1. Introduction
Electromagnetic pulses (EMPs) emitted by laser-produced plasma represent an extensively studied phenomenon. Numerous results have been obtained studying the interactions of high-power laser radiation with solid targets. The study of EMPs from plasmas created by focusing a laser beam into a homogeneous gas (laser spark) has been the subject of a few papers so far. This is surprising because laser sparks, if generated under the properly chosen conditions (i.e., absence of metallic parts of the gas cells), make it possible to study the EMP phenomena associated only with the plasma, unaffected by a solid target, its holder and the vacuum interaction chamber.
The molecular gas, chosen for performing the interaction experiments reported in this paper, is sulphur hexafluoride. There are several good reasons for this choice. At the beginning of the last century, Henri Moissan and Paul Lebeau[ Reference Moissan and Lebeau1], the French chemists, synthetized an extremely stable compound from two highly reactive elements, fluorine and sulphur. The high stability of SF6 is due to strong S-F bonds and a perfect octahedral symmetry of the molecule (Figure 1). Sulphur hexafluoride has also unique electrical properties, for example, a high electron affinity[ Reference Christophorou and Olthoff2, Reference Maller and Naidu3]. In science and technology, numerous disciplines (please see Refs. [Reference Chu4–Reference Kampfrath, Perfetti, Gericke, Frischkorn, Tegeder and Wolf11] and the numerous references cited therein) benefit from the exceptional properties of this molecule, for example, biomedicine (anaesthesia; magnetic resonance imaging; gas tamponade; ultrasound contrast agent), the chemical industry and metallurgy (non-reactive gas with a high heat capacity; blanketing gas), chemicals, especially photochemical synthesis (fluorination agent), laser science and engineering (insulating and buffer gas; reactant in chemical lasers; sensitizer in infrared laser chemistry), the nuclear industry (insulating gas; tracer; leak indicator), radiation, flame and plasma sciences (electron scavenger), microchip production (plasma etching), environmental and earth sciences (tracer), etc. However, it has reached its widest spread in the electric power industry serving as a gaseous dielectric, insulating gas in high-voltage (HV) devices, especially switches and circuit breakers. Unfortunately, SF6 molecules exhibit a strong absorption in the mid-infrared spectral range. It is therefore a gas that contributes significantly to the greenhouse effect in the atmosphere. Thus, the new source of motivation[ Reference Tian, Zhang, Cressault, Hu, Wang, Xiao, Li and Kabbaj12] appeared for the study of SF6 plasma chemical reactivity. Not only the possibilities of replacing it completely, but also of recycling it or mixing it with other gases are being studied.
Ball and stick model of sulphur hexafluoride.
It follows from the brief overview given above[ Reference Moissan and Lebeau1– Reference Tian, Zhang, Cressault, Hu, Wang, Xiao, Li and Kabbaj12] that SF6 represents a unique compound with numerous applications. Nevertheless, there is also a very strong motivation for its choice to be investigated at the PALS facility directly in the field of laser–plasma chemistry, since the first attempts to elucidate the chemical consequences of laser-induced breakdown of gaseous SF6 appearing in the 1970s[ Reference Seka, Myatt, Short, Froula, Katz, Goncharov and Igumenshchev13, Reference Kurte, Heise and Klockow14]. There are only two papers, but they contain very interesting findings that need to be confronted with results obtained using the new approaches and experimental possibilities offered by high-power lasers. The first[ Reference Seka, Myatt, Short, Froula, Katz, Goncharov and Igumenshchev13] describes the strong influence of the inner surface of the gas cell. In the present work, it is eliminated by the larger dimensions of the gas cell and only a low number of accumulated high-energy pulses. The latter[ Reference Kurte, Heise and Klockow14] differentiates between two mechanisms that control the chemical reactions initiated by the laser-induced dielectric breakdown (LIDB) plasma at different pressures. At pressures below 2.7 kPa, the decomposition yields are controlled by the rate constants of non-thermal processes associated with electron attachment to the SF6 molecule, which has uniquely high electron affinity (see Ref. [Reference Christophorou and Olthoff2] and numerous references cited therein), while the contribution of thermal decomposition increases with increasing gas pressure. At pressures exceeding 6.7 kPa, pyrolysis dominates the decomposition processes.
A specific source of EMPs, which are characterized by a short burst of electromagnetic energy, is plasma produced by the interaction of a laser pulse with a solid target or gas[ Reference Consoli, Tikhonchuk, Bardon, Bradford, Carroll, Cikhardt, Cipriani, Clarke, Cowan, Danson, De Angelis, De Marco, Dubois, Etchessahar, Garcia, Hillier, Honsa, Jiang, Kmetik, Krása, Li, Lubrano, McKenna, Metzkes-Ng, Poyé, Prencipe, Raczka, Smith, Vrana, Woolsey, Zemaityte, Zhang, Zhang, Zielbauer and Neely15]. The power, duration and frequency range of the EMP depend on the properties of the plasma and its environment, such as the interaction chamber or surrounding gas. The EMP intensity rises steeply to a maximum and then decreases more slowly. It usually has the shape of a damped sinusoidal pulse. EMPs, which are regularly detected during the interaction of femtosecond to nanosecond laser pulses with matter, are generally considered a threat to electronic devices and diagnostics and have prompted the development of various protective measures[ Reference Brown, Ayers, Felker, Ferguson, Holder, Nagel, Piston, Simanovskaia, Throop, Chung and Hilsabeck16, Reference Bradford, Woolsey, Scott, Liao, Liu, Zhang, Zhu, Armstrong, Astbury, Brenner, Brummitt, Consoli, East, Gray, Haddock, Huggard, Jones, Montgomery, Musgrave, Oliveira, Rusby, Spindloe, Summers, Zemaityte, Zhang, Li, McKenna and Neely17]. The EMP spectrum generally spans many frequency bands, from tens of MHz to the terahertz limit. The electromagnetic fields of EMPs are of primary importance not only for the safe operation of high-power and high-energy laser devices, but also for the possible application of these electromagnetic fields[ Reference Consoli, Tikhonchuk, Bardon, Bradford, Carroll, Cikhardt, Cipriani, Clarke, Cowan, Danson, De Angelis, De Marco, Dubois, Etchessahar, Garcia, Hillier, Honsa, Jiang, Kmetik, Krása, Li, Lubrano, McKenna, Metzkes-Ng, Poyé, Prencipe, Raczka, Smith, Vrana, Woolsey, Zemaityte, Zhang, Zhang, Zielbauer and Neely15].
The EMP is primarily driven by the most energetic electrons being able to pass through the plasma potential barrier (of a virtual cathode) and to escape the laser-produced plasma[ Reference Dahlbacka and Guillory18]. When a laser interacts with a solid, the escape of electrons causes positive charging of the target[ Reference Dubois, Lubrano-Lavaderci, Raffestin, Ribolzi, Gazave, Compant La Fontaine, d’Humieres, Hulin, Nicolaï, Poyé and Tikhonchuk19, Reference Poyé, Hulin, Bailly-Grandvaux, Ribolzi, Raffestin, Bardon, Lubrano-Lavaderci, Santos, Nicolaï and Tikhonchuk20]. This charge is neutralized by a return current flowing between the target and the interaction chamber through the target holder[ Reference Cikhardt, Krása, De Marco, Pfeifer, Velyhan, Krouský, Cikhardtová, Klír, Řezáč, Ullschmied, Skála, Kubeš and Kravárik21]. As this current oscillates, the target holder becomes an antenna emitting the EMP in the GHz domain. In addition, the geometry of the interaction chamber determines the MHz domain of the EMP spectrum because the electrons from the evaporating target striking the chamber walls cause the chamber to resonate at its fundamental and resonant EM frequencies[ Reference Mead, Neely, Gauoin, Heathcote and Patel22].
Ultrashort high-intensity laser pulses focused on a metal foil or a gas can generate terahertz radiation, which has been intensively studied experimentally and theoretically for applications in various fields[ Reference Herzer, Woldegeorgis, Polz, Reinhard, Almassarani, Beleites, Ronneberger, Grosse, Paulus, Hübner, May and Gopal23– Reference Englesbe, Elle, Schwartz, Garrett, Woodbury, Jang, Kim, Milchberg, Reid, Lucero, Gordon, Phillips, Kalmykov and Schmitt-Sody26]. A comparison of the EMP frequency spectra emitted by plasmas produced in gases and on metal targets shows that, despite the different mechanisms of expansion of electrons into the gas surrounding the plasma core, EMP frequencies can be assigned to the same frequency bands, especially the ultra-high frequency (UHF) band ranging between 0.3 and 3 GHz. Primarily, megahertz and gigahertz frequencies of EMPs are generated not only in various high-power laser experiments but can also be generated by flashes of hard X-rays emitted from nuclear explosions in the air and high-energy explosives, as well as partial discharges in HV systems[ Reference Longmire27– Reference Stone, Cavallini, Behrmann and Serafino30].
A similarity between EMPs generated by a laser spark and partial discharges can be seen because the observed broadband UHF spectra match with the short duration of the produced filaments or sparks. For example, the observed electronic part of the partial discharge can have a pulse rise time of 0.3–0.8 ns and an FWHM (full width at half maximum) magnitude duration of about 1.5 ns[ Reference Boggs and Stone31]. Femtosecond lasers can produce EMPs with durations longer than 100 ps, but the lifetime of the laser–plasma kernel can reach tens of nanoseconds[ Reference Liu, Lu, Ma, Feng, Ge, Zheng, Li, Chen, Dong, Wang, Wang, Teng, Wei and Zhang32]. Although data on EMPs produced by nanosecond lasers are sparse, time-resolved spectra and shadowgraph imaging of sparks demonstrate long plasma kernel duration of up to hundreds of microseconds[ Reference Harilal, Skrodzki, Miloshevsky, Brumfield, Phillips and Miloshevsky33].
Laser-driven UHF radiation from under-dense gas plasma is much weaker than from a solid target, which is grounded. In our case, electrons escaping from the plasma kernel are not only slowed down by collisions with surrounding cold gas particles, but also if they approach the inner surface of the gas cell, they do not reach the ground, as they are insulated from it by both the cell and the electrically non-conductive holder of the cell. This indicates that the source of the EMP is the plasma kernel itself. Although the question of the origin of the EMP arising from the interaction of a laser pulse with gas has not yet been fully answered, it is nevertheless inclined to the idea that the EMP is generated by electric currents in plasma[ Reference Mitrofanov, Voronin, Rozhko, Sidorov-Biryukov, Nazarov, Fedotov and Zheltikov34].
The cold ambient gas is ionized not only by the hot electrons, but also by X-rays and extreme ultraviolet (XUV) radiation from the plasma kernel. As a result, the ambient gas is transformed into a low-temperature plasma. This phenomenon has been investigated by Bartnik et al. [ Reference Bartnik, Skrzeczanowski, Czwartos, Kostecki, Fiedorowicz, Wachulak and Fok35] in SF6 using an external laser–plasma source of XUV radiation. Finally, a shock wave is generated, and further ionic and atomic species are formed, revealed by their emission in the ultraviolet (UV) and visible regions of the electromagnetic spectrum[ Reference Harilal, Skrodzki, Miloshevsky, Brumfield, Phillips and Miloshevsky33, Reference Guthikonda, Kameswari, Manikanta, Shiva, Harsha, Ikkurthi and Kiran36]. Thus, the experiments also provide useful insights into spark chemistry with respect to differences in laser absorption properties.
In this paper, we present the results of an EMP experiment conducted on the iodine photodissociation laser system PALS, which operates at a wavelength of 1315.2 nm[ Reference Jungwirth, Cejnarová, Juha, Králiková, Krása, Krouský, Krupičková, Láska, Mašek, Mocek, Pfeifer, Präg, Renner, Rohlena, Rus, Skála and Straka37]. The laser pulses with an energy of about 120 J and a length of 0.3 ns were focused into a gas cell, which does not contain any metal component, filled with SF6. In addition to EMPs, we also focused our attention on the emission of near-UV and visible radiation in the wavelength range of 300–700 nm and on identification of products formed in reactions initiated by LIDB plasmas.
2. Experimental setup
A glass cell of simple design has been used to generate laser sparks in various gases. The cell features a cylindrical body with an external diameter of 90 mm and a length of 250 mm and a BK7 glass window with the following parameters: thickness of 15 mm and diameter of 98 mm for laser beam entry (see Figure 2). This window has an antireflective coating and is mounted to the cell using a two-part Murytal® flange. The front section of the flange is machined as a single piece with an internal thread, while the rear section consists of two interlocking pieces, allowing it to be positioned over the cell collar. The Murytal® material provides high rigidity and strength, ensuring that all components are precisely manufactured for a secure fit and preventing thread damage. Moreover, it is chemically resistant. To ensure mechanical integrity, the flange system incorporates a triple-sealing arrangement. A Teflon® gasket protects the window from mechanical damage, a nitrile butadiene rubber (NBR) gasket shields the cell collar during closure, and a highly chemically resistant Kalrez® O-ring provides a tight seal between the cell collar and the window.
Gas cell – Murytal® flanges: (a) front part; (b) rear part composed of two pieces; (c) glass body of the cell; (d) BK7 window with antireflective coating; (e) Teflon® gasket; (f) Kalrez® O-ring; (g) NBR gasket.
The entire cell assembly is mounted in a three-dimensionally printed polymer socket, which is attached to a Murytal® holder. Both the socket and holder are fabricated from non-conductive polymeric materials, ensuring electrical isolation from ground. A vacuum line is connected to the cell, enabling precise control of sample pressure and concentration, as well as efficient extraction of reaction products following laser irradiation. These products are immediately analysed using gas chromatography–mass spectrometry (GC-MS). The laser beam[ Reference Jungwirth, Cejnarová, Juha, Králiková, Krása, Krouský, Krupičková, Láska, Mašek, Mocek, Pfeifer, Präg, Renner, Rohlena, Rus, Skála and Straka37] was focused into the centre of the gas cell by a lens with a focal length of 300 mm (see Figure 3 for details).
Schematic of the experimental setup (top): diagram showing a cell, focusing length and the position of the detectors used. Drawing of the cell (bottom): the image below shows a drawing that describes its dimensions, including a lens focusing a light into the centre of the gas cell.
A fibre optic spectrometer, HR4000 by Ocean Optics, was used to record the emission spectra. The spectrometer has detection range between 200 and 1100 nm and uses a 3648-element linear silicon charge-coupled device (CCD) array allowing for spectral resolution of 0.75 nm FWHM. The light from the laser spark was collected using the optical fibre facing the spark at a distance of 25 cm and no collimating optics were used. Time-integrated photography of the glowing spark was performed using a CCD camera, TM-4200 GE.
A double-ridged waveguide horn antenna (HA), Rohde & Schwarz HF907, with a bandwidth of 0.8–18 GHz was placed at an angle of 55° to the laser axis. The antenna mount made it possible to change the antenna orientation and measure both the vertically and horizontally polarized EMPs in the identical point. A loop probe, RS H 400-1, of 2.5 cm in diameter was used to detect the near H-field ranging from 5 to 3000 MHz. The antenna and loops were adjusted so that their directionality maximum was oriented towards the discharge gap centre, and the polarization of each magnetic loop approximately coincides with the direction of the discharge gap axis. The layout is shown in Figure 3.
3. Experimental results and discussion
3.1. Magnetic probe signal
In general, the plasma produced by a laser is a source of spontaneous magnetic field[ Reference Stamper38]. Perhaps the first measurement of this field was performed in a spark plasma by Korobkin and Serov[ Reference Korobkin and Serov39], and a simple model of laser spark plasma formed by the mechanism of delayed breakdown in the focal cone of a focused ns laser beam in gas was proposed by Raizer[ Reference Raizer40]. Regarding the self-generating electric and magnetic fields around a laser spark, Rohlena and Mašek[ Reference Rohlena and Mašek41] presented an assessment of various models of spark formation and their comparison with experimental findings.
In our experiment, the spontaneous magnetic field was detected 10 cm from the laser focus using a loop magnetic probe type RS H 400-1 with a diameter of 25 mm. Its orientation allowed one to record the time derivative of the azimuthal magnetic field
${\dot{B}}_{\varphi }$
induced by the pulsed electric current flowing through the plasma core, as shown in Figure 4. Please note that
${\dot{B}}_{\varphi }$
is a part of the total detected
$\dot{B}$
, which also includes the contribution of the EMP field also detected by the horn antenna 2.5 m from the spark, as described in Section 3.2. Figure 4(a) compares the time course of six probe signals S
RS together with the time course of the laser intensity, I
L, where I
L is synchronized with the S
RS in such a way that the I
L peak matches the highest positive peak of S
RS appearing at time 1 ns. The dominance of the second positive peak of S
RS is evident. Once the interaction of the laser pulse with the gas stops, the magnetic field quickly disappears, causing a rapid reduction in the energy supply to the probe, as shown in Figure 4(b). This energy was calculated using the following relationship:
$$\begin{align}{E}_\mathrm{RS}=\int {S}_\mathrm{RS}^2/R\;\mathrm{d}t,\end{align}$$
Electromagnetic radiation detected with the use of the magnetic probe localized 10 cm from the laser spark induced by a 350 ps, 125 J laser pulse focused into a cell filled with 53.3 kPa SF6. (a) Correlation of the relative laser intensity (right-hand Y scale) with the first positive peak of S RS signals of the magnetic probe, which were recorded at different shots. (b) Energy absorbed by the loop probe at shot 61812. (c) STFT of S RS for shot 61812. (d) S RS frequency spectra for shot 61812.
where R is the load impedance given by the coaxial cables and oscilloscope input. Please note that E RS(t) reaches a level of 46% of the maximum value approximately in 0.5 ns.
The short-time Fourier transform (STFT) with a Hanning window and an overlap of 22 of the S RS(t) signal presented in Figure 4(c) shows that the probe signal oscillates from 0.2 to 5 GHz, with three frequency bands dominating around 1.4, 2 and 3.2 GHz.
The used window size of ≈1/3 ns, corresponding to the FWHM of the laser intensity reveals a broadband spectrum in the range from 1 to 3 GHz with a maximum of ≈2 GHz at ≈0.5 ns. This time correlates with the maximum of the laser pulse, as shown in Figure 4(a), and therefore the frequency of ≈2 GHz could be considered as the frequency of the magnetic field generated primarily around the laser spark during the interaction of the laser pulse with the gas. This magnetic field is generated by the standard mechanism of crossed electron density (n
e) and temperature (T) gradients (
$\partial \overrightarrow{B}/\partial t\sim {n}_\mathrm{e}^{-1}\left(\mathit{\operatorname{grad}}\;T\times \mathit{\operatorname{grad}}\;{n}_\mathrm{e}\right)$
), while the electric field is supposed to be created by the polarization of the plasma due to its radial expansion across the self-generated magnetic field[
Reference Rohlena and Mašek41]. Thus, the magnetic probe signal reveals two sources of the electric and magnetic fields. One is the laser pulse itself, which, through electron density and temperature gradients, generates the observed azimuthal magnetic field, B
φ, winding around the spark plasma, whereas the electric field with E
φ = 0 is induced by a charge separation, that is, polarization of the plasma streaming radially across the self-generated magnetic field. We note that the B
φ field is detected just during the interaction of the laser with the gas; see Figures 4(a) and 4(c).
Assuming that the magnetic flux density B φ is constant within the probe’s effective area A ef, the output voltage can be calculated as follows:
$$\begin{align}{S}_\mathrm{RS}=-{A}_\mathrm{ef}\;G\frac{\mathrm{d}B}{\mathrm{d}t},\end{align}$$
where G is the attenuation of the probe, specified in the manufacturer’s datasheet[ 42] as −25 ± 5 dB (a factor of ≈ 0.056) within the frequency range of 200–1000 MHz. The current inducing the magnetic field in the magnetic probe can be evaluated by the integration of the near-field probe signal S RS, which is proportional to the time derivative of B φ:
$$\begin{align}{J}_\mathrm{RS}(t)=-\frac{1}{M}\int {S}_\mathrm{RS}(t)\mathrm{d}t,\end{align}$$
where M is the conversion coefficient representing the mutual inductance between the magnetic loop and the laser spark (conducting plasma kernel). By combining Equation (3) with Equation (2) and Ampère’s circuital law, we obtain the following:
$$\begin{align}{J}_\mathrm{RS}(t)=-\frac{2\pi r}{\mu_0}\;\frac{1}{A_\mathrm{ef}G}\int {S}_\mathrm{RS}(t)\;\mathrm{d}t,\end{align}$$
where r is the distance of the B-field probe from the laser spark. An example of the time course of
${\int}_0^t{S}_\mathrm{RS}(t)\mathrm{d}t$
is shown in Figure 5. As shown, the magnetic flux density peak reaches several tens of μT.
S
RS signal and its integral
${\int}_0^t{S}_\mathrm{RS}(t) \mathrm{d}t$
. SF6 pressure is 26.7 kPa.
Using the PALS laser, estimated values of the magnetic field intensity near the tip of the plasma can reach 0.1 T values and the intensity of the accompanying electric field can be around 100 V/cm[ Reference Rohlena and Mašek41]. Another source of electromagnetic fields is the gradient of the laser sparks, which persists in a short-term self-sustaining plasma inside the spark without being actively driven by the laser pulse, as will be elucidated in Section 3.2. Please note the frequency band around 1.4 GHz, which later appeared in the STFT only after the occurrence of 2 GHz at 1 ns (see Figure 4(c)), is the only one that dominates the far zone where the horn antenna detects the EMP; see the S HA signal shown in Figure 6.
EMP induced by a single 350 ps, 125 J laser pulse focused into a cell filled with 53.3 kPa SF6. (a) Correlation of the relative laser intensity, I L, with the first positive peak of S HA signals recorded at different shots. (b) Energy absorbed by HA for shot 61812. (c) STFT of S HA for shot 61812. (d) S HA frequency spectra for shot 61812.
Please note that in this case the probe signal is induced not only by non-radiating currents, but also by emitted EMP. Since the value of M is time independent, it can be deduced that the integral of the bipolar signal S RS(t) results in a bipolar time course of the current J RS(t). We note that only exception was an almost unipolar J RS(t) waveform obtained. According to Equation (3) and magnetic field B(t), shown in Figure 4, the peak of the current J RS(t) reaches tens of amperes and a carried charge of a few nanocoulombs.
3.2. Horn antenna signal
Sparks produced by a single near-infrared (NIR) laser pulse carrying an energy of 126 ± 4 J focused into a cell filled with SF6 at a pressure of 10.7–101.3 kPa emit EMPs, as shown in Figure 6. The horn antenna was placed 2.5 m from the laser spark at an angle of 55° to the laser vector. Figure Figure 6 shows a series of signals, S HA, obtained by repeating firing into a SF6-filled cell. Figure 6(a) also shows the time course of a laser pulse, where the first positive peaks of the signals S HA of the horn antenna match the peak of the laser intensity. The time course of the EMP emission can be characterized by the variation of the energy absorbed by the horn antenna, as shown in Figure 6(b) for shot 61812. This energy was calculated using Equation (1). The time evolution of E HA shows that the duration of the EMP exhibiting only a few oscillations is shorter than 3 ns and the corresponding decay time τ dec is of the order of a nanosecond. While E HA(t) reaches 46% of its maximum value in ≈3 ns, E RS(t) reaches it in just 0.5 ns. Figure 6(c) shows an example of the STFT of S HA detected at shot 61812, where the dominant frequency f c ≈ 1.1 GHz. This also shows that the EMP reaches its peak about 1 ns after the arrival of the maximum laser intensity. The frequency spectrum presented in Figure 6(d) reveals the dominant frequency lying in the range of the 0.8–1.5 GHz band. Frequencies from the 1.5–2.2 GHz band occur only in some shots.
The HA signals prove that the occurrence of a laser spark is accompanied by an EMP pulse. This microwave EMP is caused by time-varying currents originating from various sources such as ions, runaway electrons and slow electrons. The runaway (hot) electrons from the laser kernel move into the surrounding cold gas, where they produce secondary electrons in collisions with gas molecules. The runaway electrons thus cause the formation of an electrical double layer at the interface between the laser kernel and the surrounding gas, where the positive charge is located on the surface of the laser kernel and the negative charge is in the layer of gas touching the kernel. From a phenomenological point of view, the double layer can be considered a potential well. The positive charge of this potential well is created by the escape of hot electrons from the laser kernel, while the negative charge is created by these runaway electrons being captured by the cold gas near the core. Thus, the boundary between the kernel and the cold gas could be termed as a spark double layer (SDL). Eliezer and Hora[ Reference Eliezer and Hora43] approximated the hydrodynamic bounce frequency, ωPW, in such a potential well by the following relationship:
$$\begin{align}{\omega}_\mathrm{PW}=\frac{2\pi }{l}\sqrt{\frac{e{\phi}_0}{m}},\end{align}$$
where l is the dimension of the potential well, that is, the SDL thickness comparable to the mean free path of electrons, ϕ 0 is the SDL potential and m is the electron mass. The electric field could be found by solving Poisson’s equation for the electrostatic potential in combination with equations for the density of low-energy electrons and positive and negative ions, including the runaway electron mechanism. Please note that the temporary experimental technique does not allow us to measure this potential.
It is reasonable that the knowledge of the different periods of the EMP (frequency spectrum) and corresponding decay times on a short time scale can provide basic experimental information about the mechanism of ion production in the vicinity of the spark kernel. We note that no natural frequencies or resonant modes affected the frequency spectrum of the EMP emitted by the laser-produced spark in the gas.
The mechanism of runaway electrons in a laser spark is fundamentally different from the mechanism of runaway electrons that are produced when a laser pulse interacts with a solid target placed in the vacuum. Firstly, many orders of magnitude more electrons are generated during solid target ablation than in the laser spark mode. Secondly, the electron flux escaping from the spark is therefore many times smaller and is stopped by collisions with particles of the surrounding gas, while in the case of solid targets irradiated in a vacuum, the runaway electrons pass a long way to the walls of the vacuum chamber. Therefore, the intensity of the EMP generated in a laser spark discharge is less than in the case of solid targets irradiated in a vacuum, as shown in Figure 7. The presented comparison shows that the energy absorbed by the HA was about 4000 times higher by detecting the EMP emitted by the interaction of the laser with the copper target than by the spark produced in the SF6 by a laser delivering the same energy. However, in this case, the HA detected the EMP from the Cu plasma at 4.5 m from the target, while in the experiment with SF6 it was located only 2.5 m from the spark. We can conclude that the EMP gain from a laser spark is a thousand times smaller than when the laser interacts with solid particles placed in vacuum.
Comparison of energy absorbed by HA detecting EMPs produced by the interaction of a 150 J laser pulse with a 1 mm thin Cu target and SF6 gas at a pressure of 101.3 kPa.
Although the mechanism of broadband emission from a laser spark is not yet fully understood, there is some similarity in the EMP spectra, both when using ultrafast laser pulses and nanosecond pulses. It turns out that an important parameter is pressure, expressed, for example, in the density of the irradiated gas. At the same or higher density of gas irradiated with 30 fs laser pulses, the frequency spectra had a range of around 0.8–2 GHz[ Reference He, Wang, Deng, Feng, Xia, Hu, Zhu, Xie, Yuan, Zhang, Lu, Yang, Cheng, Li, Yan, Fang, Li, Zhou, Li, Chen, Lin and Yan44], as in our experiment. In contrast, with decreasing gas pressure, not only does the amplitude of the electromagnetic field increase, but also frequencies are higher than the 3 GHz registered by us, as shown by the experiment of Engelsbe et al. [ Reference Englesbe, Elle, Reid, Lucero, Pohle, Domonkos, Kalmykov, Krushelnick and Schmitt-Sody45]. At a pressure of 66 Pa, the 50 fs laser generated approximately a hundred times more intense EMPs than at a pressure of 84 kPa. However, 10 GHz and higher frequencies were well pronounced. In the case of PALS experiments with solid targets, frequencies higher than 3 GHz are also generated[ Reference Cikhardt, Bradford, Ehret, Agarwal, Alonzo, Andreoli, Cervenak, Ciardiello, Consoli, Davino, Dostal, Dudzak, Klir, Krasa, Krupka, Kubes, Malir, Mendez, Munzar, Novotny, Renner, Rezac, Ruiz, Santos, Sciscio, Singh, Valdova, Juha and Krus46]. These experimental results support our idea that the SDL could be a source of EMPs.
3.3. Laser spark visualization
A photograph of a glowing spark can provide a basic insight into the plasma distribution in the cell, as shown in Figure 8. Please note that this is a time-integrated image of transient laser spark emission taken in the visible spectrum. The laser pulse arrives from the right-hand side after passing through a lens with a focal length of 300 mm and then an input cell window. Luminescence of the laser-irradiated SF6 occurs as soon as the laser pulse enters the cell, where it reaches an intensity of about 5 × 109 W/cm2. As the image shows, the luminescence appears on microislands that are irregularly distributed in the cell. The life cycle of a spark can reach up to tens of microseconds[ Reference Harilal, Brumfield and Phillips47, Reference Sun, Chang, Rong, Wu and Zhang48].
Passive laser spark imaging due to LIDB plasma optical emission. The longitudinal (Hline) and radial profiles (VL) of the spark’s luminosity were extracted at the locations marked by the yellow lines in the diagram. Red arrows indicate the focused breakdown laser beam.
Figure 8 shows that the spark length is approximately 2.3 cm. This dimension can be considered the limiting dimension of a spark emitting visible radiation. However, the dimensions of the kernel with the released electrons will probably be smaller. Regardless of the mechanism of the magnetic field generation in the kernel that affects the trajectories of the boundary secondary electrons, it is evident that the number of these boundary electrons is very small. Assuming that the signal of the magnetic probe localized in the near zone is induced only by the electron current flowing through the laser spark, a rough estimate of the peak current value indicates a current of only up to 100 mA. It corresponds to a current only of about 108 electrons. Please note that the first estimate of the magnetic and electric field intensities did not consider the possibility of laser spark generation in an electronegative gas[ Reference Rohlena and Mašek41].
The laser creates a kernel consisting of fully ionized fluorine and almost fully ionized sulphur as well as electrons. Please note that although we did not measure the mass spectra of the kernel-forming ions, we can estimate the degree of ionization of the S and F elements from the spectra of polytetrafluoroethylene (PTFE) ionized with an equivalent laser energy of approximately 150 J also delivered by the PALS beam, which identified F9+ ions far from the target[ Reference Krása, Velyhan, Jungwirth, Krouský, Láska, Rohlena, Pfeifer and Ullschmied49]. The kernel formed by multiple ionized S and F ions expands into the background gas, creating a ‘bubble’ around the focus. In addition, this kernel is a source of UV and X-ray radiation, which are absorbed by SF6. This produces a secondary plasma core within SF6, in which the separation of electrons and ions also occurs.
3.4. Single-shot optical emission spectra
To help characterize a laser spark, a fibre optic spectrometer is used to analyse the emissions from the spark. The recorded spectra contain both the continuum background originating from the hot plasma kernel and the visible spectrum of recombining ions and excited atoms during laser spark quenching, as Figure 9 shows. This spectrum has a similar profile to the spectra of laser-generated sonoluminescent bubbles, which exhibit the characteristic blackbody spectrum (background continuum) observed in both laser-produced and HV discharge plasmas[ Reference Kappus, Khalid, Chakravarty and Putterman50– Reference Krile, Vela, Neuber and Krompholz52]. The observed emission spectra are affected by the dramatically changing temperature determining blackbody radiation that occurs during the early phase of spark production. For these reasons, it was not possible to perform the best fit of the continuum background using the Planck law function of blackbody radiation. Although the background spectrum has been reported in several papers, its nature is still unclear. Therefore, we simulated the background signal using three bi-Gaussian functions with central wavelengths of 412.7, 500.7 and 561.2 nm.
Optical emission spectra of laser sparks produced in SF6 (101.3 kPa, 133 J) and fit of sulphur lines: (a) S II lines at T e = 0.9 eV and n e = 1 × 1011 cm–3, (b) S III lines at T e = 2.2 eV and n e = 1 × 1017 cm–3, fluorine lines F I at T e = 0.9 eV and n e = 1×1014 cm–3, and the background signal (BS).
The presented spectroscopic lines data of sulphur and fluorine are from the National Institute of Standards and Technology (NIST) atomic spectra database[ 53]. These were superimposed on the background signal so that the resulting spectrum matched the observed spectrum. Due to the varying temperature, T e, and density, n e, of electrons during spectrum recording, no average values of these parameters were used to exactly specify spectral peaks of S and F ions and atoms. However, the spectrum was divided into three wavelength ranges of 300–460, 460–600 and 600–720 nm to help clarify the origin of the spectral lines. In the first wavelength range of 300–400 nm, the S III spectral lines dominate, which approximately correspond to T e = 2.2 eV and n e = 1 × 1017 cm–3. The decisive parameter is the electron temperature. When T e drops to about 1 eV, lines from the second range appear, which correspond mainly to S II lines. The fluorine lines F I dominate for T e = 0.9 eV and n e = 1 × 1014 cm–3 in the third range of 600–720 nm. Although we did not measure optical emission spectra (OESs) as a function of time and, thus, did not obtain time-resolved values of T e and n e, the values estimated in our experiment are like those obtained in the experiment with a laser spark produced in air with a very low pulse energy of 40–150 mJ performed by Yalçin et al. [ Reference Yalçin, Crosley, Smith and Faris54]. The value T e ≈ 1 eV obtained by Yalçin et al. was detected more than 1 μs after the end of the laser interaction. However, T e in the kernel should reach much higher values (hundreds of eV). Here, T e was estimated from the OES of plasmas produced in a SF6 gas-puff target by a focused beam of a neodymium laser delivering 15 J of energy in 1 ns[ Reference Bartnik, Dyakin, Parys, Skobelev, Faenov, Fiedorowicz and Khakhalin55].
Although the purity of the SF6 used was 99.9%, the impurity content of 0.1% in the gas and impurities absorbed on the inner surface of the cell allowed detection of the Hα line with a wavelength of 656.28 nm, as Figure 10 shows. Due to the low impurity content, the amplitude of the Hα line is small. However, the estimation of the Hα line width is crucial because it is assumed to be reciprocally correlated with the electron density of the plasma due to the Stark broadening[ Reference Yalçin, Crosley, Smith and Faris54, Reference Jasik, Heitz, Pedarnig and Veis56– Reference Hussain Shah, Iqbal, Ahmad, Khandaker, Haq and Naeem58].
Detail of the optical emission spectra of laser sparks produced in SF6 at 101.3 kPa. The arrow indicates the wavelength of the Hα spectral line.
Stark broadening can lead to asymmetric line profiles, which can be analysed by fitting a Voigt function to the observed Hα line profile to determine the FWHM, w FWHM, of the spectral line. Using this technique, which is widely used in various types of plasmas, the magnitude of the electron density, n e, can be calculated using the following relationship[ Reference Gigosos, Gonzalez and Cardenoso57]:
$$\begin{align}{n}_\mathrm{e}={\left(\frac{w_\mathrm{FWHM}}{1.098}\right)}^{1.4713}\times {10}^{17}\;\mathrm{c}{\mathrm{m}}^{-3}.\end{align}$$
Using the relationship (Equation (6)) we obtain n e ~ 1017 cm–3. This value correlates with the estimated value for the S III wavelength range shown in Figure 10.
The contribution of the Gaussian profile width to the total line is comparable to the Lorentzian width for other spectral lines, for example, the S V triplet at 703 nm. This triplet S V and the three fitted Voigt functions are shown in Figure 11. Fitting gave w G = 0.146 and w L = 0.337 being shared for all functions. The S V triplet was analysed using the Voigt function with PeakFit software.
Detail of the optical emission spectra of laser sparks produced in SF6 at 26.7 kPa. The peak corresponds to the S V triplet at 702.76, 703.00 and 703.45 nm.
3.5. Shot-to-shot reproducibility
Like other experiments dedicated to the interactions of high-power laser pulses with solids, the presented experiment exhibits significant shot-to-shot fluctuations. Fluctuations relate not only to the emission of electrons, ions and possibly products of fusion processes, but also to the emission of EMPs and the continuum background. The range of EMP fluctuations during the interaction of an approximately 370 GW laser pulse with gas is shown in Figure 12.
Time course of the energy of the horn antenna signal induced by EMPs emitted from laser spark produced in SF6 at 26.7 kPa, E L ~ 125 ± 7 J.
The time-resolved dependence of the energy absorbed by the horn antenna shows that fluctuations occur already during the first phase of the laser–SF6 interaction, that is, during the first 200 ps. The energy absorbed by the horn antenna fluctuates from 0.25 to 1.8 nJ during this period, while the fluctuations of the delivered laser energy are less than ±5%. The efficiency of converting laser energy into EMP energy, which is related to the flow of electrons escaping from the spark kernel, therefore indicates significant fluctuations in the absorption of laser radiation by the gas, as in the case of laser–solid interaction. However, please note that there is a significant difference between the two interactions, namely that the electron concentration, n e, in the case of SF6 cannot reach values higher than or equal to the critical value, n c. However, in the case of fully stripped F and S atoms, the electron density can reach values higher than n c/4, and the absorption of laser radiation can be affected by the instability of two-plasmon decay (TPD)[ Reference Seka, Myatt, Short, Froula, Katz, Goncharov and Igumenshchev13, Reference Cristoforetti, Antonelli, Atzeni, Baffigi, Barbato, Batani, Boutoux, Colaitis, Dostal, Dudzak, Juha, Koester, Marocchino, Mancelli, Nicolai, Renner, Santos, Schiavi, Skoric, Smid, Straka and Gizzi59].
Shot-to-shot fluctuations also occur in the emission of visible light, as Figure 13 shows. The curves show the average intensity recorded by the camera during three series of shots. Fresh SF6 charge was used in the first and second series, while the charge from the second series was used in the third series, but the break between them was 19 h (the average is shown by the red line labelled as ‘1st shots’). The luminosity of the first shots fluctuated around 5%. It always dropped by 20% with the second shot (see the black line labelled ‘subsequent shots’). Starting with the second shot, the luminosity fluctuated within ±10%. The subsequent shots were repeated with a period of approximately 30 min.
Intensity profile along the caustic line evaluated from spark photographs. The profiles shown are averages of the intensities obtained over three series of shots at SF6 pressure of 26.7 kPa, E L ~ 125 ± 7 J.
The shot-to-shot fluctuations in spark luminosity are different from fluctuations in the EMP emission and continuum background. While fluctuations in the luminosity of the sparks produced by the second and subsequent shots are steadily at the level of 10%, the EMP fluctuations are more pronounced, as shown in Figure 12. However, both phenomena, emission of EMPs and visible radiation, are detected at different stages of spark production and extinction and are therefore driven by different mechanisms.
3.6. Chemical change initiated by laser sparks
From a chemical point of view, the interaction experiments reported here can be divided into two groups. In the first one, gaseous SF6 contained naturally admixed moist air (N2/O2/CO2/H2O) so that the conditions corresponded to those that can be expected in the normal use of SF6 as an industrial gaseous dielectric. In the second series of experiments, SF6 contained admixtures of dry air only (N2/O2/CO2). Moisture (H2O) was excluded from all gases as well as gas handling systems and procedures used. Final products formed in reactions initiated by PALS-produced plasmas have been in both series analysed using GC-MS detection.
In samples containing the moist air, gas chromatograms reveal only three products of SF6 reactions, that is, thionyl fluoride (SOF2), sulphuryl fluoride (SO2F2) and thionyl tetrafluoride (SOF4). Yields of all three products are low (~1%). Their abundances depend on the pressure in the cell. At p(SF6) = 10.7 kPa, that is, the lowest pressure in the cell, there are SOF2 and SOF4 formed (Figure 14). If we increase the pressure of SF6 to 26.7 kPa, SOF2 and SO2F2 appear as products. At even higher SF6 pressures, that is, 53.3 and 101.3 kPa (atmospheric pressure), only one product (SOF2) is indicated. The overall (stoichiometric) reactions leading to the above-mentioned final products could be expressed as follows:
$$\begin{align*}{\mathrm{SF}}_6+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{SO}\mathrm{F}}_2+2\mathrm{HF}+{\mathrm{F}}_2,\\ {}{\mathrm{SF}}_6+2{\mathrm{H}}_2\mathrm{O}\to {\mathrm{SO}}_2{\mathrm{F}}_2+4\mathrm{HF},\\ {}{\mathrm{SF}}_6+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{SO}\mathrm{F}}_4+2\mathrm{HF}.\end{align*}$$
The gas chromatogram of SF6 (containing traces of moist air) chemically altered by LIDB plasmas induced by four laser pulses focused into the gas cell (the total pressure in the cell is 10.7 kPa) shot by shot.
However, neither HF/F2 nor SiF4 molecules have been indicated in gas chromatography records. The silicon tetrafluoride should be formed in reactions of hydrogen fluoride and/or molecular fluorine with SiO2 in the cell wall.
Contrary to the samples contaminated by moist air, the samples that do not contain traces of water vapour exhibit quite poor laser–plasma chemical reactivity. In addition to remaining SF6 and air, only sulphuryl fluoride (SO2F2) has been found in the gas cell after four and eight laser shots accumulated at initial total pressures varied from 10.7 to 101.3 kPa. Therefore, SO2F2 molecules represent a single stable product that testifies to the key role of molecular oxygen (and transient species formed from its molecule upon LIDB conditions) in the reaction mixture because water vapour is not present in these runs. Considering the situation just stoichiometrically, the overall reaction SF6 + O2 → SO2F2 + 2F2 provides sulphuryl fluoride. However, the reaction gives molecular fluorine as another product, which was not registered by GC-MS.
Notable is the absence of SiF4, which is thought to be formed by reactions of fluorine, hydrogen fluoride and other fluorine-containing reactive species with SiO2 in the glass body of the cell and its window. The SiF4 formation was observed in a narrow (1.44 cm in diameter) cell filled with SF6 in which the focused pulsed CO2 laser produced LIDB plasmas[ Reference Lin and Ronn60]. In the experiment reported here, a much larger inner diameter of the cell and the use of a long focal length lens ensure that fluorine reactants do not penetrate the mass of ambient, unirradiated gas towards the cell wall and the beam entrance window. Therefore, silicon tetrafluoride is not formed under these conditions. Both larger dimensions of the cell and a strong reduction of the gas mixture contact with carbon-containing components (e.g., O-rings, vacuum grease and flanges made of plastics) and contaminants (hydrocarbons from vacuum line) are likely responsible for an absence of CF4 formation. This product has also been frequently reported in SF6 subjected to electrical discharges[ Reference Mahdi, Abdul-Malek and Arshad61] and laser sparks[ Reference Lin and Ronn60] when fluorine-rich products and transients interact with carbon-containing species and surfaces in the gas cell.
In conclusion, we can say that the fully reproducible chemical change can be registered and quantified under the irradiation conditions applied here. Conversion efficiency and formation yields of the initial substance (SF6) and final products (SO x F y ), respectively, are both low. In addition to that, the number of products is very low, that is, only one or two products, depending on water vapour content and the pressure of the initial substance. The absence of any S x F y molecule (e.g., SF4 and/or S2F10) among products leads to the assumption that the product-forming reactions here are not stepwise unimolecular decompositions starting from SF6[ Reference Mahdi, Abdul-Malek and Arshad61– Reference Miletic, Neškovic, Veljkovic and Zmbov65], but rather bimolecular reactions of the initial substance with oxygen species (e.g., molecular and atomic oxygen, hydroxyl radicals and water molecules). All the above-mentioned findings contrast with those (especially a wide variety of products) obtained in electrical discharges between electrodes (see, for example, Refs. [Reference Kurte, Heise and Klockow14,Reference Mahdi, Abdul-Malek and Arshad61] and the references cited therein), conventional pyrolysis in a resistively heated reaction tube[ Reference Padma and Murthy66] and laser sparks induced in a narrow gas cell[ Reference Lin and Ronn60, Reference Eletskii, Klimov and Legasov67], where an interaction of plasmas (including radiation, particles and reactive species liberated from the plasma[ Reference Kurte, Heise and Klockow14, Reference Lin and Ronn60, Reference Mahdi, Abdul-Malek and Arshad61, Reference Miletic, Neškovic, Veljkovic and Zmbov65] or hot gas[ Reference Padma and Murthy66]) with solid surfaces can take place. Under our experimental conditions, the influence of solid surfaces on plasma chemical SF6 decomposition patterns seems to be significantly reduced.
4. Conclusions
SF6 plasma produced by a 350-ps, 126-J NIR laser pulse is a complex object with parameters evolving on different time scales. After the energy deposition, spontaneous relaxation of the laser spark occurs, releasing excess energy. During the interaction of the laser pulse with the gas, there is not only fragmentation and ionization of SF6, but also the escape of hot electrons from the plasma kernel, which produce a spontaneous magnetic field and emit EMPs. The EMP emission from a laser spark is very weak compared to the EMP produced when such a laser pulse interacts with a solid target placed in vacuum. This is due to the loss of energy of runaway electrons in collisions with molecules of the surrounding cold gas. The frequency of about 1.1 GHz is a typical frequency of EMPs emitted from the SF6 laser spark at atmospheric and sub-atmospheric pressures. The frequency spectrum of the spontaneous magnetic field is broader and contains three bands around 1.15, 2.1 and 3 GHz. These fields cease within 5 ns.
After being heated by the laser, the plasma undergoes a relaxation process that can last up to microseconds, during which charged particles recombine and ions and atoms emit radiation in the visible part of the spectrum. Although the evolution dynamics in recombining SF6 plasma were not measured using a time-resolved spectrometer, it was estimated that the values of n e and T e do not differ from those experimentally observed, for example, in the field of laser-induced breakdown spectroscopy (LIBS).
The primary motivation for the fabrication and engagement of the gas cell with relatively large diameter was to eliminate the effects of the walls, flanges and the beam entrance window on the plasma processes responsible for EMP generation. However, this specific feature of the cell design was also influencing the chemical change in SF6 registered under these experimental conditions. Gas chromatography showed the formation of only a very limited number of products and a low degree of conversion of SF6. This contrasts with results obtained by other researchers[ Reference Kurte, Heise and Klockow14, Reference Lin and Ronn60– Reference Eletskii, Klimov and Legasov67] in electrical discharges, electrically heated tube reactors for pyrolysis and also with laser sparks, but in small gas cells, where solids can influence SF6 decomposition mechanisms and rates, often dramatically. Under the experimental conditions described here, the laser–plasma chemical reaction system proved to be perfectly homogeneous. A detailed report on laser–plasma chemical results and their mechanistic implications (what specific physical and chemical processes are responsible for a particular chemical change; the methodology can be found in Refs. [Reference Babánková, Civiš and Juha68,Reference Juha, Civiš and Lackner69]) is being prepared to appear in a chemical journal.
The shot-to-shot fluctuations in the emission of EMPs and visible radiation reflect two fundamental stages occurring during the lifetime of the laser spark. The first is plasma produced by a laser pulse, where competing picosecond processes control the energy of electrons and their flows, generating a spontaneous magnetic field and EMPs. This phase is characterized by significant fluctuations in the magnetic field intensity and the background continuum of the visible radiation. The second phase begins after laser heating of SF6. The processes of plasma recombination and chemical reactions leading to the formation of SF6, F2, SF4 and various sulphur oxyfluorides occurring on a microsecond scale are accompanied by fluctuations in the emission of visible radiation, which, however, are much smaller compared to the fluctuations mentioned above.
Acknowledgements
Authors’ thanks go to the Czech Ministry of Education, Youth and Sports (CMEYS) for the financial support of the project No. LM2023068 (PALS RI) and to the Grant Agency of the Czech Republic (Project No. GM23-05027M).
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