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Dynamics and density distribution of laser-produced Al plasmas using optical interferometry and optical emission spectroscopy
Accepted Manuscript
Dynamics and density distribution of laser-produced Al plasmas using optical interferometry and optical emission spectroscopy Shiquan Cao , Maogen Su , Qi Min , Duixiong Sun , Pengpeng Ma , Kaiping Wang , Zhihong Jiao , Chenzhong Dong PII: DOI: Reference:
S0022-4073(18)30589-2 https://doi.org/10.1016/j.jqsrt.2018.12.029 JQSRT 6348
To appear in:
Journal of Quantitative Spectroscopy & Radiative Transfer
Received date: Revised date: Accepted date:
13 August 2018 21 December 2018 21 December 2018
Please cite this article as: Shiquan Cao , Maogen Su , Qi Min , Duixiong Sun , Pengpeng Ma , Kaiping Wang , Zhihong Jiao , Chenzhong Dong , Dynamics and density distribution of laserproduced Al plasmas using optical interferometry and optical emission spectroscopy, Journal of Quantitative Spectroscopy & Radiative Transfer (2018), doi: https://doi.org/10.1016/j.jqsrt.2018.12.029
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Two different diagnostic methods, optical interferometry and OES were used to investigate laser-produced Al plasmas in air at atmospheric pressure. Three-dimensional spatial expansion profiles of the plasma plume and shock wave of laser-produced Al plasmas in air at atmospheric pressure were presented. 2D electron density distributions of Al plasmas were obtained from the spatial dependence of the refractive index of plasma. Consistency of the results of optical interferometry and OES was verified and the advantages and disadvantages of the two diagnostic methods were discussed.
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Dynamics and density distribution of laser-produced Al plasmas using optical interferometry and optical emission spectroscopy Shiquan Caoa, Maogen Sua,b,*, Qi Mina, Duixiong Suna,b, Pengpeng Maa, Kaiping Wanga, Zhihong Jiaoa, Chenzhong Donga,b,* a
Key Laboratory of Atomic and Molecular Physics & Functional Material of Gansu Province, College of Physics
and Electronic Engineering, Northwest Normal University, Lanzhou, 730070, China b
of Chinese Academy of Sciences, Lanzhou 730070, China *
Corresponding authors.
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Joint Laboratory of Atomic and Molecular Physics, Northwest Normal University and Institute of Modern Physics
E-mail addresses: [email protected] (M. Su), [email protected] (C. Dong).
Abstract: The dynamic evolution and density distribution of laser-produced plasmas (LPP) of Al
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in air at atmospheric pressure were investigated using optical interferometry and optical emission spectroscopy, respectively. Interferograms were obtained in Mach–Zehnder interferometry with a laser pulse energy of 35 mJ and delay times from 200 ns to 6.9 µs. From the shift in interference fringes within this time interval and Taylor–Sedow theory, the expansion profiles of the shock wave were found to be hemispherical and approached planar propagation. The expansion and evolution of the plasma plume were also studied by exploiting the phase shift and refractive index
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obtained from the interferograms using the fast Fourier transformation and Abel transformation. Three-dimensional spatial expansion profiles of the plasma plume and shock wave were presented.
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In addition, two-dimensional electron density distributions of the Al plasmas were obtained from the spatial dependence of the refractive index of plasma, and compared with the results of optical emission spectroscopy. The results from the two diagnostic methods and their advantages and
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disadvantages are discussed. This work exploits two diagnostic methods to study the dynamic evolution and the density distribution of the LPP in air at atmospheric pressure and provides an
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important base reference for developing LPP applications in many fields.
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Keywords: Laser-produced plasmas; Optical interferometry; Optical emission spectroscopy.
1. Introduction Laser-produced plasmas (LPP) are formed by a high-power laser pulse focused on a solid target
surface. The material in the focus area is heated and evaporated to form a high-temperature high-density vapor that includes atoms, ions, and free electrons during laser ablation stage. In the presence of ambient gas, the vapor expands and compresses surrounding gas to produce a shock wave. After laser irradiation termination, the plasma and shock wave expand into open spaces. LPP have been researched for many years for theirs diverse applications including short-wavelength light sources [1,2], laser ion sources [3], and laser fusion [4], where the plasma 2
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expands freely into a vacuum. Other applications include laser-induced breakdown spectroscopy [5], micromachining [6], and pulsed-laser deposition [7], usually under ambient gas. Such plasma has inherent transient and inhomogeneous nature, and therefore the research on the evolution of the dynamics and diagnostics of state parameters is very important in understanding the physical properties and developing these applications [8]. Some techniques have been developed for related research. Shadowgraphy and fast photography are well-known diagnostic tools for investigating the dynamics of plasma expansion [9,10]; optical emission spectrometry (OES) as a non-contact measurement method has been widely employed for estimating plasma parameters such as
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electron temperature and density [11–13]. In addition, Langmuir probing [14], Thomson scattering [15], and laser interferometry [16–18] also provide measurements of the electron temperature and density.
Each of the diagnostic technique above has its own advantages and limitations. The combination of different diagnostic methods for dynamics evolution and state-parameter
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diagnostics of LPP is a very important approach and a current trend in research. Using shadowgraphy and interferometry, Breitling and colleagues studied the distinctive behavior in shock wave expansion and the distribution of electron density in LPP at different laser wavelengths [19]. Harilal et al. investigated the hydrodynamic expansion features of laser-produced Al plasmas in an Ar atmosphere by combining shadowgraphy and fast photography
[20]. Coons et al. measured the electron densities of laser-produced Li plasmas using
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interferometry at earlier times and spatio-temporally resolved OES at later times [21]. Although many related studies have been performing by combining different diagnostic
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methods, each diagnostic technique however operates depending on a specific principle. A verification of the results of the different diagnostic methods is very necessary. In addition, a three-dimensional spatial expansion profile of the plasma plume and shock wave is also important
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for comprehensive understanding the dynamics evolution of LPP. With the above consideration, in this work, we conducted a comparative study of the spatial evolution of the electron density using
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the results obtained from interferometry and OES. Moreover, we presented the three-dimensional spatial expansion profiles of the plasma plume and shock wave for laser-produced Al plasmas in air at atmospheric pressure and analyzed the evolution of the volume of the plasma plume and the
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spatial region of the shock wave. 2. Experiment For the experimental setups (Fig. 1), a 7-ns Nd:YAG laser (Dawa-200, Beamtech Optronics)
generating a beam of fundamental wavelength of 1064 nm is focused using a focus lens L1 ( f = 100 mm) onto a planar Al target surface to produce the plasma. The beam splitter (BS3) is used to split a small fraction of the energy to monitor the pulse energy with an energy meter. To provide a fresh target surface for each ablated spot, the target is positioned on a two-dimensional translation stage. Interferograms are obtained using a Mach–Zehnder interferometer (Fig. 1). A probe pulse is 3
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provided by a Nd:YAG laser (PRO-350, Spectra-Physics) having a frequency-doubled wavelength of 532 nm obtained using a KDP crystal. An aperture and beam expanders (of 10× magnification) are used to optimize the laser spot size to obtain a uniform probe pulse and to output a 30-mm diameter circular light spot. The probe pulse is separated into two equal intensity beams by BS1, and then reflected by mirrors M1 and M2 and joined by BS2. The plasma is situated in one arm. The interferograms are recorded using a 1200×1600-pixel CCD camera with pixel size of 4.4 µm/pixel and subsequently stored on the PC as BMP files. A 532-nm band-pass filter (BF) is placed in front of the camera to filter out the strong plasma emissions; a neutral density filter (F)
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prevents light saturation. To obtain high-quality plasma interference fringes, the lens L2 (f=250 mm) is placed in a particular position for imaging the probe beams using a 2.2× magnification determined by the principle of imaging.
OES is employed for the spatio-temporally resolved spectral measurements. The emission of plasma is collected through a quartz lens (L3) with focal length of 100 mm used to form a 1:1
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image of the plasma at the entrance slit of a spectrometer (Shamrock SR-500i, Andor) equipped with an intensified charge-coupled detector (iStar-DH734-18F-03, Andor). The spectrometer is positioned on a one-dimensional translation stage that moves along the z direction. The plasma plume is orthogonal to the slit. The target surface and the entrance slit of the spectrometer are first positioned in the same plane (x-o-y plane), which is defined as zero position of spatial detection. To perform the spatio-resolved measurements, the spectrometer moves in the opposite direction to
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the laser beam by controlling the translation stages so that the slit of spectrometer can detect different spatial slices of plasma plume and then obtains the spatio-resolved spectral data. The width of the
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entrance slit is 50 µm and the gate time fixed at 200 ns. Two digital pulse delay generators DG535 and DG645 are used to implement the time sequence control of the entire experimental setup, which can synchronize and trigger two lasers,
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spectrometer, and CCD camera for temporally resolved measurements.
Fig. 1. Schematic diagram of the optical interferometry and optical emission spectroscopy experimental setups. A: aperture, BE: beam expanders, BS: beam splitter, M: mirror, L: lens, EM: energy meter, F: neutral density filter, 4
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BF: band-pass filter, PC: personal computer.
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3. Results and discussion
Fig. 2. Optical interferograms of laser-produced Al plasma expansion in air at atmospheric pressure with a pulse energy of 35 mJ and delay times from 200 ns to 6.9 µs. The yellow dotted line and blue shaded area in each image
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represent regions of shift in interference fringes.
Fig. 2 shows a series of interferograms obtained with a pulse energy of 35 mJ and delay times
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from 200 ns to 6.9 µs. In each interferogram, the blue-shaded area represents region of shift in interference fringes outlining the shock wave in an expansion profile; the shock front is marked by
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yellow dotted lines. From Fig. 2, the expansion profiles of the shock wave are approximate to hemisphere, which grow in size with increasing delay time, however, there are no obvious changes in shape with time. This is different from the situation of air plasma, which forms a strongly prolate ellipsoid at the earlier stage and tends to a spheroid with larger time delays [22].
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Fig. 3 Time evolution of the shock-wave dimension and the velocity of laser produced Al plasmas.
Fig. 3 shows the time evolution of shock-wave dimension and expansion velocity of Al plasmas in air at atmospheric pressure (Fig. 3). The horizontal and vertical dimension of the shock wave
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are obtained from interference fringes obtained in experiments (see inset, Fig. 3). The horizontal and vertical dimension are nearly equal in value and all increase with increasing delay times from 200 ns to 6.9 µs. Therefore, the expansion profiles of the shock wave are close to being hemisphere. The shock wave can be described by a blast wave model based on the Taylor–Sedow theory: R= atb, where t is the delay time, R is the shock front, b=2/(n + 2) with n = 3, 2, and 1 for
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spherical, cylindrical, and planar shock-wave propagation, respectively; the corresponding b values are 0.4, 0.5, and 0.67 [23]. To fit the experimental data, we take the form R=R0+atb, where
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R0 is a fitted parameter included to account for any systematic offset in the data. The fittings of the horizontal and vertical expansion (blue and red solid lines, respectively, in Fig. 3) show a planar expansion in the horizontal and vertical direction with b is close to 0.67. In addition, the expansion
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velocity of the shock wave is obtained by taking derivatives of the fitted function. From Fig. 3, the velocity of the shock wave (black dash dot) decrease rapidly with increasing delay time, which is more than 1.2 km/s at 200 ns, and approaches the speed of sound at 6.9 µs. This indicates there is
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a very large shock wave energy and high speed in the initial plasma expansion, as the shock front moves away from target surface, the speed rapidly decreases along with sharp energy dissipation
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attenuating ultimately to the speed of sound. The phase shift information is extracted from the experimental interference fringes using a
two-dimensional fast Fourier transformation (2D-FFT) algorithm. The radial distribution of the refractive index of the plasmas is obtained by an inverse Abel transformation based on the Hanke– Fourier method, which assumes the plasma is axisymmetric along the incident laser beam [24,25]. Here, measurement uncertainty involves three sources: noises in the interference fringes, the extraction of fringe contours, and the Abel transformation. Generally, the numerical noise introduced through the Abel transformation creates larger uncertainty than the others [26]. In this work, to mitigate measurement uncertainty, a smoothing function is introduced in the Abel transformation. The total uncertainty is about 15%. With the contribution from free electrons, the 6
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refractive index of the plasma is less than 1. Hence, we can obtain the expansion profile of the
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plasma plume from the spatial distribution of the refractive index.
Fig. 4. Time evolution of horizontal and vertical expansion dimension of the plasma plume and the velocity of
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laser-produced Al plasmas.
The time evolution of the horizontal and vertical expansion dimension of the plasma plume (Fig. 4a) shows that with increasing delay time, the horizontal and vertical dimension all increase rapidly before 900 ns, then slowly increase towards a steady value. The horizontal dimension of plasma plume is 0.7 mm less than the vertical dimension of 0.77 mm at 200 ns, but it increases more rapidly and reaches 2.03 mm at 6.9 µs, whereas the vertical dimension is 1.8 mm. Here the
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plasma expansion is described using a drag model with 𝑅 ∝ 𝑅0 [1 − 𝑎exp(−𝛽𝑡)], where R0 is the stopping distance of the plasma plume and is the slowing coefficient [27]. Fittings of the
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horizontal and vertical expansions (Fig. 4a; blue and red solid lines, respectively) give stopping distances of 2.06 and 1.82 mm, and slowing coefficients of 0.00058 and 0.00047, respectively. The expansion velocity of the plasma plume in comparison with a shock wave (Fig. 4b) is much
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smaller and rapidly decreases with increasing delay time. The horizontal expansion velocity is also
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larger than the vertical expansion velocity, but they converge after 4µs.
Fig. 5. Three-dimensional spatial expansion profiles of a plasma plume and shock wave at the delay time of 500 ns. 7
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Fig. 5 shows the three-dimensional spatial expansion profiles of the plasma plume and shock wave at the delay time of 500 ns. The plume profile obtained from the spatial distribution of the refractive index, whereas the shock wave profile was obtained using a hemisphere approximation in accordance with its expansion characteristics. These intuitive spatial expansion images of the laser-produced Al plasmas in air at atmospheric pressure provide a clearer understanding of the dynamics. The semi-ellipsoidal plasma plume (red region) is surrounded by a shock wave (yellow region) that has separated from the plasma during the expansion. The time evolution (Fig. 6) of the plasma plume volume (red star) and the spatial region of shock wave (magenta cycle) indicate that
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they are all fitted well by a second-order polynomial, but show different evolution trends. At shorter delay times, the two are close together, less than 5 mm3. With increasing delay time, the shock wave encompasses a rapidly increasing region, much larger than the slower-increasing plasma volume, reaching 262 mm3 at 6.9 µs, nearly 20 times the volume of the plasma plume of
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13.8 mm3 at 6.9 µs.
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Fig. 6. Time evolutions of the plasma plume volume and the spatial region of the shock wave.
Electron density is a function of the refractive index n of the plasma, which is approximately
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given as Ne=2Nc(1-n), where Nc is the critical density of the probe beam, given by Nc=0me2/e2, with me the electron mass and the angular frequency of probe beam. Therefore, the two-dimensional (2D) electron density distributions can be obtained from the spatial dependence
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of the refractive index. The 2D electron density distributions as also as the 2D expansion profile of Al plasma as show in Fig. 7. At 200 ns, the plasma plume occupies a small region, the plasma core region maintains a high electron density with a maximum value of 3.4×1018 cm−3 located on the surface of the target. However, the electron density attenuates to less than 1017 cm−3 close to the edge of the plume. With increasing delay time, the plasma plume grows in volume, whereas the electron density of the plasma core decreases because of electron recombination during plasma expansion; the density has a maximum value of 1.3×1018 cm−3 at 6.9 µs. Meanwhile, the position of the plasma core gradually moves away from the target surface with time, exhibiting a similar
behavior to the laser-produced Al plasmas expansion in an Ar atmosphere reported by Harilal et 8
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al. [20].
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Fig. 7. 2D electron density distributions of Al plasmas at different delay times.
To verify the results of different diagnostic methods, OES is also employed for a comparative
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study; it is a versatile tool for the diagnosis of plasma parameters. Fig. 8 shows the measured spatially resolved emission spectra (marked by different colored lines) of the two neutral atomic lines Al I 394.40 nm and Al I 396.15 nm. The delay time is 1.9 µs, and the measurement is the
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average of ten laser shots. The spectral line intensities increase with increasing distance from the target surface, reaching a peak at 0.9 mm, and then diminishing.
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Fig. 8. Spatial resolved emission spectra of laser-produced Al plasmas at a delay time of 1.9 µs.
For the OES, the electron density of plasma is determined from the Stark broadening of the spectral lines, which is obtained by a Lorentz fitting. The relation for the electron density is [28] ,
(1)
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0
where is the full-width at half maximum (FWHM) from Lorentz fitting and ω is the electron impact parameter, obtained from [29]. We chose the neutral atomic line of Al I 394.40 nm to calculate the electron density. The line widths from Lorentz fitting at different spatial positions are listed in Table 1. In addition, the electron impact parameter is a function of the electron
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temperature, but the dependence is negligibly weak. According to our previous work, an estimate of 1 eV of the electron temperature is used to calculate the electron density. Several studies indicate that the electron densities measured using the line broadening method have an error of
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about 20%, which arising from other broadening mechanisms, such as instrumental broadening and Doppler broadening[30]. In addition, the error caused by self-absorption effect is about 15%
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for the atomic line of Al I 394.40 nm and about 5% because of Lorentz fitting and the fluctuation in the laser power density [31]. So the uncertainty is about 40% in this OES measurement.
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Table 1. Line widths (FWHM) of Al I 394.40 nm by Lorentz fitting at a delay time of 1.9 µs. Spatial position
FWHM (nm)/
(mm)
Al I 394.40 nm
0.1
0.222
0.3
0.229
0.5
0.232
0.7
0.223
0.9
0.220
1.1
0.218
1.3
0.205
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Fig. 9. Comparison of the spatial evolution of the electron density between the result of interferometry and OES at a delay time of 1.9 µs.
The electron density obtained from the OES is a mean result because of the 50-µm-wide entrance slit. Therefore, to bring results into correspondence with the results of OES, we also take
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the same mean of the results from interferometry at corresponding spatial positions. A comparison of the spatial evolution of the electron density shows a consistent spatial trend to that from interferometry and OES (Fig. 9); there is a low electron density at the position near the target surface that with increasing distance from target rises to a peak value and then falls. However the electron density from interferometry decreases faster than the result from OES at distant spatial
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positions because of limitations in line width. All of the above indicate that the two diagnostic methods provide consistent electron density results whereas interferometry performs better
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Conclusions
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through a high spatial resolution.
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Two different diagnostic methods, optical interferometry and OES, were used to investigate laser-produced Al plasmas in air at atmospheric pressure. From a series of interferograms, we obtained the evolution profile of the shock wave, showing hemispherical growth in size with
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increasing delay time. The expansion features of the shock wave fit well with the blast wave model based on the Taylor–Sedow theory in presenting a planar wave propagation. The velocity
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evolution of the shock wave was also analyzed. The expansion and evolution of the plasma plume were also studied by exploiting the phase shift and refractive index obtained from the interferograms using the fast Fourier transformation and Abel transformation. The results obtained from the drag model show the different stopping distances and slowing coefficients in the horizontal and vertical expansion. In addition, we presented the three-dimensional spatial expansion profiles of the plasma plume and shock wave and also analyzed the evolution of the volume of the plasma plume and the spatial region of the shock wave. The 2D electron density distributions of Al plasmas were obtained from the spatial dependence of the refractive index of the plasma. At shorter times, the plasma plume occupied a small region and the plasma core was located on the surface of the target and maintained a high electron density. 11
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With increasing delay time, the electron density of the plasma core decreased and the position of the plasma core gradually moved away from the target surface. We conducted a comparative study of
the spatial evolution of the electron density obtained from interferometry and OES. Our results show that the two diagnostic methods provide consistent electron density results whereas interferometry provided better details because of its high spatial resolution. With the two diagnostic methods, this work provides a further understanding of the expansion and dynamic evolution as well as the density distribution of LPP in air at atmospheric pressure and thereby
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contributes to the development of LPP applications in different fields. Acknowledgements
This work is supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the Natural Science Foundation of China (NSFC) (Grant Nos. 11874051，11364037, 11564037, 61741513).
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Dynamics and density distribution of laser-produced Al plasmas using optical interferometry and optical emission spectroscopy Shiquan Cao , Maogen Su , Qi Min , Duixiong Sun , Pengpeng Ma , Kaiping Wang , Zhihong Jiao , Chenzhong Dong PII: DOI: Reference:
S0022-4073(18)30589-2 https://doi.org/10.1016/j.jqsrt.2018.12.029 JQSRT 6348
To appear in:
Journal of Quantitative Spectroscopy & Radiative Transfer
Received date: Revised date: Accepted date:
13 August 2018 21 December 2018 21 December 2018
Please cite this article as: Shiquan Cao , Maogen Su , Qi Min , Duixiong Sun , Pengpeng Ma , Kaiping Wang , Zhihong Jiao , Chenzhong Dong , Dynamics and density distribution of laserproduced Al plasmas using optical interferometry and optical emission spectroscopy, Journal of Quantitative Spectroscopy & Radiative Transfer (2018), doi: https://doi.org/10.1016/j.jqsrt.2018.12.029
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights:
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Two different diagnostic methods, optical interferometry and OES were used to investigate laser-produced Al plasmas in air at atmospheric pressure. Three-dimensional spatial expansion profiles of the plasma plume and shock wave of laser-produced Al plasmas in air at atmospheric pressure were presented. 2D electron density distributions of Al plasmas were obtained from the spatial dependence of the refractive index of plasma. Consistency of the results of optical interferometry and OES was verified and the advantages and disadvantages of the two diagnostic methods were discussed.
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Dynamics and density distribution of laser-produced Al plasmas using optical interferometry and optical emission spectroscopy Shiquan Caoa, Maogen Sua,b,*, Qi Mina, Duixiong Suna,b, Pengpeng Maa, Kaiping Wanga, Zhihong Jiaoa, Chenzhong Donga,b,* a
Key Laboratory of Atomic and Molecular Physics & Functional Material of Gansu Province, College of Physics
and Electronic Engineering, Northwest Normal University, Lanzhou, 730070, China b
of Chinese Academy of Sciences, Lanzhou 730070, China *
Corresponding authors.
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Joint Laboratory of Atomic and Molecular Physics, Northwest Normal University and Institute of Modern Physics
E-mail addresses: [email protected] (M. Su), [email protected] (C. Dong).
Abstract: The dynamic evolution and density distribution of laser-produced plasmas (LPP) of Al
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in air at atmospheric pressure were investigated using optical interferometry and optical emission spectroscopy, respectively. Interferograms were obtained in Mach–Zehnder interferometry with a laser pulse energy of 35 mJ and delay times from 200 ns to 6.9 µs. From the shift in interference fringes within this time interval and Taylor–Sedow theory, the expansion profiles of the shock wave were found to be hemispherical and approached planar propagation. The expansion and evolution of the plasma plume were also studied by exploiting the phase shift and refractive index
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obtained from the interferograms using the fast Fourier transformation and Abel transformation. Three-dimensional spatial expansion profiles of the plasma plume and shock wave were presented.
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In addition, two-dimensional electron density distributions of the Al plasmas were obtained from the spatial dependence of the refractive index of plasma, and compared with the results of optical emission spectroscopy. The results from the two diagnostic methods and their advantages and
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disadvantages are discussed. This work exploits two diagnostic methods to study the dynamic evolution and the density distribution of the LPP in air at atmospheric pressure and provides an
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important base reference for developing LPP applications in many fields.
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Keywords: Laser-produced plasmas; Optical interferometry; Optical emission spectroscopy.
1. Introduction Laser-produced plasmas (LPP) are formed by a high-power laser pulse focused on a solid target
surface. The material in the focus area is heated and evaporated to form a high-temperature high-density vapor that includes atoms, ions, and free electrons during laser ablation stage. In the presence of ambient gas, the vapor expands and compresses surrounding gas to produce a shock wave. After laser irradiation termination, the plasma and shock wave expand into open spaces. LPP have been researched for many years for theirs diverse applications including short-wavelength light sources [1,2], laser ion sources [3], and laser fusion [4], where the plasma 2
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expands freely into a vacuum. Other applications include laser-induced breakdown spectroscopy [5], micromachining [6], and pulsed-laser deposition [7], usually under ambient gas. Such plasma has inherent transient and inhomogeneous nature, and therefore the research on the evolution of the dynamics and diagnostics of state parameters is very important in understanding the physical properties and developing these applications [8]. Some techniques have been developed for related research. Shadowgraphy and fast photography are well-known diagnostic tools for investigating the dynamics of plasma expansion [9,10]; optical emission spectrometry (OES) as a non-contact measurement method has been widely employed for estimating plasma parameters such as
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electron temperature and density [11–13]. In addition, Langmuir probing [14], Thomson scattering [15], and laser interferometry [16–18] also provide measurements of the electron temperature and density.
Each of the diagnostic technique above has its own advantages and limitations. The combination of different diagnostic methods for dynamics evolution and state-parameter
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diagnostics of LPP is a very important approach and a current trend in research. Using shadowgraphy and interferometry, Breitling and colleagues studied the distinctive behavior in shock wave expansion and the distribution of electron density in LPP at different laser wavelengths [19]. Harilal et al. investigated the hydrodynamic expansion features of laser-produced Al plasmas in an Ar atmosphere by combining shadowgraphy and fast photography
[20]. Coons et al. measured the electron densities of laser-produced Li plasmas using
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interferometry at earlier times and spatio-temporally resolved OES at later times [21]. Although many related studies have been performing by combining different diagnostic
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methods, each diagnostic technique however operates depending on a specific principle. A verification of the results of the different diagnostic methods is very necessary. In addition, a three-dimensional spatial expansion profile of the plasma plume and shock wave is also important
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for comprehensive understanding the dynamics evolution of LPP. With the above consideration, in this work, we conducted a comparative study of the spatial evolution of the electron density using
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the results obtained from interferometry and OES. Moreover, we presented the three-dimensional spatial expansion profiles of the plasma plume and shock wave for laser-produced Al plasmas in air at atmospheric pressure and analyzed the evolution of the volume of the plasma plume and the
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spatial region of the shock wave. 2. Experiment For the experimental setups (Fig. 1), a 7-ns Nd:YAG laser (Dawa-200, Beamtech Optronics)
generating a beam of fundamental wavelength of 1064 nm is focused using a focus lens L1 ( f = 100 mm) onto a planar Al target surface to produce the plasma. The beam splitter (BS3) is used to split a small fraction of the energy to monitor the pulse energy with an energy meter. To provide a fresh target surface for each ablated spot, the target is positioned on a two-dimensional translation stage. Interferograms are obtained using a Mach–Zehnder interferometer (Fig. 1). A probe pulse is 3
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provided by a Nd:YAG laser (PRO-350, Spectra-Physics) having a frequency-doubled wavelength of 532 nm obtained using a KDP crystal. An aperture and beam expanders (of 10× magnification) are used to optimize the laser spot size to obtain a uniform probe pulse and to output a 30-mm diameter circular light spot. The probe pulse is separated into two equal intensity beams by BS1, and then reflected by mirrors M1 and M2 and joined by BS2. The plasma is situated in one arm. The interferograms are recorded using a 1200×1600-pixel CCD camera with pixel size of 4.4 µm/pixel and subsequently stored on the PC as BMP files. A 532-nm band-pass filter (BF) is placed in front of the camera to filter out the strong plasma emissions; a neutral density filter (F)
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prevents light saturation. To obtain high-quality plasma interference fringes, the lens L2 (f=250 mm) is placed in a particular position for imaging the probe beams using a 2.2× magnification determined by the principle of imaging.
OES is employed for the spatio-temporally resolved spectral measurements. The emission of plasma is collected through a quartz lens (L3) with focal length of 100 mm used to form a 1:1
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image of the plasma at the entrance slit of a spectrometer (Shamrock SR-500i, Andor) equipped with an intensified charge-coupled detector (iStar-DH734-18F-03, Andor). The spectrometer is positioned on a one-dimensional translation stage that moves along the z direction. The plasma plume is orthogonal to the slit. The target surface and the entrance slit of the spectrometer are first positioned in the same plane (x-o-y plane), which is defined as zero position of spatial detection. To perform the spatio-resolved measurements, the spectrometer moves in the opposite direction to
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the laser beam by controlling the translation stages so that the slit of spectrometer can detect different spatial slices of plasma plume and then obtains the spatio-resolved spectral data. The width of the
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entrance slit is 50 µm and the gate time fixed at 200 ns. Two digital pulse delay generators DG535 and DG645 are used to implement the time sequence control of the entire experimental setup, which can synchronize and trigger two lasers,
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spectrometer, and CCD camera for temporally resolved measurements.
Fig. 1. Schematic diagram of the optical interferometry and optical emission spectroscopy experimental setups. A: aperture, BE: beam expanders, BS: beam splitter, M: mirror, L: lens, EM: energy meter, F: neutral density filter, 4
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BF: band-pass filter, PC: personal computer.
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3. Results and discussion
Fig. 2. Optical interferograms of laser-produced Al plasma expansion in air at atmospheric pressure with a pulse energy of 35 mJ and delay times from 200 ns to 6.9 µs. The yellow dotted line and blue shaded area in each image
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represent regions of shift in interference fringes.
Fig. 2 shows a series of interferograms obtained with a pulse energy of 35 mJ and delay times
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from 200 ns to 6.9 µs. In each interferogram, the blue-shaded area represents region of shift in interference fringes outlining the shock wave in an expansion profile; the shock front is marked by
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yellow dotted lines. From Fig. 2, the expansion profiles of the shock wave are approximate to hemisphere, which grow in size with increasing delay time, however, there are no obvious changes in shape with time. This is different from the situation of air plasma, which forms a strongly prolate ellipsoid at the earlier stage and tends to a spheroid with larger time delays [22].
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Fig. 3 Time evolution of the shock-wave dimension and the velocity of laser produced Al plasmas.
Fig. 3 shows the time evolution of shock-wave dimension and expansion velocity of Al plasmas in air at atmospheric pressure (Fig. 3). The horizontal and vertical dimension of the shock wave
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are obtained from interference fringes obtained in experiments (see inset, Fig. 3). The horizontal and vertical dimension are nearly equal in value and all increase with increasing delay times from 200 ns to 6.9 µs. Therefore, the expansion profiles of the shock wave are close to being hemisphere. The shock wave can be described by a blast wave model based on the Taylor–Sedow theory: R= atb, where t is the delay time, R is the shock front, b=2/(n + 2) with n = 3, 2, and 1 for
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spherical, cylindrical, and planar shock-wave propagation, respectively; the corresponding b values are 0.4, 0.5, and 0.67 [23]. To fit the experimental data, we take the form R=R0+atb, where
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R0 is a fitted parameter included to account for any systematic offset in the data. The fittings of the horizontal and vertical expansion (blue and red solid lines, respectively, in Fig. 3) show a planar expansion in the horizontal and vertical direction with b is close to 0.67. In addition, the expansion
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velocity of the shock wave is obtained by taking derivatives of the fitted function. From Fig. 3, the velocity of the shock wave (black dash dot) decrease rapidly with increasing delay time, which is more than 1.2 km/s at 200 ns, and approaches the speed of sound at 6.9 µs. This indicates there is
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a very large shock wave energy and high speed in the initial plasma expansion, as the shock front moves away from target surface, the speed rapidly decreases along with sharp energy dissipation
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attenuating ultimately to the speed of sound. The phase shift information is extracted from the experimental interference fringes using a
two-dimensional fast Fourier transformation (2D-FFT) algorithm. The radial distribution of the refractive index of the plasmas is obtained by an inverse Abel transformation based on the Hanke– Fourier method, which assumes the plasma is axisymmetric along the incident laser beam [24,25]. Here, measurement uncertainty involves three sources: noises in the interference fringes, the extraction of fringe contours, and the Abel transformation. Generally, the numerical noise introduced through the Abel transformation creates larger uncertainty than the others [26]. In this work, to mitigate measurement uncertainty, a smoothing function is introduced in the Abel transformation. The total uncertainty is about 15%. With the contribution from free electrons, the 6
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refractive index of the plasma is less than 1. Hence, we can obtain the expansion profile of the
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plasma plume from the spatial distribution of the refractive index.
Fig. 4. Time evolution of horizontal and vertical expansion dimension of the plasma plume and the velocity of
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laser-produced Al plasmas.
The time evolution of the horizontal and vertical expansion dimension of the plasma plume (Fig. 4a) shows that with increasing delay time, the horizontal and vertical dimension all increase rapidly before 900 ns, then slowly increase towards a steady value. The horizontal dimension of plasma plume is 0.7 mm less than the vertical dimension of 0.77 mm at 200 ns, but it increases more rapidly and reaches 2.03 mm at 6.9 µs, whereas the vertical dimension is 1.8 mm. Here the
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plasma expansion is described using a drag model with 𝑅 ∝ 𝑅0 [1 − 𝑎exp(−𝛽𝑡)], where R0 is the stopping distance of the plasma plume and is the slowing coefficient [27]. Fittings of the
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horizontal and vertical expansions (Fig. 4a; blue and red solid lines, respectively) give stopping distances of 2.06 and 1.82 mm, and slowing coefficients of 0.00058 and 0.00047, respectively. The expansion velocity of the plasma plume in comparison with a shock wave (Fig. 4b) is much
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smaller and rapidly decreases with increasing delay time. The horizontal expansion velocity is also
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larger than the vertical expansion velocity, but they converge after 4µs.
Fig. 5. Three-dimensional spatial expansion profiles of a plasma plume and shock wave at the delay time of 500 ns. 7
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Fig. 5 shows the three-dimensional spatial expansion profiles of the plasma plume and shock wave at the delay time of 500 ns. The plume profile obtained from the spatial distribution of the refractive index, whereas the shock wave profile was obtained using a hemisphere approximation in accordance with its expansion characteristics. These intuitive spatial expansion images of the laser-produced Al plasmas in air at atmospheric pressure provide a clearer understanding of the dynamics. The semi-ellipsoidal plasma plume (red region) is surrounded by a shock wave (yellow region) that has separated from the plasma during the expansion. The time evolution (Fig. 6) of the plasma plume volume (red star) and the spatial region of shock wave (magenta cycle) indicate that
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they are all fitted well by a second-order polynomial, but show different evolution trends. At shorter delay times, the two are close together, less than 5 mm3. With increasing delay time, the shock wave encompasses a rapidly increasing region, much larger than the slower-increasing plasma volume, reaching 262 mm3 at 6.9 µs, nearly 20 times the volume of the plasma plume of
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13.8 mm3 at 6.9 µs.
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Fig. 6. Time evolutions of the plasma plume volume and the spatial region of the shock wave.
Electron density is a function of the refractive index n of the plasma, which is approximately
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given as Ne=2Nc(1-n), where Nc is the critical density of the probe beam, given by Nc=0me2/e2, with me the electron mass and the angular frequency of probe beam. Therefore, the two-dimensional (2D) electron density distributions can be obtained from the spatial dependence
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of the refractive index. The 2D electron density distributions as also as the 2D expansion profile of Al plasma as show in Fig. 7. At 200 ns, the plasma plume occupies a small region, the plasma core region maintains a high electron density with a maximum value of 3.4×1018 cm−3 located on the surface of the target. However, the electron density attenuates to less than 1017 cm−3 close to the edge of the plume. With increasing delay time, the plasma plume grows in volume, whereas the electron density of the plasma core decreases because of electron recombination during plasma expansion; the density has a maximum value of 1.3×1018 cm−3 at 6.9 µs. Meanwhile, the position of the plasma core gradually moves away from the target surface with time, exhibiting a similar
behavior to the laser-produced Al plasmas expansion in an Ar atmosphere reported by Harilal et 8
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al. [20].
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Fig. 7. 2D electron density distributions of Al plasmas at different delay times.
To verify the results of different diagnostic methods, OES is also employed for a comparative
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study; it is a versatile tool for the diagnosis of plasma parameters. Fig. 8 shows the measured spatially resolved emission spectra (marked by different colored lines) of the two neutral atomic lines Al I 394.40 nm and Al I 396.15 nm. The delay time is 1.9 µs, and the measurement is the
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average of ten laser shots. The spectral line intensities increase with increasing distance from the target surface, reaching a peak at 0.9 mm, and then diminishing.
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Fig. 8. Spatial resolved emission spectra of laser-produced Al plasmas at a delay time of 1.9 µs.
For the OES, the electron density of plasma is determined from the Stark broadening of the spectral lines, which is obtained by a Lorentz fitting. The relation for the electron density is [28] ,
(1)
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0
where is the full-width at half maximum (FWHM) from Lorentz fitting and ω is the electron impact parameter, obtained from [29]. We chose the neutral atomic line of Al I 394.40 nm to calculate the electron density. The line widths from Lorentz fitting at different spatial positions are listed in Table 1. In addition, the electron impact parameter is a function of the electron
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temperature, but the dependence is negligibly weak. According to our previous work, an estimate of 1 eV of the electron temperature is used to calculate the electron density. Several studies indicate that the electron densities measured using the line broadening method have an error of
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about 20%, which arising from other broadening mechanisms, such as instrumental broadening and Doppler broadening[30]. In addition, the error caused by self-absorption effect is about 15%
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for the atomic line of Al I 394.40 nm and about 5% because of Lorentz fitting and the fluctuation in the laser power density [31]. So the uncertainty is about 40% in this OES measurement.
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Table 1. Line widths (FWHM) of Al I 394.40 nm by Lorentz fitting at a delay time of 1.9 µs. Spatial position
FWHM (nm)/
(mm)
Al I 394.40 nm
0.1
0.222
0.3
0.229
0.5
0.232
0.7
0.223
0.9
0.220
1.1
0.218
1.3
0.205
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Fig. 9. Comparison of the spatial evolution of the electron density between the result of interferometry and OES at a delay time of 1.9 µs.
The electron density obtained from the OES is a mean result because of the 50-µm-wide entrance slit. Therefore, to bring results into correspondence with the results of OES, we also take
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the same mean of the results from interferometry at corresponding spatial positions. A comparison of the spatial evolution of the electron density shows a consistent spatial trend to that from interferometry and OES (Fig. 9); there is a low electron density at the position near the target surface that with increasing distance from target rises to a peak value and then falls. However the electron density from interferometry decreases faster than the result from OES at distant spatial
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positions because of limitations in line width. All of the above indicate that the two diagnostic methods provide consistent electron density results whereas interferometry performs better
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Conclusions
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through a high spatial resolution.
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Two different diagnostic methods, optical interferometry and OES, were used to investigate laser-produced Al plasmas in air at atmospheric pressure. From a series of interferograms, we obtained the evolution profile of the shock wave, showing hemispherical growth in size with
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increasing delay time. The expansion features of the shock wave fit well with the blast wave model based on the Taylor–Sedow theory in presenting a planar wave propagation. The velocity
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evolution of the shock wave was also analyzed. The expansion and evolution of the plasma plume were also studied by exploiting the phase shift and refractive index obtained from the interferograms using the fast Fourier transformation and Abel transformation. The results obtained from the drag model show the different stopping distances and slowing coefficients in the horizontal and vertical expansion. In addition, we presented the three-dimensional spatial expansion profiles of the plasma plume and shock wave and also analyzed the evolution of the volume of the plasma plume and the spatial region of the shock wave. The 2D electron density distributions of Al plasmas were obtained from the spatial dependence of the refractive index of the plasma. At shorter times, the plasma plume occupied a small region and the plasma core was located on the surface of the target and maintained a high electron density. 11
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With increasing delay time, the electron density of the plasma core decreased and the position of the plasma core gradually moved away from the target surface. We conducted a comparative study of
the spatial evolution of the electron density obtained from interferometry and OES. Our results show that the two diagnostic methods provide consistent electron density results whereas interferometry provided better details because of its high spatial resolution. With the two diagnostic methods, this work provides a further understanding of the expansion and dynamic evolution as well as the density distribution of LPP in air at atmospheric pressure and thereby
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contributes to the development of LPP applications in different fields. Acknowledgements
This work is supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the Natural Science Foundation of China (NSFC) (Grant Nos. 11874051，11364037, 11564037, 61741513).
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