PRAMANA c© Indian Academy of Sciences Vol. 82, No. 1— journal of January 2014

physics pp. 147–152

Benefits of cryogenic cooling on the operationof a pulsed CO2 laser

UTPAL NUNDYBH-2-76, Kendriya Vihar, Kharghar, Sector-11, Navi Mumbai 410 210, IndiaE-mail: unundy@yahoo.co.in

DOI: 10.1007/s12043-013-0654-9; ePublication: 5 January 2014

Abstract. The paper presents results of a theoretical model of a pulsed electron beam controlledCO2 laser (EBCL) to investigate the effect of cooling on the laser gas mixture. It is shown thatcryogenic cooling can significantly improve the performance of the laser. The efficiency of anEBCL improved from 20% to 25.3% by cooling it to 200 K. The improvement is mainly due to thedecrease of thermal population of the CO2 (0 1 0) vibration level.

Keywords. Pulsed CO2 laser; electron beam controlled laser; simulation of pulsed CO2 laser.

PACS Nos 42.55.Lt; 42.60.Lh; 42.60.Rn

1. Introduction

Cryogenic cooling has been extensively used for ‘CO’ lasers. Such lasers operate at30–50% efficiency [1]. However, cryogenic cooling is not so popular with CO2 lasers.Theoretical considerations indicate that the efficiency of a CO2 laser can be improvedconsiderably with cryogenic cooling. These arguments are presented in this paper. Aroom temperature electron beam controlled CO2 laser (EBCL) [2] and also a theoreticalmodel for it [3], were developed. The model uses the experimentally obtained dischargevoltage and current data to predict an output energy of 71.5 J with an efficiency of 20%,which is in good agreement with the experiment. It will be interesting to find out the effectof cooling on the performance of this laser. This paper presents the results of a theoreticalinvestigation to calculate the output energy and efficiency of the same laser, when it iscooled to 200 K. Since an actual experiment was not carried out, in the model [4], firstthe discharge is simulated and then this data are used to evaluate the laser performance.This model predicts an output energy of 117.4 J with 25.3% efficiency.

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2. Laser system

Though the laser system has been described previously [2], for completeness, a briefdescription is provided here. In the EBCL developed, a thermionic gun is used to generatea wide-area electron beam. The high-voltage electron beam is injected into the laserchamber. Here it causes secondary electrons to be produced due to the ionization ofthe components of the laser gas mixture. These secondary electrons can then initiate adischarge, which in turn pumps the laser gas mixture.

The laser uses a −130 kV electron beam with an area of 100 cm × 10 cm. Because ofthe design of the anode used, the discharge produced is restricted to the dimension of 6 cm(height) × 10 cm (width) × 70 cm (length). To operate the discharge in switch mode,a 1.3 μF capacitor is directly connected across the electrodes separated by 6 cm, andcharged to 28 kV. This voltage is below the breakdown voltage of the 1:1:8, CO2:N2:Hegas mixture at 1 atm and hence no discharge occurs. Now, when the electron beam isswitched on, the conductivity of the gas mixture increases and the discharge is produced.The capacitor discharges partially, with a residual voltage remaining on it, at the end of thedischarge. Though the electron beam lasts for 6 μs, the model predicts that the dischargelasts for ∼25 μs.

For modelling the laser the optical cavity consists of a gold mirror of 20 m radiusof curvature and a ZnSe plane output coupler of 90% reflectivity. Both the mirrors arecircular with 10 cm diameter, thus addressing the full discharge cross-section of 10 cm× 6 cm. The theoretical modelling is carried out for two cases, with the laser chamberat room temperature and with the laser chamber cooled to 200 K. However, before wepresent the results of the model, let us understand the parameters of a pulsed CO2 laserwhich are affected by cooling.

3. Effect of cooling on laser performance

Let us refer to figure 1, the energy level diagram of the CO2 laser to understand theparameters that are affected by gas temperature.

The laser action takes place between two rotational sublevels of the (0 0 1) and (10 0) vibration levels of CO2. After pumping of various vibration levels, there is redis-tribution of population among the levels due to vibration relaxation processes. Fewof these are indicated in the diagram. These are: k – resonant transfer rate betweenN2 (V = 1) level and CO2(0 0 1) level; k24 – transfer rate between (1 0 0) and (0 2 0)levels due to Fermi resonance; k2 – intramode transfer rate between (0 2 0) and (0 1 0)levels; k13 – intermode transfer rate between (0 0 1) and (0 1 0) levels; k3 – vibrationto translation relaxation rate of the (0 1 0) level. This last relaxation rate is relativelyslow and acts as a bottleneck. Also the (0 1 0) level is close to the ground level and thedischarge heating causes the thermal population of this level to be substantial and restrictthe laser performance. The performance of the laser is decided by (1) small signal gaincoefficient of the laser, (2) vibration relaxation rates, and (3) thermal population of (0 10) level. Let us now see how temperature affects these parameters.

148 Pramana – J. Phys., Vol. 82, No. 1, January 2014

Benefits of cryogenic cooling on the operation of a pulsed CO2 laser

Figure 1. Energy level diagram of the CO2 laser.

3.1 Influence of temperature on small signal gain coefficient

Let T be the gas temperature. Small signal gain coefficient g is given by

g = σulfu�Nv, (1)

where σul is the stimulated emission cross-section at the line centre, fu is the rotationpartition function and �Nv is the population inversion between upper and lower vibrationlevels. The stimulated emission cross-section is inversely proportional to the linewidth.The collision-broadened linewidth is a product of particle density, collision cross-sectionand gas velocity. Gas velocity is proportional to T 1/2 and particle density is inverselyproportional to temperature. Thus, linewidth varies as T −1/2 and σul varies as T 1/2. Therotation partition function fu is given by

fu = (2J + 1)hcB

kTexp

(−hCB

kTJ (J + 1)

),

Jm =[

kT

2hcB

]1/2

− 1

2or (2Jm + 1) =

[2kT

hcB

]1/2

. (2)

Here J is the rotation quantum number, h is the Planck’s constant, c is the velocity oflight, B is the rotational constant for CO2 molecule and Jm is the quantum number ofthe rotational level having maximum population. Since laser action involves rotationallevels having the maximum population, the above equation shows that fu varies withtemperature as T −1/2. It can be seen from eq. (1), that if pumping is the same at thetwo temperatures, �Nv is the same, and small signal gain coefficient is independent oftemperature.

3.2 Effect of temperature on vibration relaxation rates

Taylor and Bitterman [5] have provided data about the temperature dependence of vibra-tion relaxation rate constants. From these data, the variation with temperature of only two

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Table 1. Values of k and k3 at three temperatures.

Temperature (K) 200 230 300

k (10−13 cm3 s−1) 6.6 6.15 5.4k3 (106 s−1) 1.54 1.73 2.45

rate constants k and k3 can be ascertained. In table 1, we provide the values of these rateconstants at three temperatures.

Thus cooling has a mixed effect, on lasing, nitrogen to CO2 transfer rate increases,which is desirable, but the relaxation of (0 1 0) level slows down, which is detrimental.

3.3 Effect of temperature on thermal population of (0 1 0) level

As (0 1 0) level is at 0.08 eV from the ground state, its thermal population density issensitive to the gas temperature. In table 2 the values of thermal population of (0 1 0)level at three temperatures are presented.

If one wants to discharge water from a reservoir, he will fix the exit port as closeas possible to the base. Similarly, the benefit of extracting more energy from the laserrequires the thermal population of (0 1 0) level to be as small as possible.

4. Simulation methodology and results

The electron beam ionizes the laser gas species and creates a source term, which is pro-portional to the electron beam current density in the gas and the gas density [6]. Asthe cooling increases the gas density, the source term is higher in the cooled gas. Thiscauses the discharge current to be higher in the second case. In figures 2 and 3, thedischarge current and the laser pulse are presented for room temperature and cooled oper-ation respectively. In both cases, the reflectivity of the output coupler is 90%. Table 3lists the discharge energy, output energy and efficiency for the two cases.

There is a rise of gas temperature during the discharge pulse. The model does not takeinto account this temperature variation. Hence, for each case the temperature rise wasestimated and it was assumed that the gas is at this constant elevated temperature, which isan average of the initial and final gas temperatures. In the case of cooling this temperaturewas 230 K, and for room-temperature operation this temperature was 350 K. The valuesof vibration relaxation rate constants (except k and k3, whose temperature variations aredescribed in §3) were taken from Tyte [7]. The values of ionization coefficient, attachmentcoefficient and drift velocity, required to calculate the discharge current, were taken from

Table 2. Thermal population of (0 1 0) level at three temperatures.

Temperature (K) 200 230 350

Population density (1016/cc) 3.38 5.38 12.57

150 Pramana – J. Phys., Vol. 82, No. 1, January 2014

Benefits of cryogenic cooling on the operation of a pulsed CO2 laser

0.0 5.0x10-6 1.0x10-5 1.5x10-5 2.0x10-5 2.5x10-5

0.0

2.0x103

4.0x103

6.0x103

8.0x103

1.0x104

1.2x104

1.4x104

1.6x104

Lase

r P

ower

(K

W)

Time (Second)

0

500

1000

1500

2000

2500

Dis

char

ge c

urre

nt (

Am

p)

I

I-Calculated Discharge current

P1-Calculated laser power

P1

Figure 2. Discharge current and laser power (300 K).

Judd [8]. To evaluate the discharge pumping of the vibration levels of CO2 and N2, theelectron excitation rates provided by Judd [8] were used. However, as mentioned in ref.[3], to match experiment with theory for room-temperature operation, electron excitationof the lower (1 0 0) level was neglected, and the rates of excitation of the (0 0 1) level wasdoubled. The same criterion has also been used in the simulation with 200 K operation. Toascertain the contribution of relaxation rates on lasing, the room-temperature relaxationrates were used deliberately, in the simulation for 200 K. The energy in this case was119.1 J, indicating that the relaxation rates do not influence the output energy greatly.

0.0 5.0x10-6 1.0x10-5 1.5x10-5 2.0x10-5 2.5x10-5

0.0

2.0x103

4.0x103

6.0x103

8.0x103

1.0x104

1.2x104

1.4x104

1.6x104

1.8x104

2.0x104

Lase

r P

ower

(K

W)

Time (Sec)

0

1000

2000

3000

4000

Dis

char

ge c

urre

nt (

Am

p)

I

I-Calculated Discharge current

P1-Calculated laser power

P1

Figure 3. Discharge current and laser power (200 K).

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Utpal Nundy

Table 3. Comparison of EBCL operation with and without cooling.

Temperature (K) Discharge energy (J) Laser energy (J) Efficiency (%)

200 464 117.4 25.3300 358.5 71.5 20

5. Conclusion

The paper presents theoretical modelling results to demonstrate that the efficiency of apulsed CO2 laser can be enhanced considerably by cryogenic cooling. Operating a EBCLat 200 K, an efficiency of 25% could be achieved. However, this require development ofcryogenically-cooled closed loop gas circulation schemes, and laser chambers which canoperate at cryogenic temperatures, as has been developed in Russia [9]. The cooling opensup new applications for the CO2 laser, which are otherwise not possible. For example, apulsed CO2 laser operating at 16 μm [4] has to be cryogenically cooled, and will requiresuch a set-up. Also this technology will be very helpful for developing high-energy elec-tron beam controlled CO laser systems, which can have diverse practical applications, andthese systems operate best with cryogenic cooling.

References

[1] M M Mann, D K Rice and R G Eguchi, IEEE J. Quantum Electron QE-10, 682 (1974)[2] V P Singal, R Vijayan, B S Narayan, D J Biswas and U Nundy, Infrared Phys. Technol. 44, 69

(2003)[3] U Nundy, Theoretical investigations on the working of an electron beam controlled CO2 laser,

DAE–BRNS National Laser Symposium (NLS-21)(BARC, Mumbai, 6–9 Feb. 2013)[4] U Nundy and M Kumar, Pramana– J. Phys. 79(6), 1425 (2012)[5] R L Taylor and S Bitterman, Rev. Mod. Phys. 41(1), 26 (1969)[6] J D Daughtery, Principles of laser plasmas edited by G Bekefi (Wiley, New York, 1976)

p. 369[7] D C Tyte, Advances in quantum electronics edited by D W Goodwin (Academic Press,

London, 1970) Vol. 1, p. 129[8] O P Judd, J. Appl. Phys. 45(10), 4572 (1974)[9] A A Ionin, Quatum Electron 23(2), 9 (1993)

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