In situ measurements of the spectral reflectance of metallic mirrors at the H α line in a low density Ar–H plasma

The efﬁcient and reliable control and monitoring of the quality of the optical properties of mirrors is an open problem in laboratory plasmas. Until now, the measurement of the reﬂectance of the ﬁrst mirrors was based on the methods that require additional light calibration sources. We propose a new technique based on the ratio of the red- and blue-shifted emission signals of the reﬂected hydrogen atoms which enables the in situ measurement of the spectral reﬂectance of metallic mirrors in low-density Ar–H or Ar–D plasmas. The spectral reﬂectance coefﬁcients were measured for C, Al, Ag, Fe, Pd, Ti, Sn, Rh, Mo, and W mirrors installed in the linear magnetized plasma device PSI-2 operating in the pressure range of 0.01-0.1 Pa. The results are obtained for the H α line using the emission of fast atoms induced by excitation of H atoms through Ar at a plasma-solid interface by applying a negative potential U = − 80, . . . , − 220 V to the mirror. The agreement between the measured and theoretical data of reﬂectance is found to be within 10% for the investigated materials (except for C). The spectra also allow us to efﬁciently determine the material of the mirror.


I. INTRODUCTION
The accuracy and reliability of spectroscopic measurements in laboratory plasmas crucially depend on the physical properties of the optical components used. Usually, the accurate modeling and measurements of transmission, reflectance, polarization properties, etc., have to be performed well in advance of many experiments. For example, if an absolute intensity of a certain spectral line is measured, the transmittance of the complete optical path must be known. Here, the essential elements are the plasma facing mirrors that guide the emission from the plasma to the spectrometers or cameras. Mostly being placed inside the vacuum vessel, these mirrors may be damaged by exposure to the plasma (e.g., erosion and deposition) as for instance in fusion plasmas 1 or due to irritation induced by laser pulses. 2 The degradation of mirrors reduces the actual transmittance of the optical path so that a new calibration is required. Two practical solutions for this problem exist. In the most frequently applied method, a calibration lamp must be installed in front of the mirror to re-measure the reflectance. Either the calibration source must be placed inside the plasma volume or the mirror must be taken out. In the second and less frequently used approach, the measurements of the spectral reflectance can be monitored using another external source such as a laser. 3 However, this technique is often limited by the additional optical access to the mirror. Until now, no better practical method is known allowing for in situ measurements of the reflectance of plasma a) s.dickheuer@fz-juelich.de facing mirrors without removing it from the plasma and without using an additional calibration source. A more practical diagnostic to monitor the modification of surfaces, such as spectral reflectance, surface morphology, or polarization properties, is desired for fusion, 4 laser produced, or technological plasmas. 5,6 A new method for measuring the spectral reflectance of electrical conductive surfaces such as metallic mirrors is proposed in this paper. It relies on the stimulated Balmer lines' emission in an Ar-H mixed plasma induced by fast hydrogen atoms. No additional calibration source is required, and there is no need to remove the mirror from the plasma. The calibration source is the plasma itself, and the fast atoms are generated as a result of the controlled plasma-surface interaction. The paper is structured as follows: In Sec. II, the background of the new diagnostic technique will be explained in detail. In Sec. III, we present the experimental results achieved by using the new diagnostic technique. The conclusion and outlook is given in Sec. IV.

II. DOPPLER-SHIFTED REFLECTANCE MEASUREMENT
The idea of this approach is sketched in Fig. 1. We consider the Doppler effect in front of a mirror. If an atom with velocity v moves toward the observer [ Fig. 1(a), top], then the measured emission of the spectral lines is blue-shifted relative to the emission induced by an atom at rest according to the Doppler effect, i.e., ∆λ/λ 0 = (λ b − λ 0 )/λ 0 = v/c, where λ 0 is the unshifted wavelength of the transition, λ b is the measured   9 where the fitting parameters depend on the choice of the projectile-target system.
wavelength, and c is the speed of light in a vacuum. The photon emission is usually isotropic. In this case, if the emission of atoms occurs on the distances l λ 0 much smaller than the dimension of the mirror S (l λ 0 S r) and the latter is much less than the distance r between the observer and the mirror, then the photons reflected at the mirror will be detected at the red-shifted wavelength λ r [ Fig. 1(a), bottom]. The intensity of the red-shifted signal is reduced relative to the intensity of the blue-shifted signal by the reflectance of the mirror. The spectral reflectance at the wavelength λ 0 can be calculated by The profile of the blue-shifted component is in general determined by the different broadening mechanisms in the plasma such as the Doppler or Stark broadening. In the case of pure mirror-like reflectance, the whole profile of the red-shifted signal must be symmetrical to the blue-shifted one and only its amplitude is reduced. The emission of the Balmer lines induced by fast hydrogen or deuterium atoms in the plasma represents the most suitable atomic system to realize this scheme of measurements in laboratory plasmas. Among all elements at the same energy, the Doppler-shift is the largest for hydrogen or deuterium. Extensive experimental studies of emission of atoms at the plasma surface interface in low pressure discharges and fusion plasmas demonstrated the enhanced emission of the Balmer lines in the presence of noble gases such as argon. [10][11][12][13] In fact, it was already mentioned in earlier studies [14][15][16][17] that the photons reflected at the surface could provide an additional source of emission at the red-shifted wavelengths. However, in high pressure discharges (10-100 Pa), the observed signal is a complex superposition of emission 15,18,19 induced by the incident and reflected atoms. The incident fast atoms are produced as the result of the charge-exchange recombination between the ions, being accelerated in the sheath, and the background molecules or atoms. The backscattered or reflected atoms are the result of the neutralization of the incident ions at the plasma surface. The emission of the incident atoms in the sheath enables access to the measurements of the Stark effect. 20 However, it restricts the measurement of the reflectance, according to the scheme in Fig. 1(b) considerably. In these high pressure discharges, both the directly observed emission and the reflected emission are superpositions of emission from the incident and reflected atoms. Additionally, the Stark splitting complicates the separation of lines.
In low pressure discharges, the situation is especially favorable to realize the measurements of reflectance. A recent study of the emission of fast atoms in the linear magnetized plasma, operating in the pressure range of 0.01-0.1 Pa, 21 has proven that the observed signal is induced by the reflected atoms only. 13 The following conditions are required to enable in situ measurements of the spectral reflectance in the plasma: and Here l cx = 1/(n g σ cx ) is the mean-free path of the chargeexchange recombination of the ions in the sheath (with the neutral gas density n g = p/k B T g , where p is the neutral gas pressure, k B is the Boltzmann constant, T g is the neutral gas temperature, and σ cx is the charge-exchange cross section), d is the sheath thickness, and l λ 0 = v τ is the characteristic distance the atoms move before emitting a photon at the wavelength λ 0 , where τ = 1/ k A ik is the lifetime of the excited level i and A ik is the Einstein coefficient for the transition from i to k, whereas the sum extends over all lower lying levels k. Condition (2) guarantees the absence of the signal produced by the incident atoms in the sheath, impacted by the Stark effect. Condition (3) guarantees that the photons are emitted outside the sheath avoiding the impact of a strong electric field, and thus, no Stark effect on the observed line emission is expected. In order to create fast reflected atoms in a low-density plasma, the ions need to be accelerated toward the mirror surface. To achieve this, the applied potential in the presented experiments can be varied between U = −80 and −220 V. At the surface, the ions are neutralized and backscattered as fast atoms. 22 They leave the surface with a certain energy and angular distribution, 7,8 as schematically shown in Fig. 1(b, top). So, for instance, for the H or D atom scattered on heavy Z materials such as W or Mo, the over-cosine angular distribution of the reflected atoms is expected. 7 The emission profile of the reflected atoms is schematically shown in Fig. 1(b) (bottom). Depending on the observation angle θ 0 , the blue-shifted signal of the atoms is also partially observed at the red-shifted wavelengths and vice versa: the spectral interval of the directly observed photons is [λ 0 (1 − v/c), λ 0 (1 + v/c·sin(θ 0 ))], and the indirectly detected signal shown in Fig. 1 The value of the spectral reflectance R(λ 0 ) can be determined by the ratio between the non-overlapping parts of the red-and blue-shifted parts of the spectrum [compare Eq. (1)].
A demonstration that the emission of fast atoms can be applied for the spectral reflectance measurements has been shown in recent papers. 10,13 It is reported that the strongest signal of the Balmer lines generated by the reflected atoms is observed for Ar-H mixed plasmas (at flow ratios close to 1:1) where the signal depends solely on the relative kinetic energy in atom-atom collisions. 13 The kinetic energy of reflected atoms can be selectively controlled by the applied potential. In this way, the emission of fast atoms can be switched on and off as required.
The focus of this paper is to show that the signal induced by reflected atoms in low-density Ar-H plasmas can be used as an effective diagnostic tool to derive the values of spectral reflectance of metallic mirrors without additional calibration source and without removing the mirror from the plasma. Spectra were measured for a set of various mirror materials and different negative potentials.

III. EMISSION SPECTRA OF THE H α LINE AT DIFFERENT MIRROR MATERIALS
The measurements of emission were carried out in the linear plasma device PSI-2. 21,23 The plasma is generated by a hot cathode arc discharge utilizing a hollow LaB 6 cathode. The plasma particles, created in the cathode region, move in the axial direction and are radially confined by a cylindrical magnetic field of 0.1 T generated by six magnetic field coils. The magnetic field and the geometry of the setup in the cathodeanode region reduce the extent plasma radius to r ≈ 5 cm. Via an inlet system single gases or gas mixtures with a variable gas flow can be produced in the vacuum chamber resulting in neutral gas pressures (measured during discharge) between 0.01 and 0.1 Pa. The electron density is in the range of n e ∼ 10 10 -10 12 cm −3 , and typically the electron temperature is in the range of T e ∼ 4-10 eV. 21 The working gas flow of either 40 or 80 sccm for both H 2 and Ar gases was selected in the present experiments. Figure 2 shows the plasma profiles of electron density, electron temperature, and plasma potential for Ar-H plasma measured by using a single Langmuir probe. The electron density is on the order of 5·10 10 cm −3 , the electron temperature is about 5-7 eV, and the plasma potential is about −25 V. More detailed information about the device and its operation range can be found in Refs. 21 and 23.
The mirrors are brought into the plasma using a side manipulator at the distance of approximately 2 m downstream from the cathode. The area of the mirror is 169 mm 2 and the thickness is 2 mm. In the radial direction, the mirror is located at r ≈ 2.5 cm in the density maximum of the hollow profile, as shown in Fig. 2. The spectral emission of the fast atoms is measured at two different lines of sight, corresponding to the angles of 35 • and 90 • . We note that the measurements at the angle of 90 • do not provide the reflectance data since the line of sight is parallel to the mirror surface. The spectrum is measured with a high-resolution echelle spectrometer being connected with the PSI-2 device by optical fibers which are approximately 50 m long. The dispersion and resolution of the spectrometer are ∼1 pm/pixel and ∼5 pm/pixel at 6562.7 Å, respectively. The wavelength calibration is performed using a deuterium-hydrogen calibration lamp by fitting the measured H α and D α lines on the detector to the fine-structure resolved intensities of both lines. In all cases, the H α line measurements are performed using a 656 nm filter in front of the spectrometer entrance slit to avoid the appearance of other orders on the detector. The integration time is 300 s for all presented spectra. First, we show that at applied voltages U between −80 and −220 V, the experimental conditions allow us to measure the spectral reflectance of metallic mirrors according to Eqs. (2) and (3). The electron density of 5 × 10 10 cm −3 , electron temperature of 6 eV, gas pressure of 0.1 Pa, and kinetic energy of the atoms of 100 eV are assumed here. Using the expression for the Child-Langmuir sheath 24 in the low-collisional regime, one obtains a sheath thickness of d ≈ 0.5 mm. The mean-free path of ions can be estimated as l cx ≈ 2.6 m using the value for the charge-exchange cross section of σ cx = 3 × 10 −15 cm 2 (taken from the work of Janev et al. 25 ) and a neutral gas density n g of 1.25 × 10 12 cm −3 , assuming a neutral gas pressure of 0.1 Pa and a neutral gas temperature of 0.5 eV. Finally, the distance the atoms move before they can emit the detectable amount of photons in the case of the H α line l λ 0 is equal to 1.4 mm (assuming a hydrogen atom with an energy of 100 eV and a lifetime of excited n = 3 levels τ = 10 ns 26 ). This distance is also less than the characteristic size of the mirror of 13 mm. Thus, all the necessary conditions at the PSI-2 device are fulfilled to measure the spectral reflectance of metallic mirrors. Figure 3 shows the measured spectra along both lines of sight for different applied potentials for the Pd mirror. Taking the Doppler effect into account, the wavelength scales of the spectra are plotted as energy scales, whereas the negative energy values correspond to observed wavelengths smaller than the wavelength of the unshifted line. The spectra consist of a strong background H α line 27 and a very weak D α line. No emission induced by the reflected atoms could be observed at the floating potential U = −30 V. By increasing the absolute value of the negative potential to 80 V, the rapid rise of emission of the reflected atoms becomes visible in Figs. 3(a) and 3(b). The observed intensity increases and the line becomes broadened. The strongest intensity for both lines of sight is achieved at a negative potential between −120 and −140 V. Further increase in the absolute potential leads to the reduction in the intensity while the width of the redand blue-shifted wings increases. In all cases of the applied negative potential, the measured spectra in (a) reproduce the scheme shown in Fig. 1(b) (bottom). The red-shifted signal behaves identically to the blue-shifted one. By contrast, the profiles are symmetrical for 90 • observation [ Fig. 3(b)]. Also in this case, the observed energy of the emission correlates with the applied negative potential. The steepness of the gradient of emission is also reduced. By increasing the absolute amplitude of the applied voltage to 140 V and higher, the emission induced by neutralization of H + 2 at the surface becomes visible. This fact is especially pronounced in Fig. 3(a) as no overlap with the D α line is observed here for the red-shifted interval. By increasing the absolute applied voltage to the values of 200 V and higher, one obviously observes the emission induced by the fast H(H + 2 ) atoms in the plasma as well as by the change in the slope of the Doppler-shifted component. 18 On the one hand, we confirm the observation from high density plasma discharges, 15 but on the other hand, by adding Ar into the hydrogen plasma, we could not detect the considerable reduction in the concentration of H + in favor of molecular ions H + 2 or H + 3 . However, as the calculation of the spectral reflectance from measurements is only based on the ratio between the redand blue-shifted intervals, the source of emission is of a weak importance. In Fig. 4, the measurements for the line of sight of 35 • for the Fe and C mirrors are shown. As one can see, the red-shifted part for both elements is different, but the behavior for different applied potentials is identical to the Pd mirror. The difference can be explained with the different reflectance coefficients and the different atomic masses of the materials. The atomic mass changes the energy of the backscattered atoms [according to Eq. (4)] and thus the shape of the Doppler-shifted components. The measured spectra for C, Al, Ag, Ti, and W at the applied electrostatic potential of −100 V are shown in Fig. 5. Two effects are clearly observed. First, the ratio between the red-and blue-shifted signals changes dramatically for different materials. Second, the broadening of emission clearly correlates with the atomic mass, especially for the low Z elements. Thus, for instance, for the C mirror, the red-shifted signal is very weak and the width of the emission is the lowest among all investigated materials. In the case of the Al mirror, the picture becomes quite opposite. The red-shifted signal approaches in its intensity the blue-shifted one. The wings of the emission at the blue-and red-shifted wavelengths increase too. For the Ag mirror, the profile becomes practically symmetric. For Mo, the red-shifted signal is again reduced with respect to the blue-shifted one. The increase in the red-shifted signal is observed again for the Sn mirror, and in the case of W, the red-shifted signal is nearly the half of the blue-shifted one. Whereas the measurements of reflectance depend on the ratio of the signals only, it is worth analyzing if the broadening of the emission for different materials corresponds to the general expectations. Thus, for instance, if the observed emission is caused by the reflected atoms only, then the signal is extended over the wider spectral or energy interval for higher masses of the mirror material. According to the classical formula 28 of the elastic binary collisions, the maximal kinetic energy of the reflected atoms E m is equal to where E 0 is the incident energy of the ions, E m is the maximal energy of the reflected atoms, m is the mass of deuterium or hydrogen atoms, and M is the atomic mass of the mirror material. We note that Eq. (4) is expressed in the laboratory frame and the angle θ 0 is the angle between the surface normal and the line of sight. Moreover, we note that Eq. (4) is only used to calculate an upper limit of the energy because the observed emission is a result of inelastic collisions. In the lowdensity limit of plasma operation, the maximal kinetic energy of the incident ions is approximately equal to E 0 ≈ e(U − U p ), where U is the applied negative potential and U p is the plasma potential. The measured plasma potential of the PSI-2 plasma at the position of the mirror is of −25 V, as exemplified in Fig. 2 transferred to the potential energy of the n = 3 levels of H atoms by excitation by argon atoms. Depending on the source of excitation of the fast atoms, e.g., excitation either by the ground level or by metastable levels of argon, the value δE = 10.2 eV or δE = 0.12 eV must be added to the value E p m to be comparable with Eq. (4). In Fig. 6, the comparison between the measured energy of the reflected atoms and the calculated one using Eq. (4) is shown. The dashed line shows the normalized energy of the atoms calculated according to Eq. (4), and the experimental energies are derived from the emission spectra of fast atoms. For the investigated materials, the measured energies E p m deviate not more than 10% from the calculated energies E m . The elements with a low Z number (Z < 20) reproduce the theoretical curve well. The data points for materials with Z > 20 spread stronger, because with a greater mass the ratio E p m /E m slowly reaches the value of 1 which makes it more difficult to detect the difference. Furthermore, most of the data points show a systematically lower energy compared to the calculated one: E p m /E m ≈ 0.8..0.9 as neither plasma potential nor the energy offset of 0.12 or 10.2 eV was considered in Eq. (4). The spectral reflectance of the different materials could be obtained by dividing the non-overlapping part of the reflected and direct signal of the reflected atoms in the symmetrical energy intervals of the spectra [E p m · sin 2 (θ 0 ):E p m ], as shown in Fig. 5. The corresponding integrals I r and I b and the errors σ r and σ b were calculated using the trapezoidal rule. 29 Finally, the error for the measured reflection coefficient is determined using the Gaussian error propagation formula First, we show the results of the measurements as a function of applied negative potential for C, Fe, and Pd. Each mirror was exposed to the plasma for about 150 min. They were put under the floating potential for about 10 min, and the spectrum where N + is the ion density of hydrogen atoms, R N is the particle reflection coefficient for hydrogen, N Ar,Ar * is the density of argon or metastable argon, 13 and σ(E 0 ) √ E 0 is the rate coefficient of excitation. Following from Eq. (6), the formula eU is used for fitting the measured integrals I b . Figure 7(a) shows very good agreement between the measured integral and the theoretical expectation. This supports our hypothesis that the blue-shifted signal is only generated by the reflected atoms. The applied potential changes the emission rate coefficient and consequently the Doppler-shifted emission. Thus, the Doppler-shifted components can be switched on and off only by varying the applied potential. If no electrostatic potential is applied, no Doppler-shifted emission will be detectable (compare, e.g., Fig. 3).
In the case of Fe and Pd [ Fig. 7(b)], the derived spectral reflectance seems to be only weakly dependent on the applied potential in the σ range and remains close to the literature values of 0.57 and 0.74 30 for all the applied potentials. A reduction in the measured reflectance is observed of the order of 5%. For C, the first value of reflectance is equal to 0.35 exceeding the literature value by more than a 50%, but for higher absolute values of applied potential, the measured ratio In this case, the emission of fast atoms is weak and the separation from the background component is difficult [ Fig. 4(b)]. Increasing the energy of the incoming ions results in stronger emission induced by fast atoms. As a consequence, the signalto-background ratio increases and the reflectance can be better calculated. For the mirrors of Fe and Pd, the weak variation of the measured reflectance is most probably the consequence of the weak molecular lines in the spectral region and the uncertainty of the background subtraction. In order to prove the latter fact, the Pd mirror was exposed for about 2 h in the same plasma at the applied potential of −140 V. The time dependence of the reflectance is shown in Fig. 8. Indeed within the error bars, no variation of the reflectance is detected. Also the measurements in the laboratory, before and after exposing the mirror to the plasma, indicated by the red data points only show variation of spectral reflectance of the order of 1%-2%. Apparently, the ion flow of Ar ions only weakly and slowly changes the optical properties of the mirror surface at the used plasma conditions. The comparison between the measured and the literature values of reflectance for the investigated materials is shown in Fig. 9. The data were obtained at U = −80 V for Fe and Pd; U = −100 V for Ag, W, Mo, Al, and Sn; U = −120 V for C; U = −140 V for Rh; and U = −180 V for Ti. The experimentally in situ determined reflectances are all close to the literature listed values. This fact clearly confirms that the ratio between the red-and blue-shifted signals can be used to determine the reflectance. The deviation from the literature values is at maximum ≈15%. Except for C, W, and Al, the deviation is approximately 5%. For C, the big difference can be explained with the weak red-shifted component, which makes the determination of the reflectance difficult, as explained before. For the tungsten mirror, the reflectance is larger than the theoretical value from the work of Werner et al. 30 This is also observed in other experiments, where the tungsten reflectance was measured. The difference between the experimental results for tungsten reflectance from the work of Minissale et al. 32  to the theoretical calculations of Rakić et al. 33 and Werner et al. 30

IV. CONCLUSION AND OUTLOOK
In this paper, we presented a new spectroscopic technique, the DSRM (Doppler-Shifted Reflectance Measurement) diagnostic, which provides the possibility to measure the spectral reflectance of surfaces of electrically conductive materials in low-density Ar-H plasmas 36 without the additional use of calibration lamps or lasers. The necessary condition to measure spectral reflectance is the absence of emission due to charge exchange processes in the plasma sheath. The measurements rely only on the Doppler-shifted stimulated emission of the fast atoms reflected at the plasma-solid interface. 13 Active control of the Doppler-shifted stimulated emission is performed by varying the applied electric potential to the mirror surface. In this way, the kinetic energy of the fast reflected atoms can be controlled, and in turn, the intensity of the stimulated emission can be changed. No or very weak Doppler-shifted emission is observed for −30 V, but the emission starts to rise at applied electric potentials above −80 V. The integral over the blue-shifted emission is proportional to the square root of the kinetic energy of the ions, confirming that the signal is induced by reflected atoms only. A comparison of the measured data with the literature listed reflectance values for mirrors of several materials (C, W, Fe, Mo, Ti, Pd, Rh, Sn, Al, and Ag) shows an agreement within 15%. In spite of the obvious limitations in the precision of the measurements, e.g., the errors of order of 1%-2% in the specialized mirror laboratories could be hardly achieved using the proposed technique, the Doppler-shifted reflectance measurements can be used in lowdensity plasma applications where the access to the mirrors is limited.
We note, nevertheless, that the measurements were performed only for mirror-like surfaces, e.g., the analysis assumes the symmetry (except for relative intensity) between the blue-and red-shifted profiles. However, in the case of the diffusive surfaces, the analysis probably breaks as the red-shifted emission moves toward the passive component, although the upper limit at the red-shifted wavelength is independent of the surface quality. As a result, the separation between the direct and reflected signals could be more difficult to perform.
In the forthcoming experiments, we are going to address this issue by measuring the transition from the specular to the diffusive regime and by measuring the spectral reflectance of diffusive surfaces. The polarization technique can also be applied to distinguish between the different components of the spectral reflectance for some of the materials.

ACKNOWLEDGMENTS
We thank the complete PSI-2 team for the technical and experimental support and the maintenance of the PSI-2 device.