- Email: [email protected]
Spatio-temporal evolution of laser-induced air plasma in the stage of laser pulse action
Optics Communications 289 (2013) 114–118
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Spatio-temporal evolution of laser-induced air plasma in the stage of laser pulse action Jian Tang, Duluo Zuo n, Tao Wu, Zuhai Cheng Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 April 2012 Received in revised form 3 August 2012 Accepted 29 August 2012 Available online 25 October 2012
Spatially and temporally resolved emission spectra of laser-induced air plasma in the stage of laser pulse action were studied. Due to the expansion of laser supported detonation wave and shielding effect at the critical surface for CO2 laser radiation, a behavior of spatial separation of the radiative plasma along the radial direction was clearly recognized. Based on the Stark broadening, we investigated the spatio-temporal evolution of the electron density and temperature of the plasma, which was evaluated by fitting the measured spectral profile to the summation of Voigt profiles of all spectral lines in a selected spectral range. The electron density was distributed densely around the focal point and thinly near the plasma edge at early times. On the contrary, the electron temperature around the focal point was a minimum at early times but became a maximum at later times. Unlike the spatiotemporal resolution results of post-pulse in previous work, the results in the present work revealed the information related to the processes of laser energy deposition. & 2012 Elsevier B.V. All rights reserved.
Keywords: Laser-induced plasma Spectroscopy Spatio-temporal evolution Imaging spectroscopy
1. Introduction When a high-power laser beam is focused into a gas, a fully ionized plasma can be created near the focal point of the laser beam. The emission spectra of excited atoms and molecules of the plasma are extensively applied to determine the elemental composition of the analyte [1]; furthermore, the blast wave accompanied with air plasma induced by a pulsed CO2 laser is adopted for laser propulsion [2] and laser plasma drag reduction [3]. In the past decade, researchers have made a great effort on improvement of the sensitivity of laser-induced breakdown spectroscopy (LIBS), the efficiency of laser propulsion and laser plasma drag reduction, however, an investigation of the laserplasma processes taking place during laser-induced plasma (LIP) could help us to get a better understanding how the laser parameters affect the applications mentioned above both temporally and spatially. As the two main parameters to figure the interactions between laser and plasma, an interest in the plasma diagnosis of spatiotemporal evolution of the electron density and temperature in LIP in application of LIBS and laser propulsion was increased last decade. Jones et al. [4] used a triple Langmuir probe to investigate the time dependence of the electron temperature and number density in the plasma of the lightcraft qualitatively. Siegel et al.
n
Corresponding author. Tel./fax: þ 86 027 87792355. E-mail address: [email protected] (D. Zuo).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.08.096
[5] and Aragon et al. [6,7] employed the spectrally resolved imaging technique to estimate spatial distribution of the electron density and temperature in plasmas, and analyzed the expansion and cooling processes of LIP after the termination of laser pulse. Camacho et al. [8] examined the time-resolved optical emission spectral lines of laser-induced air plasma generated by a transversely excited atmospheric (TEA) CO2 laser. Zhang et al. [9] reported the formation of the plasma channel at the early stage of laser-induced air plasma by using optical interferometry. Shimamura et al. [10] utilized the optical interferometry to determinate the electron density distribution of laser-induced air plasma at the later stage of laser pulse, indicated that the laser energy was absorbed perfectly in the laser-supported detonation (LSD) regime, and the precursor electrons ahead of the shock wave drove the expansion of plasma in the direction opposite to the incident laser. Despite numerous spatially and temporally resolved measurements of electron density and temperature had been carried out in the previous work [4–10], few of them evaluated the evolution in the processes of laser energy deposition, from which we might appreciate how the laser parameters affect LIP temporally and spatially, and specifically, for the air breakdown by pulsed CO2 laser in laser propulsion and laser plasma drag reduction in the present work. We performed a TEA CO2 laser-induced air plasma experiment to obtain the evolution of the electron density and temperature during the stage of a pulse action. The parabolic reflector used in this study was similar with the Bohn-bell parabolic reflector from the DLR (German Aerospace Center)
J. Tang et al. / Optics Communications 289 (2013) 114–118
[11]. In addition, we accomplished the Voigt line profile fitting model to calculate the electron density and temperature of LIP, and then discussed the processes of laser energy deposition.
115
of instrumental broadening was estimated as 0.2 nm when the 300 grooves/mm gratings were used.
3. Spectral fitting model 2. Experimental setup A GaAs plane plate was employed to obtain the spatially and temporally resolved emission spectra of the plasma at a front-on observation, which transmit the CO2 laser radiation highly and reflect the visible radiation of LIP as depicted in Fig. 1(a). The plasma was generated in atmospheric pressure air by focusing the TEA CO2 laser pulse, with the pulse energy of 1 J and full width at half maximum (FWHM) of 70 ns. The typical pulse waveform of laser radiation was presented in Fig. 2. An aluminum parabolic reflector was used to focus the pulsed laser radiation to initiate air breakdown, with the focal length of 10 mm. Two achromatic lens were utilized to image the plasma 1:1 onto the entrance slit of the spectrograph, with a slit width of 20 mm. In this way, the spatial resolved spectra of plasma emission along the radial direction were detected by the vertical array of CCD. A time-gated ICCD system (PI-MAX-1300, 1340 1300 pixels, Princeton Instrument Inc.) was employed to provide the temporal resolution of plasma. The spectrograph used in the experiment was SP2750i of Princeton Instruments, Inc., with a focus length of 750 mm. The synchronization in the experiment was realized by the synchronous output signal of the digital oscilloscope TDS7154B of Tektronix, when it was triggered by the electromagnetic interference of pulsed discharge detected by a probe connected to it. The jitter between the trigger output and the beginning of laser pulse or plasma radiation was less than 10 ns. The intensity response of the measurement system was calibrated with a standard deuterium tungsten–halogen calibration light source (DH-2000-CAL, Ocean Optics Inc.). Furthermore, the wavelength calibration of the spectrometer was achieved with several standard atom lamps (Ar, Kr, Ne,Xe, and Hg). The full width
The emission intensity corresponding to the transition from level m to n was evaluated from the Boltzmann statistical law and the classical theory, assuming that the LIP in this experiment was in the local thermodynamic equilibrium (LTE) state and optically thin Z 1 1 g Em Imn ¼ hnmn Amn N A m exp f ðnÞdn, ð1Þ 4p Q ðTÞ kT 0 where NA was the number density of the excited particle; Q(T) was the partition function; Amn was the transition probability; nmn was the spontaneous radiation frequency; gm was the statistical weight; Em was the energy of the excited energy level; k was the Boltzmann’s constant; h was the Planck’s constant; T was the electron temperature; the function f(n) was the Voigt line profile. The values of Amn, gm, Em, and nmn were from NIST database [12]. The Voigt line profile function f(n) was calculated using the polynomial approximations proposed by Kuntz et al. [13,14]. The broadening mechanisms contributed to the plasma spectral line broadening by which the shape of the width of f(n) was determined were estimated listed in Table 1 [15]. The Stark broadening from electron collision and Doppler broadening were the primary mechanisms in this experiment, where the FWHM of Stark broadening related to the electron density was calculated from the impact theory [16]
DnL ¼
11:37 2=3 1=3 0 C 4 v ne J ðbÞ, 2p
ð2Þ
where C4 was the quadratic Stark constant; v was the mean velocity of electron; ne was the electron density; J0 (b) was the non-adiabatic correcting factor. In this work, an algorithm was established to fit the spectral emission profiles and compare them to the experimental spectral profiles, where the broadening of the spectral lines and the intensity-ratio between each spectral line were very sensitive to the local density of electron and temperature, respectively. The intensity of each wavelength I(li) in the spectral fitting model were evaluated for the entire spectral profiles as the form below Iðli Þ ¼
p X
Ij ðli Þ
ði ¼ 1,2,:::,qÞ,
ð3Þ
j¼1
Fig. 1. Experimental setup (a) and the LIP geometry (b).
where p was the number of transition spectral lines; q was the number of wavelength pixels. The routine was carried out by a least-squares procedure to find the best reproduction of the experimental profiles, and obtain the electron density and temperature simultaneously. Similar with the spectral model of Glumac [17], we chose the region from 498 nm to 520 nm to the fitting model to evaluate the electron density and temperature. Firstly, there were only N II lines observed in this region [12]. Secondly, the spectral lines in the spectral fitting region were originated from higher-excited Table 1 The estimated FWHM of each broadening contribution.
Fig. 2. Typical pulse waveform of TEA CO2 laser radiation.
Broadening
FWHM magnitude (nm)
Natural broadening Doppler broadening Resonance broadening Stark broadening [16] Vander Waals broadening
10 4 10 2 10 3 10 1 Lower than 10 3
116
J. Tang et al. / Optics Communications 289 (2013) 114–118
levels and terminated in excited levels, and hence the optically thin assumption was adequate [18]. Thirdly, there were not any resonance lines in this selected spectral range, which were most affected by self-absorption. As Fig. 3 illustrated the resulting
profiles of LIP, numerous N II spectral lines overlap to form three main envelopes at around 500, 504, and 518 nm, in which the contribution of continuum spectra had been deducted. The fitted and measured profiles in Fig. 3 added a background factitiously for a legible comparison.
4. Results and discussion 4.1. Images of laser-induced air plasma
Fig. 3. Example of a measured spectral line profile fitted with the Voigt profile.
The visualization of the LIP expansion progress was captured by ICCD, a sequence of instantaneous images was taken of each independent laser-induced breakdown event, with the gate time of 50 ns. The ionization of the cold ambient gas was provided by the propagation of the laser absorption wave [10], and the shape of the LIP expansion was similar with the laser spot as inspection in Fig. 4. The corresponding spectrally resolved imaging measurement of the 20 mm-central slice of the LIP was depicted in Fig. 5, from 0.05 ms to 4 ms with the respect to laser pulse onset. To show a legible plasma image, the intensity at t¼ 0.05 ms in Figs. 4 and 5 were multiplied by 9 and 35, respectively. The optical breakdown of air occurred at t¼0.05 ms after laser pulse onset, with the initial radius of ignition region about 0.5 mm. The resulting plasma absorbed laser energy by two different absorption processes, multi-photon ionization and inverse bremsstrahlung absorption, accompanying with intense continuum emission, as showed at t¼0.05 ms and 0.1 ms in Fig. 5. Subsequently, the remainder energy of the laser pulse was absorbed consecutively by the laser absorption wave, resulting in the expansion of LIP into the background gas, and together with the appearance of N II lines emission envelopes at 500 nm, 504 nm, and 518 nm. An evident spatial separation along the radial direction in this period was clearly recognized, weak around the focal point and strong near the plasma edge. We conjectured that the spatial separation behavior was caused by the expansion of laser
Fig. 4. Images of LIP evolution and the detected part in this paper.
Fig. 5. Images of radial spectral emission distribution of LIP.
J. Tang et al. / Optics Communications 289 (2013) 114–118
117
Fig. 6 demonstrated the radial distribution of electron density and temperature of LIP calculated by the spectral fitting model in the duration of laser pulse, taken at 0.3 ms, 0.9 ms, 1.5 ms and 3 ms. In Fig. 6, the plasma showed a relative minimum electron density along the laser axis, the similar phenomenon was also found by Zhang et al. [9], who interpreted in terms of high velocity of the plasma expanding in the radial direction. The maximum electron density was up to about 1.2 1019 cm 3 at the outer region at the radial position around r ¼ 70.3 mm. The electron density at early times exceeded the critical density (nc ¼1019 cm 3) which results in the reflection of the CO2 laser beam at this critical surface, where the plasma frequency became higher than the laser frequency [19]. As a result of the plasma shielding of laser energy around the focal point, the plasma outside the critical surface was heated by the reflected laser radiation once again, therefore, as showed in Fig. 6(b) (t ¼0.3 ms, 0.9 ms and 1.5 ms), the maximum electron temperature did not correspond to the maximum electron density position, the maximum temperature was up to about 40000 K at the region outside the critical surface r ¼ 70.75 mm when t¼0.3 ms. At the same time, the electron temperature at the plasma center (r ¼0 mm) was slightly higher than that at critical density region, this may be interpreted as the effect of the hightemperature plasma generated at the beginning of optical breakdown. However, as the cooling processes of the plasma at later
times (t¼ 3 ms), the radial distribution of the electron density became homogeneous, and the electron temperature at the plasma edge decreased sharply. Fig. 7 presented the temporal evolutions of the electron density and temperature of laser-induced air plasma at three radial points, 0 mm, 0.3 mm and 0.75 mm. The electron density exhibited a monotonously decreasing behavior all the time, while the electron density at the outer region near the critical surface (r ¼0.3 mm) was higher than others for the first 0.9 ms. At the meantime, the evolution of the electron temperature showed three different stages. In the duration of the first 0.5 ms, as a result of the cutoff of the laser beam transmission at the critical density surface, the plasma center could not be heated by the laser radiation, and hence the electron temperature at r ¼0 mm, 0.3 mm had a faster decay rate than that at r ¼0.75 mm. As time elapsed, the laser radiation could transmit through the outer plasma after disappearance of the critical surface, then the plasma center were heated by laser radiation, naturally, the temperature at r ¼0.3 mm increased earlier than plasma at r ¼0 mm. Finally, after the termination of laser pulse, because of adiabatic expansion of the plasma and recombination of electrons and ions, we noted an appreciable temperature decreased at later times. Results in our work were different from the radial distribution given by Aragon et al. [6,7] who indicated that the electron density and temperature had maximums in the center part of the plasma. Firstly, the captured temporal windows were different. Aragon et al. selected the stage after the termination of laser pulse, and only examined the adiabatic expansion of LIP. But in our work, the temporal windows along with the processes of plasma heating were selected. In the duration of laser pulse, the plasma had a steep spatial gradient, leading to the radical expansion of plasma with high velocity. Meanwhile, accompanied by the injection of laser energy, enhanced plasma density was formed outside the axis. Secondly, the wavelength of laser radiation was different. In our experiments, the air plasma around
Fig. 6. Radial distribution of the electron density (a) and temperature (b).
Fig. 7. Temporal evolution of the electron density (a) and temperature (b).
absorption wave and the opacity of the plasma around the focal point for CO2 radiation, which would be discussed in the latter sections. In the later stage of the plasma evolution, due to the decreasing of laser radiation, the recombination of electrons and ions became dominant, the spatial distribution of the radiative plasma was homogenized gradually until the emission extinguished eventually. 4.2. Spatio-temporal evolution of the electron density and temperature
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J. Tang et al. / Optics Communications 289 (2013) 114–118
the focal point was ionized rapidly above the critical density and became opaque for CO2 laser radiation, while the critical density for a Nd:YAG laser (l ¼ 1.06 mm) was 1021 cm 3. Namely, compared with Nd:YAG laser, the electron density was more easily to reach the critical value of CO2 laser. Therefore, the CO2 laser could not heat the plasma inside the critical surface, resulting in temperature minimum at the plasma center. 4.3. Verification of the existence of LTE In the case of transient and inhomogeneous plasma, if the variation of the plasma thermodynamic parameters were sufficiently slow both temporally and spatially, while the McWhirter criterion was fulfilled at the same time, Omenetto et al. [20,21] consider the plasma to be in LTE state. ne Z
2:55 1011 1=2 T ðDEÞ3 , /gS
ð4Þ
T ðt þ trel ÞTðtÞ ne ðt þ trel Þne ðtÞ {1 {1, TðtÞ ne ðtÞ
ð5Þ
TðxÞT x þddif f ne ðxÞne x þ ddif f {1 {1, TðxÞ ne ðxÞ
ð6Þ
breakdown by pulsed CO2 laser. The optical breakdown of air occurred at t ¼0.05 ms after the onset laser pulse, with the initial radius of ignition region about 0.5 mm. Due to the expansion of laser absorption wave and the shielding effect at the critical surface, the plasma exhibited the separate behavior along the radial direction, where the plasma was divided into two regions by the critical surface. In the region with the electron density above the critical density, the local plasma became opaque and the laser radiation could not transmit into the plasma center; in the outer region with the electron density under the critical density, the plasma absorbed the energy of the laser radiation, and hence the electrons in this region were strongly heated. However, once the laser beam propagated through into the plasma center, the electron temperature at the plasma center ascended gradually. Finally, subsequent to the termination of laser pulse, as the adiabatic expansion of LIP and the cooling processes with the ambient air, the electron density and temperature decreased sharply.
References
where /gS was the quantum mechanical correction factor; DE was the largest energy gap in the transitions; trel and ddiff were the relaxation time of the plasma and the diffusion length during the relaxation time, respectively, the value of these two characteristic parameters of N II was about 4 10 8 s and 3.4 10 3 mm while the LIP characterized by ne ¼2 1018 cm 3 and T¼35000 K in our study. With the measured electron density and temperature in LIP, the Eqs. (4)–(6) relations were fulfilled suggesting the existence of LTE in plasma in our study.
5. Conclusions Thanks to spectrally resolved imaging technique, the transverse cross-section of LIP was imaged onto the entrance slit of a spectrometer to perform spatially and temporally resolved measurements. As the plasma in our study was characterized by hightemperature and high-density, the collision processes dominated all other processes and the deviations from LTE were negligible. The electron density and temperature of LIP were evaluated by fitting the measured spectral profiles to the summation of Voigt line profiles, in the selected spectral range from 480 nm to 520 nm. Unlike most of the works on LIBS which mainly investigated the post-pulse evolution, we studied the evolution of LIP at the stage of laser energy deposition, specifically for the air
[1] Alejandro Molina, Peter M. Walsh, Christopher R. Shaddix, Shane M. Sickafoose, Linda G. Blevins, Applied Optics 45 (2006) 4411. [2] A.A. Ageichik, M.S. Egorov, Y.A. Rezunkov, A.L. Sarfronov, V.V. Stepanov, AIP Conference Proceedings 702 (2004) 49. [3] A.C. Oliveira, M.A.S. Minucci, P.G.P. Toro, J.B. Chanes, L.N. Myrabo, AIP Conference Proceedings 997 (2008) 379. [4] J.E. Jones, T.S. Wang, Proceedings of the 37th AIAA/ASME/SAE/ASEE Joint Propulation Conference, 2001, p. 3796. [5] J. Siegel, G. Epurescu, A. Perea, F.J. Gordillo-Vazquez, J. Gonzalo, C.N. Afonso, Spectrochimica Acta Part B 60 (2005) 915. [6] C. Aragon, F. Penalba, J.A. Aguilera, Applied Physics A 79 (2004) 1145. [7] J.A. Aguilera, C. Aragon, Spectrochimica Acta Part B 62 (2007) 378. [8] J.J. Camacho, L. Diaz, M. Santos, L.J. Juan, J.M.L. Poyato, Journal of Applied Physics 107 (2010) 083306. [9] H. Zhang, J. Lu, Z. Shen, X. Ni, Optics Communications 282 (2009) 1720. [10] K. Shimamura, K. Hatai, K. Kawamura, A. Fukui, A. Fukuda, Journal of Applied Physics 109 (2011) 084910. [11] W.O. Schall, W.L. Bohn, H.A. Eckel, W. Mayerhofer, W. Riede, E. Zeyfang, Proceedings of SPIE 4065 (2000) 472. [12] Available from: /http://physics.nist.gov/cgi-bin/ASD/lines1.plS. [13] M. Kuntz, Journal of Quantitative Spectroscopy and Radiative Transfer 57 (1997) 819. [14] W. Ruyten, Journal of Quantitative Spectroscopy and Radiative Transfer 86 (2004) 231. [15] N. Konjevic, Physics Reports 316 (1999) 339. [16] I.I. Sobel’man, Introduction to the Theory of Atomic Spectra, Pergamon Press, New York, 1972. [17] N. Glumac, G. Elliott, M. Boguszko, AIAA Journal 43 (2005) 1984. [18] S.S. Harilal, B.O. Shay, M.S. Tillack, Journal of Applied Physics 98 (2005) 013306. [19] H. Hora, Laser Plasmas and Nuclear Energy, Plenum Press, New York, 1975. [20] D.W. Hahn, N. Omenetto, Applied Spectroscopy 64 (2010) 335A. [21] G. Cristoforetti, A.D. Giacomo, M. Dell’Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, N. Omenetto, Spectrochimica Acta Part B 65 (2010) 86.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Spatio-temporal evolution of laser-induced air plasma in the stage of laser pulse action Jian Tang, Duluo Zuo n, Tao Wu, Zuhai Cheng Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 April 2012 Received in revised form 3 August 2012 Accepted 29 August 2012 Available online 25 October 2012
Spatially and temporally resolved emission spectra of laser-induced air plasma in the stage of laser pulse action were studied. Due to the expansion of laser supported detonation wave and shielding effect at the critical surface for CO2 laser radiation, a behavior of spatial separation of the radiative plasma along the radial direction was clearly recognized. Based on the Stark broadening, we investigated the spatio-temporal evolution of the electron density and temperature of the plasma, which was evaluated by fitting the measured spectral profile to the summation of Voigt profiles of all spectral lines in a selected spectral range. The electron density was distributed densely around the focal point and thinly near the plasma edge at early times. On the contrary, the electron temperature around the focal point was a minimum at early times but became a maximum at later times. Unlike the spatiotemporal resolution results of post-pulse in previous work, the results in the present work revealed the information related to the processes of laser energy deposition. & 2012 Elsevier B.V. All rights reserved.
Keywords: Laser-induced plasma Spectroscopy Spatio-temporal evolution Imaging spectroscopy
1. Introduction When a high-power laser beam is focused into a gas, a fully ionized plasma can be created near the focal point of the laser beam. The emission spectra of excited atoms and molecules of the plasma are extensively applied to determine the elemental composition of the analyte [1]; furthermore, the blast wave accompanied with air plasma induced by a pulsed CO2 laser is adopted for laser propulsion [2] and laser plasma drag reduction [3]. In the past decade, researchers have made a great effort on improvement of the sensitivity of laser-induced breakdown spectroscopy (LIBS), the efficiency of laser propulsion and laser plasma drag reduction, however, an investigation of the laserplasma processes taking place during laser-induced plasma (LIP) could help us to get a better understanding how the laser parameters affect the applications mentioned above both temporally and spatially. As the two main parameters to figure the interactions between laser and plasma, an interest in the plasma diagnosis of spatiotemporal evolution of the electron density and temperature in LIP in application of LIBS and laser propulsion was increased last decade. Jones et al. [4] used a triple Langmuir probe to investigate the time dependence of the electron temperature and number density in the plasma of the lightcraft qualitatively. Siegel et al.
n
Corresponding author. Tel./fax: þ 86 027 87792355. E-mail address: [email protected] (D. Zuo).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.08.096
[5] and Aragon et al. [6,7] employed the spectrally resolved imaging technique to estimate spatial distribution of the electron density and temperature in plasmas, and analyzed the expansion and cooling processes of LIP after the termination of laser pulse. Camacho et al. [8] examined the time-resolved optical emission spectral lines of laser-induced air plasma generated by a transversely excited atmospheric (TEA) CO2 laser. Zhang et al. [9] reported the formation of the plasma channel at the early stage of laser-induced air plasma by using optical interferometry. Shimamura et al. [10] utilized the optical interferometry to determinate the electron density distribution of laser-induced air plasma at the later stage of laser pulse, indicated that the laser energy was absorbed perfectly in the laser-supported detonation (LSD) regime, and the precursor electrons ahead of the shock wave drove the expansion of plasma in the direction opposite to the incident laser. Despite numerous spatially and temporally resolved measurements of electron density and temperature had been carried out in the previous work [4–10], few of them evaluated the evolution in the processes of laser energy deposition, from which we might appreciate how the laser parameters affect LIP temporally and spatially, and specifically, for the air breakdown by pulsed CO2 laser in laser propulsion and laser plasma drag reduction in the present work. We performed a TEA CO2 laser-induced air plasma experiment to obtain the evolution of the electron density and temperature during the stage of a pulse action. The parabolic reflector used in this study was similar with the Bohn-bell parabolic reflector from the DLR (German Aerospace Center)
J. Tang et al. / Optics Communications 289 (2013) 114–118
[11]. In addition, we accomplished the Voigt line profile fitting model to calculate the electron density and temperature of LIP, and then discussed the processes of laser energy deposition.
115
of instrumental broadening was estimated as 0.2 nm when the 300 grooves/mm gratings were used.
3. Spectral fitting model 2. Experimental setup A GaAs plane plate was employed to obtain the spatially and temporally resolved emission spectra of the plasma at a front-on observation, which transmit the CO2 laser radiation highly and reflect the visible radiation of LIP as depicted in Fig. 1(a). The plasma was generated in atmospheric pressure air by focusing the TEA CO2 laser pulse, with the pulse energy of 1 J and full width at half maximum (FWHM) of 70 ns. The typical pulse waveform of laser radiation was presented in Fig. 2. An aluminum parabolic reflector was used to focus the pulsed laser radiation to initiate air breakdown, with the focal length of 10 mm. Two achromatic lens were utilized to image the plasma 1:1 onto the entrance slit of the spectrograph, with a slit width of 20 mm. In this way, the spatial resolved spectra of plasma emission along the radial direction were detected by the vertical array of CCD. A time-gated ICCD system (PI-MAX-1300, 1340 1300 pixels, Princeton Instrument Inc.) was employed to provide the temporal resolution of plasma. The spectrograph used in the experiment was SP2750i of Princeton Instruments, Inc., with a focus length of 750 mm. The synchronization in the experiment was realized by the synchronous output signal of the digital oscilloscope TDS7154B of Tektronix, when it was triggered by the electromagnetic interference of pulsed discharge detected by a probe connected to it. The jitter between the trigger output and the beginning of laser pulse or plasma radiation was less than 10 ns. The intensity response of the measurement system was calibrated with a standard deuterium tungsten–halogen calibration light source (DH-2000-CAL, Ocean Optics Inc.). Furthermore, the wavelength calibration of the spectrometer was achieved with several standard atom lamps (Ar, Kr, Ne,Xe, and Hg). The full width
The emission intensity corresponding to the transition from level m to n was evaluated from the Boltzmann statistical law and the classical theory, assuming that the LIP in this experiment was in the local thermodynamic equilibrium (LTE) state and optically thin Z 1 1 g Em Imn ¼ hnmn Amn N A m exp f ðnÞdn, ð1Þ 4p Q ðTÞ kT 0 where NA was the number density of the excited particle; Q(T) was the partition function; Amn was the transition probability; nmn was the spontaneous radiation frequency; gm was the statistical weight; Em was the energy of the excited energy level; k was the Boltzmann’s constant; h was the Planck’s constant; T was the electron temperature; the function f(n) was the Voigt line profile. The values of Amn, gm, Em, and nmn were from NIST database [12]. The Voigt line profile function f(n) was calculated using the polynomial approximations proposed by Kuntz et al. [13,14]. The broadening mechanisms contributed to the plasma spectral line broadening by which the shape of the width of f(n) was determined were estimated listed in Table 1 [15]. The Stark broadening from electron collision and Doppler broadening were the primary mechanisms in this experiment, where the FWHM of Stark broadening related to the electron density was calculated from the impact theory [16]
DnL ¼
11:37 2=3 1=3 0 C 4 v ne J ðbÞ, 2p
ð2Þ
where C4 was the quadratic Stark constant; v was the mean velocity of electron; ne was the electron density; J0 (b) was the non-adiabatic correcting factor. In this work, an algorithm was established to fit the spectral emission profiles and compare them to the experimental spectral profiles, where the broadening of the spectral lines and the intensity-ratio between each spectral line were very sensitive to the local density of electron and temperature, respectively. The intensity of each wavelength I(li) in the spectral fitting model were evaluated for the entire spectral profiles as the form below Iðli Þ ¼
p X
Ij ðli Þ
ði ¼ 1,2,:::,qÞ,
ð3Þ
j¼1
Fig. 1. Experimental setup (a) and the LIP geometry (b).
where p was the number of transition spectral lines; q was the number of wavelength pixels. The routine was carried out by a least-squares procedure to find the best reproduction of the experimental profiles, and obtain the electron density and temperature simultaneously. Similar with the spectral model of Glumac [17], we chose the region from 498 nm to 520 nm to the fitting model to evaluate the electron density and temperature. Firstly, there were only N II lines observed in this region [12]. Secondly, the spectral lines in the spectral fitting region were originated from higher-excited Table 1 The estimated FWHM of each broadening contribution.
Fig. 2. Typical pulse waveform of TEA CO2 laser radiation.
Broadening
FWHM magnitude (nm)
Natural broadening Doppler broadening Resonance broadening Stark broadening [16] Vander Waals broadening
10 4 10 2 10 3 10 1 Lower than 10 3
116
J. Tang et al. / Optics Communications 289 (2013) 114–118
levels and terminated in excited levels, and hence the optically thin assumption was adequate [18]. Thirdly, there were not any resonance lines in this selected spectral range, which were most affected by self-absorption. As Fig. 3 illustrated the resulting
profiles of LIP, numerous N II spectral lines overlap to form three main envelopes at around 500, 504, and 518 nm, in which the contribution of continuum spectra had been deducted. The fitted and measured profiles in Fig. 3 added a background factitiously for a legible comparison.
4. Results and discussion 4.1. Images of laser-induced air plasma
Fig. 3. Example of a measured spectral line profile fitted with the Voigt profile.
The visualization of the LIP expansion progress was captured by ICCD, a sequence of instantaneous images was taken of each independent laser-induced breakdown event, with the gate time of 50 ns. The ionization of the cold ambient gas was provided by the propagation of the laser absorption wave [10], and the shape of the LIP expansion was similar with the laser spot as inspection in Fig. 4. The corresponding spectrally resolved imaging measurement of the 20 mm-central slice of the LIP was depicted in Fig. 5, from 0.05 ms to 4 ms with the respect to laser pulse onset. To show a legible plasma image, the intensity at t¼ 0.05 ms in Figs. 4 and 5 were multiplied by 9 and 35, respectively. The optical breakdown of air occurred at t¼0.05 ms after laser pulse onset, with the initial radius of ignition region about 0.5 mm. The resulting plasma absorbed laser energy by two different absorption processes, multi-photon ionization and inverse bremsstrahlung absorption, accompanying with intense continuum emission, as showed at t¼0.05 ms and 0.1 ms in Fig. 5. Subsequently, the remainder energy of the laser pulse was absorbed consecutively by the laser absorption wave, resulting in the expansion of LIP into the background gas, and together with the appearance of N II lines emission envelopes at 500 nm, 504 nm, and 518 nm. An evident spatial separation along the radial direction in this period was clearly recognized, weak around the focal point and strong near the plasma edge. We conjectured that the spatial separation behavior was caused by the expansion of laser
Fig. 4. Images of LIP evolution and the detected part in this paper.
Fig. 5. Images of radial spectral emission distribution of LIP.
J. Tang et al. / Optics Communications 289 (2013) 114–118
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Fig. 6 demonstrated the radial distribution of electron density and temperature of LIP calculated by the spectral fitting model in the duration of laser pulse, taken at 0.3 ms, 0.9 ms, 1.5 ms and 3 ms. In Fig. 6, the plasma showed a relative minimum electron density along the laser axis, the similar phenomenon was also found by Zhang et al. [9], who interpreted in terms of high velocity of the plasma expanding in the radial direction. The maximum electron density was up to about 1.2 1019 cm 3 at the outer region at the radial position around r ¼ 70.3 mm. The electron density at early times exceeded the critical density (nc ¼1019 cm 3) which results in the reflection of the CO2 laser beam at this critical surface, where the plasma frequency became higher than the laser frequency [19]. As a result of the plasma shielding of laser energy around the focal point, the plasma outside the critical surface was heated by the reflected laser radiation once again, therefore, as showed in Fig. 6(b) (t ¼0.3 ms, 0.9 ms and 1.5 ms), the maximum electron temperature did not correspond to the maximum electron density position, the maximum temperature was up to about 40000 K at the region outside the critical surface r ¼ 70.75 mm when t¼0.3 ms. At the same time, the electron temperature at the plasma center (r ¼0 mm) was slightly higher than that at critical density region, this may be interpreted as the effect of the hightemperature plasma generated at the beginning of optical breakdown. However, as the cooling processes of the plasma at later
times (t¼ 3 ms), the radial distribution of the electron density became homogeneous, and the electron temperature at the plasma edge decreased sharply. Fig. 7 presented the temporal evolutions of the electron density and temperature of laser-induced air plasma at three radial points, 0 mm, 0.3 mm and 0.75 mm. The electron density exhibited a monotonously decreasing behavior all the time, while the electron density at the outer region near the critical surface (r ¼0.3 mm) was higher than others for the first 0.9 ms. At the meantime, the evolution of the electron temperature showed three different stages. In the duration of the first 0.5 ms, as a result of the cutoff of the laser beam transmission at the critical density surface, the plasma center could not be heated by the laser radiation, and hence the electron temperature at r ¼0 mm, 0.3 mm had a faster decay rate than that at r ¼0.75 mm. As time elapsed, the laser radiation could transmit through the outer plasma after disappearance of the critical surface, then the plasma center were heated by laser radiation, naturally, the temperature at r ¼0.3 mm increased earlier than plasma at r ¼0 mm. Finally, after the termination of laser pulse, because of adiabatic expansion of the plasma and recombination of electrons and ions, we noted an appreciable temperature decreased at later times. Results in our work were different from the radial distribution given by Aragon et al. [6,7] who indicated that the electron density and temperature had maximums in the center part of the plasma. Firstly, the captured temporal windows were different. Aragon et al. selected the stage after the termination of laser pulse, and only examined the adiabatic expansion of LIP. But in our work, the temporal windows along with the processes of plasma heating were selected. In the duration of laser pulse, the plasma had a steep spatial gradient, leading to the radical expansion of plasma with high velocity. Meanwhile, accompanied by the injection of laser energy, enhanced plasma density was formed outside the axis. Secondly, the wavelength of laser radiation was different. In our experiments, the air plasma around
Fig. 6. Radial distribution of the electron density (a) and temperature (b).
Fig. 7. Temporal evolution of the electron density (a) and temperature (b).
absorption wave and the opacity of the plasma around the focal point for CO2 radiation, which would be discussed in the latter sections. In the later stage of the plasma evolution, due to the decreasing of laser radiation, the recombination of electrons and ions became dominant, the spatial distribution of the radiative plasma was homogenized gradually until the emission extinguished eventually. 4.2. Spatio-temporal evolution of the electron density and temperature
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the focal point was ionized rapidly above the critical density and became opaque for CO2 laser radiation, while the critical density for a Nd:YAG laser (l ¼ 1.06 mm) was 1021 cm 3. Namely, compared with Nd:YAG laser, the electron density was more easily to reach the critical value of CO2 laser. Therefore, the CO2 laser could not heat the plasma inside the critical surface, resulting in temperature minimum at the plasma center. 4.3. Verification of the existence of LTE In the case of transient and inhomogeneous plasma, if the variation of the plasma thermodynamic parameters were sufficiently slow both temporally and spatially, while the McWhirter criterion was fulfilled at the same time, Omenetto et al. [20,21] consider the plasma to be in LTE state. ne Z
2:55 1011 1=2 T ðDEÞ3 , /gS
ð4Þ
T ðt þ trel ÞTðtÞ ne ðt þ trel Þne ðtÞ {1 {1, TðtÞ ne ðtÞ
ð5Þ
TðxÞT x þddif f ne ðxÞne x þ ddif f {1 {1, TðxÞ ne ðxÞ
ð6Þ
breakdown by pulsed CO2 laser. The optical breakdown of air occurred at t ¼0.05 ms after the onset laser pulse, with the initial radius of ignition region about 0.5 mm. Due to the expansion of laser absorption wave and the shielding effect at the critical surface, the plasma exhibited the separate behavior along the radial direction, where the plasma was divided into two regions by the critical surface. In the region with the electron density above the critical density, the local plasma became opaque and the laser radiation could not transmit into the plasma center; in the outer region with the electron density under the critical density, the plasma absorbed the energy of the laser radiation, and hence the electrons in this region were strongly heated. However, once the laser beam propagated through into the plasma center, the electron temperature at the plasma center ascended gradually. Finally, subsequent to the termination of laser pulse, as the adiabatic expansion of LIP and the cooling processes with the ambient air, the electron density and temperature decreased sharply.
References
where /gS was the quantum mechanical correction factor; DE was the largest energy gap in the transitions; trel and ddiff were the relaxation time of the plasma and the diffusion length during the relaxation time, respectively, the value of these two characteristic parameters of N II was about 4 10 8 s and 3.4 10 3 mm while the LIP characterized by ne ¼2 1018 cm 3 and T¼35000 K in our study. With the measured electron density and temperature in LIP, the Eqs. (4)–(6) relations were fulfilled suggesting the existence of LTE in plasma in our study.
5. Conclusions Thanks to spectrally resolved imaging technique, the transverse cross-section of LIP was imaged onto the entrance slit of a spectrometer to perform spatially and temporally resolved measurements. As the plasma in our study was characterized by hightemperature and high-density, the collision processes dominated all other processes and the deviations from LTE were negligible. The electron density and temperature of LIP were evaluated by fitting the measured spectral profiles to the summation of Voigt line profiles, in the selected spectral range from 480 nm to 520 nm. Unlike most of the works on LIBS which mainly investigated the post-pulse evolution, we studied the evolution of LIP at the stage of laser energy deposition, specifically for the air
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