Benefits of cryogenic cooling on the operation of a pulsed CO 2 laser

Transcription

1 PRAMANA c Indian Academy of Sciences Vol. 82, No. 1 journal of January 2014 physics pp Benefits of cryogenic cooling on the operation of a pulsed CO 2 laser UTPAL NUNDY BH-2-76, Kendriya Vihar, Kharghar, Sector-11, Navi Mumbai , India unundy@yahoo.co.in DOI: /s ; epublication: 5 January 2014 Abstract. The paper presents results of a theoretical model of a pulsed electron beam controlled CO 2 laser (EBCL) to investigate the effect of cooling on the laser gas mixture. It is shown that cryogenic cooling can significantly improve the performance of the laser. The efficiency of an EBCL improved from 20% to 25.3% by cooling it to 200 K. The improvement is mainly due to the decrease of thermal population of the CO 2 (0 1 0) vibration level. Keywords. Pulsed CO 2 laser; electron beam controlled laser; simulation of pulsed CO 2 laser. PACS Nos Lt; Lh; Rn 1. Introduction Cryogenic cooling has been extensively used for CO lasers. Such lasers operate at 30 50% efficiency [1]. However, cryogenic cooling is not so popular with CO 2 lasers. Theoretical considerations indicate that the efficiency of a CO 2 laser can be improved considerably with cryogenic cooling. These arguments are presented in this paper. A room temperature electron beam controlled CO 2 laser (EBCL) [2] and also a theoretical model for it [3], were developed. The model uses the experimentally obtained discharge voltage 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 effect of cooling on the performance of this laser. This paper presents the results of a theoretical investigation to calculate the output energy and efficiency of the same laser, when it is cooled to 200 K. Since an actual experiment was not carried out, in the model [4], first the discharge is simulated and then this data are used to evaluate the laser performance. This model predicts an output energy of J with 25.3% efficiency. Pramana J. Phys., Vol. 82, No. 1, January

2 2. Laser system Utpal Nundy Though the laser system has been described previously [2], for completeness, a brief description is provided here. In the EBCL developed, a thermionic gun is used to generate a wide-area electron beam. The high-voltage electron beam is injected into the laser chamber. Here it causes secondary electrons to be produced due to the ionization of the components of the laser gas mixture. These secondary electrons can then initiate a discharge, 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 of the 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, and charged to 28 kv. This voltage is below the breakdown voltage of the 1:1:8, CO 2 :N 2 :He gas mixture at 1 atm and hence no discharge occurs. Now, when the electron beam is switched 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 the discharge. Though the electron beam lasts for 6 μs, the model predicts that the discharge lasts for 25 μs. For modelling the laser the optical cavity consists of a gold mirror of 20 m radius of curvature and a ZnSe plane output coupler of 90% reflectivity. Both the mirrors are circular 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 chamber at room temperature and with the laser chamber cooled to 200 K. However, before we present the results of the model, let us understand the parameters of a pulsed CO 2 laser which are affected by cooling. 3. Effect of cooling on laser performance Let us refer to figure 1, the energy level diagram of the CO 2 laser to understand the parameters that are affected by gas temperature. The laser action takes place between two rotational sublevels of the (0 0 1) and (1 0 0) vibration levels of CO 2. After pumping of various vibration levels, there is redistribution of population among the levels due to vibration relaxation processes. Few of these are indicated in the diagram. These are: k resonant transfer rate between N 2 (V = 1) level and CO 2 (0 0 1) level; k 24 transfer rate between (1 0 0) and (0 2 0) levels due to Fermi resonance; k 2 intramode transfer rate between (0 2 0) and (0 1 0) levels; k 13 intermode transfer rate between (0 0 1) and (0 1 0) levels; k 3 vibration to translation relaxation rate of the (0 1 0) level. This last relaxation rate is relatively slow and acts as a bottleneck. Also the (0 1 0) level is close to the ground level and the discharge heating causes the thermal population of this level to be substantial and restrict the laser performance. The performance of the laser is decided by (1) small signal gain coefficient of the laser, (2) vibration relaxation rates, and (3) thermal population of (0 1 0) level. Let us now see how temperature affects these parameters. 148 Pramana J. Phys., Vol. 82, No. 1, January 2014

3 Benefits of cryogenic cooling on the operation of a pulsed CO 2 laser Figure 1. Energy level diagram of the CO 2 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 = σ ul f u N v, (1) where σ ul is the stimulated emission cross-section at the line centre, f u is the rotation partition function and N v is the population inversion between upper and lower vibration levels. The stimulated emission cross-section is inversely proportional to the linewidth. The collision-broadened linewidth is a product of particle density, collision cross-section and gas velocity. Gas velocity is proportional to T 1/2 and particle density is inversely proportional to temperature. Thus, linewidth varies as T 1/2 and σ ul varies as T 1/2.The rotation partition function f u is given by f u = (2J + 1) hcb ( kt exp hcb ) J (J + 1), kt [ ] kt 1/2 J m = 1 [ ] 2kT 1/2 2hcB 2 or (2J m + 1) =. (2) hcb Here J is the rotation quantum number, h is the Planck s constant, c is the velocity of light, B is the rotational constant for CO 2 molecule and J m is the quantum number of the rotational level having maximum population. Since laser action involves rotational levels having the maximum population, the above equation shows that f u varies with temperature as T 1/2. It can be seen from eq. (1), that if pumping is the same at the two temperatures, N v is the same, and small signal gain coefficient is independent of temperature. 3.2 Effect of temperature on vibration relaxation rates Taylor and Bitterman [5] have provided data about the temperature dependence of vibration relaxation rate constants. From these data, the variation with temperature of only two Pramana J. Phys., Vol. 82, No. 1, January

4 Utpal Nundy Table 1. Values of k and k 3 at three temperatures. Temperature (K) k (10 13 cm 3 s 1 ) k 3 (10 6 s 1 ) rate constants k and k 3 can be ascertained. In table 1, we provide the values of these rate constants at three temperatures. Thus cooling has a mixed effect, on lasing, nitrogen to CO 2 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 is sensitive 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 close as possible to the base. Similarly, the benefit of extracting more energy from the laser requires 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 proportional to the electron beam current density in the gas and the gas density [6]. As the cooling increases the gas density, the source term is higher in the cooled gas. This causes the discharge current to be higher in the second case. In figures 2 and 3, the discharge current and the laser pulse are presented for room temperature and cooled operation respectively. In both cases, the reflectivity of the output coupler is 90%. Table 3 lists 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 take into account this temperature variation. Hence, for each case the temperature rise was estimated and it was assumed that the gas is at this constant elevated temperature, which is an average of the initial and final gas temperatures. In the case of cooling this temperature was 230 K, and for room-temperature operation this temperature was 350 K. The values of vibration relaxation rate constants (except k and k 3, whose temperature variations are described in 3) were taken from Tyte [7]. The values of ionization coefficient, attachment coefficient 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) Population density (10 16 /cc) Pramana J. Phys., Vol. 82, No. 1, January 2014

5 Benefits of cryogenic cooling on the operation of a pulsed CO 2 laser Laser Power (KW) 1.6x x x x x x x10 3 I I-Calculated Discharge current P1-Calculated laser power P Discharge current (Amp) 2.0x x x x x x10-5 Time (Second) Figure 2. Discharge current and laser power (300 K). 0 Judd [8]. To evaluate the discharge pumping of the vibration levels of CO 2 and N 2,the electron excitation rates provided by Judd [8] were used. However, as mentioned in ref. [3], to match experiment with theory for room-temperature operation, electron excitation of the lower (1 0 0) level was neglected, and the rates of excitation of the (0 0 1) level was doubled. The same criterion has also been used in the simulation with 200 K operation. To ascertain the contribution of relaxation rates on lasing, the room-temperature relaxation rates were used deliberately, in the simulation for 200 K. The energy in this case was J, indicating that the relaxation rates do not influence the output energy greatly. 2.0x x x10 4 I I-Calculated Discharge current P1-Calculated laser power 4000 Laser Power (KW) 1.4x x x x x x10 3 P Discharge current (Amp) 2.0x x x x x x10-5 Time (Sec) Figure 3. Discharge current and laser power (200 K). 0 Pramana J. Phys., Vol. 82, No. 1, January

6 Utpal Nundy Table 3. Comparison of EBCL operation with and without cooling. Temperature (K) Discharge energy (J) Laser energy (J) Efficiency (%) Conclusion The paper presents theoretical modelling results to demonstrate that the efficiency of a pulsed CO 2 laser can be enhanced considerably by cryogenic cooling. Operating a EBCL at 200 K, an efficiency of 25% could be achieved. However, this require development of cryogenically-cooled closed loop gas circulation schemes, and laser chambers which can operate at cryogenic temperatures, as has been developed in Russia [9]. The cooling opens up new applications for the CO 2 laser, which are otherwise not possible. For example, a pulsed CO 2 laser operating at 16 μm [4] has to be cryogenically cooled, and will require such a set-up. Also this technology will be very helpful for developing high-energy electron beam controlled CO laser systems, which can have diverse practical applications, and these 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 CO 2 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) 152 Pramana J. Phys., Vol. 82, No. 1, January 2014