lated by the empirical method of Brokaw. The approxi- mation results as well as the references are given in Table I. The hydrogen (and the neon-hydrogen mixture, as well) has two different approximations. This is because of the dissociation of hydrogen molecules which increases rap- idly at gas temperatures higher than 1600 K resulting in intensification of the heat extraction from zone I to zone 11.

Fig. 8 shows the radial profiles of the gas temperature in tube A for q, = 4 W/cm3 (curves 1 and 2 ) and qv = 5 W/cm3 (curves 3 and 4 ) which is 50 and 65 percent, respectively, of the average input power from the HV rec- tifier equal to 1.2 kW. The wall temperature is considered to be constant at 800 K.

At fixed power deposition the profiles with 0.3 torr H, (curves 1 and 3) and in pure 15 torr Ne (curves 2 and 4 ) differ factually only in zone I. The maximum temperature difference occurs in the center-in neon it is 150-200 K higher. Concerning the average gas temperature in neon it is only about 100 K higher than in the mixture of 15 torr Ne and 0.3 torr H2.

Thus, heat modeling has shown that the hypothesis of the thermal nature of the hydrogen effect has a limited opportunity to be plausible since the variations of the gas temperature caused by the addition of 0.3 torr H2 are too small.

E. Temporal Course of the Electron Density During the Excitation Pulse

The significant increase of the plasma resistance during the discharge pulse when hydrogen is added to neon buffer might be attributed to an increase of the frequency of elec- tron collisions and/or the decreased electron density.

Thus we have made an attempt to calculate the temporal course of the electron density during the excitation. To that purpose we used a method for calculating the con- ductance of the multicomponent gas mixture containing

JOURNAL OF QUANTUM ELECTRONICS. VOL. 24, NO. 9. SEPTEMBER 1988

TABLE I

Gas Temperature K B a Ref.

Ne 800-3000 9.7 X 0.685 [8]

H2

15 torr Ne and 0.3 torr H, 1600-2600 1.84 X 1.54 'lo]

191 800- 1600 4.4 x 1

1600-2600 4.4 X IO-*' 7.56 9.3 X 0.695 800- 1600

Nore: B and a are fork in W . m-' . K - ' .

' 16 8 0 a r,mm 16

Fig. 8. Radial profiles of the plasma gas temperature in tube A. Curves 1 and 2 are for qtj = 4 W/cm3 and curves 3 and 4 are for q,, = 5 W/cm3. The temperature profiles in 15 torr Ne and 0.3 torr Hz are shown by curves 1 and 3, and in 15 torr Ne by curves 2 and 4. The arrows locate zone I having diameter 2Rl.

negative ions. The method is reported in [20] and has proved confidence in an equilibrium and a nonequilibrium plasma.

The CuBr laser plasma comes from two initial compo- nents-neon and copper bromide. The molecules of CuBr dissociate to copper and bromine atoms in the pulsed dis- charge. A number of studies have ascertained that CuBr dissociates completely during the discharge. Moreover, it has been found that no reconstitution of CuBr molecules occurs in a pulse interval of 60 ps long [ 1 11. The copper atoms have the lowest ionization potential and they are actually the only source of electrons during the discharge. Meanwhile, bromine demonstrates high electron affinity resulting in the production of negative bromine ions Br- , yet with electrons of heat energy [12 ] . The negative bro- mine ions are the dominant negative particles in the plasma of the CuBr laser by the reason of their high sta- bility and the instability of bromine molecules [ 121-[ 141.

The addition of hydrogen complicates the constitution of the CuBr laser plasma. It is necessary to take into ac- count the dissociation of hydrogen molecules and the for- mation of negative hydrogen ions H- as well as the even- tual occurrence of other intercomponent formations. Among them are the molecules of HBr which appear to be very unstable in the electron environment dissociating yet by electron impacts at a heat energy of 0 . 2 eV [12 ] .

In accordance with the calculation method in Table I1 are given the momentum transfer cross sections for elastic collisions of electrons with the heavy particles of the CuBr laser plasma and their respective references. Some of the

ASTADJOV er al.: CuBr LASER WITH HYDROGEN ADDITIVES 1933

TABLE I1

Gas Momentum Transfer Component Cross Section A* Ref.

Ne 1.6E ' I 6 c u 500E-' Br 12.6

1181 H,

H 21E - ' I 2 [I91

In (E + 1.46) E + 1.46

46.21

Note: E is electron energy in eV

cross sections were not in the required analytic form re- quiring us to approximate the available numerical data an- alytically. The momentum transfer cross section for bro- mine was evaluated using the Chapman-Enskog theory by the potential functions of Lennard-Jones.

According to [ 121 the equilibrium constants are expo- nential functions of temperature. Thus, the electron at- tachment constants have the form for hydrogen.

k H - = Tr.5 exp (23.287 - O.747/Te) (12) which is taken from [20] and for bromine

kBr- = Tf.5 exp (24.237 - 3.546/Te) (13)

which is an approximation based on data from [13]. The constants dimension is cm-3 and the electron temperature T, is in eV.

In this way was approximated the equilibrium constant of the dissociation of hydrogen molecules:

-

kHz = exp ( 8 - 51 200/7') (14) where kH2 is in torr and T is the average gas temperature in K.

The time dependence of the electron density has been computed employing equations which follow below:

n, = 1.244 x 10" T2IR.J (15) where ne is electron density in cmp3, R is the plasma re- sistance in ohms, and the electron temperature T, is in eV. J is an integral having the form

1 OT,

E 2 . 5 / ( K 1 + K 2 ) exp ( -E/T,) dE (16) J = lo where

Kl = (ni/9 x 10") In ( 1 + 2.4 x lo2' T : / n + ) (17) accounts for the Coulomb scattering of the electrons on ions, and K2 is for the total scattering of electrons on all neutrals:

K2 = 3.5 X 104(p/7') c.5E1.5

* C A ; ( l - X , - Y,)Qe; (18) i

where

A, = p,/p, X, = pj'/pj and Yj = pj/pj. (19)

tive and negative). The quantities pi, p: , and pJr are, re- spectively, the total partial pressure, the positive ion pres- sure, and the negative ion pressure of thej-neutral plasma component, all in torr. The total gas pressure is p = C j pj, and Q , is the momentum transfer cross section of electron e l p i c collisions with the neutrals of the j com- ponent in A2.

The quantity Yj can be obtained from

Y; = ( 1 - Xj)/(l + C , / n e ) (20) where

kH- (for hydrogen)

kBr- (for bromine).

For calculation of I;. we use the value of ne obtained from (15) by the preceding computational cycle.

In our model we have assumed that only copper under- goes ionization and the degree of ionization is about 0.5. (It is interesting to note that when the copper ionization degree varies from to 1 the electron density changes within f 6 percent.)

An important aspect of the modeling is the temporal course of the electron temperature during the discharge. In accordance with [14] we consider it to be an exponen- tial function of time:

Te = Teo exp ( - t / t c ) 9 (21) where t , is the entire duration of the current pulse and T,, the electron temperature at the moment of gas breakdown (conditioned to be when the current reaches 10 A ) . The time constant t, has been averaged to 185 ns. The most indefinite quantity is Teo. We have specified it to three values-4, 7, and 10 eV. This energetic interval (4-10 eV ) includes the peak electron temperature which is con- sidered to be in copper vapor laser. Thus, the maximum variations of the electron density owing to the high indef- initeness of the electron temperature course (plus the in- definiteness due to the copper ionization degree) are within f36 percent.

Equations (12)-(2 1) have been solved on a personal computer, Pravets Model 8M. Fig. 9 shows the temporal course of the electron density during the excitation pulse in pure neon and various hydrogen additives. Curve 1 is in 15 torr Ne, curve 2 is in 15 torr Ne and 0.3 torr H2 and, curve 3 is in 15 torr Ne and 1 torr H2. It is easy to see that the curves have different trends. Curves 1 and 2 are approximately exponents until about 100 ns after the excitation start. Curve 3 cannot be approximated by one exponent. Another difference is the initial electron density (conditioned to be at a current of 10 A ) which in our opinion truly reflects the differences of the prepulse elec- tron density. In pure neon it is 2.7 k 0.1 x 10l2 cmp3. The addition of hydrogen results in a reduction of the ini- tial electron density. With 0.3 torr H2 it is 8.6 +_ 0.5 X

10" cmp3 and with 1 torr H? it decreases to 7 rf: 0.5 X The electron energy E is in eV, n , is the density of the

positive ions, and ni is the total density of all ions (posi- 10" cmp3. The maximum electron density in pure neon is about 1015 ~ m - ~ , with 0.3 torr H2 about lOI4 cmp3, and

1934 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 24. NO. 9. SEPTEMBER 1988

10 -6

K d . cm3/5

.

. cm3/s

/ /

0 50 100 150 t,ns 200

Fig. 9. Temporal course of the electron density ne during the excitation pulse Curve 1 is in 15 torr Ne, curve 2 in 15 torr Ne and 0 .3 torr H,, and curve 3 is in 15 torr Ne and 1 torr H,.

10-10

with 1 torr H2 about 4 X 1013 ~ m - ~ . Concerning the fluc- tuations of the electron density (which are most pro- nounced in curve 2) they presumably occur because the fluctuations of the power deposition in the discharge.

If we assume that the electron density is an exponential function of time:

ne = neo exp ( A t ) (22) where A is the rate of the electron multiplication, curves 1 and 2 can be featured by the following rates, respec- tively, A = 0.043 ns-' and A = 0.06 ns-'. Curve 3 has a more complicated trend. During the first 10-15 ns the multiplication rate is 0.1-0.2 ns-' degrading afterwards (between 15 and 50 ns) to A = 0.05 ns-' and A = 0.03 ns-' between 50 and 80 ns after the excitation start.

F. Detachment of Electrons From Negative Hydrogen Ions by Electron Impacts

The analysis of the temporal course of the electron den- sity has shown that the effect of hydrogen consists of the decrease of the prepulse electron density and the increase of the multiplication rate of electrons during the initial stage of the discharge. The reason for the decrease of the prepulse density of electrons is the electrons affinity of hydrogen to produce negative ions [21], [22].

In order to clear up the mechanism of the intensification of electron multiplication when hydrogen is added to neon we have investigated the problem of the detachment of electrons from negative hydrogen ions H- by electron im- pacts. Based on rich experimental data [23], [24], [25], we did an analytical approximation of the detachment cross section Qd of electrons for the reaction

e + H- + 2e + H. (23) It was found to be

Qd = 1.76(0.045E0.2 - E-' In (0.12E))-' (24)

where Qd is in A2 and E is the electron energy in eV. The detachment rate for the process (23) has been cal-

culated as well. The electron distribution is considered to be Maxwellian. The electron detachment rate kd for the process (23) and the ionization rate ki for copper atoms versus the electron temperature are displayed in Fig. 10. The analytic form of the cross section for copper ioniza-

1 0 - 1 2 L L , 0 - 1 2 0 L 8 Te,eV 12

Fig. 10. Detachment rate kd of electrons from negative hydrogen ions H - and ionization rate k, of copper atoms by electron impacts versus the electron temperature T,.

tion we have used is

Qi = 6.2(E - 7.8) E-' .2 (25)

and it is an averaged value of the ionization cross sections for copper used in [15] and [26]. The dimensions of Qi is in A2 and the electron energy E is in eV.

It is easy to see that kd is much greater than ki - kd 1s at least order of magnitude greater than ki, and when T, < 2 eV then kd = (lo2 - lo4) ki. Taking into account that the attachment rate for electrons to form H- is not less than cm3/s [22] the duration of the interpulse interval (above 50 p s ) is sufficiently long to produce not less than 10'2-10'3 cm3 H- density. In this way the elec- tron detachment dominates over the copper ionization es- pecially in the early stage of the discharge, which mostly contributes to the self-terminating laser oscillation.

The effect of hydrogen probably would occur in other metal vapor lasers if kd > k y where k y is the ionization rate of the respective metal M by electron impacts. This is the presumable reason for the improved performance of gold vapor laser reported in [27].

111. CONCLUSION The major result of our parametric study is the expla-

nation of the hydrogen effect which consists in shielding (and shunting) of the direct electron ionization of copper atoms by another electron-generating process. In our case it is the electron detachment from negative hydrogen ions. The recent absorption measurements which we have made establish more copper in the ground state when hydrogen is added. It is found [ 111 that in a CuBr laser medium containing 0.3 torr H2 added to 15 torr Ne only 20 percent of the ground state copper is depleted during the excita- tion pulse contrasting with 60 percent of it in 15 torr Ne.

The existance of an optimum value of the hydrogen pressure implies that there might be an optimum multi- plication rate of electrons and/or an optimum prepulse electron density. Concerning the concrete value of the op- timum pressure equal to 0.3 torr H2 it is possible not to be a fixed constant but to be specified by the size of the

ASTADJOV et al.: CuBr LASER WITH HYDROGEN ADDITIVES 1935

laser medium, the buffer gas, the excitation parameters, etc. The excitation parameters comprise the pulsed energy per unit volume (0.1-0.3 mJ/cm3), the average power input per unit volume (1-5 W/cm3), the electric field intensity (150-250 V/cm), etc.

Possibly our version is incomplete and does not explain all aspects of the hydrogen effect on the operation of CuBr laser and other metal vapor lasers. Additional strong ef- fects might occur by reason of the electronic-vibrational excitation of hydrogen molecules which fraction nearly one-half in the early stage of the discharge. According to [ 81, under experimental conditions similar to ours elec- trons losses for vibrational excitation of H2 levels could be as high as 90 percent of their energy.

Considering the major processes which allow the hy- drogen effect to take place in the neon-hydrogen plasma it is clear why this effect has been already observed in the pure copper vapor laser [28] and the pure gold vapor laser [27]. It is likely that the hydrogen effect will appear in other self-terminating (or even pulsed) lasers if they are as technologically accomplished as the commercial cop- per and gold vapor lasers.

ACKNOWLEDGMENT The authors would like to thank Dr. Petrash, Dr. Isaev,

and Dr. Kazaryan of the P. N. Lebedev Physical Institute, U. S. S. R . Academy of Sciences, for helpful comments and discussion.

REFERENCES D. N. Astadjov, G. G. Petrash, N. V. Sabotinov, and N. K. Vuch- kov, “Long-lived sealed-off CuBr laser,” Opt. Commun., vol. 51,

N. V. Sabotinov, N. K. Vuchkov, and D. N. Astadjov, “Progress in CuBr laser,” in Tech. Dig . , Con$ Lasers, Electro-Opt. San Fran- cisco, CA: OSA, 1986, paper WE 3. D. N. Astadjov, N. V. Sabotinov, and N. K. Vuchkov, “Effect of hydrogen on CuBr laser power and efficiency,” in Europhys. Con$ Abstracts, Second Int. Con$ -Trends Quantum Electron. Bucha- rest, Romania: Euro Phys. Soc., 1985, paper l.C.3.1. - , “Effect of hydrogen on CuBr laser power and efficiency,” Opt. Commun., vol. 56, pp. 279-282, 1985. D. N. Astadjov, N. K. Vuchkov, A. A. Isaev, G. G. Petrash, I. V. Ponomarev, and N. V. Sabotinov, “The relaxation of metastable cop- per atoms in a CuBr laser emitting regular pulses,” Kvant. Elektron., vol. 14, no. 2, pp. 396-399, 1987. R. A. J. Shelton, “Vapour pressures of the solid copper halides,” Trans. Faraday Soc., vol. 57, pp. 2113-2116, 1961. N. B. Vargaftik, Thermophysical Properties of Matter. Gosenergoiz- dat, 1956. A. V. Eletski, L. A. Palkina, and B. M. Smirnov, Transfer Phenom- ena in Partly Ionized Plasma. N. B. Vargaftik, Yu. D. Vasilevskaya, “Transfer coefficients of dis- sociating hydrogen,” Teplojizika vis. temp., vol. 7 , no. 5, pp. 913- 917, 1969. R. C. Reid and T . K. Sherwood, The Properties of Gases and Liq- uids. Leningrad: Khimiya, 1971, D. N. Astadjov and A. A. Isaev et a l . , to be published. V. N. Kondratiev and E. E. Nikitin, Chemical Processes in Gases. Moscow: Nauka, 1981. B. P. Nikolski, Ed., Chemist Handbook, vol. 3. Moscow: Khimya, 1964. M. J. Kushner and F. E. C. Culick, “A model for the dissociation pulse, afterglow, and laser pulse in Cu/CuCI double pulse laser,” J. Appl. Phys., vol. 51, no. 6 , pp. 3020-3032, 1980. A. Kh. Mnatsakanyan, G. V. Naidis, and N. P. Shternov, “Electron distribution over energies in mixtures of copper vapor and neon or helium,” Kvant. Elektron., vol. 5 , no. 3, pp. 597-602, 1978.

pp. 85-86, 1984.

Moscow: Atomizdat, 1975.

1161 S. Trajmar, W. Williams, and S. K. Srivastava, “Electron-impact cross sections for Cu atoms,” J. Phys. B: Atom. Molec. Phys., vol. 10, no. 16, pp. 3323-3333, 1977. K. M. Arefiev, Transfer Phenomena in Gas and Plasma. Leningrad: Energoatomizdat, 1983. A. G. Engelhardt and A. V. Phelps, “Elastic and inelastic collision cross sections in hydrogen and deuterium from transport coeffi- cients,” Phys. Rev., vol. 131, no. 5 , pp. 2115-2128, 1963. B. E. Golant, A. P. Jilinski, and S . A. Sakharov, The Essentials of Plasma Physics. Moscow: Atomizdat, 1977. Yu. G. Chernov, “About conductivity of multicomponent gas mix- tures,” Teplojizika vis. temp., vol. 8 , no. 5 , pp. 934-939, 1970. H. Massey, Negative Ions. London: Cambridge Univ. Press, 1976. V. D. Rusanov and A. A. Fridman, “Physics of chemically active plasma,” M. Nauka, 1984. D. S. Walton, B. Peart, and K. T . Dolder, “A measurement of cross sections for detachment of electrons from H- by a method employing inclined ion and electron beams,” J. Phys. B: Atom. Molec. Phys., vol. 4 , no. IO, pp. 1343-1348, 1971. D. F. Dance, M. F. Hamson, and R. D. Rundel, “A measurement of the cross-section for detachment of electrons from H- by electron impact,” Proc. Roy. Soc. A , vol. 299, pp. 525-537, 1967. G. Tisone and L. Branscomb, “Detachment of electrons from H- and D- negative ions by electron impact,” Phys. Rev., vol. 170, pp. 169- 183, 1968. D. A. Leonard, “A theoretical description of the 5106 A pulsed cop- per vapor laser,” IEEE J. Quantum Electron., vol. QE-3, pp. 380- 381, 1967. 2. G. Huang, H. Y. Shan, Y. Huo and H. Wang, “A gold-vapor laser using Ne-H, as buffer gas,” Appl. Phys. B, vol. 44, pp. 57-59, 1987. Z. G. Huang, K. Namba, and F. Shimizu, “Influence of molecular gases on the output characteristics of a copper vapor laser,” Japan. J . Appl. Phys., vol. 25, no. 11, pp. 1677-1679, 1986.

Dimo N. Astadjov was born in Tolbuchin, Bul- garia in 1955. He received the degree in physics from Sofia University, Sofia, Bulgaria, in 1981.

Since 1981 he has been a research physicist with the Institute of Solid State Physics, Bulgarian Academy of Sciences. His research interests in- clude copper and copper bromide vapor lasers.

Mr. Astadjov is a member of the Bulgarian Physical Society.

Nikolay K. Vuchkov was born in Sofia, Bulgaria, in 1949. He received the degree in physics from Sofia University in 1975 and the Ph.D. in quan- tum electronics from the Lebedev Physical Insti- tute, Moscow, U.S.S.R. His dissertation research concerned physical processes limiting the CuBr laser lifetime.

Since 1975 he has been with the Institute of Solid State Physics, Bulgarian Academy of Sci- ences. His research interests include CW and pulsed metal vapor lasers.

Dr. Vuchkov is a member of the Bulgarian Physical Society

Nikola V. Sabotinov was born In Bourgas, Bul- garia in 1941. He received the degree in physics from Sofia University, Sofia, Bulgaria, in 1967 and the Ph.D. degree from the Institute of Solld State Physics, Bulgarian Academy of Sciences in 1976. His doctoral research concerned He-Cd and He-Se lasers. He is a Senior Research Physicist and the Head of the Metal Vapor Lasers Group, Institute of Solid State Physics, Bulgarian Acad- emy of Sciences, where he has worked on He-Ne lasers and since 1970 has been involved mainly in

the research and development of metal vapor lasers. Currently, his research interests include CW positive columns, hollow cathode and RF-excited metal vapor lasers, as well as pulsed metal vapor and metal halide vapor lasers. He has published over 70 papers in this area

Dr. Sabotinov is a member of the Bulgarian Physlcal Society.