1 INTRODUCTION

If the discharge current contains a constant and a variable component, then under certain conditions the plasma passes into a new, acoustoplasmic state [1–3]. The influence of the variable component of the discharge current can be decomposed into a successive increase and decrease in current between the minimum and maximum values [4]. The increase can be represented as the application of a pulsed electric field, and the decrease – as a recombining plasma [5, 6]. When a pulsed electric field is applied to an equilibrium plasma (at the stage of current increase), the degree of ionization will lag behind the temperature increase, and if the duration of the pulsed voltage is less than the time of complete relaxation of the plasma parameters, then an “under-ionized plasma” appears, in which all three types of distributions may be absent: Boltzmann, Maxwell, and Saha [4]. With a decrease in the electric field, ionization decreases more slowly than the temperature, and a “recombining” plasma arises. In an acoustoplasmic discharge, due to a continuous change in the discharge current, the modes of “under-ionized” and “recombining” plasma occur continuously and replace each other with the frequency of current modulation. In this case, the discharge cannot be characterized at all by any temperature, and neither the description of the plasma within the framework of the two-temperature model nor the description of non-equilibrium plasma using several temperatures (electronic, natural gas, vibrational, rotational) is possible [4, 7, 8]. Due to the self-consistency of processes in plasma, changes in different degrees of freedom are interconnected, and a deviation from equilibrium in one of the degrees of freedom can lead to a deviation from equilibrium in other degrees of freedom [9, 10]. The use of probe methods [11, 12] for acoustoplasma is undesirable, because probes affect the discharge, and spectroscopy remains one of the few methods for determining plasma parameters [13, 14]. In [2, 3, 15], it was reported that a strong spectral line was obtained in the red region of the spectrum.

2 EXPERIMENT

The experiment is described in [3] in detail. The laser mixture was studied CO2 : N2 : He = 1 : 1 : 8, pure nitrogen, and various mixtures containing and not containing nitrogen. The strongest emission line was obtained in the mixture CO2 : N2 : He = 1 : 1 : 8. The pressure in the discharge tube was varied from 10 to 5000 Pa, and the constant and variable components of the discharge current could be varied separately from 1 to 30 mA, that is, the current modulation depth (the ratio of the variable to the constant component) varied from 0 to 1. The discharge current modulation frequency f varied from 0.1 to 50 kHz. In the experiment, the visible region of 300–800 nm was studied, and in this work, the region with a strong line near 650 nm is considered in detail.

3 RESULTS AND DISCUSSION

Figure 1 shows the experimentally obtained spectrum with a resolution of 0.1 nm. Only the band of the first positive system (FPS) of nitrogen is shown (electronic transition B3Пg → A3\(\Sigma _{u}^{ + }\)).

Fig. 1.
figure 1

Spectrum taken with a modernized IKS-51 spectrograph with a resolution of 0.1 nm. CO2 : N2 : He = 1 : 1 : 8; P0 = 200 Pa; I0 = 21 mA; U = 2.58 kV; I~ = 17.2 mA.

Full size image

A high-intensity spectral line is visible between the lines at 654.48 and 662.36 nm of the FPS spectrum of nitrogen (up to 17 times more than neighboring lines). In the same area, there is a red line of hydrogen H - alpha 656.3 nm. Hydrogen could have come from adhesive joints. In this case, hydrogen would always be present, but in our plasma of helium and carbon dioxide without nitrogen, there was no strong line, and in pure nitrogen plasma such a line was present but 3–4 times weaker than in a 1:1:8 mixture. It was concluded that the strong red line is caused by nitrogen.

In Fig. 1, each small rectangle represents a separate rotational band for the corresponding vibrational level (individual rotational lines merge). The strong red line lies between transitions with vibrational quantum levels (7 → 4; λ = 654.5 nm) and (6 → 3; λ = 662.4 nm). Because the distance between the centers of adjacent lines at 654.48 and 662.36 nm is about 8 nm, the width of the strong line at the base is approximately equal to 1/10 of this distance, that is, about 0.8 nm, and the FWHM is 0.3 ± 0.1 nm. Experiments have shown that at the modulation frequency f = 0.1 kHz, the intensity of the strong red spectral line is several times weaker than at the frequency 10 kHz. Because the red line is very strong, the remaining vibrational-rotational bands are almost invisible (due to normalization to the white level when printing).

To check that there is no spectrum transfer (of the photo mixing type) due to the nonlinear interaction of various spectral lines of nitrogen with the emission line of the 10.6 μm CO2 laser, one of the discharge tube windows was replaced with germanium, the other remained glass. A laser beam with a power density of up to 10 W/cm2 entered the tube through a germanium window. There were no changes in the visible spectrum. Then an assumption was put forward about the emission line at the forbidden transition. In 1927 A.S. Bowen [16] proved that the incomprehensible spectral lines observed in the spectra of some nebulae can be explained by radiation on forbidden transitions. The appearance of forbidden lines is most likely if their upper state is the metastable state of the atom. Under laboratory conditions, the probability of destruction of a metastable state in collisions is much greater than the probability of a forbidden transition. Therefore, radiation at forbidden transitions is rarely observed under laboratory conditions. This was first noted by S. Mrozovsky [17]. In outer space, due to the large extent of objects and the low probability of collisions (because the concentration of particles is much lower than in laboratory conditions), astronomers can observe radiation at forbidden transitions. In particular, the emission of two forbidden lines of singly ionized nitrogen is observed (λ = 654.81 and 658.36 nm). This is the first negative system (FNS) of nitrogen-electronic transition B2\(\Sigma _{u}^{ + }\) → X2\(\Sigma _{g}^{ + }\) (Fig. 10 in [3]). Forbidden lines are also present in auroras and the glow of the night sky. In our experiments, a line near 658.36 nm was observed more often, which corresponds to the transition 3P2 – 1D2.

It was pointed out in [18] that two types of forbidden radiation can be obtained in discharge tubes. The intensity decreases with increasing current for lines of the first type, and they are associated with the mechanism of spontaneous emission. For lines of the second type, the intensity increases in proportion to the square of the current density, and they are associated with the mechanism of stimulated emission. The mechanism of spontaneous emission is associated with multipole emission, for which the selection rules differ from dipole electric, and lines forbidden for dipole radiation become allowed for multipole radiation [18, 19]. The mechanism of stimulated emission is associated with ionic fields, or with external electric and magnetic fields, which can be considered constant at distances comparable to the size of an atom.

In outer space, the spontaneous mechanism should prevail because of the low density of the gas. Under laboratory conditions, at much higher gas densities, the stimulated emission mechanism may predominate. It is this result that was obtained in our experiments at pressures of 10–600 Pa, which is much higher than in outer space. In the acoustoplasmic mode of the discharge in the discharge tube and the laser mixture, various mixtures containing nitrogen, and pure nitrogen, a spectral line of high intensity was obtained precisely in this region. In our experiments, the intensity of the strong line increases with both the current strength and the depth of current modulation. Thus, we can speak about the mechanism of stimulated emission.

It was assumed that the acoustoplasmic state removes the prohibition of the probability, the emission from the metastable transition becomes greater than the probability of quenching by collisions, and a strong spectral line appears at the forbidden transition. Because the probability of a decrease in the population of a metastable transition remains less than the probability of a reduction in the population due to radiation for the allowed lines of the entire standard vibrational-rotational transition, then the resulting emission line will be narrower and stronger, which is what we observe in the experiment. The paper [18] considers the theory of dipole electric radiation forced by a constant electric field. Moreover, the action of a constant field is considered a limiting case of a variable periodic field with a frequency equal to zero. In our experiments, we produce low-frequency modulation of current and electric discharge voltage, but for variable periodic fields, radiation is resonant. Acoustic oscillations in plasma result in the fact that an external force (concerning a diatomic nitrogen molecule) leads to an increase in oscillations inside the molecule at certain frequencies. As a result, the intensity of one of the vibrational bands in the vibrational spectrum of the nitrogen molecule can be significantly increased, so much that the effect of Rahman scattering is possible. But with Rahman scattering, it is possible to violate some of the prohibition rules and generate a forbidden (under normal conditions) transition [18].

Another explanation has to do with precession. The mechanism is as follows: the diatomic nitrogen molecule is a molecular top. At the frequencies of acoustoplasmic resonances in the discharge tube, the amplitude of linear oscillations of the molecule increases as a whole. As a result, there will again be a change in the intensities of individual lines in the vibrational-rotational spectrum, and Rahman scattering is possible. The emerging Coriolis force changes the rules of prohibition, and the direction of the Coriolis force is changing every half of the period of acoustic oscillations. As a result, we can get radiation on some forbidden transitions. For different directions of rotation of molecular tops, the Coriolis forces will be different, and the competition of transitions will narrow the emission line.

According to our estimates, at the frequency of the first longitudinal acoustic mode, the acoustic pressure is about 0.2 Pa. In the frequency range of 10 kHz, the acoustic pressure increases so much that it can change the discharge trajectory on off-axis modes [20]. According to our estimates, the kinetic energy of acoustic vibrations of a nitrogen molecule can reach 10–2 eV. A sufficiently long exposure (comparable to the period of acoustics) of such a large energy can remove the ban on radiation from forbidden transitions. In our case, the pressure may exceed 10 Pa. Then the vibrational velocity of the nitrogen molecule can reach 200 m/s; the kinetic energy of a nitrogen molecule can exceed 10–2 eV. All this we observe in the experiment.

4 CONCLUSION

In an acoustic plasma containing nitrogen at a pressure of 200–600 Pa, a spectral emission line of high intensity (up to 17 times more than the neighboring lines of the FPS spectrum of nitrogen) was obtained in laboratory conditions in the region of forbidden lines at 654.81 and 658.36 nm. Usually, such forbidden emission lines were observed only by astronomers in the spectra of some nebulae at pressures many orders of magnitude lower, and the intensity of the forbidden lines was comparable to the neighboring lines of the FPS spectrum of nitrogen. In a laser mixture, a strong line was obtained in the acoustoplasmic discharge regime in various combinations containing nitrogen and pure nitrogen. In gas mixtures containing no nitrogen, this line was not observed. As possible mechanisms to obtain such a strong line, precession around the direction of acoustic oscillations and stimulated Rahman scattering is considered. Thus, the strong line that results is not a spontaneous but a stimulated emission mechanism. This will probably make it possible to make an acoustoplasmic laser that simultaneously produces in the IR and red regions of the spectrum.