Cavity confinement microwave enhanced laser-induced plasma modulation method: Improvement in signal intensity and repeatability

Abstract

Microwave-enhanced laser-induced breakdown spectroscopy (ME-LIBS) is a promising analysis technique for trace element detection with the advantage of high signal intensity. However, the shot-to-shot repeatability of the ME-LIBS signal is relatively low, which affects the precision of the result and limits quantification performance. A cavity confinement microwave-enhanced laser-induced plasma (CC-ME-LIP) modulation method is proposed to improve the repeatability of the ME-LIBS signal. During the plasma evolution, cavity confinement provides an environment that regulates plasma around the microwave probe, controls plasma expansion, and minimizes interaction with the atmosphere. This behavior enhances the stability of the plasma morphology, leading to improved signal repeatability. In addition, confinement increases the energy transfer process within the plasma by the superimposition of two methods, resulting in a stronger signal intensity. The CC-ME-LIP modulation method is applied to the brass sample. The relative standard deviation (RSD) of the different copper and zinc lines has been reduced, along with an improvement of the intensity enhancement factor (IEF). For example, Cu 521.820 nm line RSD reduced from 29.11% (ME-LIBS) to 17.12% (CC-ME-LIBS) with an IEF of 1.08. The result demonstrated that the proposed approach significantly improves the repeatability of the ME-LIBS signal, thereby increasing the overall signal quality. To gain a deeper understanding, a detailed analysis of the mechanisms behind the increased signal intensity and improved repeatability was further investigated.

Graphical abstract

Keywords

microwave-enhanced laser-induced breakdown spectroscopy / plasma modulation / cavity confinement / intensity enhancement / pulse-to-pulse repeatability

1 Introduction

Microwave-enhanced laser-induced breakdown spectroscopy (ME-LIBS) is an attractive analytical technique that significantly shows promising strength in enhancing the signal strength of traditional laser-induced breakdown spectroscopy (LIBS) [1−4]. It has been extensively studied in various domains such as nuclear fuel analysis [5−7], metal alloy [8−10], and characterization of combustion emission products [11]. ME-LIBS is a variant of laser-induced breakdown spectroscopy in which microwaves are added into laser-induced plasma as an external energy source. The electromagnetic field component of the microwave radiations accelerates electrons within the laser-induced plasma (LIP), increasing their kinetic energy. The increased kinetic energy of the electrons is transferred to ions and neutral particles through collisions, leading to a significant enhancement in signal intensity. Besides high signal intensity, many studies have also reported its effect on the expansion of plasma volume [12], the enlargement of plasma lifetime [13], the reduction of self-absorption and self-reversal effects [14, 15], the detection of isotopes [16], and an improved limit of detection (LOD) [17]. However, despite these significant advantages, the ME-LIBS signal largely suffers from poor signal repeatability. Several factors contribute to the low RSD of the ME-LIBS signal, however, the stability of microwave-enhanced laser-induced plasma (ME-LIP), the source of the emission signal is likely the primary reason. Typically, microwaves interact with the LIP rather than the sample itself [18]. This interaction involves a complex energy transfer process between microwaves, LIP, and the surrounding environment. The microwaves directly affect the plasma morphological fluctuations and characteristics parameters which in turn affect the quality of raw signals. Improving the ME-LIP can help to achieve the high signal repeatability of ME-LIBS.

The modulation of ME-LIP can be a unique approach to resolving this problem. Plasma modulation is the modification of LIP in which the plasma evolution process changes. It can be of two types: (i) physical modification such as applying a cavity or a magnetic field around the plasma and (ii) environmental modification such as changing the environmental pressure or surrounding gases through which plasma interacts [19]. Many researchers have applied different/above-mentioned methods to enhance signal repeatability by modifying the LIP evolution process [20]. Hou et al. [21] applied cylindrical cavity confinement around LIP and showed the reduction in the RSD of carbon line (C(I) 193.09 nm) up to 21% and 36% for laser energies 80 mJ and 130 mJ. In a separate study, Fu et al. [22] studied the plasma evolution process and the shockwave phenomenon under rectangular cavity confinement and observed the phenomenon of reflected shockwave and plasma compression and amalgamate of reflected shockwave into plasma. Khan et al. [23] applied a magnetic field around LIP and studied the signal repeatability and sensitivity of plasma generated on an Al target. The repeatability of the Mg and Si emission lines was improved from 23% to 12% and 25% to 14%, respectively. Zhang et al. [24] studied the effect of ambient pressure on the signal quality of LIBS signal at an optimized spatiotemporal window. The variations in RSD and signal strength at various pressures show that the RSD of the signal decreased with decreasing surrounding pressure from 100 kPa to 5 kPa. To improve the quality of the LIBS signal, Yu et al. [25] studied the effects of the ambient gas properties such as molecular weight, ionization energy, and thermal capacity on LIP. Different compositions of gas mixtures of He, Ne, and Ar were utilized to improve titanium alloy plasma and found a significant decrease in RSD. Additionally, some recent studies have also highlighted the integration of machine learning to further improve LIBS analytical capabilities [26, 27]. Among these, cavity confinement appears to be an effective method to increase signal repeatability by providing a control environment for plasma expansion and minimizing external atmospheric influence on its evolution.

In this work, the cavity confinement microwave-enhanced laser-induced plasma (CC-ME-LIP) modulation method is proposed to improve the repeatability of the ME-LIBS signal by exploring the effect of cavity confinement on ME-LIP. Unlike in a typical open environment, the entire process of plasma generation, microwave addition, plasma expansion, and cooling occurs within a confined space. We recorded and compared the relative standard deviation (RSD) of the optical emission lines for four different types of LIBS systems: (i) conventional LIBS, (ii) cavity confinement LIBS (CC-LIBS), (iii) microwave-enhanced LIBS (ME-LIBS), (iv) cavity confinement microwave-enhanced LIBS (CC-ME-LIBS), and found the lowest RSD (10%) in the CC-ME-LIBS. To investigate the impact of the cavity on plasma stability, we conducted ultrafast imaging to observe the temporal evolution of the plasma in each case. Furthermore, the mechanism behind the enhanced signal intensity is analyzed by studying the effect of the cavity on various factors such as plasma volume, microwave power absorption, plasma temperature, and electron number density. Finally, sample ablation characteristics in the combined microwave and cavity environment are discussed in detail.

2 Experimental setup and methods

2.1 Experimental setup

The schematic diagram of an experimental setup of the CC-ME-LIBS system is shown in Fig.1. A Q-switched Nd:YAG laser, operating at a wavelength of 1064 nm, with a pulse duration of 6 ns, a repetition frequency of 1 Hz, and laser energy of 90 mJ was used to generate plasma on the sample surface. The laser beam was reflected by a 45° dichroic mirror (Thorlabs, cutoff wavelength 805 nm, transmission band at 400−788 nm, and reflection band at 823−1300 nm) and focused onto the sample surface by a quartz lens of focal length 50 mm. The sample was mounted on a 3D (X–Y–Z) linearly motorized stage with a speed of 1 mm/s to ensure that each laser shot encountered a fresh sample surface. Emission from the LIP transmits through the dichroic mirror and is collected into the optical fiber of the spectrometer by a fused silica plano-convex lens with a focal length of 50 mm. The optical emission was then transmitted to a three-channel spectrometer (Avanta’s, spectral range: 180–650 nm, resolution: 0.1 nm). The spectrometer delay time and integration time were 1 μs and 1 ms, respectively. An intensified charged coupled device (ICCD) was used to capture the plasma images. Integration times of 5 ns, 10 ns, 50 ns, and 100 ns were selected, for the plasma images taken between 5 to 90 ns, 100 to 200 ns, 500 to 1000 ns, and 2000 ns, respectively.

Fig.1 Schematic diagram of the experimental setup.

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A solid-state microwave generator (WSPS-2450-3K-MCWF00) operating in pulse mode at a frequency of 2450 MHz was used to inject microwaves into the ablation plume. The microwave was set to an output power of 400 W with a pulse width of 1 ms, and a repetition frequency of 1 Hz. A flexible coaxial cable (50 ohms) was used to guide the microwave power to the microwave probe. The horizontal distance between the microwave probe and the laser beam was fixed at 1mm. A rigid coaxial cable (RG402), having a diameter and lengths of the inner conductor is 1.63 mm and 32 mm and outer conductors are 6.35 mm and 88 mm was used to form a microwave probe. The outer copper and insulation layer were removed and only the inner silver copper plate remained after making its tip pointed. A metal chamber with an opening on each side was used to avoid microwave leakage. The opening was covered with nickel mesh (hole size is 0.8 mm × 0.4 mm, thickness 0.08 mm) to pass light and block microwave radiations. A digital delay generator was used to synchronize the laser pulse, microwave pulse, spectrometer, and ICCD. For plasma confinement, a cylindrical cavity made up of aluminum (6061) is used in this work. The diameter and height of the cavity were optimized as 5 mm and 2 mm. The confinement was positioned 1 mm above the sample surface and a laser was shot through the cavity hole. A confocal microscope was used to measure the ablation crater at a magnification of 20. Copper alloy (ZBY902) was used as a target, which was polished with sandpaper and then rinsed with alcohol. The main components of the copper alloy are listed in Tab.1.

Tab.1 The elemental concentrations (wt.%) in copper alloy ZBY902.

ZBY902	Cu	Zn	Pb	Fe
Wt.%	64.43	33.45	1.87	0.167

2.2 Methods

Cavity confinement is an easy-to-apply LIP modification method both for laboratory and for online/in-situ analysis. The assertion of applying a cavity to improve the ME-LIP relies on the fact that it can confine and stabilize the plasma, thereby mitigating external influences and promoting more controlled and repeatable plasma characteristics. Besides the impacts of reduced plasma volume and improved morphology, additional effects of confinement on the microwave power absorption, the energy transfer within the plasma, and the sample will be discussed in detail. The effect brought by the cavity is classified as the effect on ME-LIP (marked I), the effect on microwave power absorption (marked II), and the effect on the sample (marked III) as shown in Fig.2. Various investigation methods are used to verify these effects.

Fig.2 Schematic diagram illustrating the potential impact of cavity confinement.

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The influence on plasma is further divided into two categories: impacts on plasma expansion and the energy transfer within the plasma. Regarding the plasma expansion part, the temporal evolution images of plasma were chosen as a medium of study to verify the cavity effect on plasma stabilization and repeatability improvement on the ME-LIBS signal. In addition, cavity confinement also increases the energy transfer process within plasma due to which the state of plasma changes. Therefore, the calculation of plasma state parameters (plasma temperature T and electron density ne) will be chosen as a medium of study to verify the impact on signal strength. Moreover, increasing microwave power absorption can enhance the lifetime of plasma, therefore, calculation of plasm lifetime is considered an indirect way to verify the confinement effect on MW power absorption. The computation of crater volume and ablation mass was used as an investigation tool to determine the combined CC-ME-LIBS effect on the target surface.

3 Result and discussion

3.1 Signal quality improvement using the CC-ME-LIP modulation technique

The four types of setups are named as (i) conventional LIBS, (ii) cavity confinement LIBS (CC-LIBS), (iii) microwave-enhanced LIBS (ME-LIBS), (iv) cavity confinement microwave-enhanced LIBS (CC-ME-LIBS) were studied and compared as shown in Fig.3. For each system, 20 spectra at 20 different locations from the sample surface were used to calculate the average signal intensity enhancement factor and pulse-to-pulse RSD.

Fig.3 Four types of LIBS systems: (a) conventional LIBS, (b) CC-LIBS, (c) ME-LIBS, and (d) CC-ME-LIBS.

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Tab.2 shows the intensity enhancement factor (IEF) and RSD values of different spectral lines for LIBS, CC-LIBS, ME-LIBS, and CC-ME-LIBS. It can be seen that cavity confinement greatly reduced the signal uncertainty of the ME-LIBS signal from ~29% to ~17%. At the same time, the signal intensity of the CC-ME-LIBS was also enhanced for the various Cu and Zn lines in the brass sample.

Tab.2 IEF and RSD for LIBS, CC-LIBS, ME-LIBS, CC-ME-LIBS.

Intensity enhancement factor (IEF)
Lines (nm)	Zn I 481.053	Zn I 472.215	Cu I 515.323	Cu I 521.820	Zn I 462.980	Zn I 468.013	Fe I 470.494	Pb I 507.635
CC-LIBS	1.07	1.08	1.00	1.00	1.16	1.06	1.17	1.16
ME-LIBS	1.03	1.04	1.01	1.01	1.11	1.02	1.14	1.12
CC-ME-LIBS	1.08	1.10	1.08	1.08	1.23	1.10	1.28	1.25
Relative standard deviation (RSD)
LIBS	13.75%	17.42%	21.37%	18.78%	19.66%	20.97%	21.86%	20.25%
CC-LIBS	13.01%	17.41%	20.99%	17.79%	19.18%	20.84%	21.80%	20.01%
ME-LIBS	17.10%	22.34%	23.89%	29.11%	27.16%	24.69%	30.40%	28.66%
CC-ME-LIBS	10.41%	14.96%	16.21%	17.12%	16.13%	16.94%	18.13%	17.43%

3.2 Factors affecting the signal uncertainty reduction and mechanism analysis

This section analyzes the mechanism behind the improved signal reliability of the CC-ME-LIP modulation method. As mentioned earlier, plasma instability is a key factor leading to low signal repeatability in ME-LIBS. When extra microwave energy is added to LIP, it expands into a larger volume. This increased expansion of the ME-LIP intensifies its interaction with the surrounding atmosphere, leading to the fluctuation in plasma morphology. Ikeda et al. [28] showed an 18 times increase in plasma volume when microwaves were added to LIP as shown in Fig.4. The high expansion of the ME-LIP can subsequently increase the interaction with the atmospheric air environment. Khumaeni et al. [6] generated ME-LIP under different gas environments (Ar and He) at varied pressures to avoid the molecular emission band produced due to the high interaction of ME-LIP with the surrounding atmosphere. The interaction between the expanding plasma and surrounding gases can involve complex dynamics, including temperature and pressure gradients, which influence the mixing process and ionization of the medium, leading to high instability of ME-LIP.

Fig.4 Plasma vlume without (a) and with (b) microwaves [28].

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Fu et al. [29] studied the morphology fluctuation in laser-induced plasma at an initial expansion stage and showed that when plasma interacts with the surrounding atmosphere, a morphologically unstable evolution phenomenon happens, transforming the “stable plasma” into a “fluctuating plasma” as shown in Fig.5. A process of back-pressing happens in the plasma’s frontier region due to a counterbalancing force (generated because of shockwaves) towards the surface of the sample. When the sample surface experiences an opposing force, a rebound phenomenon will happen at the plasma front. Due to this, the plasma frontier part collides with the bottom region, making overall plasma morphology unstable.

Fig.5 Plasma morphological fluctuation at an early stage [29].

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When microwaves are injected into LIP, it does not directly affect the back press and crash-down phenomenon, as this process occurs much before 100−300 ns, the complete absorption of microwaves into LIP (~μs) [30]. However, this critical morphological process occurs at an early stage buried the seed of instability, which was later amplified during microwave interaction with LIP, its expansion, and mixing with environmental gas. This pre-instability of LIP itself also affects the transfer of microwave energy into LIP. If the plasma is not evenly distributed around the microwave probe, the transfer of microwave energy may not be uniform. In such cases, certain regions of the plasma may absorb more energy than others. Variations in heating can lead to uneven ionization (i.e., different temperatures and electron densities at different positions of plasma). Thus, it can be considered that the enhanced atmospheric interaction caused by large plasma volume, and uneven energy transfer due to the non-uniform distribution of LIP, increases the morphology fluctuation of plasma and produces instabilities. Therefore, the changes in plasma expansion/volume (by size) and plasma stability (by position) caused by the cavity should be the most concern.

To investigate the plasma morphological fluctuation, an ultrafast imaging camera is used to observe the temporal behavior of plasma. Fig.6(a)−(d) show the time evolution images of plasma from 5 to 2000 ns in each case. Two important parameters (fluctuation in plasma core position and size) were extracted by analyzing these images quantitively. Since the plasma core accounts for the majority of its emission intensity, more spatial stability in the plasma core would likewise result in reliable emission detected by optical instruments [21].

Fig.6 Plasma evolution images from 5 ns to 2000 ns. Each image was an average of ten pulses and was normalized by its highest intensity.

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The movement of the plasma core in the Y direction for both ME-LIBS and CC-ME-LIBS is shown in Fig.7. The plume core position is determined by calculating the average ordinate value of pixels in each plasma image that falls within the top 5% brightness range. In the ME-LIBS, the position of the hot plasma core maintains an abrupt expansion and moves in an irregular path throughout the evolution period, leading to inconsistent emission signals. Initially, the plasma shows expansion at 30 ns, after which it falls to 100 ns, rises again at 160 ns and then further moves back. However, in the CC-ME-LIBS, the hot plasma core initially fluctuated till 200 ns as in the earlier period there were no reflected shockwaves to compress the plasma plume. After that, the plasma core maintains a steady spatial position till the middle of the evolution period (1 μs). In this duration, the plasma core moves toward a certain direction in the cavity case. This could be explained as the laser focusing position was not precise at the center of the cavity, thus the reflective shockwave from one side of the cavity wall reached the plasma earlier than that from the other side, leading to the plasma core moving towards a particular direction. Above 1us, the plasma dissipated greatly and the plasma core positions did not make much sense anymore. Additionally, at this time the plasma intensity was so low that it could be disregarded in terms of its contribution to the plasma emission. In the cavity case, the ME-LIP core exhibited more stable evolution, and the core position was closer to the target surface, compared to the microwave environment.

Fig.7 Plasma core height in ME-LIBS and CC-ME-LIBS.

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To further understand the CC-ME-LIBS signal stabilizing effect, changes in plasma core sizes were also observed and plotted against delay time for both ME-LIBS and CC-ME-LIBS as shown in Fig.8. To calculate the core size, we defined the plasma boundary as 80% of the maximum image intensity. The plasma in the microwave environment shows a large core size and undergoes an abrupt expansion and diminution, throughout the evolution period, indicating fluctuations in its morphology. However, in the CC-ME-LIBS, from the beginning, the plasma maintains a smaller and stable core size close to the surface of the sample. The reflected shockwave from the cavity wall compresses plasma and produces a smaller and steady plasma core. The proportion of stable signals in the spectral data increases with the extent to which the plasma maintains a stable morphology, lowering the spectral signal’s RSD.

Fig.8 Plasma core size in ME-LIBS and CC-ME-LIBS.

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The morphological fluctuation of 10 plasma images from 10 laser pulses at each configuration is shown in Fig.9(a)−(d). The plasma morphology is confined in CC-LIBS compared to LIBS as shown in Fig.9(a) and (b). However, in the case of ME-LIBS, the morphology of the plasma fluctuates violently compared to traditional LIBS as shown in Fig.9(c). On the contrary, the plasma morphology of ME-LIP in a cavity environment is more stable and uniform as shown in Fig.9(d).

Fig.9 Plasma images at 1000 ns, showing morphological fluctuation (a) LIBS, (b) CC-LIBS, (c) ME-LIBS, and (d) CC-ME-LIBS.

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To conduct a more quantitative analysis of the variations in plasma morphology, the pixel-to-pixel RSD of ten plasma images was calculated as displayed in Tab.3. The greatest RSD value for microwave LIBS indicates a large variation in microwave plasma. However, the smaller value of pixel-to-pixel RSD in the CC-ME-LIBS demonstrates that the plasma morphology becomes more repeatable under cavity confinement.

Tab.3 The RSD values of pixels from 10 plasma images at 1000 ns.

Case	LIBS	CC-LIBS	ME-LIBS	CC-ME-LIBS
Mean value of RSD pixels	7.36%	5.08%	10.14%	3.54%

Consequently, the reflected shockwaves from the cavity wall compress the plasma plume into smaller volumes and produce a smaller core area. This compressing effect reduces the interaction between the plasma and the surrounding atmosphere, which stabilizes the core position and allows more uniform heating, thereby mitigating morphological fluctuations and producing a more repeatable signal.

3.3 Factors affecting the signal intensity enhancement and mechanism analysis

This section covered the factors responsible for the signal intensity enhancement through the CC-ME-LIP modulation technique. Cavity confinement not only reduces the signal uncertainty of ME-LIBS but also plays a significant role in enhancing signal strength. As mentioned above, the energy transfer process within the plasma is highly affected by the superimposition of two methods such that the expanding plasma plume is compressed into a smaller volume by the shock wave’s reflection upon encountering the cavity wall. This increases the collision probability between particles, resulting in more excitations of atoms and ions. At the same time, confinement increases plasma density around the microwave probe, as microwaves are continuously transferring electromagnetic energy to the plasma, which further improves the microwave heating rate. Thus, both the increased “heating effect” of the microwave and the “compressing effect” of the cavity promote the collision and subsequent transition within the plume. This effect significantly increases the electron number density and temperature within the plasma, producing signal enhancement. The effect of the cavity on plasma volume, microwave power absorption, and plasma state parameters, was investigated quantitively to understand the mechanism of signal intensity enhancement under the CC-ME-LIP modulation method.

For plasma volume measurement, an average of 10 plasma images at 1000 ns has been shown in Fig.10(a)−(d) in each configuration. The plume circumference was measured with image J analysis software and typical edge detection and pixel counting techniques. The approach involves modifying the color threshold to identify maximum and minimum plume edges, creating a binary image for automatic edge recognition, and inverting the image to accurately quantify plume area and circumference. To convert measurements from pixels to millimeters, a ruler image was obtained using the same camera settings.

Fig.10 Average plasma images at 1000 ns (a) LIBS, (b) CC-LIBS, (c) ME-LIBS, and (d) CC-ME-LIBS.

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The area of the plasma images and their subsequent volume calculation have been presented in Tab.4. The results indicate that as we apply the cavity around ME-LIP, the average area of plasma decrease indicates a reduction in plasma volume. This decrease in volume naturally increases the number of particles per unit volume. An increase in the number density of particles increases the frequency of collisions between plasma species (electrons, ions, and neutral atoms), resulting in more frequent excitation of atoms and ions and enhanced emission intensities. However, the plasma volume is greater compared to the CC-LIBS, because of the injected microwave energy which contributes to additional volume due to the expansion effect.

Tab.4 The volume, area, and radius of average plasma images at 1000 ns.

Case	Plasma volume (mm3)	Plasma area (mm2)	Plasma radius (mm)
LIBS	401.20	52.20	5.76
CC-LIBS	350.95	47.74	5.51
ME-LIBS	616.20	69.49	6.65
CC-ME-LIBS	393.20	51.50	5.73

Ikeda et al. [31] investigated the changes in plasma lifetime and plasma volume by changing microwave input power at fixed laser energy. The large microwave input power resulted in the enlargement of plasma as well as a longer plasma lifetime. Thus, the indirect way to evaluate the increased microwave absorption power into plasma is to compare the plasma lifetime in both ME-LIBS and CC-ME-LIBS. The relative values of plasma lifetime are represented by the plasma decay time. The time of plasma decay is calculated by applying the fit of an exponential decay curve to the image intensity data and then determining the time constant of decay. The average plasma image intensity was calculated by defining the plasma boundary “1/e” of the maximum intensity of each plasma image. Fig.11 shows the variation of the average plasma image intensity over time in the ME-LIBS and CC-ME-LIBS. The intensity was lower than that from the ME-LIBS at earlier delay times. This could be explained as the delay of shockwave reflection and plasma compression at the earliest plasma expansion stage. However, at a later delay time, the plasma intensity in the CC-ME-LIBS was prominently higher than that in the ME-LIBS and lasted up to 2500 ns.

Fig.11 Mean intensity of plasma image.

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Tab.5 shows that the plasma decay time at CC-ME-LIBS is slightly longer than at ME-LIBS. This indicates that the lifetime of ME-LIBS plasma further increases in the confinement environment. A prolonged plasma lifetime is an indication of increased microwave power absorption due to the cavity confinement. Moreover, an increased plasma lifetime means there is more time available for the excitation and emission of photons from the excited species. As a result, the population of excited species within plasma increases, leading to higher signal intensity.

Tab.5 Plasma decay time at ME-LIBS and CC- ME-LIBS.

Case	ME-LIBS	CC-ME-LIBS
Plasma decay time (ns)	1372.26	1388.40

To further verify the superimposition effect of the combined application of ME-LIBS and CC-LIBS techniques, the electron temperature and number density were calculated for four types of LIBS configurations. The Boltzmann plot method was used to calculate the plasma temperature [32]. The Boltzmann equation is as follows:

(1)$\ln \left({\displaystyle \frac{{\lambda }_{ki}{I}_{ki}}{A_{ki}{g}_k}}\right)=\ln \left({\displaystyle \frac{N}{Z}}\right)-{\displaystyle \frac{E_k}{{KT}_e}},$

where $\lambda$ is the wavelength, $I$ is the integrated intensity, $A$ is the transition probability, $g$ is the statistical weight, $N$ is the number density, $Q$ is the partition function, $E_k$ is excitation energy, $K$ is the Boltzmann constant, $T_e$ is the electron temperature. The slope of the graph of $\ln \left(\frac{{\lambda }_{ki}{I}_{ki}}{A_{ki}{g}_k}\right)$ versus $E_k$ for the observed transition lines yield a value of plasma temperature [32]. As seen in Fig.12(a), four Cu I lines from various excitation states were used to construct the Boltzmann plots.

Fig.12 (a) Boltzmann plot for plasma temperature by Cu I 510.554 nm, 515.323 nm, 521.820 nm, and 529.251 nm lines. (b) Cu 515.323 nm line broadening for electron number density in LIBS, CC-LIBS, ME-LIBS, and CC-ME-LIBS.

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Using the electron impact parameter w and the Stark width of Cu I 515.323 nm, as demonstrated in Eq. (2), the electron density was computed. The Cu I 515.323 nm line was fitted using the Lorentz profile, and the Stark width was determined by taking the full width at half maximum (FWHM), which was found to be 0.275 nm, 0.333 nm, 0.313 nm, and 0.334 nm for LIBS, CC-LIBS, ME-LIBS, and CC-ME-LIBS, respectively, as illustrated in Fig.12(b). The value of the stark broadening parameter $\omega$ for Cu I 515.323 nm used for the calculation of electron number density is 0.346 nm [33, 34]. The plasma temperature and electron density were calculated, as shown in Tab.6,

Tab.6 Plasma temperature and electron number density in the LIBS, CC-LIBS, ME-LIBS, and CC-ME-LIBS.

Case	Plasma temperature Te (K)	Electron density (1015 cm−3)
LIBS	10857	4.74
CC-LIBS	11698	5.75
ME-LIBS	11249	5.40
CC-ME-LIBS	11727	5.76

(2)$\mathrm{\Delta }{\lambda }_{1/2\left(\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{k}\right)}=2\omega \left({\displaystyle \frac{N_e}{{10}^{16}}}\right).$

Compared with the ME-LIBS, plasma temperature, and electron density are found to increase in the CC-ME-LIBS. This enhancement is attributed to the combined effects of the two techniques, i.e., under cavity confinement, the reflected shock wave compresses the plasma causing the plume to become more elongated and narrower, with more dense volume, and a frequent collision rate. Additionally, electromagnetic energy is efficiently supplied to the plasma by the microwave probe. After absorbing electromagnetic energy, the electrons gain kinetic energy and accelerate, leading to increased collision with atoms and ions generating more excited species. As a result, the plasma in the CC-ME-LIBS system exhibits higher temperatures and electron densities compared to ME-LIBS. However, when we compared the temperature and number density values of ME-LIBS with the CC-LIBS, the result was inconsistent with our expectations. In the CC-LIBS, the plasma temperature and electron density are higher than that of ME-LIBS. This may be due large distance between the sample and the microwave probe, which weakens the probability of fully penetrating microwaves inside the plasma and leads to lower plasma temperatures and electron densities compared to CC-LIBS. However, the plasma temperature and electron number density are higher for ME-LIBS than LIBS, because the microwave still provides a high-temperature environment at the periphery of plasma. As a result, free electrons can be propelled by the microwave electromagnetic field and gain the kinetic energy needed to excite nearby atoms and ions through repeated electron−atom and/or electron−ion collisions.

In the CC-ME-LIP modulation method, both the “compressing effect” produced by a reflected shockwave from the cavity wall and the “heating effect” by increased electromagnetic energy of microwaves play an important role in improving the overall quality of the LIBS signal. For signal repeatability, the “compressing effect” condenses the plasma plume into a smaller volume. This reduction minimizes plasma−atmospheric interaction and stabilizes core position fluctuation. The overall stability of the plasma enhanced and, as a result, improved signal repeatability. For signal intensity, both the “heating effect” and the “compressing effect” contribute to the increased energy transfer process within the plasma, enhancing microwave absorption power and prolonging plasma lifetime. This effect leads to significant particle collisions and subsequent excitation. As a result, plasma temperature and electron number density increase, thereby enhancing signal intensity.

The process involved is the combined effect of microwave energy and cavity confinement to improve plasma signal quality. Microwave heating increases plasma temperature and electron number density, enhancing signal intensity. The compressing effect caused by cavity walls stabilizes plasma morphology, reducing core position fluctuations and increasing signal repeatability. Additionally, microwaves prolong the plasma lifetime and increase energy transfer, allowing more particle collisions and improved emission intensity. These effects together result in a stable, high-intensity plasma, which provides reliable, repeatable signals for LIBS analysis.

3.4 Effect on sample ablation characteristics

This section describes the effect of combined cavity and microwave effect on sample ablation characteristics, such as ablation mass and ablation volume. Fig.13(a)−(d) display the three-dimensional structure of the sample’s ablation crater observed using a confocal microscope after 50 laser pulses under each configuration. Tab.7 shows the corresponding volume and ablation mass calculation.

Tab.7 Ablation crater volume and mass in each case.

Case	Volume (μm3)	Ablation mass (μg)
LIBS	7.85 × 106	70.33
CC-LIBS	7.66 × 106	68.63
ME-LIBS	8.23 × 106	73.44
CC-ME-LIBS	6.80 × 106	60.92

Fig.13 Three-dimensional shape of the sample ablation crater: (a) LIBS, (b) CC-LIBS, (c) ME-LIBS, and (d) CC-ME-LIBS.

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In ME-CC-LIBS, the volume of the ablation crater decreases compared to ME-LIBS, because of the increases in the density of plasma within the confined space. This causes a plasma shielding effect to occur, leading to the reduction of the sample ablation mass. However, the sample volume and ablation mass were found to be increased in the case of ME-LIBS as shown in Fig.13(c). When microwave energy is absorbed into the plasma, it expands and becomes less dense due to which more and more laser energy can reach the sample, causing higher ablation.

4 Conclusion

In this work, a CC-ME-LIP modulation method was applied to improve the shot-to-shot repeatability of the microwave-enhanced laser-induced breakdown spectroscopy (ME-LIBS) signal. CC-ME-LIBS was utilized to control plasma expansion and stabilize plasma morphology. The results showed that under the CC-ME-LIP modulation method, the RSD of different Cu and Zn lines has been improved along with an increase in signal intensity. Additionally, a detailed mechanism analysis of enhanced signal intensity and improved repeatability was carried out for the CC-ME-LIBS. For signal repeatability, the smaller plasma core area and stabilized core position reduced overall morphology fluctuation, which in turn improved stability. For signal intensity, an increase in the energy transfer process within plasma, enhances the electron number density and plasma temperature, thereby increasing signal strength. Furthermore, the smallest ablation mass and crater volume show that sample ablation does not contribute to signal enhancement for CC-ME-LIBS. Thus, we conclude that for CC-ME-LIBS, plasma generates and evolves in a confined space rather than in an ordinary open environment. In such a case, ME-LIP is characterized by smaller volume, prolonged lifetime, higher temperature and electron density, stable core position, and reduced morphological fluctuation, resulting in enhanced signal intensity and improved repeatability.

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Novelty statements

The goal of this study is to use the CC-ME-LIBS modulation approach to increase the shot-to-shot repeatability of ME-LIBS signals. While earlier research has mostly concentrated on enhancing signal intensity in ME-LIBS, this work presents a method of using cavity confinement to improve signal stability over several laser pulses.

Acknowledgements

The authors are grateful for the financial support from the National Key Research and Development Program of China (No. 2023YFB4102900), the Carbon Neutrality and Energy System Transformation (CNEST) Program led by Tsinghua University, and Huaneng Group Science and Technology Research Project (No. HNKJ22-H105).

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