A potential optical approach for diagnosis of the local magnetic field near the surface of the first wall/divertor tiles by Zeeman effect using polarization-resolved laser-induced breakdown spectroscopy

Magnetic field measurement is the basic diagnosis to obtain the physical engineering parameters of magnetic confinement fusion device and the macro information of plasma discharge. The real-time diagnosis of magnetic field distribution near the plasma-facing components (PFCs) surface provides the important information on the migration and transport model of key elements. In this work, a remote, in-situ approach for the magnetic field measurement near the surface of PFCs by the polarization-resolved laser-induced breakdown spectroscopy (LIBS) based on Zeeman effect is proposed and implemented. The Zeeman characteristics of the emission spectra of laser-induced W, Mo and C plasmas were verified in the laboratory by using different magnetic field configurations. According to the polarization characteristics of the Zeeman sublines of the LIBS spectrum, the intensity and direction of the external local magnetic field were successively identified by using a linear polarizer. Subsequently, a linear array fiber was utilized to determine the polarity of the external magnetic field. And finally, the magnetic field intensity near the lower edge surface of the tungsten baffle of the Experimental Advanced Superconducting Tokamak (EAST) upper divertor was measured when the field coils were demagnetized. This method can supplement the experimental data near the PFCs for the magnetic field configuration of the magnetic confinement fusion device and provide a reference for the wall element analysis model diagnosed by LIBS.

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Introduction
The magnetic measurement method is the basic diagnostic technology for the magnetic confinement fusion device to obtain the physical engineering parameters of device and the macro information of plasma discharge [1].The acquisition of magnetic field information is very important for the operation of the fusion device, the control of plasma discharge parameters and the related physical diagnosis [2].For example, this information can be used to derive the basic parameters such as plasma current and displacement, and can also be used to study the magnetohydrodynamics (MHD) behavior and turbulence in plasma [3].
At present, there are several conventional magnetic measurement methods in fusion devices, which have their own advantages and are suitable for different measurement occasions.The magnetic probes are widely used in fusion devices because of its simple measurement principle, low cost and local measurement ability [4,5].The Hall probes have high accuracy and are excellent in measuring static magnetic fields [6,7].However, these two kinds of probes are commonly used to measure the magnetic fields at fixed locations in the plasma boundary region (outside the scrape off layer).The magnetic field configuration of the device is reconstructed by the measured values at these fixed positions.When magnetic probe measurements are unavailable in some regions or when reconstructed magnetic field near the wall surface at some position need further verification, it is desired to employ a non-contact magnetic field measurement method with a wide range of adjustable measurement positions.The motional Stark effect diagnosis enables local measurement of the magnetic field inside the plasma (magnetic field strength, pitch angles, safety factor), and has been applied on some devices such as DIII-D tokamak and Korea Superconducting Tokamak Advanced Research (KSTAR) in recent years [8][9][10].However, the prerequisite that its application must depend on the neutral beam injection limits its application scope.The cross polarization scattering meter (provides measurement information of magnetic field fluctuation) and laser polarimeter interferometer have been successfully applied to diagnose the magnetic field inside the plasma because of their large measuring range and high measuring accuracy [11][12][13].The intractable problems of them include the complexity of the measurement system as well as the high cost.Based on the respective characteristics of the above magnetic measurement technologies, they have been combined to reflect the magnetic field configuration of the device operation.Nevertheless, the real-time experimental data on the distribution of magnetic fields near the plasma-facing components (PFCs) in fusion devices need to be further mutual verified and supplemented, especially for the regions where the magnetic probe measurements are unavailable.Other auxiliary magnetic measurement methods may be meaningful in cases, where magnetic probe measurements are not possible or calculations of the magnetic field can be very imprecise.For instance, some complementary or optimized magnetic measurement methods are currently being developed to address the dynamic magnetic field distributions in stellarators (complex magnetic structures), spherical tokamaks (magnetic probes are hardly inserted in the inboard side of the plasma), and Z-pinch machines [4,14,15].In this work, the development of a non-intrusive method for measuring magnetic field distribution on the wall surface, which is not affected by the different wall material and does not take into account the problems of high thermal load and high-energy particle bombardment, is valuable for perfecting and verifying the information obtained by conventional magnetic diagnosis.Meanwhile, the real-time information of magnetic field distribution near the wall surface could provide the important information on the migration and transport of key elements on the first wall surface, so as to further understand the process of the plasma-wall interaction [16].
Laser-induced breakdown spectroscopy (LIBS) is a realtime and in-situ active analysis technique, which is recognized as a great potential analytical method for wall element diagnosis due to its advantages of non-intrusive, large-area scanning, fast and multi-element analysis capability [17,18].In the past two decades, LIBS has been applied to multiple fusion devices and a series of studies have been carried out [19].For example, some valuable results has been obtained related to the fuel retention problems, impurity migration problem and the wall treatment problems such as the lithiation, boronization, and siliconization from the Experimental Advanced Superconducting Tokamak (EAST), KSTAR, Wendelstein 7-X (W7-X), Frascati Tokamak Upgrade (FTU) and other devices, which are concerned by International Thermonuclear Experimental Reactor (ITER) [20][21][22][23][24].However, due to the complex and harsh working conditions of the fusion device and the intricate physical process of laser-induced plasma, these LIBS results are mostly qualitative or semi-quantitative results [25].The complex and variable magnetic field within the fusion device is a significant factor that limits the quantitative accuracy of LIBS [26,27].The effect of magnetic fields on LIBS signals has been investigated in the laboratory and in the linear plasma devices such as the Magnum-PSI and the PSI-2, but the external magnetic fields of them are known and fixed [28,29].However, in practical applications, LIBS requires the real-time information on the diagnosis of wall surface element composition during the plasma discharge, discharge gaps, field coils excitation and demagnetization, and the wall treatment process.Frequent variation makes the magnetic field distribution near the PFCs surface always unknown.Previous reports have shown that the intensity, direction and polarity of the magnetic field all affect the LIBS measurements [15,30,31].At the same time, Wu et al found that the emission spectrum of laser-induced plasma shows obvious Zeeman splitting under an external magnetic field, which means that it seems feasible to use the Zeeman splitting to measure the magnetic field distribution near the PFCs [32].
In this work, an approach of the Zeeman effect magnetic field measurement by polarization-resolved laser-induced breakdown spectroscopy (PRLIBS) (ZEMF-PRLIBS) was proposed and implemented.A spectrograph equipped with a high-resolution grating and specially optimized experimental parameters were used for spectral acquisition under the external magnetic field.Four magnetic field configurations and characteristic spectral lines selected for the elements of three PFCs were used to verify the Zeeman effect on the laserinduced plasmas under the external magnetic field.A linear polarizer was designed to measure the strength and direction of the external magnetic field in steps, and a linear array fiber was used subsequently to measure the polarity of the external magnetic field.At last, this approach was used on EAST to measure the magnetic field intensity near the lower edge surface of the tungsten (W) baffle of the upper divertor during the toroidal field demagnetized process.These results confirm the feasibility of using LIBS to measure the magnetic field distribution near the surface of PFCs in real-time, provide valuable data support for the magnetic field configuration of the fusion device and provide a reference for the analysis model of element content distribution on the wall surface.

Experimental setup and measured sample
The schematic diagram of the LIBS experimental setup is illustrated in figure 1, which is based on our previous work [31].The setup comprises various components, including a nanosecond laser system (Brilliant Eazy, Quantel), an energy attenuation system integrated by an λ/2 waveplate and prism splitter, a spectrometer (Andor-SR750) with ICCD (Andor iStar 340T), a digital delay generator (DG645), a 1D translation stage, various optical elements, transverse magnet, vacuum equipment and a computer.The Q-switched Nd-YAG laser with Gaussian mode operates at a wavelength of 1064 nm with a pulse width of 5 ns, a repetition rate of 2 Hz, and an energy stability of 5%.Throughout the experiment, the laser energy was maintained at 150 mJ by adjusting the energy attenuation system without affecting spot quality.The laser beam was reflected by a small dichroic mirror and then focused onto the sample surface through a plano-convex quartz lens (diameter-10 cm) with a focal length of 50 cm.The area of the ablation craters was measured as ∼5.28 × 10 −3 cm 2 using confocal microscopy (Micromesure 2, France STIL).Therefore, the average laser power density on the sample surface is estimated at 5.68 GW cm −2 .To simulate the vacuum environment of tokamak, the pressure in the vacuum chamber was reduced to ∼1 × 10 −5 mbar by using a rotary and a turbo-molecular pump.
The W, molybdenum (Mo), and carbon (C) were used as experimental samples due to these materials are the PFCs materials in the fusion devices [33].These samples were placed in the middle of the slit of the permanent magnet, as depicted in figure 2. Permanent magnets and samples were placed in a vacuum chamber.A one-dimensional stage was used to move the sample to obtain a fresh surface and avoid the effect of ablation craters on spectral intensity.The laserinduced plasma expands in the presence or absence of a magnetic field.The Nd-Fe-B permanent magnets in size of length × width = 50 × 50 mm 2 were used to generate a nearly-uniform magnetic field.By changing the thickness of the magnet, the configurations of magnetic field with strengths of 0 T, 0.25 T, 0.6 T, 0.64 T (designed for figure 2(b)), 0.76 T, 0.9 T, and 1.1 T were obtained and their gap is always fixed at 7 mm to ensure the same spatial constraints.As measured by a Gauss meter (CESTSEN, HT-20), the magnetic field strength is nearly uniform in the area of 40 × 40 mm 2 in the center of the gap cross section.The plasma size of laser ablation is generally about 10 mm, as shown in figure 11.Therefore, positioning the sample at the center of the magnetic field ensures that the laser-ablated plasma experiences a nearly uniform magnetic field strength.Due to the presence of hole with a diameter of 16 mm drilled into one side of the magnet in the magnetic field configuration shown in figure 2(b), the uniformity of the magnetic field strength is relatively reduced.Nonetheless, this configuration is only intended to verify the polarization characteristics of the LIBS spectrum in a magnetic field rather than to measure the magnetic field strength, which is deemed acceptable.Two aluminum (Al) blocks of the same size to the permanent magnets were used as the magnetic field-free case for comparison.Two optical collection paths were used to measure the strength, direction and polarity of the magnetic field.First, the collection path perpendicular to the laser direction in figure 1 was used to determine the intensity and direction of the magnetic field, which corresponds to figures 2(a) and (b). Figure 2(a) depicts the LIBS collection path along the x direction, whereas figure 2(b) illustrates the LIBS collection path along the z direction.Note that only the magnets and iron mounts in figure 2(b) were drilled to accommodate LIBS spectroscopic analysis along magnetic field lines.The 2400 grooves/mm grating (spectral range is about 7 nm) were selected to investigate the Zeeman splitting of spectral lines on this collection method.Second, the collection path coaxial with the laser direction in figure 1 was used to determine the polarity of the magnetic field, which corresponds to figures 2(c) and (d).The 1200 grooves/mm grating (spectral range is about 14 nm) were selected on this collection method.The object distance of both collection paths is twice the image distance.An optical fiber bundle composed of 18 linear array fibers with a core diameter of 350 µm (numerical aperture ≈ 0.22) was used to collect the emission light of plasma.Hence, the length of the total collection region and the spatial resolution of plasma by experimental measurement was about 12.6 mm and 0.7 mm, respectively.In order to mitigate random errors in spectral detection, ten laser pulses were accumulated for signal averaging, and five data sets were collected for each sample.All of the gate width of the LIBS experiment was set to 10 µs.

The splitting distance of spectral line under magnetic field
During the cooling process of the laser-induced plasma, the ions and atoms transit from high-energy levels to low-energy levels, radiating light corresponding to the emission lines.When exposed to a uniform external magnetic field, the coupling of the orbital angular momentum L and spin angular momentum S of an atom or ion changes, causing its energy levels to split.The energy shift ∆E due to the L-S coupling and the magnetic field is given by the equations (1) and (2) [34], where g J and g ′ J are the Lande factor for the corresponding upper and lower energy levels, which can also be obtained by consulting the NIST database [35], µ B is the Bohr magneton, M J and M ′ J are the magnetic quantum number of upper and lower energy levels, B is the strength of the magnetic field, J, L and S are the total, angular and spin quantum number, respectively.Hence, the splitting distance ∆λ of spectral line under a magnetic field can be derived from the following equations ( 3) and ( 4) [36], where e and m e are the charge and mass of the electron, λ 0 is the wavelength without the external magnetic field, c is the velocity of light.Based on the equation ( 4), the splitting distance ∆λ of spectral lines is proportional to the strength of the external magnetic field, which means that it can used to determine the value of the magnetic field strength.Meanwhile, the splitting distance ∆λ also depends on the λ 0 and the value of g J M J − g ′ J M ′ J .Under the same external magnetic field, the larger the spectral line corresponds to λ 0 and/or the larger the value of g J M J − g ′ J M ′ J , and the larger the splitting distance ∆λ.

Theoretical intensity and polarization characteristics of spectral splitting lines under magnetic field
It is well known that according to the quantum mechanics, the energy level with the angular quantum number J will splits into 2J + 1 Zeeman sub-levels under the action of the external magnetic field.Under the constraints of the selection rule, the transitions between different Zeeman sub-levels (M J and M J ′ ) will produce Zeeman sub-lines with different wavelengths.The electric dipole transition will produce the π sublines in the Zeeman split when ∆M J = 0, and produce the σ sublines (σ r and σ b ) when ∆M J = ±1.σ b represents the sublines with a wavelength less than the π sublines while σ r represents the sublines with a wavelength greater than the π sublines.
According to the Spontaneous radiation relation and considering the polarization state of the Zeeman splitting spectral line, the relative intensity distribution of each Zeeman subline can be derived as shown in table 1.Meanwhile, the polarization characteristics of each Zeeman subline of the spectrum under the external magnetic field are shown in figure 3(a).
When viewed perpendicular to the direction of magnetic field (along the x and y directions), both π sublines and σ sublines exhibit a linearly polarization state.The π sublines are always parallel to the magnetic field direction and the σ sublines are always perpendicular to the magnetic field direction.When observed parallel to the magnetic field direction (along the z direction), the σ b sublines are right-handed circular polarization state, the σ r sublines are left-handed circular polarization state, while the π sublines does not appear.Therefore, the intensity variation of each Zeeman subline of spectral lines when viewed from different angles is exhibited in figure 3(b).It is derived from equations ( 5) and ( 6) [36], where θ is an angle between the line of sight and magnetic field B, θ = 0 • means the line of sight is parallel to the magnetic Table 1.Theoretical intensity of Zeeman sublines [34]. Transition Intensity of π lines (∆M J = 0) Intensity of σr lines (M J → M J + 1)  1, respectively.Based on the equations ( 5) and ( 6), the direction of the external magnetic field can be calculated at a fixed viewing angle.

Influence of spectral profile broadening mechanism on magnetic field measurement
The broadening of spectral profile directly affects the resolution of magnetic field strength.Excessive line broadening and asymmetrical profile will significantly attenuate the limits of detection and accuracy of magnetic field measurements.The spectral profile broadening of LIBS are mainly caused by resonance broadening, instrument broadening, Stark effect and Doppler effect [37][38][39].
Resonance broadening occurs when excited atoms collide with ground state atoms of same species or are affected by their electrostatic field.The W I-505.33 nm, Mo I-553.30nm and C II-658.29 nm selected in this work are not associated with the resonance state, so the resonance broadening is negligible.
In the process of collecting the light emitted by the plasma, the light is diffracted after passing through the spectrometer slit.It will cause the spectral profile to form a certain broadening.The instrument broadening of this experimental system is fixed, and the average value is 0.022 nm measured by argon mercury lamp (Hg I-546.08 nm, Ar I-696.54 nm).
The electric field generated by the electrons and ions of the plasma will affect the state of the luminous particles.The energy level of the particle shifts or splits in the electric field, which shifts the wavelength position of the spectral line and broadens the spectral profile.Stark broadening of spectral lines is commonly used to calculate plasma electron density.The broadening and frequency shift caused by Stark effect can be expressed by equations ( 7) and (8), respectively [40], where w S and d S are the full width at half maximum (FWHM) broadening and frequency shift of the line, respectively.w e is the electron impact width parameter (half width at half maximum-HWHM), N e and T e are the plasma electron density and electron temperature, respectively.Note that the units of N e and T e in equation ( 7) are cm −3 and Kelvin, respectively.A is the ion broadening parameter, d e is the electron impact shift.Due to the small ionic contribution to Stark broadening, the second term of equation ( 7) can be ignored.In vacuum, the N e and T e of laser-induced plasma rapidly decrease with time.Increasing the gate delay for spectrum acquisition while ensuring sufficient signal intensity will reduce the contribution of stark effect.In our previous work, the temporal evolution of N e of W, Mo and C has been systematically studied [31,32].Consequently, the gate delays for W, Mo and C were set to 400 ns, 500 ns and 250 ns according to the characteristics of the sample itself, respectively [41].Under this condition, the Stark broadening of three elements were less than 0.008 nm, which is smaller than the instrument broadening.
While the Stark shift is typically smaller than the Stark width, and ranges from 0% to 30% for most lines [42].Apparently, it can be ignored.The particles of the laser-induced plasma move rapidly with respect to the spectral collection system.The parts of the particles which move away from the spectrograph produce spectral profile shifted towards the red.While the parts of the particles which move towards the spectrograph will be shifted towards the blue.The shift of frequency is Doppler shift, which can be roughly expressed as the equation ( 9) [43].The corresponding profile broadening is Doppler broadening, it is estimated from equation (10) [44], ) 1/2 (10) where λ d and w d are the wavelength position caused by the Doppler effect and FWHM broadening of the line, respectively.λ c is the ideal wavelength position, v 0 is the expansion velocity of particles, a is the angle between the expanding direction of the particle and the signal detector.M is the atomic mass in amu and T is the plasma temperature in Kelvin.Note that the units of w d and λ c in equation ( 10) are nm.According to our previous work, the v 0 of W I, Mo I and C II were about 16 km s −1 , 19 km s −1 and 30 km s −1 , respectively [41].When the spectrum is collected in coaxial with the laser as shown in figure 1, the wavelength shift estimated by equation ( 9) of W, Mo and C were 0.027 nm, 0.035 nm and 0.066 nm, respectively.The values have exceeded the instrument broadening and are not conducive to magnetic field measurement.Therefore, a collection method perpendicular to the laser direction was adopted to measure the magnetic field.Moreover, due to the large gate delay in spectral acquisition, the calculated T e of the W, Mo and C were all less than 1 eV, and the w d estimated from equation (10) were 0.0028 nm, 0.0043 nm and 0.015 nm, respectively.The results indicate that the w d of W and Mo can be ignored, while the C needs to be considered.The shape of the spectral line is a convolution between Gaussian and Lorentz profiles (Voigt function).The above broadening phenomena exist: instrumental, Doppler effect for the Gaussian contributions and resonance, Stark effect for the Lorentzian contributions.The Lorentz and Gauss parameters (FWHM) of W and Mo were 0.022 nm and 0.008 nm, while those of C were 0.037 nm and 0.008 nm, respectively.

Effect of Lorentz force on spectral spatial evolution behavior
The laser produced plasma is not only a transient process but also a complex system of electrons, charged ions and atoms.This leads to complex interactions between the plasma and the magnetic field that require some theoretical calculations or numerical simulation such as MHD model to explain.The Lorentz's law and the generalized form of Ohm's law based on the MHD model is given as equations ( 11) and (12), respectively [45], where F is the Lorentz force on the charged particle in a magnetic field, v is the mass flow velocity, E and B are the electric and magnetic fields, J is the electron conduction current and σ 0 is the conductivity and electron density.In our previous work, the spatiotemporal evolution behavior of W and Mo plasma with or without magnetic field have been systematically investigated and the related physical processes have been attempted to describe.After the gate delay (>200 ns), the magnetic field has a more obvious effect on the spectrum and plasma plume.As the magnetic field acts on the laser ablation plasma, the charged particles in the plasma are subject to the Lorentz force F. The reversal of magnetic field polarity directly leads to the change of ion rotation direction.The large Larmor radius of the ions allows them to leave the bulk of the plasma, and the electron magnetization prevents the electrons from neutralizing the ion charge.This produces a charge separation.The J produces a force in the direction of the plasma expansion and decelerates the bulk of plasma causing confinement.The J × B force acts to push the plasma until the magnetic pressure is balanced by the plasma pressure.This process leads to Joule heating of the electrons, enabling them to excite higher-charge states and promote electron collisional ionization.It should be noted that this is just a simple physics picture of single particle.However, the real situation is much more complicated, involving magnetohydrodynamics (MHD) and the transient evolution of laser ablation plasma (recombination, collisional ionization, and drag effect of plasma species).The Larmor radius of W II, Mo II and C II ions are estimated to be 28.0 mm, 17.3 mm, and 3.42 mm under a uniform magnetic field at 1.1 T, respectively.The corresponding cyclotron frequencies of W II, Mo II and C II ions are estimated to be 9.1 × 10 4 Hz, 1.7 × 10 5 Hz, and 1.4 × 10 6 Hz, respectively.Due to the existence of multiple charge states and complex spatiotemporal evolution process of laser-induced plasma, these calculated values may not accurately represent the real trajectory of species.Nevertheless, it seems to be feasible to identify the polarity of the external magnetic field based on the characteristic that the ions will shift in opposite directions under reverse polarity.This is well demonstrated by the spatial distribution behavior of the spectrum, as described in section 4.4.

The influence of Zeeman effect on LIBS spectral lines profile
Whether the emission line of laser-induced plasma in the external magnetic field conforms to the Zeeman effect theory needs to be verified.Hence, the configuration shown in  figure 2(a) was used and the gate delay of the spectral acquisition was optimized so that the spectrum resolution under the current experimental conditions is optimal [31].The comparison of spectral line profiles of W, Mo and C under different magnetic field intensities are shown in figure 4. It can be seen that under the strong magnetic field of 1.1 T, the profile of the spectral lines presents different degrees of widening and diverse shapes.This is caused by the difference value of the electron configuration J and the Lande factor g for these spectral lines, as described in section 3.1.However, for the complex conditions of magnetic field measurement in tokamak, not only the suitable value of J and g, but also the large transition probability and long luminous lifetime are necessary.Three spectral 'strong lines' suitable for magnetic field measurements near the surface of W, Mo and C component were selected and their spectral parameters are shown in table 2. Compared to other spectral lines, they have the larger wavelengths, the longer luminous lifetimes, and the larger values of J and g.The corresponding values of J and g for three spectral lines are presented in figure 5.The figure 5 also shows the transitions of W I-505.33 nm, Mo I-553.30nm and C II-658.29 nm in the regions where the magnetic field intensity is equal to or greater than 0. In the presence of an external magnetic field, W I-505.33 nm will split into 7 Zeeman sublines, Mo I-553.30nm will split into 13 Zeeman sublines, and C II-658.29 nm will split into 4 Zeeman sublines.These Zeeman sublines are superimposed to create the different shapes of the spectral lines shown in figure 4.This means that even at a magnetic field strength of 1.1 T, it is difficult to judge the magnetic field strength only by experimental spectral fitting at the current spectral resolution.While it seems to be a feasible method to determine the magnetic field strength by comparing the experimental spectra with the numerical simulation spectra.
As depicted in figures 6 (a), (c) and (e), the experimental spectra of the three elements agrees well with the numerical simulation spectra at 1.1 T. It should be noted that the experimental profiles of the W I-505.33 nm and C II-658.29 nm lines do not perfectly coincide with the numerical simulation profiles at the peaks.The physical mechanism of this phenomenon remains to be further investigated and understood.The numerical simulation spectra is derived from the superposition of each Zeeman subline, as shown in figures 6(b), (d) and (f ).The spectral lines profile was fitted by the Voigt function, and the wavelength and relative intensity of each Zeeman subline were calculated by section 3. The well agreement between the experimental spectra and the numerical simulation spectra proves that the proposed method is reasonable to measure the magnetic field intensity.Meanwhile, as can be seen from figure 6, the σ b sublines are distributed in the short wavelength position, the σ r sublines are distributed in the long wavelength position, and the π sublines are distributed in the middle of them.This phenomenon will provide an important role for the application of linear polarizers in the measurement and analysis of magnetic fields by LIBS, as shown in sections 4.2 and 4.3.In addition, it should be emphasized that the spectral line profile of LIBS widens under the external magnetic field have been confirmed.Neglecting the influence of Zeeman splitting on spectral line broadening, especially in strong magnetic fields, will result in the calculated density of the laser ablation plasma being higher than the true value.This density error will directly lead to inaccuracies in the LIBS quantitative results obtained based on the calibration-free method.
Therefore, it is necessary to consider the Zeeman effect to calculate the electron density of plasma under magnetic field by using Stark broadening method.

The application of linear polarizer in magnetic field strength measurement
As shown in figure 3(a), the light emitted by σ and π lines has completely different polarization characteristics, so the polarization characteristics of LIBS spectrum under the external magnetic fields need to be verified.The experimental configuration in figure 2(a) was used to investigate the spectral characteristics of LIBS with the change of the linear polarizer angles.The results are presented in figure 7. The extinction ratio of a linear polarizer is 1000:1.The 0 • represents that the light transmission axis of the linear polarizer only allows the π sublines to pass through, while 90 • represents that the linear polarizer only allows the σ sublines to pass through.The characteristic lines of the three elements appear only as the π sublines at 0 • and only as the σ sublines at 90 • .The spectral intensity variation with the angles of the linear polarizer should follow the Malus' law, as shown in equation ( 13) [46], where α is the angle between the polarization direction of the incident light and the transmittance axis of the linear polarizer as shown in figure 1.Let the polarization direction vector of the incident light be − → E 0 , and the transmission axis direction vector of the polarizer be − → E p .Then, α can be represented as the angle between these two vectors: is the spectral intensity after passing through the line polarizer, I (α = 0) is the spectral intensity after passing through the line polarizer when α is 0 • , respectively.In the absence of magnetic field, the spectral intensity of Mo I-553.30nm almost unchanged with the angles of the polarizer, indicating that it is unpolarized.While in the presence of magnetic field, the variation of the Zeeman subline intensities of σ and π with the polarizer angles agree well with the theoretical values, as illustrated in figure 7(d).
It has been proved that the π sublines can be blocked when the light transmission axis of the line polarizer is in the same direction as the σ sublines.This method could be more conducive to the measurement of magnetic field, as shown in figures 8(a)-(c).According to equation ( 4) and table 1, it can be calculated that the wavelength position and relative intensity of σ b and σ r sublines for the three characteristic lines are centrosymmetric in the absence of π sublines.This means that as long as the experimental spectral lines are fitted with Voigt function to get the splitting distance of the two peaks, the strength of the external magnetic field can be easily calculated.Obviously, this method is very suitable for measurement under the weak magnetic fields.The experimental values of the three elements calculated by this method under different magnetic field intensities are shown in figure 8(d).The experimental results are in good agreement with the theoretical values (measured by a Gauss meter).Under this experimental condition, the detection limits of the external magnetic field intensity measured by LIBS for W, Mo and C are 0.45 T, 0.40 T and 0.41 T, respectively.This is due to the splitting distance caused by the Zeeman effect under a weak magnetic field is less than or equal to the instrument broadening (0.022 nm) [47].Therefore, a high-resolution spectrometer such as 3600 grooves/mm grating will further improve the detection limits of LIBS for magnetic field strength measurements.Likewise, the higher resolution of the spectrometer will obtain better resolution for magnetic field strength.Moreover, the effect of linear polarizers can not only help judge the strength of the external magnetic field, but also roughly judge the direction of the magnetic field.For example, based on the angles corresponding to the σ and π sublines shown in figure 3(a), it can be determined that the direction of the magnetic field lies in the two-dimensional plane consisting of x-z axis as shown in figure 2(a).The more detailed determination of magnetic field direction is described in section 4.3.

The application of linear polarizer in magnetic field direction measurement
As the direction of the magnetic field is determined in a twodimensional plane, the equations ( 5) and ( 6) are used to further determine the direction of the magnetic field.But before that, the experimental configuration shown in figure 2(b) was used to obtain the LIBS spectra when observed parallel to the magnetic field direction.The profile of spectral lines of W I-505.33 nm, Mo I-553.30nm and C II-658.29 nm without the linear polarizer are shown in figure 9(a).It seems that the spectral lines have no π sublines but only σ b and σ r sublines under the external magnetic field of 0.64 T. A linear polarizer was used to further determine if there is no π sublines, as depicted in figure 9(b).Under the external magnetic field, the spectral line intensity of the three elements is almost unaffected by the angles of the line polarizer.This means that the LIBS emission lines observed parallel to the magnetic field only present the σ b and σ r sublines with the circularly polarized state, as shown in figure 3(a).The intensity of the circular polarization state presented by σ sublines does not change with the angles of the linear polarizer.The slight jitter in the spectral intensity in figure 9(b) is due to the instability of the LIBS signal, which   is similar to the amplitude of the change in the black boxes in figure 7(d).Therefore, it is feasible for equations ( 5) and ( 6) to be used to judge the direction of the magnetic field.
The comparison of lines profile of (a) W I-505.33 nm, (b) Mo I-553.30nm and (c) C II-658.29 nm at the observation angles of θ = 0 • , 30 • , 60 • and 90 • by spectral numerical simulation are presented in figures 10(a) and (c).Due to the σ and π have different variation trend and proportion with viewing angles-θ, the total spectral lines manifest diverse shapes.As mentioned above, the use of a linear polarizer can quickly calculate the magnetic field strength and determine the twodimensional plane corresponding to the magnetic field direction.There are two feasible methods that can be used to judge the viewing angles-θ.First, when the magnetic field intensity is determined, the numerical simulation spectra with various θ are compared with the spectra obtained by the experiment (without the linear polarizer).The numerical simulation spectra with the highest similarity correspond to the observation angle θ, as shown in figure 6 (θ = 90 • ).Alternatively, due to the spectral intensity of the σ sublines is always constant 1  2 I ′ σ in the direction perpendicular to the projection of the magnetic field line, the spectral intensity obtained without the linear polarizer minus the spectral intensity obtained through the linear polarizer (the transmittance axis is perpendicular to the projection of the magnetic field line) is 1 2 I ′ σ cos 2 (θ).The transmittance of the linear polarizer near the wavelength of 553 nm is about 90%.By this method, as shown in figure 10(d), the viewing angles-θ of Mo I-553.30nm was calculated as 87.68 • .The results are in good agreement with the theoretical values θ = 90 • .The direction of the magnetic field is then deduced from the viewing angles-θ.

Determining magnetic field polarity by spectral spatial distribution
After the strength and direction of the magnetic field are determined, the judgment of its polarity is the final task to be solved.For this purpose, the polarity change is achieved by flipping the magnet, as indicated in figures 2(c) and (d).As mentioned above, a linear array fiber was used to investigate the spectral spatial distribution behavior under the different polarities of magnetic field.The spectral spatial distribution behaviors of W, Mo and C at 0 T, 1.1 T-N and 1.1 T-S are indicated in figure 11, respectively.The gate delay for W, Mo, and C were set to 400 ns, 500 ns, and 150 ns respectively.The gate width for all three elements was set to 10 µs.The 1.1 T-N corresponds to the experimental configuration shown in figure 2(c) and the 1.1 T-S corresponds to the experimental configuration indicated in figure 2(d).In the absence of magnetic field, the laser-induced W, Mo, and C plasmas expand freely and their spectral spatial behaviors are symmetrically distributed along the laser spot center.However, when the external magnetic field of 1.1 T is present, the plasma is obviously constrained and its spatial behavior shows opposite behavior under different polarity.As described in section 3.4, the charged particles are shifted sideways by the Lorentz force under an external magnetic field.The different polarity of the magnetic field naturally leads to the opposite spectral spatial distribution behavior.
Laser-induced plasma is a complex system composed of electrons, ions and neutral particles [48].Not only that, it is a transient process full of collision, ionization and recombination.Although the atoms such as W and Mo do not seem to be affected by the Lorentz force, the fact that the spatial distribution behavior of the atoms still drift to one side should be caused by the recombination of ions, which has been confirmed by previous work [31].This means that the control of temporal acquisition parameters is also important for determining the polarity of the magnetic field.Due to the drift effect caused by the complex recombination process of ions, the acquisition parameters for W I-505.33 nm and Mo I-553.30nm need to be adjusted with respect to the large gate delay to determine the polarity, whereas the acquisition parameters for C II-658.29 nm do not.Therefore, in this work, the spatial distribution behavior of the spectra can be used to distinguish the polarity of the magnetic field after optimizing the temporal acquisition parameters.The specific method is that when the magnetic field direction is determined, the optical fiber with spatial resolution ability is placed perpendicular to the magnetic field direction, and then the polarity of the magnetic field is further determined according to the spatial distribution behavior of the spectra.In addition, it should be noted that the measurement information of magnetic field strength and polarity will also have an important impact on the LIBS signal collection and quantitative analysis results.Improper collection method or measurement under the varying magnetic field strength will affect the accuracy of LIBS diagnosis results [49].

Local magnetic field measurement on EAST upper divertor
After the laboratory demonstration of the principle of the ZEMF-PRLIBS, the magnetic field intensity near the surface of lower edge of the W upper divertor-baffle in EAST device was measured.The schematic diagram of the ZEMF-PRLIBS experimental system for the upper divertor on EAST is shown in figure 12(a).The length of the collection light path of the whole ZEMF-PRLIBS system was about 3.5 m.The spectrometer of the ZEMF-PRLIBS system was also equipped with a 2400 grooves/mm grating.The ZEMF-PRLIBS system is mounted on the H flange of the EAST.A reflecting mirror placed in the vacuum chamber is used to scan the laser from the baffle to the dome area of upper divertor.In this work, the variation of the magnetic field intensity near the surface of the lower edge of the W baffle with the demagnetization of the toroidal field coils of the EAST was systematically measured.The spectral line profile of the W I-505.33 nm with or without the linear polarizer before demagnetization of the EAST toroidal field coils is illustrated in the figure 12(b).In this case, i.e. in the presence of only toroidal magnetic field, the direction of the magnetic field is apparent.The spectral intensities of σ and π were obtained without the linear polarizer, while only the spectral intensities of σ were obtained when the axis of the linear polarizer is perpendicular to the direction of magnetic field.This is consistent with the conclusions stated above.Meanwhile, the spectral line profile of W I-429.46 nm with or without the linear polarizer also confirms this result.When the light transmission axis of the polarizer was placed parallel to the direction of the magnetic field, W I-429.46 nm exhibits only the π sublines.While when the light transmission axis of the polarizer was placed perpendicular to the direction of the magnetic field, W I-429.46 nm exhibits only the σ sublines.The wavelength position and relative intensity distribution of Zeeman sublines corresponding to W I-429.46 nm can be seen in the work of Beigman et al [36].The light transmission axis of the linear polarizer was placed perpendicular to the direction of the magnetic field, and then the magnetic field intensity near the surface of the W wall changes with the demagnetization of the EAST, as shown in figure 12(d).The variation of magnetic field intensity (B t ) with EAST demagnetization follows the Ampère's circuital law, as shown in equation ( 14), where µ 0 is the permeability of vacuum, N is the number of turns of the coil (N of EAST toroidal coil is 16 × 130), I is the coil current and R is the distance from the toroidal coil.The R corresponding to the wall surface detected by ZEMF-PRLIBS is about 1.427 m (the large radius of EAST is 1.85 m).It can be seen that the B t is linearly correlated with the decrease of the toroidal coil current, which is consistent with the calculated value of Ampère's circuital law.The slight difference between the measured results of ZEMF-PRLIBS and theoretical calculation may arise from errors in spectral analysis and variations in coil currents (The toroidal coil was in demagnetization state during ZEMF-PRLIBS measurement).In the discharge gap of EAST operation, the magnetic field intensity near the W wall surface can exceed 3.1 T, which is also similar with the results measured by the magnetic probe [50].The measurement results of ZEMF-PRLIBS and magnetic probe need to be further verified in the future work.In contrast, the magnetic field strength during the wall treatment is only several thousand Gauss or 0 T. Therefore, the influence of magnetic field intensity should be considered when measuring and analyzing the composition and content of elements on the wall surface by LIBS.In addition, it should be noted that due to the current experimental conditions, the accuracy of ZEMF-PRLIBS method for measuring magnetic field strength still needs further investigation.The higher the wavelength resolution of the spectrometer under certain experimental parameters, the more accurate the ZEMF-PRLIBS results of the magnetic field intensity.Employing gratings with more grooves/mm, such as the 3600 grooves/mm, is an effective means to improve the detection accuracy of ZEMF-PRLIBS method.
In short, ZEMF-PRLIBS could be used as a potential insitu measurement method for the magnetic field near the wall surface in fusion devices.In real-time magnetic field measurements, the application of ZEMF-PRLIBS methods to different operating conditions in fusion devices still needs to address the following issues.Firstly, due to the absence of discharge plasma during plasma discharge gaps, field coils excitation and demagnetization, etc.The ZEMF-PRLIBS method can accurately determine relevant magnetic field information, as demonstrated by results obtained in lab and EAST.Secondly, even during fusion device discharges or discharge wall cleaning, the ZEMF-PRLIBS method can still obtain the highresolution spectra.These spectra comprise light emitted by laser-induced plasma and discharge plasma radiation.In this case, the collecting optical path of the string lines and the Doppler effect caused by high-speed motion of the particle flow in the discharge plasma may cause errors in determining the magnetic field information.However, due to the collection efficiency of the ZEMF-PRLIBS optical system, the contribution of light radiated by discharge plasma (chord integral) from the high-field side of the wall surface outweighs that from the low-field side.Furthermore, the luminescent radiation lifetime of laser-induced plasma in vacuum is only a few µs, resulting in a significant contribution to spectral intensity compared to discharge plasma radiation near the wall surface.Therefore, optimizing the acquisition gate width (several µs) can further significantly mitigate potential errors from background plasma.It is imperative to further validate the accuracy of magnetic field information obtained by the ZEMF-PRLIBS approach during different discharge conditions at different locations in future work.

Conclusions
In this work, a real-time and in-situ measurement method, ZEMF-PRLIBS, for the magnetic field intensity, direction and polarity near the wall surface in fusion device was proposed.The suitable spectral characteristic lines for W, Mo and C wall materials were selected for analysis of magnetic field measurements.The specific steps are as follows: 1.The experimental spectra with only σ Zeeman sublines can be obtained by using a linear polarizer, and the splitting distance of the spectral fitting peak can be calculated.And then the magnetic field intensity and its direction (located in which two-dimensional plane) will be obtained.2. Under the premise of determining the magnetic field intensity, the numerical simulation spectra at different viewing angles can be compared with the experimental spectra without the linear polarizer to determine the magnetic field direction.Alternatively, the experimental spectra without the linear polarizer is subtracted from the spectra with only σ Zeeman sublines with the linear polarizer.The difference of them can be derived from the magnetic field direction.3.Under the premise of determining the magnetic field direction, the optical fiber with spatial resolution ability can be placed perpendicular to the magnetic field direction, and then the polarity of the magnetic field is further determined according to the spatial distribution behavior of the spectra.
The use of linear polarizers verifies the polarization characteristics of laser-induced W, Mo and C plasmas in an external magnetic field.Based on the polarization characteristics of laser-induced plasma and the related theory of Zeeman effect, the magnetic field in the laboratory and near the W divertor surface of the EAST were systematically measured using ZEMF-PRLIBS approach.The results are in good agreement with those of Gauss meter and magnetic probe.In the future, ZEMF-PRLIBS will measure and analyze the magnetic field strength under different discharge conditions at different locations in the EAST, providing the data support for correction of element composition analysis results of wall surface and construction of boundary magnetic field configuration.
We would like to express our special gratitude to the editors and reviewers of the Nuclear Fusion journal for their highly constructive contribution on our paper.

Figure 2 .
Figure 2. Configuration of the transverse magnetic field at the collection path along the (a) x-direction, (b) z-direction, (c) y-direction and (d) y-direction-field reversal, respectively.

Figure 3 .
Figure 3.The (a) polarization characteristics and the (b) theoretic intensity variation of each Zeeman subline of spectrum when viewed from different angles.

Figure 4 .
Figure 4. Comparison of spectral line profiles of (a) W, (b) Mo and (c) C under different magnetic field intensities.The θ is 90 • .

Figure 5 .
Figure 5.The transitions of (a) W I-505.33 nm, (b) Mo I-553.30nm and (c) C II-658.29 nm in the regions where the magnetic field intensity is equal to or greater than 0.

Figure 6 .
Figure 6.Comparison of experimental and numerical simulation profiles of (a) W I-505.33 nm, (c) Mo I-553.30nm and (e) C II-658.29 nm and the modeled spectra of Zeeman sublines of (b) W I-505.33 nm, (d) Mo I-553.30nm and (f ) C II-658.29 nm under the magnetic field of 1.1 T. The θ is 90 • .

Figure 7 .
Figure 7.Comparison of characteristic line profiles of (a) W I-505.33 nm, (b) Mo I-553.30nm and (c) C II-658.29 nm at polarization angles α of 0 • and 90 • , respectively.The variation of (d) spectral normalized intensity of Mo I-553.30nm with polarization angles with or without magnetic field.α = 0 • represents that the light transmission axis of the linear polarizer only allows the π sublines to pass through, while α = 90 • represents that the linear polarizer only allows the σ sublines to pass through.The θ of (a)-(d) are 90 • .

Figure 8 .
Figure 8.The characteristic line profiles of (a) W I-505.33 nm, (b) Mo I-553.30nm and (c) C II-658.29 nm with the variation of magnetic field intensity at the condition that the linear polarizer only allows the σ sublines to pass through, respectively.(d) Comparison of experimental and theoretical values of Zeeman splitting of three elements under various magnetic field intensities.'SD' stands for the splitting distance, which is calculated by the difference between the fitted central wavelengths of the two peaks.The θ is 90 • .

Figure 9 .
Figure 9. (a) The profile of spectral lines of W I-505.33 nm, Mo I-553.30nm and C II-658.29 nm when observed parallel to the magnetic field direction.(b) The variation of intensity of W I-505.33 nm, Mo I-553.30nm and C II-658.29 nm at the different linear polarizer angles when observed parallel to the magnetic field direction (θ is 0 • ).The magnetic field strength is 0.64 T.

Figure 10 .
Figure 10.Comparison of simulated spectral lines profile of (a) W I-505.33 nm, (b) Mo I-553.30nm and (c) C II-658.29 nm at the observation angles of θ = 0 • , 30 • , 60 • and 90 • , respectively.(d) Comparison of the spectral profile of Mo I-553.30nm obtained without the linear polarizer and obtained with the linear polarizer (the transmittance axis is perpendicular to the projection of the magnetic field).

Figure 11 .
Figure 11.Comparison of spatial distribution characteristics of W spectra at (a) 0 T, (b) 1.1 T-N and (c) 1.1 T-S, respectively.Comparison of spatial distribution characteristics of Mo spectra at (d) 0 T, (e) 1.1 T-N and (f ) 1.1 T-S, respectively.Comparison of spatial distribution characteristics of C spectra at (h) 0 T, (i) 1.1 T-N and (g) 1.1 T-S, respectively.The white dotted line represents the center of the laser spot.

Figure 12 .
Figure 12.(a) Schematic diagram of ZEMF-PRLIBS experimental system for the upper divertor on EAST.(b) The spectral line profile of the W I-505.33 nm with or without the linear polarizer when the current It of the toroidal field coil is 11 000 A. The light transmission axis of the polarizer is placed perpendicular to the magnetic field.(c) The spectral line profile of the W I-429.46 nm with or without the linear polarizer when the current It of the toroidal field coil is 11 000 A. The light transmission axis of the polarizer is placed perpendicular to and parallel to the magnetic field, respectively.(d) Comparison between the measured value of magnetic field strength by ZEMF-PRLIBS and the calculated value of Ampère's circuital law under the toroidal coil current It.The measured point is near the surface of lower edge of the upper divertor-baffle.