Longitudinal Power Distribution and Corresponding Temperature Distribution in a RF Waveguide CO2 Laser (2006)

The output power of a gas laser can not be increased by increasing the input power due to the increase of the gas temperature. As the temperature of the laser gas mixture increases up to 600K, the ampliflcation of the amplifying medium decreases rapidly and so the output power decreases. In this paper, longitudinal power distribution and corresponding temperature distribution along the CO2 waveguide laser are studied theoretically. Efiect of voltage and current distributions along and transverse to the electrode direction respectively are accounted for the studies. It is seen that the temperature decreases exponentially along the length of the electrodes on both sides of the feed point. DOI: 10.2529/PIERS060829221216 Several papers (1) have already described the huge potentiality of large area difiusion cooled RF capacitive discharges for the construction of medium | to high power CO2 lasers for materials processing. Indeed, some industrial sources based on this technology are presently appearing (2). However, there exist some open problems that limit the simple scaling of the above-mentioned technique to higher power segments. One of the major problem is certainly the attainment of a uniform gain medium excitation because of transmission line efiects (3) naturally determined by electrode dimensions comparable with the exciting RF wavelength. Typical counter measures to this di-culty are the adoption of sectioned discharges or the use of reactive elements along the electrodes. The principles for the correct design of systems based on these schemes are well established in the case of narrow channel devices (4{6), in which the equivalent-line characteristic impedance is mainly determined by the electrode structure. In (7) it is demonstrated that the same smoothing principals could be applied to wide channel high power discharges provided that the in∞uence of the discharge loading be taken into account. Indeed, from the analysis carried out in (7), it is possible to conclude that the main role played by the discharge loading is that of determining a new equivalent transmission line whose charac- teristic impedance is closer to that produced by the capacitance of the ion sheaths surrounding the electrodes rather than by the channel capacitance. This efiect determines the voltage and thus power distribution closer to a lossless-line rather than lossy-line models. Moreover (8,9), the typical impedances of sheaths and neutral plasma for the mixtures and pressure of the interests for CO2 laser construction produce distributions hardly distinguishable from uniform transmission line models (7,10,11). In this paper the temperature distribution along the longitudinal direction of the electrodes is studied theoretically by considering the longitudinal power distribution by applying the trans- mission line theory. Voltage distribution is considered along the longitudinal direction while the current in transverse direction of the electrodes. The voltage and current distributions along the electrodes are given by solving the simple transmission line difierential equations (2,7,10{12):