Influence of the electric field frequency on the performance of a RF excited CO <Subscript>2 </Subscript> waveguide laser

An analysis is presented of the effect of the RF frequency on the active media of CO2 waveguide lasers. It is found that the characteristics are improved with increasing RF frequency because the space charge sheath width decreases with increasing excitation frequency. We also found that the sheath width decreases with the discharge current; this fact was never discussed before. The higher the exciting frequency the higher is the maximum input power of the discharge in the stable low current mode. It is attractive to extend the input power while keeping the discharge in this mode. Finally, a stabilizing excitation technique is described for the inherent unstable region of the discharge. It is well known that the best performance of C O 2 waveguide lasers is obtained with RF excitation [1-6]. The choice of the used excitation frequency was mainly determined by practical arguments like the available power supplies. Its impact on the laser performance has not been studied thoroughly. So far this problem received little attention. There are two main points of view. There is the opinion that a change of frequency influences only the properties of the quasi-neutral plasma of the active medium [-2,7]. The other one is that the frequency changes the thickness of the charge sheaths near the electrodes so that the energy deposition into the quasineutral plasma and consequently the laser output are influenced [8,9]. The theoretical background for these considerations was discussed either phenomenologically or qualitatively. In a previous paper we presented the laser characteristics of the CO2 waveguide system with RF discharge [5]. The present paper, based on the previous model, will analyse the mechanism of laser excitation as it depends on various parameters, especially on the RF field frequency. 1 Initial assumptions and system description The system that will be analysed theoretically is our experimental device [4, 5] having a waveguide discharge volume of 2.25 × 2.25 x 370 mm 3. The used gas mixture is CO2-Nz-He (1:1:8) at a pressure of 100 Tort. The RF voltage is by means of parallel shunt inductors homogeneously applied to the two parallel electrodes. The field distribution in the discharge is calculated by solving the Poisson equation with the appropriate boundary conditions determined by the oscillating voltage over the electrodes. Because of the homogeneity of the RF discharge the problem is treated one-dimensionally with the coordinate x perpendicular to the electrode surfaces. The Boltzmann equation for the electron energy distribution is then solved by using the relevant cross-sections for the electronic excitations, vibrational excitations, dissociation of the CO2 molecule and the ionisations of N2 and CO2. The discharge heat is removed through both electrodes and through the ceramic side walls of the cavity. The considered frequencies of the electric field are in the range from 62 to 233 MHz. The relaxation frequency of the electron drift velocity is assumed to be larger than the frequency of the electric field. This condition limits the field frequency. Due to the time dependent plasma formation of the discharge, the discharge current is not in phase with the externally applied voltage. The current is not even harmonic. For that reason the Fourier analysis is applied to calculate the relevant parameters like impedance and energy deposition. The effects of the dissociation products, carbon monoxide and oxygen, on the discharge are also taken into account. The laser field is described by the fundamental waveguide mode EH11. The cavity losses are described by a distributed loss ~ = 10 -4 cm-1 and the outcoupling through one mirror is obtained by a transmission T = 5%, while the other mirror is considered as a 100% reflector. The variable parameters are the frequency and the input RF power. A more detailed description of the present model and its justification are given in [5]. 576 2 The effect of the space charge on the laser process With the method described in [5] we calculated numerically the laser parameter values for three discharge frequencies which are 62, 125 and 223 MHz. At first, all calculations are performed for 200 W input power. The results are shown in Table 1. The voltage amplitudes over the electrodes show a significant frequency dependence for constant input power. It is seen that the reduced electric field strength (E/N) in the quasi-neutral central plasma (the root-mean-square, RMS value) is not sensitive to the discharge frequency. Its value is near the optimum value for the excitation of the upper level. Both the gas temperature and the discharge current change slowly with frequency. In contrast to that, the electric field and the structure of the discharge impedance change significantly. Since the impedance of the discharge due to plasma formation kinetics is nonlinear with the applied voltage it is found that the current deviates from the harmonic Table 1. Frequency [MHz] 62 125 223 Voltage amplitude 324 202 167 Modulus [Q] of discharge impedance 129 72.1 56.9 Cosine of the angle between the first 0.508 0.719 0.828 current harmonic and the voltage to the electrodes Active resistance R~ [O] 65.6 51.8 47.1 Reactive resistance X+ [~2] 111 50.1 31.8 Full current amplitude Im [A] 2.36 2.59 2.74 The first harmonic current [A] 2.51 2.80 2.93 amplitude I0 Difference between full current 0.6 0.8 0.8 value and its first harmonic [%] Reduced electric field in a quasi-neutral 1.86 1.99 1.99 plasma ERMs/N [V cm 2 10-16 ] Reduced electric field close to the 33.2 21.7 14.7 electrodes ERMs/N [V cm 2 10-16] Gas temperature at the centre of 493 511 515 the discharge gap [K]