Figure
1.
Schematic diagram of LIBS system.
| Citation: |
Long CHEN, Zuojun CUI, Weifu GAO, Ping DUAN, Zichen KAN, Congqi TAN, Junyu CHEN. Effect of ion stress on properties of magnetized plasma sheath[J]. Plasma Science and Technology, 2024, 26(2): 025001. DOI: 10.1088/2058-6272/ad0d4f
|
In the plasma sheath, there is a significant gradient in ion velocity, resulting in strong stress on ions treated as a fluid. This aspect has often been neglected in previous sheath studies. This study is based on the Braginskii plasma transport theory and establishes a 1D3V sheath fluid model that takes into account the ion stress effect. Under the assumption that ions undergo both electric and diamagnetic drift in the presheath region, self-consistent boundary conditions, including the ion Bohm velocity, are derived based on the property of the Sagdeev pseudopotential. Furthermore, assuming that the electron velocity at the wall follows a truncated Maxwell distribution, the wall floating potential is calculated, leading to a more accurate sheath thickness estimation. The results show that ion stress significantly reduces the sheath thickness, enhances ion Bohm velocity, wall floating potential, and ion flux at the wall. It hinders the acceleration of ions within the sheath, leading to notable alterations in the particle density profiles within the sheath. Further research indicates that in ion stress, bulk viscous stress has the greatest impact on sheath properties.
In recent years, laser-induced breakdown spectroscopy (LIBS) has been extensively researched and applied [1]. The technology has been investigated in various areas, including soil organic matter [1‒4] and heavy metal detection [5‒7], atmospheric environmental monitoring [8‒10], water quality monitoring [11, 12], and industrial testing [13, 14].
The demand for enhancing the detection of elements is increasing with the widespread implementation of LIBS technology. However, the low analysis accuracy and high detection limit result from the weak spectral signal intensity. Consequently, the issues of poor spectral quality and high detection limit have emerged as critical challenges in commercialization and industrialization [1, 15‒19]. Many scholars had studied LIBS signal enhancement methods. Prochazka et al examined the enhancement effect of three combinations of laser pulses [20]. The experimental results demonstrated that the spectral signal intensity of the multi-pulse configuration was 12 times higher than that of SP-LIBS. Effenberger Jr et al achieved significant enhancement in spectral intensity by controlling the gas composition and pressure in the sample’s vacuum chamber and optimizing the delay time between DP-LIBS lasers [21‒23]. Shen et al and Popov et al had obtained significant enhancement effects by using the utilization of parallel panel confinement devices, cylindrical space confinement devices, and hemispherical confinement devices [24‒26]. The compression effect of these space confinement devices on the plasma was increasing, with the hemispherical space confinement device demonstrating the most pronounced compression effect and exhibiting a notable enhancement effect on plasma spectral enhancement. In recent years, magnetic field confinement had been employed by researchers to increase plasma temperature by intensifying particle collisions within the plasma, thereby leading to the emission of more photons. Li et al utilized two permanent magnets (NdFeB) to create a magnetic confinement device with a constant magnetic field. Under the influence of an external magnetic field, the spectral intensity of copper plasma atoms and ions was enhanced, while the spectral intensity of non-metallic silicon plasma remained unaltered. Both space confinement and magnetic confinement resulted in increased plasma temperature and electron density, with enhancement coefficients reaching up to 3 for V and Mn [27, 28]. Furthermore, Guo et al discovered that the spectral intensity can be significantly enhanced by elevating the sample temperature to 250 °C and employing a cylindrical space confinement device, with experimental results demonstrating a 2.5-fold increase [29]. Kexue et al utilized laser ablation and fast pulsed discharge plasma spectroscopy (LA-FPDPS) to substantially increase atomic emission of lead and arsenic in soil laser plasma [30]. Xu et al employed laser-induced breakdown spectroscopy (LIBS) and mid-infrared spectroscopy (FTIR-ATR) in conjunction with multivariate techniques to detect soil organic matter [2]. By utilizing spark discharge and dual laser-induced breakdown spectroscopy, Habibpour et al increased the plasma temperature by 18% and enhanced the degree of ionization [31].
In LIBS technology, there are numerous approaches to enhancing the spectral intensity of soil heavy metals. The majority of researchers employ methods such as multi-pulse excitation, spatial constraint devices, and sample pretreatment to augment the spectral signal. Within these enhancement methods, the primary strategy involves increasing the probability of particle collisions to release a greater number of photons, thereby achieving the objective of spectral enhancement. However, in these studies, the spectral acquisition commonly involves the utilization of a fiber optic probe or lens collection method to enhance the spectral signal by increasing the plasma within the fixed solid angle of collection. Upon the laser pulse interacting with the sample surface, resulting plasma exhibits outward radiation in a hemispherical shape. Subsequently, the spectrum is collected from a single direction through a fiber optic probe or lens. The solid angle of this acquisition method is limited. Until now, there have been relatively few studies on enhancing spectral intensity through the use of multi-directional collection of plasma. Hence, this paper introduces a method for multi-directional collection of plasma spectrum and designs a PSCD. By utilizing this device, more plasma information is gathered to effectively enhance the spectral intensity.
The schematic diagram of the experimental device used in this work is shown in figure 1. The laser beam is generated by a Q-switched Nd:YAG laser (wavelength: 1064 nm, energy: 0‒400 mJ, pulse width: 8 ns, repetition rate: 1‒10 Hz). The laser energy is regulated by the injection voltage of the laser power supply.
The laser emits a laser beam with a wavelength of 1064 nm and a spot diameter of 7 mm, which is reflected 90° downward through the mirror, and through the dichroic mirrors (R > 98% @ 400‒872 nm, T > 90% @ 932‒1300 nm), the laser beam is vertically focused to the sample surface using focusing lens with a focal length of 120 mm to generate light. Light radiation is collected by focusing lens, and then coupled to spectrometer (Andor, SR-500i) with ICCD detector by dichroic mirrors and flat convex lens. The spectral range of Shamrock SR-500i spectrometer is 200‒975 nm, the diffraction grating is 1200 lines/mm @ 500 nm, and the resolution is 0.07 nm. The laser and spectrometer are synchronously controlled by a digital pulse generator (BNC575, Berkeley Nucleonics Corp, USA), and the spectrometer is triggered by the Q-switching signal of the laser. The sample is placed 2 mm in front of the lens focus. The experiment is conducted in an air environment with atmospheric pressure, temperature of 20 °C and ambient relative humidity of 25%. In the experiment, 15 spectra are collected from different positions of each sample, and each spectrum is obtained by 5 times of accumulation, reducing the impact of system error on the experiment.
In this study, we designed a kind of device, which aims to collect the light radiated outwards more effectively, so as to achieve the purpose of spectral signal enhancement. The device is based on the reflection principle of light. First, the optical path is abstracted, and the light propagation is abstracted as the propagation of an optical path. The two-dimensional model is
| Y2=2px. | (1) |
The focus point is K(p2,0). The tangent line of the paraboloid at any point A(x0,√2px0) on the parabola was made, and the tangent slope at this point is
| Kt=√p2x0. | (2) |
The normal of the parabola is at point A, and the slope of the normal at this point is
| Kn=−√2x0p. | (3) |
The focus point K(p2,0) is used as the sample point. The slope of optical path 1 is calculated using the known coordinates of points A and K
| K1=√2px0x0−p2. | (4) |
The slope of optical path 2 after A-point reflection is K2. According to the reflection principle of the light source, the incidence angle is equal to the reflection angle, that is
| K1−Kn1+K1Kn=K2−Kn1+K2Kn. | (5) |
The calculation result is
| K2=0. | (6) |
That is, the light source of light path 2 is parallel to the X-axis. From this, it can be concluded that light in different directions can be collected into parallel light after passing through the PSCD, so as to achieve the purpose of collecting light in different directions.
The diameter of the flat convex lens is 25.4 mm. The top diameter (2r) and depth (h) (vertical distance from the bottom opening to the top opening) of the PSCD are the main optimized parameters that determine the actual shape of the device. In the process of device optimization, the larger the equivalent solid angle, the larger the proportion of light that can be projected onto the lens. The formula for solid angle is given as follows:
| Ω=AR2. | (7) |
In this equation, A is the surface area of the spherical crown corresponding to the flat convex lens, and R is the radius of the spherical surface. It is known that the diameter of the flat convex lens is 25.44 mm, and the distance from the sample is 118 mm, that is, the radius of the spherical surface R=118.68 mm, and the solid angle is Ω1=0.036 sr.
Under the PSCD, the equivalent solid angle is
| Ω2=2π−2π(R−R⋅h/√r2+h2)R+Ω1. | (8) |
In this equation, r represents the radius of the top opening of the PSCD, and h represents the depth of the device. In ideal conditions, the energy flux in units of solid angle is
| dϕ=IdΩ. | (9) |
In this equation, I is the emission intensity and ϕ is the energy flux. According to formulas (8) and (9), the equivalent solid angle will vary with changes in r and h. The collection solid angle is closely related to the energy flux of the flat convex lens. The number of plasma radiation reaching the flat convex lens will also vary with different solid angles. The energy flux of the flat convex lens will also vary with different parameter combinations, as shown in figure 2(b).
From figure 2(b), it can be seen that when the top opening diameter of the device is around 10 mm and the depth is around 35 mm, the energy flux of the device is poor and the collection effect is the worst. When the diameter of the device is 25.4 mm and the depth is 20.0 mm, the energy flux of the device is high, the more spectral information of the plasma reflects to the flat convex lens, and the reflected light has good directionality. Therefore, the device parameters we designed are 25.4 mm in diameter and 20.0 mm in depth, and Ω2=5.34 sr. According to the parabolic characteristics, the bottom opening diameter (line segment DE) is 7.4 mm. Based on this, a three-dimensional model is established by rotating 180° around the X-axis as the central axis.
Aluminum materials have the advantages of easy molding, low cost, and high temperature resistance. Therefore, aluminum substrates are chosen for the PSCD. Firstly, stamping molds are manufactured based on the 3D model, and then aluminum plates are stamped and polished. Finally, a vacuum aluminum coating process is used to coat the inner cavity, and the device with reflective effect is obtained. The reflectivity of the inner cavity is 88.2% ± 2%.
As shown in figure 3, when studying the enhancement effect of the PSCD, the device was placed vertically above the sample and keep the laser light path coincident with the rotation axis of the PSCD. After a series of ionization processes, the generated light presents a semi-spherical outward divergence. After being reflected by the device, the light radiation propagates vertically upwards, passes through the flat convex lens, and is then reflected by the dichroic mirrors and focused by the flat convex lens before finally being collected by the spectrometer.
In this paper, the test sample is made of standard soil GBW07403 and Pb(NO3)2, Cr(NO3)2·9H2O and Cd(NO3)2 respectively in a specific proportion. The content of chromium in standard soil is very low and can be ignored. The sample was thoroughly stirred with deionized water, then dried, put into a grinder to be fully ground and screened to obtain soil powder containing specific concentrations of Pb, Cr and Cd. Finally, 5 g of soil powder was taken and put into the tablet press, and a pressure of 50 MPa was applied for 30 min for tableting. The content of self-made soil samples is shown in table 1.
| Sample No. | Pb | Cr | Cd | |||||
| Concentration (wt%) | Deviation (wt%) | Concentration (wt%) | Deviation (wt%) | Concentration (wt%) | Deviation (wt%) | |||
| 1 | 0.2 | 0.015 | 0.2 | 0.016 | 0.2 | 0.015 | ||
| 2 | 0.3 | 0.018 | 0.3 | 0.018 | 0.3 | 0.016 | ||
| 3 | 0.4 | 0.019 | 0.4 | 0.017 | 0.4 | 0.017 | ||
| 4 | 0.5 | 0.020 | 0.5 | 0.017 | 0.5 | 0.014 | ||
| 5 | 0.6 | 0.017 | 0.6 | 0.015 | 0.6 | 0.016 | ||
| 6 | 0.7 | 0.015 | 0.7 | 0.015 | 0.7 | 0.017 | ||
| 7 | 0.8 | 0.014 | 0.8 | 0.016 | 0.8 | 0.016 | ||
DownLoad:
CSV
The spectral signal is greatly weakened or directly swallowed due to the influence of laser energy and acquisition delay time. In this paper, the parameters were optimized based on the above factors to achieve the optimal experimental parameters. Laser energy directly affects the plasma temperature and ionization degree, then affects the spectral intensity. The spectral radiation is mainly continuous background radiation at the initial stage of plasma production. Continuous background spectral radiation decayed rapidly, and the attenuation time of the peak intensity of the characteristic spectra is relatively long, as time went on. The characteristic spectral line gradually becomes clear with the passage of time, which is conducive to the analysis of the characteristic spectral line. It is shown that the delay time directly affected the intensity of the characteristic spectra. Therefore, this study optimized the acquisition parameters to obtain better characteristic spectral lines. The results showed that when the laser energy is 80 mJ, the acquisition delay time is 3000 ns, and the defocus amount is −2 mm, the characteristic spectral line intensity reached the maximum value.
The spectral signal was collected in the wavelength range of 380‒460 nm. The three characteristic spectral lines of Pb I 405.78 nm, Cr I 425.43 nm and Cd II 441.57 nm were selected to explore the influence of the collection device on the spectral intensity. The signal-to-noise ratio (SNR) of the spectra of samples 4 and 7, and the enhancement rate of the spectral intensity by the PSCD are shown in table 2.
| Spectral intensity | SNR | |||||
| Sample 4 |
Sample 7 |
Sample 4 | Sample 7 | |||
| Pb I 405.78 nm | Without device | 105518.79 (a.u.) | 109716.22 (a.u.) | 21.40 | 9.86 | |
| With device | 111229.04 (a.u) | 122040.40 (a.u.) | 24.72 | 11.53 | ||
| Enhancement rate (%) | 5.41% | 11.23% | 16.65% | 17.02% | ||
| Cr I 425.43 nm | Without device | 146816.28 (a.u) | 204474.58 (a.u.) | 3.36 | 3.54 | |
| With device | 188721.78 (a.u) | 244263.94 (a.u.) | 3.47 | 3.80 | ||
| Enhancement rate (%) | 28.54% | 19.45% | 3.46% | 7.40% | ||
| Cd II 441.57 nm | Without device | 33913.29 (a.u.) |
36817.51 (a.u.) |
2.32 | 2.50 | |
| With device | 42123.17 (a.u.) |
50057.81 (a.u.) |
3.15 | 3.25 | ||
| Enhancement rate (%) | 24.21% | 35.96% | 36.22% | 30.01% | ||
DownLoad:
CSV
Figure 4 showed the plasma emission spectra of sample 4 and sample 7 with and without device. From figure 4(a), it can be seen that after using this device, the spectral intensity of the elements is enhanced. The enhancement rate is up to 29%, and the signal-to-noise ratio is increased by 36%. Compared with the absence of device, the baseline intensity is not significantly enhanced, while the background noise is enhanced. From figure 4(b), it can be seen that the spectral intensity enhancement rate of sample 7 reached 36% and the signal-to-noise ratio increased by 30% after using the device. The signal-to-noise ratio of the spectrum has been improved, and the quality of the spectral signal has also been improved. Compared with sample 4, the spectral intensity was significantly enhanced when the content of Pb, Cr and Cd in the soil sample was doubled. The PSCD had an enhancement effect on the samples of both concentrations. This may be due to the increase in the number of characteristic spectra generated by the plasma transition after the concentration is doubled, and the device collects more plasma. The above results show that the PSCD has the effect of improving the signal intensity.
The analysis showed that the enhancement effects of the PSCD on different elements were different, and the enhancement rate fluctuated at different concentrations. This may be due to the differences in the values of transition probability and transition energy level for the three elements, as well as variations in element concentrations and fluctuations in laser energy, resulting in changes in the number of free particles generated by ablation. This may be the main reason for the inconsistent enhancement effect of the device.
During the optimization of device parameters, the energy flux of the flat convex lens increased several times. This is only valid under the condition of a uniform distribution of plasma in space. PSCD can collect spectral information from multiple spatial directions, and its enhancement rate is positively correlated with the equivalent solid angle. However, in the experimental process, the distribution of plasma in different spatial directions is non-uniform. The plasma geometry was hemispherical [32], and each axial position corresponded to plasma slices with different transverse expansions caused by density gradients in the plasma. Therefore, the plasma radiation distribution varies in different directions. Spectral intensity can differ several times at different collecting angles [33]. It is likely that the light radiation directly collected by the flat convex lens constitutes a significant portion, while the collected portion by the PSCD is only a small fraction. This could be one of the reasons why the actual results may not match the enhanced effects predicted in theory.
In addition, using a PSCD can increase the energy flux of a plano-convex lens several times in theoretical analysis. However, when a device is used to collect the generated plasma and pass it through a focusing lens, some of the plasma ceases to be parallel light and cannot be reflected by the dichroic mirror or collected by the collection lens after reflection. Much of the spectral information that is ultimately collected cannot be collected by the spectrometer, so the spectral intensity enhancement effect is very limited. It may be one of the main factors affecting the enhancement effect.
Many scholars had utilized the spatial constraint method to compress plasma in a reverse manner by utilizing the shockwaves produced by pulsed laser ablation on the sample surface. This technique increases the probability of particle collision in the compressed plasma, resulting in a significant enhancement of radiation intensity [24‒26]. Since the device adopts a cavity structure, the possibility of signal enhancement due to the spatial constraint effect cannot be ruled out. To further investigate the impact of the PSCD on spectral intensity, we took the measure of coating the reflective surface of the device in black to eliminate its reflection effect on the plasma. Subsequently, an anti-reflection collection device will be employed for experimental analysis.
Figure 5 illustrates the spectral intensities of samples 4 and 7 under no device and non-reflective collection device conditions. It was observed that the spectral intensities of Pb, Cr, and Cd elements in both samples were reduced when the non-reflective collection device was utilized. Analysis reveals that under the influence of the non-reflective collection device, all spectral lines exhibit a slight weakening effect, with a relatively inconspicuous rate of intensity decay. Based on the analysis above, it could be concluded that under the condition of no reflection, the device may have a slight attenuating effect on spectral lines. This could be attributed to the black coating on the reflecting surface of the PSCD, which absorbs certain amount of plasma, leading to a weakened intensity of the spectral lines. Research had shown that the spatial confinement effect of the device under the condition of no reflection was extremely weak. Therefore, the signal enhancement effect was not due to spatial confinement, and the influence of the device’s spatial structure on the spectral signal can be negligible.
Plasma temperature is a crucial parameter for characterizing plasma as it directly affects the intensity of characteristic spectral lines. The research on traditional methods of spectral enhancement aims to increase particle collisions, thereby raising the plasma temperature and enhancing the spectral signals under the same acquisition conditions. Therefore, we investigated the mechanism of enhancing spectral signals in PSCD based on the analysis of plasma temperature variations.
The transient nature of LIBS results in the plasma being in a state of local thermal equilibrium. In this study, the Boltzmann plot method was employed to measure the plasma temperature using the atomic line intensity of the Cr element. The relationship between the intensity of emission spectra and energy levels can be expressed as follows:
| lnIijλgiAij=−EikBT+lnCSFUS(T). | (10) |
Where Iij is the signal intensity response value of the spectrometer, Cs is the particle density of the transition, Aij is the probability of the transition, gi is the statistical weight of the Ei level, kB is the Boltzmann constant, T is the plasma temperature, F is the experimental parameter, and US(T) is the partition function. According to experimental data, we plotted Boltzmann diagrams for two samples using both PSCD and non-plasma spectroscopic collection devices, as shown in figure 6. It can be observed from the figure that the plasma temperature of sample 7 was higher than that of sample 4. Based on the analysis of plasma temperatures of samples 4 and 7 using both non-plasma spectroscopic collection devices and PSCD, no significant variation between the two was observed. Therefore, this further confirms that the enhancement of the spectral signal was not caused by intensified particle collisions. Our experimental results demonstrate that the PSCD did not lead to an increase in plasma temperature, indicating that it did not produce more plasma. On the contrary, the device achieved spectral enhancement by effectively collecting the existing spectral information. In other words, it successfully enhanced the spectral signals by efficiently capturing them. Further confirmation of the lack of spatial confinement of plasma by the cavity structure of the PSCD was obtained through the observed variation in plasma temperature. This finding aligns with our previous research conclusion on the non-reflective collection device.
The spectral intensity was effectively enhanced by PSCD with the experimental parameters unchanged. After 3.1 research, it was found that the signal enhancement rate of sample 7 was higher than that of sample 4. In order to study the enhancement rate under different heavy metal concentrations, the fitting curves of the concentration and spectral intensity of samples 1‒6 without device and with PSCD were established.
Theoretically, signal enhancement of characteristic spectral lines can further reduce the detection limit. In order to confirm that the PSCD can effectively reduce the detection limit, the detection limit (LOD) without device and with device was calculated according to formula (11).
| LOD=3σS. | (11) |
Among them, σ is the relative standard deviation of the background signal, and S is the slope of the quantitative analysis curve. The five characteristic data were selected before and after the lowest intensity of continuous background noise on the left side of Pb I 405.78 nm and Cr I 425.43 nm at each concentration, when calculating σ. These five feature data were averaged, and then their relative standard deviation was calculated. The relationship between the concentration of Pb, Cr and Cd elements and the spectral intensity was plotted, as shown in figure 7. The quantitative analysis curves of the two elements were fitted. According to the calibration curve, the curve slopes of the three elements without device and with device were obtained. The calculated LOD values for Pb, Cr, and Cd elements without the device condition are 5.295 ppm, 2.337 ppm, and 1.989 ppm, respectively. The LOD values for Pb, Cr, and Cd elements were 4.934 ppm, 1.436 ppm, and 1.387 ppm, respectively, when using the PSCD. Therefore, the detection capability of the calibration curve is improved by using a PSCD.
Figure 7(a) displayed the fitted curve of the characteristic spectral intensity of Pb I 405.78 nm as a function of concentration. It could be observed that the R2 value had improved. From figure 7(b), it could be observed that there was a strong linear relationship between the spectral intensity and the concentration gradient when using the PSCD. The fitted curve of Cr I 425.43 nm showed a higher R2 value than without the device, indicating that the PSCD could improve the fitting performance. Figure 7(c) displayed the fitted curve of the characteristic spectral intensity of Cd II 441.57 nm as a function of concentration. It could be observed that the R2 value had improved. The enhancement rates at different concentrations were calculated based on the calibration curves from figures 7(a)–(c), as shown in figure 8. It could be observed from figure 8 that the PSCD had an enhancing effect on the spectral signals at different concentrations. Although the enhancement rates exhibited some fluctuations, but generally showed an upward trend. The PSCD had different effects on the spectral signals at different element concentrations. The reason for this might be due to the increase in the number of characteristic spectral lines generated by plasma transitions as the concentration increased. Therefore, the PSCD could collect more spectral information.
Additionally, the impact of PSCD on uncertainty was discussed. Figure 9 compares the relative standard deviation (RSD) of the three elements with and without PSCD. The diagram showed a certain decrease in RSD under the influence of PSCD. This could be attributed to uneven and fluctuating expansion velocities in different directions caused by the varying lateral and longitudinal expansion velocities of the plasma [33], leading to unstable spectral signals in a single direction. PSCD was used to collect spectral signals in different spatial directions in order to mitigate the impact of varying expansion speeds on spectral signal fluctuations, thus reducing the influence of plasma evolution on spatial uncertainty. On the other hand, table 2 indicates a noteworthy enhancement in characteristic spectral intensity with the application of PSCD, whereas the level of continuous background radiation remains insignificant, ultimately resulting in a substantial improvement in SNR. Hence, PSCD aids in reducing the spectral signal’s uncertainty and enhancing the repeatability of the spectrum [34].
In this work, a novel PSCD was designed based on the principle of mathematical parabola. A three-dimensional model was established by rotating the parabolic two-dimensional model 180° along the X-axis. Compared with the case without the device, it was found that the PSCD could effectively improve the spectral intensity by 45%, the SNR of the spectra by 36%, respectively. After calculations, it was found that the plasma temperature did not change significantly with or without the device. This also indicates that the device does not have spatial confinement effects and can be ignored. Finally, the enhancement effect of spectral under concentration gradient was studied, and the fitting curve between concentration and spectral intensity was established. Linear fitting R2 improved by up to 0.054, while LOD decreased by a maximum of 0.901. The effectiveness of the PSCD in the detection of heavy metals in soil has been verified. This study provides a new idea for the research of LIBS spectral intensity enhancement method in other application fields.
This paper was supported by Department of Science and Technology of Jilin Province of China (Nos. YDZJ202301ZYTS481, 202202901032GX, and 20230402068GH).
| [1] |
Lymberopoulos D P and Economou D J 1994 J. Vac. Sci. Technol. A 12 1229 doi: 10.1116/1.579300
|
| [2] |
Conrads H and Schmidt M 2000 Plasma Sources Sci. Technol. 9 441 doi: 10.1088/0963-0252/9/4/301
|
| [3] |
Chankin A V 1997 J. Nucl. Mater. 241–243 199 doi: 10.1016/S0022-3115(96)00505-3
|
| [4] |
Gao Q D and Chen X P 2003 Phys. Plasmas 10 1389 doi: 10.1063/1.1562478
|
| [5] |
Chen F F 1995 Phys. Plasmas 2 2164 doi: 10.1063/1.871477
|
| [6] |
Kersten H et al 2001 Contrib. Plasma Phys. 41 598 doi: 10.1002/1521-3986(200111)41:6<598::AID-CTPP598>3.0.CO;2-Z
|
| [7] |
Sheridan T E and Goree J 1991 Phys. Fluids B 3 2796 doi: 10.1063/1.859987
|
| [8] |
Liu J Y, Wang Z X and Wang X G 2003 Phys. Plasmas 10 3032 doi: 10.1063/1.1584048
|
| [9] |
Chen X P 1998 Phys. Plasmas 5 804 doi: 10.1063/1.872768
|
| [10] |
White F M 2011 Fluid Mechanics 7th ed (New York: McGraw-Hill
|
| [11] |
Landau L D and Lifshitz E M 1987 Fluid Mechanics 2nd ed (Oxford: Butterworth-Heinemann
|
| [12] |
Batchelor G K 2000 An Introduction to Fluid Dynamics (Cambridge: Cambridge University Press
|
| [13] |
Chorin A J, Marsden J E 1993 A Mathematical Introduction to Fluid Mechanics 3rd ed (New York: Springer-Verlag
|
| [14] |
Dhawan R and Malik H K 2021 Plasma Sci. Technol. 23 045402 doi: 10.1088/2058-6272/abeb03
|
| [15] |
El Ghani O, Driouch I and Chatei H 2020 Phys. Plasmas 27 083701 doi: 10.1063/5.0010080
|
| [16] |
Paul R et al 2020 Phys. Plasmas 27 063520 doi: 10.1063/5.0004796
|
| [17] |
Moulick R, Adhikari S and Goswami K S 2019 Phys. Plasmas 26 043512 doi: 10.1063/1.5090537
|
| [18] |
Li Y Z et al 2022 Phys. Rev. Lett. 128 085002 doi: 10.1103/PhysRevLett.128.085002
|
| [19] |
Dhawan R and Malik H K 2020 Vacuum 177 109354 doi: 10.1016/j.vacuum.2020.109354
|
| [20] |
Hatami M M 2021 Sci. Rep. 11 9531 doi: 10.1038/s41598-021-88894-1
|
| [21] |
Basnet S and Khanal R 2019 AIP Adv. 9 095030 doi: 10.1063/1.5109102
|
| [22] |
Sharma G et al 2020 Phys. Scr. 95 035605 doi: 10.1088/1402-4896/ab5548
|
| [23] |
Dhawan R and Malik H K 2020 Chin. J. Phys. 66 560 doi: 10.1016/j.cjph.2020.06.007
|
| [24] |
Liu J Y, Wang F and Sun J Z 2011 Phys. Plasmas 18 013506 doi: 10.1063/1.3543757
|
| [25] |
Wang Z X et al 2004 J. Plasma Phys. 70 577 doi: 10.1017/S002237780400282X
|
| [26] |
Ou J et al 2013 Phys. Plasmas 20 063502 doi: 10.1063/1.4811474
|
| [27] |
Zhao X Y, Zhang B K and Wang C X 2020 Phys. Plasmas 27 113705 doi: 10.1063/5.0018339
|
| [28] |
Dhawan R and Malik H K 2023 J. Appl. Phys. 133 043303 doi: 10.1063/5.0120616
|
| [29] |
Dhawan R, Kumar M and Malik H K 2020 Phys. Plasmas 27 063515 doi: 10.1063/5.0003242
|
| [30] |
Malik L and Tevatia A 2021 Defence Sci. J. 71 137 doi: 10.14429/dsj.71.15762
|
| [31] |
Malik L et al 2021 Mater. Today: Proc. 38 191
|
| [32] |
Guo S S et al 2020 Plasma Sci. Technol. 22 125301 doi: 10.1088/2058-6272/abb455
|
| [33] |
Tang R X et al 2019 Phys. Plasmas 26 043509 doi: 10.1063/1.5091676
|
| [34] |
Jung M et al 2018 Phys. Plasmas 25 013507 doi: 10.1063/1.5010713
|
| [35] |
Takahashi Y et al 2020 J. Phys. D: Appl. Phys. 53 235203
|
| [36] |
Wang T T, Li J J and Ma J X 2016 Phys. Plasmas 23 123519 doi: 10.1063/1.4972094
|
| [37] |
Wang T T 2017 The effect of electron reflection and ion viscosity on magnetized plasma sheath PhD Thesis University of Science and Technology of China, Hefei, China (in Chinese)
|
| [38] |
Li J J, Ma J X and Wei Z A 2013 Phys. Plasmas 20 063503 doi: 10.1063/1.4811479
|
| [39] |
Wang T T, Ma J X and Wei Z A 2015 Phys. Plasmas 22 093505 doi: 10.1063/1.4930208
|
| [40] |
Chen L et al 2022 Plasma Sci. Technol. 24 074011 doi: 10.1088/2058-6272/ac57fe
|
| [41] |
Zou X et al 2020 Plasma Sci. Technol. 22 125001 doi: 10.1088/2058-6272/abb3dc
|
| [42] |
Chen L et al 2023 Plasma Sci. Technol. 25 035003 doi: 10.1088/2058-6272/aca502
|
| [43] |
Chen F F 1974 Introduction to Plasma Physics (New York: Plenum
|
| [44] |
Braginskii S I 1965 Reviews of Plasma Physics (New York: Consultants Bureau
|
| [45] |
Dhawan R and Malik H K 2020 J. Theor. Appl. Phys. 14 121 doi: 10.1007/s40094-020-00369-2
|
| [1] | Long CHEN, Yehui YANG, Yuhao AN, Ping DUAN, Shaojuan SUN, Zuojun CUI, Zichen KAN, Weifu GAO. Modeling of magnetized collisional plasma sheath with nonextensive electron distribution and ionization source[J]. Plasma Science and Technology, 2023, 25(3): 035003. DOI: 10.1088/2058-6272/aca502 |
| [2] | Suresh BASNET, Raju KHANAL. Kinetic simulation of an electronegative plasma with a cut-off distribution and modified Bohm criterion[J]. Plasma Science and Technology, 2020, 22(4): 45001-045001. DOI: 10.1088/2058-6272/ab5720 |
| [3] | G C DAS. Some studies on transient behaviours of sheath formation in dusty plasma with the effect of adiabatically heated electrons and ions[J]. Plasma Science and Technology, 2017, 19(9): 95002-095002. DOI: 10.1088/2058-6272/aa750c |
| [4] | LIU Huiping(刘惠平), ZOU Xiu(邹秀), QIU Minghui(邱明辉). Sheath Criterion for an Electronegative Plasma Sheath in an Oblique Magnetic Field[J]. Plasma Science and Technology, 2014, 16(7): 633-636. DOI: 10.1088/1009-0630/16/7/01 |
| [5] | M. M. HATAMI, A. R. NIKNAM. Characteristics of Positive Ions in the Sheath Region of Magnetized Collisional Electronegative Discharges[J]. Plasma Science and Technology, 2014, 16(6): 552-556. DOI: 10.1088/1009-0630/16/6/02 |
| [6] | DUAN Ping(段萍), ZHOU Xinwei(周新维), LIU Yuan(刘媛), CAO Anning(曹安宁), QIN Haijuan(覃海娟), CHEN Long(陈龙), YIN Yan(殷燕). Effects of Magnetic Field and Ion Velocity on SPT Plasma Sheath Characteristics[J]. Plasma Science and Technology, 2014, 16(2): 161-167. DOI: 10.1088/1009-0630/16/2/13 |
| [7] | M. M. HATAMI. The Properties of the Space-Charge and Net Current Density in Magnetized Plasmas[J]. Plasma Science and Technology, 2013, 15(12): 1169-1173. DOI: 10.1088/1009-0630/15/12/01 |
| [8] | LI Jiajia, HU Zhanghu, SONG Yuanhong, WANG Younian. Effects of Fast-Ion Injection on a Magnetized Sheath near a Floating Wall[J]. Plasma Science and Technology, 2013, 15(1): 1-6. DOI: 10.1088/1009-0630/15/1/01 |
| [9] | JI Yankun, ZOU Xiu, LIU Huiping. Bohm Criterion in a Magnetized Plasma Sheath[J]. Plasma Science and Technology, 2011, 13(5): 519-522. |
| [10] | XIANG Nong, HU Yemin, OU Jing. Bohm criterion for collisionless sheaths in two-ion-species plasmas[J]. Plasma Science and Technology, 2011, 13(4): 385-391. |
| 1. | Ma, H.-J., Xie, H.-S., Sun, G.-L. et al. Simulation of ion cyclotron range of frequencies heating in the proton-boron plasma of the spherical tokamak. Plasma Physics and Controlled Fusion, 2025, 67(2): 025019. DOI:10.1088/1361-6587/ada8dc |
| 2. | Jiang, X., Shi, Y., Song, S. et al. Physics design of current drive and strategy of heating system for EHL-2 spherical torus. Plasma Science and Technology, 2025, 27(2): 024012. DOI:10.1088/2058-6272/adae71 |
| 3. | Chen, J.K., Jiang, X.C., Ma, H.J. et al. Numerical investigation of electron cyclotron and electron Bernstein wave current drive in EXL-50U spherical torus.. Fusion Engineering and Design, 2025. DOI:10.1016/j.fusengdes.2025.114800 |
| 4. | Liu, Z., Zhang, J., Wu, K. et al. Interaction between the core and the edge for ion cyclotron resonance heating based on artificial absorption plasma model. Plasma Science and Technology, 2024, 26(10): 105103. DOI:10.1088/2058-6272/ad60f5 |
| 5. | Liu, M.-S., Xie, H.-S., Wang, Y.-M. et al. ENN's roadmap for proton-boron fusion based on spherical torus. Physics of Plasmas, 2024, 31(6): 062507. DOI:10.1063/5.0199112 |
| 1. | Ma, H.-J., Xie, H.-S., Sun, G.-L. et al. Simulation of ion cyclotron range of frequencies heating in the proton-boron plasma of the spherical tokamak. Plasma Physics and Controlled Fusion, 2025, 67(2): 025019. DOI:10.1088/1361-6587/ada8dc |
| 2. | Jiang, X., Shi, Y., Song, S. et al. Physics design of current drive and strategy of heating system for EHL-2 spherical torus. Plasma Science and Technology, 2025, 27(2): 024012. DOI:10.1088/2058-6272/adae71 |
| 3. | Chen, J.K., Jiang, X.C., Ma, H.J. et al. Numerical investigation of electron cyclotron and electron Bernstein wave current drive in EXL-50U spherical torus.. Fusion Engineering and Design, 2025. DOI:10.1016/j.fusengdes.2025.114800 |
| 4. | Liu, Z., Zhang, J., Wu, K. et al. Interaction between the core and the edge for ion cyclotron resonance heating based on artificial absorption plasma model. Plasma Science and Technology, 2024, 26(10): 105103. DOI:10.1088/2058-6272/ad60f5 |
| 5. | Liu, M.-S., Xie, H.-S., Wang, Y.-M. et al. ENN's roadmap for proton-boron fusion based on spherical torus. Physics of Plasmas, 2024, 31(6): 062507. DOI:10.1063/5.0199112 |
Figures(10) / Tables(1)
Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Sample No. | Pb | Cr | Cd | |||||
| Concentration (wt%) | Deviation (wt%) | Concentration (wt%) | Deviation (wt%) | Concentration (wt%) | Deviation (wt%) | |||
| 1 | 0.2 | 0.015 | 0.2 | 0.016 | 0.2 | 0.015 | ||
| 2 | 0.3 | 0.018 | 0.3 | 0.018 | 0.3 | 0.016 | ||
| 3 | 0.4 | 0.019 | 0.4 | 0.017 | 0.4 | 0.017 | ||
| 4 | 0.5 | 0.020 | 0.5 | 0.017 | 0.5 | 0.014 | ||
| 5 | 0.6 | 0.017 | 0.6 | 0.015 | 0.6 | 0.016 | ||
| 6 | 0.7 | 0.015 | 0.7 | 0.015 | 0.7 | 0.017 | ||
| 7 | 0.8 | 0.014 | 0.8 | 0.016 | 0.8 | 0.016 | ||
DownLoad:
CSV
| Spectral intensity | SNR | |||||
| Sample 4 |
Sample 7 |
Sample 4 | Sample 7 | |||
| Pb I 405.78 nm | Without device | 105518.79 (a.u.) | 109716.22 (a.u.) | 21.40 | 9.86 | |
| With device | 111229.04 (a.u) | 122040.40 (a.u.) | 24.72 | 11.53 | ||
| Enhancement rate (%) | 5.41% | 11.23% | 16.65% | 17.02% | ||
| Cr I 425.43 nm | Without device | 146816.28 (a.u) | 204474.58 (a.u.) | 3.36 | 3.54 | |
| With device | 188721.78 (a.u) | 244263.94 (a.u.) | 3.47 | 3.80 | ||
| Enhancement rate (%) | 28.54% | 19.45% | 3.46% | 7.40% | ||
| Cd II 441.57 nm | Without device | 33913.29 (a.u.) |
36817.51 (a.u.) |
2.32 | 2.50 | |
| With device | 42123.17 (a.u.) |
50057.81 (a.u.) |
3.15 | 3.25 | ||
| Enhancement rate (%) | 24.21% | 35.96% | 36.22% | 30.01% | ||
DownLoad:
CSV
