Erosion sensor using time-resolved cavity ring-down spectroscopy for Hall thrusters.

A high-sensitivity sensor to measure titanium atom density based on time-resolved cavity ring-down spectroscopy (CRDS) was developed to monitor the wall erosion and predict the lifetime of Hall thrusters. The minimum detection limit for the sensor was dependent on the discharge current oscillation in the Hall thruster. A Volterra engine management system was employed for time-resolved measurements to develop the time-resolved CRDS system, which was synchronized to the discharge current oscillation. The results confirmed that the path-integrated number density of sputtered titanium atoms was synchronized with the discharge current oscillation. The minimum detection limit was decreased by ∼30% from 2 × 1012 to 6 × 1011 m-2.

field are applied. The magnetic field is applied using the inner and outer coils, while the electric field is applied using a potential difference between the anode and outer cathode. Electrons are emitted from the cathode and used for both ionization and neutralization. The electrons from the cathode are trapped by the magnetic field, and a Hall current is induced along the azimuthal direction due to the E×B drift. The high-energy electrons collide with and ionize the neutral particles of the propellant, which generates ions and electrons. The produced ions are accelerated in the acceleration channel by the electric field to generate thrust as the reaction force. The electrons emitted from the cathode and those produced by ionization then progress towards the anode due to the electric field.
In a Hall thruster, electrons exist in the acceleration channel without any space-charge limitations. Thus, a high thrust density can be achieved, which allows Hall thrusters to be more compact than ion thrusters. In addition, the thrust-to-power ratio of Hall thrusters exceeds that of ion thrusters. 5 Therefore, the thrust is greater for Hall thrusters under the same operating conditions, as a constant electric power is generated by the solar cell. Such a process effectively shortens the transition period to reach the desired orbit. The 702SP launched by Boeing used an ion thruster (the XIPS-25) with a thrust-to-power ratio of 37 mN/kW and required approximately 6 months to reach the target orbit. The Eutelsat 172B launched by Airbus used Hall thrusters (the PPS-5000) with a thrust-to-power ratio of 64 mN/kW and took approximately 4 months to attain the target orbit. In addition to the approximately 4000 hours of operation required for orbital rising, more than 3000 hours of operation were required for north/south station keeping.
The primary factor that limits the lifetime of Hall thrusters is wall erosion due to ion sputtering. 6 Therefore, measuring sputter erosion is essential to evaluate thruster lifetimes. However, conventional long-term wear tests are extremely costly in terms of both human resources and time. 7 Moreover, there are numerous experimental parameters to consider, and the erosion of the Hall thruster wall is relatively slow, which makes conventional measurement approaches impractical. Therefore, in situ and high sensitivity measurement systems for sputter erosion are required. Lee et al. demonstrated the effectiveness of sputter measurement systems based on cavity ring-down spectroscopy (CRDS) for erosion measurements in electric propulsion systems. 8,9 CRDS is a type of laser absorption spectroscopy that permits quantitative in situ measurements. [10][11][12][13] In CRDS, an optical cavity composed of two high-reflection mirrors confines the incident laser beam. This beam is reflected multiple times using mirrors, and if the mirror reflectivity is 99.95%, the length of the probe optical path is expanded up to 2000 times, leading to extremely sensitive measurements. When the absorbing species has the same excitation wavelength as the emission wavelength of the laser in the cavity, the species absorbs the laser energy. The transmitted light is called the "ring-down signal," where the ring-down time is defined as how long it takes the signal to decrease below a factor of 1/e. The ring-down time is calculated using the attenuation time of the transmitted light by fitting an exponential decay curve, as illustrated by the black line in Fig. 1

. The
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absorbance and density of the sputtered atoms can be calculated using the ring-down time. Therefore, CRDS is a promising method to perform in situ erosion measurements in Hall thrusters.
The use of CRDS to perform such measurements requires overcoming several challenges.
Fluctuations in the absorbance due to changes in the density of the sputtered particles are one limitation that affects the detection limit. Discharge current oscillations are caused by fluctuations in the plasma density. The ion flux that collides with the wall surface is transient, which causes a variable amount of wear. A previous study showed that the ion current that flows into the wall is synchronized with the discharge current oscillations. Therefore, the absorbance histogram has two peaks with a relatively high minimum detection limit . 14 These observations were ascribed to oscillations in erosion in association with the discharge current oscillation of the Hall thruster at approximately 20 kHz. If the histogram does not have a Gaussian distribution, the measurement uncertainty is derived from random errors and other potential causes, such as fluctuations in the density of sputtered atoms. Thus, a conventional time-averaged CRDS system has a large measurement uncertainty. To reduce this uncertainty, CRDS measurements should be performed during each phase of the discharge current oscillations. Therefore, it is essential to synchronize the erosion measurement system with discharge current oscillations using a time-resolved system. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

A. CRDS system
A schematic diagram of the CRDS system is presented in Fig. 2. A Littrow external cavity diode laser (DL100 pro, Toptica) was used to measure the transition line of titanium at 394.86708 nm in air 15 by scanning the wavelength range from 394.86424 to 394.87224 nm. The mode-hop-free scanning range was approximately 20 GHz with a laser linewidth below 10 MHz, corresponding to 5.2×10 -6 nm.
The probe laser was divided into probe and reference light using beam splitters. The probe light was chopped using a trigger when the ring-down signal exceeded a pre-defined threshold and was modulated to the first-order diffracted light using an acousto-optic modulator (AOM). The laser intensity was reduced using a neutral density (ND) filter to avoid absorption saturation. The peak laser power coupled into the cavity was 1.8 μW; therefore, the peak power in the cavity corresponding to the peak ring-down signal was estimated at 3.6 mW 16 with a mirror reflectivity of 99.95%. The laser passed the cavity 30 mm downstream of the Hall thruster. The cavity length was 0.55 m, and the signal was detected using a photomultiplier tube (PMT). The reference light was used for optogalvanic spectroscopy to obtain the relative frequency of the laser with respect to the absorption frequency of Ti 48 . The light was chopped using an optical chopper and passed through a hollow-cathode lamp (HCL) with a titanium electrode. The titanium spectrum contains numerous peaks due to its hyperfine structure. 17 The spectra were separated as An etalon (free spectral range = 1.5 GHz) was used as the frequency reference. A titanium This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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target was set 30 mm downstream of the laser path. The head of an M6 (10 mm) hexagonal bolt was used as the target. During operation of the Hall thruster, the ions were exhausted before colliding with the titanium target, which caused sputtering of titanium atoms that could be detected in the absorption signal. As a result, the high-reflection mirrors were contaminated with sputtered particles from the Ti target and the wall of the vacuum chamber, which reduced the mirror reflectivity.
Therefore, a gas purge system as created using a 3D printer was installed. This system dispensed a uniform flow of Ar gas fromr four directions to each of the mirrors. In addition, the thruster and high-reflection mirrors were installed in a carbon cylindrical box. The mirrors and thruster were then separated with a carbon wall, and an iris was used for the laser path.
A typical ring-down signal and profiles for the discharge voltage and current are presented in The reference point was observed 2.2 μs after the ring-down signal exceeded 1.4 V, which was set as the threshold because the AOM shutter closed completely within 2.2 μs. When the ring-down signal was attenuated, the decrease from the reference point was fit using an exponential function to calculate the ring-down time and absorbance.
In this work, the discharge current oscillation was locked at 20 kHz using a Volterra engine management system to synchronize the time-resolved measurement with the discharge current oscillation. The Volterra engine is a harmonized power processing unit that can lock the discharge current oscillation at a constant frequency. 18,19 The time of the obtained ring-down signal was then aligned with the normalized time of the oscillation. Thus, the ionization instability in the Hall thruster could be controlled, and the discharge current oscillation could be locked at the applied frequency. The time resolution was set to one-tenth of the oscillation cycle at 5 μs, with a frequency resolution of 1 GHz (wavelength resolution of 0.52 pm).
The phase of the discharge current oscillation dictates the normalized time, which is defined as: The data for fitting were obtained 2.2 μs after the ring-down signal exceeded the threshold due to delay in the devices. The ring-down times were collected with a relative frequency and normalized time for the time-resolved measurements. In the time-averaged CRDS measurements, the ring-down time was averaged in a given laser frequency bin. In the time-resolved CRDS measurements, the ring-down time was averaged over a given laser frequency bin and a given normalized time. Thus, the bin for the time-resolved CRDS measurements was finer than that of the time-averaged results.
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To verify the effect of the time-resolved CRDS, the same data sets were analyzed using both time-resolved and time-averaged methods. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. The propellant was xenon gas, and the flow rate was controlled using mass flow controllers.

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The mass flow rates at the anode and cathode were 0.68 and 0.27 mg/s, respectively. To reduce the This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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influence of heat on the mirrors, the Hall thruster was mounted inside an isotropic graphite box.
During a given experiment, 0.15 mg/s of argon flowed in front of the high-reflection mirrors to avoid contamination by sputtered particles from the target and vacuum chamber walls.

FIG. 4.
Exterior of a Hall thruster.

C. Vacuum facility
The measurements were conducted inside a cylindrical vacuum chamber with a diameter of 1.0 m and length of 1.2 m. The chamber was made of titanium-free SUS304 stainless steel; therefore, it did not affect the CRDS titanium measurements. The chamber was attached to a rotary pump, two turbomolecular pumps, and a cryogenic pump to provide an ultimate pressure below 7.0×10 -4 Pa and an operating pressure of 1.0×10 -2 Pa.

A. Absorbance
The time-averaged CRDS spectrum was calculated using the ring-down time, as shown in Fig.   5. The sample absorbance along the optical axis, (), was calculated as: 16 where ( , ) is the absorption coefficient of the target atoms, x is the position along the optical This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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axis, is the optical length, is the speed of light, ( ) is the ring-down time when sputtered titanium atoms exist in the cavity, and 0 ( ) is the ring-down time when the optical cavity is empty.
The transmitted light is called the "ring-down signal," and the ring-down time is the time at which the transmitted light is reduced to 1/e times its initial value. The absorbance and density of the sputtered atoms was calculated using the ring-down time with absorbers, ( ), and without absorbers, 0 ( ), which can be expressed as follows: where R is the mirror reflectance.
If the absorbance is balanced by the absorption and induced emission, as in Ref. 20, the total absorbance can be expressed as: where is the state degeneracy, and is the state degeneracy.
Integrating Eq. (2) over the frequency and using Eqs. (5) and (6) when assuming the population ratio for the state to state species is negligible provides the integrated absorption coefficient as: Therefore, Integrating this equation along the cavity axis gives the path-integrated number density of the ground This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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Here, the population ratio of the excited to the ground state species is assumed to be negligible due to the small ratio of the excited electron temperature in the plume region to the energy difference between the ground and the excited states of the target resonance line at 3.14 eV. The transition parameters for the ground state of Ti atoms are presented in Table I. 23 During measurements, the laser scan cannot cover the entire absorption line profile because the  Table II.

FIG. 5.
Time-averaged spectrum calculated using the ring-down time.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.   25 of the spatial distribution of the differential sputtering yield. 26 The density of sputtered titanium atoms in the ground state is relatively low around the central axis. As a result, two peaks appear at the relative frequencies of -4.5 and 4.5 GHz. The measurement uncertainty for the time-averaged measurements was calculated to be 29.9 parts-per-million (ppm; 1 ppm corresponds to 10 -6 ), which was evaluated using the standard deviation as shown in Fig. 5. Thus, the path-integrated number density and uncertainty were 1×10 13 and 2×10 12 m -2 , respectively. The uncertainty was 20%, which is relatively large because the absorbance histogram of the bins from -4 to -5 GHz reveals a bimodal distribution instead of unimodal, as shown in Fig. 6. As this was not a Gaussian distribution, the uncertainty was assessed using the standard deviation instead of the standard error. This histogram was obtained from a total of 241 ring-down signals and shows how often each absorbance was obtained in a given This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

B. Time-resolved CRDS
The time-resolved CRDS absorbance signals are given in Fig. 7. The absorbance was large when the normalized time was from 0.4 to 0.5 with a relative frequency from -4 to -5 GHz or 4 to 5 GHz. In contrast, the absorbance was small when the normalized time was 0.0 to 0.2 and 0.8 to 1.0. respectively (the individual points in Fig. 7 were calculated using the data set in Fig. 8 or Fig. 9).
The central axis of the distribution was 97.9 ppm for the 0.4 to 0.5 bin and 86.6 ppm for the 0.1 to 0.2 bin. These data suggest that the amount of sputtered titanium atoms varied over time. In addition, Fig. 8 can be considered as unimodal, indicating a homoscedastic distribution. Therefore, for the time-resolved CRDS measurements, the uncertainty can be evaluated using the standard error and was evaluated as 6.36 ppm. In contrast, the histogram for the -4 to -5 GHz bins for the normalized times of 0.1 to 0.2 did not have a unimodal distribution; therefore, the uncertainty was evaluated from the data variability, which is large compared with the 0.4 to 0.5 GHz bins. This is because the amplitude of the discharge current was not always the same every cycle, giving a fluctuating ion beam current into the target. Consequently, the amount of sputtered titanium atoms was non-uniform, even with the same normalized time.
The absorbance spectrum for normalized times between 0.4 to 0.5 is presented in Fig. 10. These data presented are related to the horizontal line in Fig. 7 for a normalized time from 0.4 to 0.5. In this This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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case, the fitting results indicate that the FWHM of the assumed Gaussian function was 6.3 GHz, and the frequency shift was 6.7 GHz. In addition, a 10% fitting error was assumed for the Gaussian function.
Finally, the path-integrated number density was estimated for each normalized time. Time variations for the path-integrated number density of titanium atoms with the discharge current and voltage are shown in Fig. 11. The path-integrated number density oscillated from 8.3×10 12 to 1.08×10 13 m -2 with the discharge current, which yields an uncertainty of 6×10 11 m -2 . Compared with the conventional time-averaged CRDS, which has a path-integrated number density of 1×10 13 m -2 and uncertainty of 2×10 12 m -2 , the time-resolved CRDS reduces the uncertainty by 30%. In addition, the path-integrated number density appears to lag slightly behind the discharge current. This phenomenon is ascribed to the fact that xenon ions take approximately 1 μs to reach the target, whereas the produced titanium atoms require approximately 2 μs to cross the laser path. Therefore, the peak path-integrated number density shifted by a normalized time of 0.06 relative to the discharge current. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

IV. CONCLUSION
A titanium erosion sensor based on time-resolved CRDS was developed to assess wall erosion in Hall thrusters. The time-resolved CRDS results confirm that the path-integrated number density of sputtered titanium particles oscillated from 8.3×10 12 to 1.08×10 13 m -2 with the discharge current.
Additionally, the studies permitted measuring the uncertainty by assessing the standard error, which improved the uncertainty from 2×10 12 to 6×10 11 m -2 compared to the time-averaged CRDS. The proposed system proved effective at sensing titanium erosion and is suitable to optimize the lifetime of Hall thrusters.
In this study, the spectrum was fit using a Gaussian distribution for simplicity. A finite-element method for the sputtering 27 using the Thompson distribution 28 will be examined in future work. In addition, the intention is to measure the sputtered atom density from the wall using the time-resolved This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI:10.1063/1.5127788