Table 1 presents the results of the experiment.
Table 1
C | 2200 pF | 1650 pF | 1500 pF | 1320 pF | 1000 pF | 750 pF |
UC | 6580 V | 7600 V | 7970 V | 8500 V | 9760 V | 11270 V |
P | 945 mW | 960 mW | 992 mW | 945 mW | 1025 mW | 1110 mW |
P1 | 450 mW | 478 mW | 505 mW | 492 mW | 580 mW | 645 mW |
P0 | 160 mW | 167 mW | 174 mW | 165 mW | 184 mW | 189 mW |
Figure 1 shows the dependence of power on the storage capacity.
With an increase in capacity, the radiation power decreases by 14.9%, and the single-pass radiation power decreases by 30.2%. ASE power is reduced by 15.3%. In general, this indicates a decrease in the efficiency of excitation of the active medium in terms of both the generation power and the brightness amplification [21] related to the single-pass gain.
Figures 2a-f show waveforms of voltage at the GDT (V), current through the GDT (I), as well as the radiation pulse (E).
It can be seen that the increase in the capacity of the storage capacitor leads to the increase in the excitation pulse duration, which is associated with an increase in the time constant of the discharge circuit. There is also a shift of the beginning of the generation pulse relative to the voltage pulse on the GDT.
Next, we evaluate the pumping parameters in more detail, primarily the time and amplitude values of the excitation pulses. A waveform of the instantaneous power pulse was obtained by multiplying the voltage pulse on the GDT and the current pulse through the GDT.. Integrating it over time, we obtain the energy of the excitation pulse. It is obvious that the ratio of the energy entering the active medium before the start of the generation pulse, before its end, and the total energy determines the excitation efficiency. The energy entering the medium after the generation pulse is clearly spent on heating the plasma.
Figure 3 shows power waveforms and calculated energy for a 750 pF storage capacitor. The total pump energy is ~ 30 mJ, with the stored energy in the capacitor being ~ 48 mJ. The efficiency of energy transfer in the GDT is 63.2%. In this case, the pump energy before the start of the lasing pulse is ~ 4 mJ, the energy until the end of the lasing pulse is ~ 22 mJ, and the energy until the end of the lasing pulse (0.1 from the maximum) is ~ 20 mJ.
Similar measurements were made for all storage capacitors. The results are shown in Table 2.
Table 2
C, pF | 750 | 1000 | 1320 | 1500 | 1650 | 2200 |
Total calculated energy, mJ | ~ 30 | ~ 31 | ~ 39 | ~ 33 | ~ 38 | ~ 42 |
Energy transfer efficiency, % | 63,2 | 65,4 | 80,8 | 69,9 | 78,7 | 87,9 |
Energy before the start of the lasing pulse, mJ | ~ 4 | ~ 4 | ~ 4 | ~ 3 | ~ 3 | ~ 3 |
Energy until the end of the lasing pulse, mJ | ~ 22 | ~ 17 | ~ 20 | ~ 15 | ~ 16 | ~ 14 |
Energy until the end of the lasing pulse (0.1 from the maximum), mJ | ~ 20 | ~ 18 | ~ 18 | ~ 15 | ~ 15 | ~ 15 |
Thus, with an increase in capacitance from 750 pF to 2200 pF, the pump energy (directly on the active element) increased from ~ 30 mJ to ~ 42 mJ, i.e. energy transfer efficiency increased from 63.2–87.9%. In our opinion, this is due to the matching of the active element, discharge circuit, and power source. In this case, a decrease in the pump energy entering the medium before the end of the generation pulse is observed, which has a greater effect on the population inversion and, accordingly, the excitation efficiency. The energy until the end of the lasing pulse, when determining the end of the pulse at a level of 0.1 from the maximum, decreases from ~ 20 mJ to ~ 15 mJ with an increase in the storage capacitance from 750 pF to 2200 pF, respectively. We can conclude that, for a storage capacitance of 750 pF, ~ 33% of the energy is spent on heating the active medium, while for a storage capacitance of 2200 pF this value is 64.2%, which significantly reduces the excitation efficiency. It can be seen that the ratio of the energy before the start of the excitation pulse to the total energy decreases from 13.7–7.7%. The nonlinear change is most likely associated with the permissible deviation of the KVI-3 capacitance from the nominal value as the voltage increases, as well as with some resonant processes in the discharge circuit. Note that in the absence of voltage, the capacitance value measured using the device coincided with the nominal value.
Modeling of the active medium kinetic processes
The experimental configuration was also studied using a mathematical model. For this purpose, the kinetic model presented in [22] was used. The model analysis will make it possible to evaluate in more details the influence of pump parameters on the plasma medium features, such as electron temperature, concentration of the atoms in various energy states, etc. To simulate pumping, a simplified circuit of the discharge circuit was used, taking into account the inductive and capacitive components of the GDT resistance. The waveforms obtained in the model for three different capacities are presented in Fig. 4. The active resistance of the active medium is a function of time, determined by the spatiotemporal distribution of the concentration and temperature of the electrons of the active medium [22]. Figure 5 shows the changes of the active part of the plasma resistance during the time. The pre-pulse resistance of the active medium was the same for all capacitance values due to the fact that the pre-pulse distribution of electron concentration and their temperature were almost identical. This is a consequence of the fact that concentration and temperature are sufficiently inertial so that their prepulse values were determined by the pump energy rather than the shape of the pump pulse. The same is true for the Cu atom population in the lower operating level (metastable). It is worth noting that the peak resistance value is almost identical for all capacitances, i.e. the GDT is the similar type of load for the power source, even with a multiple change in the capacitance of the storage capacitor.
The values of ASE and radiation power were calculated in the model. For all configurations considered (the same as in the experiment), the laser power was 0.94–0.99 W, with the maximum being achieved for 1320 and 1500 pF. This spread is insignificant and fits into the model error, which can be seen, in particular, when comparing the model values with the experimental ones. The ASE power in the model also varies slightly for different capacities and is equal to ~ 0.19 W. The total energy input per pulse directly into the active medium was 30–33 mJ for all capacities, i.e. energy losses in the electrical circuit were weakly dependent on the pumping mode. Some difference in the behavior of the energy transfer efficiency in the model from the experiment is mainly due to the fact that the model did not take into account the dependence of the characteristics of the components of the pump circuit on voltage, as well as the simplicity of the model of components of the discharge circuit, primarily the switch element. For capacities of 1320–2200 pF, the behavior of the radiation power coincides with the model results, however, for capacitors of 750 and 1000 pF, a noticeable increase in the radiation power was observed in the experiment, which was not in the model results. This can be explained by a probable decrease in the loss of electrical energy for heating cold zones in the GDT at low capacitance values (sufficiently fast discharge), which results in a slight change in pumping conditions and an increase in its real efficiency. However, such an increase in radiation power is not due to fundamental factors associated with the kinetics of heated zones of the active medium, judging by the simulation results.
In Fig. 6 shows the active medium inversion formation for the green line in the center of the GDT. It can be seen that the pumping efficiency of the upper operating level is almost the same at different capacities. At the same time, for smaller capacitances (faster discharge), the lower operating level is populated somewhat more strongly (the peak population value of the lower operating level increases by approximately 8% when the capacitance decreases from 2200 pF to 1320 pF and from 1320 pF to 750 pF in Fig. 6). At relatively low frequencies, which were used in this work, this difference has little effect on the pre-pulse concentration of copper atoms in the metastable state (lower operating level), which at the center of the GDT was ~ 6∙1011 cm− 3 for the green line and ~ 6∙1010 cm− 3 for the yellow line. Since the active medium is pumped by Joule heating of the electron gas, it is also of interest to consider the change in electron temperature during the discharge, which is shown in Fig. 7.
Figure 7 shows that the electron temperature is weakly inertial and begins to increase almost simultaneously with an increase in the pumping voltage and current. Since the discharge had excess power to form lasing, a population inversion is formed at the beginning of pumping (from the point of view of the deposited energy), which is confirmed by Fig. 6 and calculation of the energy input before the generation pulse in the experiment (see Table 2). The main “useful” pump power occurs during the period of time when a population inversion has already been formed and is maintained by maintaining the electron temperature above 2 eV, necessary to create a population inversion (see [23] and references therein). In this case, maintaining such a high electron temperature leads to active ionization of the active medium, which is why the active resistance of the plasma quickly decreases (Fig. 5). As a result, due to the low active resistance of the GDT, ensuring a pump power high enough to maintain the electron temperature requires a further increase in the current. Thus, in practice, the duration of the existence of a population inversion can be limited not only by the growth of the population of the lower operating level [24], but also by the ionization of the active medium.