Discharging fused silica optics occluded by an electrostatic drive D. Ugolini, C. Fitzgerald, I. Rothbarth, and J. Wang Citation: Review of Scientific Instruments 85, 034502 (2014); doi: 10.1063/1.4867248 View online: http://dx.doi.org/10.1063/1.4867248 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Shock temperatures in fused silica measured by optical technique J. Appl. Phys. 53, 4512 (1982); 10.1063/1.331191 Observation of surface flaws in fused silica optical fibers Appl. Phys. Lett. 30, 155 (1977); 10.1063/1.89315 Optical frequency dependence of the photoelastic coefficients of fused silica J. Appl. Phys. 47, 4024 (1976); 10.1063/1.323228 Total Optical Attenuation in Bulk Fused Silica Appl. Phys. Lett. 20, 264 (1972); 10.1063/1.1654141 Optical Determinations of OH in Fused Silica J. Appl. Phys. 37, 3911 (1966); 10.1063/1.1707952
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 034502 (2014)
Discharging fused silica optics occluded by an electrostatic drive D. Ugolini,a) C. Fitzgerald, I. Rothbarth, and J. Wang Department of Physics and Astronomy, Trinity University, San Antonio, Texas 78212, USA
(Received 15 December 2013; accepted 18 February 2014; published online 10 March 2014) Charge accumulation on test masses is a potentially limiting noise source for gravitational-wave interferometers, and may occur due to exposure to an electrostatic drive (ESD) in modern test mass suspensions. We verify that an ESD can cause charge accumulation on a fused silica test mass at a rate of 8 × 10−16 C/cm2 /h. We also demonstrate a charge mitigation system consisting of a stream of nitrogen ionized by copper feedthrough pins at 3750 VAC. We demonstrate that the system can neutralize positive and negative charge from 10−11 C/cm2 to 3 × 10−14 C/cm2 in under 2 h. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4867248] I. INTRODUCTION
Charging is a potentially limiting noise source for gravitational-wave interferometers1–3 and other precision measurements of gravitational effects.4, 5 At the Laser Interferometer Gravitational-Wave Observatory (LIGO),6 charge may build up on the surface of suspended fused silica test masses through contact with other materials.7 Static charge could attract dust to the test mass surface, increasing absorption and making thermal compensation more difficult,8 while moving charges would generate fluctuating electric fields that could displace the test mass at frequencies in the interferometer’s sensitive band. The GEO 6009 and Advanced LIGO10 test mass suspensions place each test mass adjacent to a reaction mass with an electrostatic drive (ESD) for fine position control. The ESD is a pattern of high voltage electrodes of alternating polarity; the resulting electric field attracts the dielectric test mass material. Prokhorov and Mitrofanov have found that the ESD causes charge redistribution and a potential noise contribution, with charge accumulating near electrodes of opposite polarity.11 Excess charge can be removed with UV light via the photoelectric effect, but in this case the ESD would occlude the charged surface, and UV light has been shown to create color centers that could increase the absorption of reflective coatings.12 Reid et al.13 are experimenting with conductive oxide thin film coatings to prevent inhomogeneous surface charge distributions. Such coatings would have the advantage of working passively (i.e., not requiring interruption of an experiment to neutralize surface charge), but it is a substantial challenge to change the optical coating without introducing increased absorption or additional mechanical losses. Buchman et al.14 have suggested using alternating beams of electrons and positive ions to neutralize both polarities of charge on an optic. Discharging was demonstrated at Trinity University using nitrogen ions generated by electrons from thermionic emission of a filament,15 and at MIT using nitrogen ionized via contact with high voltage needles.16 But the former technique worked very slowly, while the latter required a sophisticated scratch-built ionizer. a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0034-6748/2014/85(3)/034502/5/$30.00
The purpose of this paper is to verify the charging effects of an electrostatic drive, and demonstrate charge neutralization with nitrogen ionized by a simple high voltage vacuum feedthrough that would be easy to install or replace at a gravitational-wave observatory.
II. EXPERIMENTAL SETUP
The charge measurements were made with a capacitive device called a Kelvin probe. A charge layer on a sample induces a voltage that causes opposite charge to flow to the surface of the probe element. Modulating the capacitance creates an alternating current signal proportional to the potential difference between the probe and sample, which depends on the magnitude of charge on the sample.17 We used a Kelvin Probe S from Besocke delta phi GmbH, which has a 2.5 mm diameter electrode vibrated vertically at an amplitude of 0.5 mm by a PZT. One lead of the AC signal was connected to a lock-in amplifier while the other was grounded to the vacuum chamber. The probe was calibrated by measuring a conducting sample at fixed voltage from −30 V to +30 V, with results shown in Figure 1. Treating the sample as an infinite sheet, one volt of electric potential corresponds to 5.04 × 10−14 C/cm2 . Combining this with the data in Figure 1, we find that the 0.1 mV minimum sensitivity of the probe corresponded to a charge density of approximately 10−15 C/cm2 . Note that the nonzero probe reading at zero applied volts is a constant offset that is a function of the sample material, which will cancel out when we measure charge buildup through the change in probe signal over time. All measurements must be taken in vacuum, since surface charge is rapidly neutralized by water vapor at atmospheric pressure. The layout of our vacuum chamber is shown in Figure 2. Our sample, a representative of Advanced LIGO test mass materials, was a superpolished Corning 7980 fused silica substrate, 7.6 cm in diameter and 0.25 cm thick, with a 30 layer, quarter-wave stack of titania-doped tantala/silica with silica as the top layer as a high reflection coating on one side. The sample rests on a cylindrical aluminum holder, which is attached to a 150 mm translation stage. At one end, the ESD is mounted horizontally 1 mm above the sample, while at the other end, the Kelvin probe is mounted on two perpendicular
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FIG. 1. Kelvin probe calibration.
translation stages, allowing us to make 2.5 cm square maps of charge density. Thus the sample can be kept under the ESD during exposures, and then shifted over to the Kelvin probe for charge measurements. The ESD consists of three microscope slides epoxied together into a rectangular plate large enough to occlude the entire surface of the sample. One side of the plate is covered with a sheet of Kapton insulation, onto which are epoxied the electrode pattern, consisting of six steel strips 3 mm wide with 4 mm gaps between neighboring strips. The strips are wired to two HV power supplies such that each strip is alternate in polarity to its nearest neighbors. When discharging the sample with ionized nitrogen, the ESD is grounded. Our ionizers were Kurt Lesker 5 kV power feedthroughs with either two or eight copper pins. Unless otherwise stated, the pins were trimmed such that the tips were directly below the nitrogen inlet, and the tips filed to points. The power source was a France 7500V 30 mA neon sign transformer attached to a Variac for voltage control. Each pin was connected through a 3.8 watt, 5 M resistor to the transformer’s center tap, for a maximum voltage of 3750 VAC. When the pins are
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FIG. 3. Sample scan from ESD charging measurement; the charge magnitude is calculated by averaging the heights of the two peaks above the center trough.
at a large positive voltage, they attract electrons from nitrogen atoms, creating positive ions, and similarly a negative voltage results in negative ions. Relative measurements of ion production were made with a sampling electrometer consisting of two wires extending across the diameter of the nitrogen inlet section of the vacuum system. A 10V, 0.1 Hz square wave is applied to one, and the current signal from the other is converted to a voltage by a 1 M resistor in a simple low-noise amplifier circuit. III. CHARGE ACCUMULATION FROM ELECTROSTATIC DRIVE
We exposed our sample test mass to the ESD electrodes at ± 600 V for two weeks, followed by two weeks with the ESD feedthroughs grounded, followed by two more weeks with the 600 V terminals reversed. We used LabView to automate scans of the test mass every 12 h. Each scan consisted of 21 measurements at 1 mm intervals along a line perpendicular to the ESD electrodes. The initial scan is subtracted from each to give the change in probe signal since the beginning of the experiment. Figure 3 shows the results of a scan near the end of the initial two-week charging period. The scan shows three peaks, two positive and one negative, at 7 mm intervals, precisely what we would expect from 3 mm wide electrodes spaced 4 mm apart at alternating voltages (the other three peaks are outside of our available scan range). We first calculated the difference in probe signal between neighboring peaks, represented by the two solid black arrows in Figure 3. Averaging these two numbers gave us a measure of the magnitude of charge accumulation at that time. Figure 4 shows the charge magnitude as a function of time. Fitting a line to each region of the plot gives the following charging rates:
r ESD active: 8 × 10−16 C/cm2 /h; r ESD off: (−8 ± 1) × 10−17 C/cm2 /h; r ESD polarity reversed: −1.2 × 10−15 C/cm2 /h.
FIG. 2. Cross-sectional view of experimental setup (not to scale).
Charge relaxation due to surface conductivity should cause the initial charging rate (which is working against the relaxation) to be slower than the discharging rate with the
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FIG. 4. Test mass charge magnitude versus ESD exposure time.
ESD polarity reversed (which is working with the relaxation), and that the difference should be twice the discharging rate with the ESD off. The rate with polarity reversed is in fact faster, but the difference is more than four times the discharge rate with the ESD off, suggesting another physical effect may be present. An exponential fit to the charge data with the ESD off yields a relaxation time constant of 3700 ± 900 h. This is a factor of three smaller than the time constant measured by Prokhorov and Mitrofanov, but this ratio and the time constant value are consistent with previous measurements of our test mass.7 The discrepancy is due to differing methods of cleaning the test mass prior to measurements, which cause different levels of surface conductivity; the Prokhorov/Mitrofanov sample was cleaned in an ultrasound bath with acetone, producing a cleanliness on par with an Advanced LIGO optic at installation, while our sample is dry-wiped, arguably a better representation of the surface cleanliness after months or years of use. The average charging/discharging rate is 10−15 C/cm2 /h, roughly an order of magnitude less than the previous measurement by Prokhorov and Mitrofanov.11 The higher surface conductivity of our sample should result in a slower charging rate, but not by a full factor of ten. Coating differences are unlikely to contribute, since we have previously measured similar discharging rates on coated and uncoated surfaces of the same substrate.12 One possible explanation is that the charging rate is a strong function of the separation between ESD and sample, since we would expect the effect of the ESD to be greater when it is close to the sample. This would also explain the difference in peak amplitudes in Figure 3, if the sample were not perfectly parallel to the ESD, than an electrode that was slightly closer to the sample would generate a larger peak. IV. DISCHARGING WITH IONIZED NITROGEN
We began by determining the optimal nitrogen flow rate for ion generation. Gas from a cylinder of compressed nitrogen flowed through a metering valve into our vacuum chamber. By adjusting the metering valve while pumping on the
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FIG. 5. Ion flux as a function of steady-state pressure (proportional to flow rate).
system, we reached a steady-state pressure proportional to the nitrogen flow rate. We then measured the ion flux with the sampling electrometer as a function of pressure, with the results shown in Figure 5. Ion generation was a maximum between 50 and 60 mTorr. This result was insensitive to the spacing between the two electrometer wires and to the height of the high voltage pins above the sampling electrometer, so we do not believe recombination downstream of the pins affected the measurement at higher pressures. At 55 mTorr, when the turbopump was shut off, the pressure increased at 13 mTorr per second. Given an approximate volume of 0.02 m3 for our system, this corresponds to a nitrogen flow rate of 3.4 × 10−4 L/s, or about 4 × 10−7 kg/s. We use this flow rate for the remainder of our measurements. With the two-pin feedthrough, ion production was evenly balanced between positive and negative ions. But with the eight-pin feedthrough at voltages as low as 75% of the maximum, nitrogen gas discharge occurs, characterized by a large increase in positive ion production and a decrease in negative ions almost to zero. Since the two-pin feedthrough never exhibited this behavior, we used it exclusively for the subsequent measurements. We also measured ion generation versus pin length by starting with an unmodified feedthrough, shortening the pins by approximately 20 mm at a time, reinstalling in the system, and measuring the relative ion production with the sampling electrometer at a fixed nitrogen flow rate. The results are shown in Figure 6. Recall from Figure 2 that the feedthrough is installed on one end of a cross; the central region of the cross extends from 43 mm to 83 mm away from each end. The ion flux appears to increase linearly as the pin extends across this region, implying that ions are being generated along the full length of the pin, not just the tip. The peak at a length of 100 mm may imply that ion production is greater at the tip than elsewhere, and decreases when the tip is no longer in direct line-of-sight to the nitrogen inlet. For each measurement of discharge rate, the test mass was charged by wiping vigorously with a Kimwipe and then pumping down to vacuum. The nitrogen metering valve was
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FIG. 6. Ion production versus pin length. The region between the dashed lines is where the nitrogen inlet is directly above the end of the pin.
FIG. 8. Measured (diamonds) and predicted (solid line) test mass charge versus ionized nitrogen exposure time.
set to give a steady-state pressure of 55 mTorr. The charge level was measured at 64 points in an 8 × 8 grid with 3 mm spacing between points, and the absolute value of these readings were summed to obtain an overall surface charge level. The test mass was then moved under the ESD and voltage was applied to the ionizing pins for 10 min intervals. After each exposure the high voltage was shut off and the test mass was moved back to the Kelvin probe for another measurement. Figure 7 shows a result common to all our measurements—the rate of discharge was exponentially related to the amount of charge on the test mass surface:
A typical example of discharging a test mass is shown in Figure 8. The points represent charge density measurements, while the solid curve is a least-squares fit of Eq. (2) to the data. The fit matches well until the data sharply levels off at a charge density of 3 × 10−14 C/cm2 , or 30 times the minimum sensitivity of our Kelvin probe. The fitted values of a and b imply that even with a large starting charge density of 10−11 C/cm2 , the test mass will reach minimum charge density in under 2 h.
dQ = aQ0 e−bQ/Q0 , − dt
In summary, we have verified charge accumulation from an electrostatic drive at a rate of 8 × 10−16 C/cm2 /h. We have demonstrated charge mitigation with nitrogen ionized by high voltage pins, with the nitrogen flow perpendicular to the pins and generating ions along the entire pin length. We have derived an equation for charge magnitude as a function of time which is an excellent fit to the data, and which predicts discharging from 10−11 C/cm2 to below 3 × 10−14 C/cm2 in under 2 h. By using only minor variations on commercially available vacuum hardware, this ionizing system should be easier to service and replace at gravitational-wave observatories. Absorption measurements of the test mass are still required to ensure the reflective coating is not being damaged by the ion flow.
(1)
where Q0 is the initial charge level, Q is the current charge level, and a and b are unitless positive constants insensitive to the choice of Q0 . Treating Q as a function of time, this differential equation can be solved to yield: Q(t) = −
Q0 ln abt + e−b . b
(2)
V. CONCLUSIONS
ACKNOWLEDGMENTS
The authors would like to thank Valery Mitrofanov, Stuart Reid, and Rai Weiss for their advice, suggestions, and assistance. This work was supported by the National Science Foundation under Grant No. PHY-1068760. This article has been assigned LIGO Document No. LIGO-P1300108. 1 R.
FIG. 7. Measured exponential dependence of discharge rate on charge density.
Weiss, LIGO Technical Note LIGO-T960137 (1996), see http://www. ligo.caltech.edu/docs/T/T960137-00.pdf. 2 S. Rowan, S. M. Twyford, R. Hutchins, and J. Hough, Class. Quantum Grav. 14, 1537 (1997). 3 P. Bender, A. Brillet, I. Ciufolini, A. M. Cruise, C. Cutler, K. Danzmann, F. Fidecaro, W. M. Folkner, J. Hough, P. McNamara, M. Peterseim, D. Robertson, M. Rodrigues, A. Rüdiger, M. Sandford, G. Schäfer, R.
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Schilling, B. Schutz, C. Speake, R. T. Stebbins, T. Sumner, P. Touboul, J.-Y. Vinet, S. Vitale, H. Ward, and W. Winkler, MPQ Report No. 233 (1998). 4 S. Buchman, C. W. F. Everitt, B. Parkinson, J. P. Turneaure, R. Brumley, D. Gill, G. M. Keiser, and Y. Xiao, Adv. Space Res. 25, 1177 (2000). 5 E. G. Adelberger, B. R. Heckel, and A. E. Nelson, Annu. Rev. Nucl. Part. Sci. 53, 77 (2003). 6 B. Abbott et al., Rep. Prog. Phys. 72, 076901 (2009). 7 Ugolini, R. Amin, G. Harry, J. Hough, I. Martin, V. Mitrofanov, S. Reid, S. Rowan, and K-X. Sun, in Proceedings of the 30th International Cosmic Ray Conference, Merida, Mexico, 3–11 July 2007. 8 R. Lawrence, D. Ottaway, P. Fritschel, and M. Zucker, Opt. Lett. 29, 2635 (2004). 9 M. Hewitson, K. Danzmann, H. Grote, S. Hild, J. Hough, H. Luck, S. Rowan, J. R. Smith, K. A. Strain, and B. Willke, Class. Quantum Grav. 24, 6379 (2007).
Rev. Sci. Instrum. 85, 034502 (2014) 10 G.
M. Harry for the LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084006 (2010). 11 L. G. Prokhorov and V. P. Mitrofanov, Class. Quantum Grav. 27, 225014 (2010). 12 D. Ugolini, M. Girard, G. M. Harry, and V. P. Mitrofanov, Phys. Lett. A 372, 5741 (2008). 13 S. Reid, I. W. Martin, A. Cumming, L. Cunningham, M. M. Fejer, G. Hammond, A. Heptonstall, J. Hough, A. Markosyan, P. Murray, R. Route, S. Rowan, and K. Tokmakov, Class. Quantum Grav. 29, 035002 (2012). 14 S. Buchman, R. L. Byer, D. Gill, N. A. Robertson, and K-X. Sun, Class. Quantum Grav. 25, 035004 (2008). 15 D. Ugolini, Q. Funk, and T. Amen, Rev. Sci. Instrum. 82, 046108 (2011). 16 R. Weiss, LIGO Technical Note LIGO-T1100332 (2011). 17 L. Kronik and Y. Shapira, Surf. Sci. Rep. 37, 1 (1999).
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 034502 (2014)
Discharging fused silica optics occluded by an electrostatic drive D. Ugolini,a) C. Fitzgerald, I. Rothbarth, and J. Wang Department of Physics and Astronomy, Trinity University, San Antonio, Texas 78212, USA
(Received 15 December 2013; accepted 18 February 2014; published online 10 March 2014) Charge accumulation on test masses is a potentially limiting noise source for gravitational-wave interferometers, and may occur due to exposure to an electrostatic drive (ESD) in modern test mass suspensions. We verify that an ESD can cause charge accumulation on a fused silica test mass at a rate of 8 × 10−16 C/cm2 /h. We also demonstrate a charge mitigation system consisting of a stream of nitrogen ionized by copper feedthrough pins at 3750 VAC. We demonstrate that the system can neutralize positive and negative charge from 10−11 C/cm2 to 3 × 10−14 C/cm2 in under 2 h. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4867248] I. INTRODUCTION
Charging is a potentially limiting noise source for gravitational-wave interferometers1–3 and other precision measurements of gravitational effects.4, 5 At the Laser Interferometer Gravitational-Wave Observatory (LIGO),6 charge may build up on the surface of suspended fused silica test masses through contact with other materials.7 Static charge could attract dust to the test mass surface, increasing absorption and making thermal compensation more difficult,8 while moving charges would generate fluctuating electric fields that could displace the test mass at frequencies in the interferometer’s sensitive band. The GEO 6009 and Advanced LIGO10 test mass suspensions place each test mass adjacent to a reaction mass with an electrostatic drive (ESD) for fine position control. The ESD is a pattern of high voltage electrodes of alternating polarity; the resulting electric field attracts the dielectric test mass material. Prokhorov and Mitrofanov have found that the ESD causes charge redistribution and a potential noise contribution, with charge accumulating near electrodes of opposite polarity.11 Excess charge can be removed with UV light via the photoelectric effect, but in this case the ESD would occlude the charged surface, and UV light has been shown to create color centers that could increase the absorption of reflective coatings.12 Reid et al.13 are experimenting with conductive oxide thin film coatings to prevent inhomogeneous surface charge distributions. Such coatings would have the advantage of working passively (i.e., not requiring interruption of an experiment to neutralize surface charge), but it is a substantial challenge to change the optical coating without introducing increased absorption or additional mechanical losses. Buchman et al.14 have suggested using alternating beams of electrons and positive ions to neutralize both polarities of charge on an optic. Discharging was demonstrated at Trinity University using nitrogen ions generated by electrons from thermionic emission of a filament,15 and at MIT using nitrogen ionized via contact with high voltage needles.16 But the former technique worked very slowly, while the latter required a sophisticated scratch-built ionizer. a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0034-6748/2014/85(3)/034502/5/$30.00
The purpose of this paper is to verify the charging effects of an electrostatic drive, and demonstrate charge neutralization with nitrogen ionized by a simple high voltage vacuum feedthrough that would be easy to install or replace at a gravitational-wave observatory.
II. EXPERIMENTAL SETUP
The charge measurements were made with a capacitive device called a Kelvin probe. A charge layer on a sample induces a voltage that causes opposite charge to flow to the surface of the probe element. Modulating the capacitance creates an alternating current signal proportional to the potential difference between the probe and sample, which depends on the magnitude of charge on the sample.17 We used a Kelvin Probe S from Besocke delta phi GmbH, which has a 2.5 mm diameter electrode vibrated vertically at an amplitude of 0.5 mm by a PZT. One lead of the AC signal was connected to a lock-in amplifier while the other was grounded to the vacuum chamber. The probe was calibrated by measuring a conducting sample at fixed voltage from −30 V to +30 V, with results shown in Figure 1. Treating the sample as an infinite sheet, one volt of electric potential corresponds to 5.04 × 10−14 C/cm2 . Combining this with the data in Figure 1, we find that the 0.1 mV minimum sensitivity of the probe corresponded to a charge density of approximately 10−15 C/cm2 . Note that the nonzero probe reading at zero applied volts is a constant offset that is a function of the sample material, which will cancel out when we measure charge buildup through the change in probe signal over time. All measurements must be taken in vacuum, since surface charge is rapidly neutralized by water vapor at atmospheric pressure. The layout of our vacuum chamber is shown in Figure 2. Our sample, a representative of Advanced LIGO test mass materials, was a superpolished Corning 7980 fused silica substrate, 7.6 cm in diameter and 0.25 cm thick, with a 30 layer, quarter-wave stack of titania-doped tantala/silica with silica as the top layer as a high reflection coating on one side. The sample rests on a cylindrical aluminum holder, which is attached to a 150 mm translation stage. At one end, the ESD is mounted horizontally 1 mm above the sample, while at the other end, the Kelvin probe is mounted on two perpendicular
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FIG. 1. Kelvin probe calibration.
translation stages, allowing us to make 2.5 cm square maps of charge density. Thus the sample can be kept under the ESD during exposures, and then shifted over to the Kelvin probe for charge measurements. The ESD consists of three microscope slides epoxied together into a rectangular plate large enough to occlude the entire surface of the sample. One side of the plate is covered with a sheet of Kapton insulation, onto which are epoxied the electrode pattern, consisting of six steel strips 3 mm wide with 4 mm gaps between neighboring strips. The strips are wired to two HV power supplies such that each strip is alternate in polarity to its nearest neighbors. When discharging the sample with ionized nitrogen, the ESD is grounded. Our ionizers were Kurt Lesker 5 kV power feedthroughs with either two or eight copper pins. Unless otherwise stated, the pins were trimmed such that the tips were directly below the nitrogen inlet, and the tips filed to points. The power source was a France 7500V 30 mA neon sign transformer attached to a Variac for voltage control. Each pin was connected through a 3.8 watt, 5 M resistor to the transformer’s center tap, for a maximum voltage of 3750 VAC. When the pins are
Rev. Sci. Instrum. 85, 034502 (2014)
FIG. 3. Sample scan from ESD charging measurement; the charge magnitude is calculated by averaging the heights of the two peaks above the center trough.
at a large positive voltage, they attract electrons from nitrogen atoms, creating positive ions, and similarly a negative voltage results in negative ions. Relative measurements of ion production were made with a sampling electrometer consisting of two wires extending across the diameter of the nitrogen inlet section of the vacuum system. A 10V, 0.1 Hz square wave is applied to one, and the current signal from the other is converted to a voltage by a 1 M resistor in a simple low-noise amplifier circuit. III. CHARGE ACCUMULATION FROM ELECTROSTATIC DRIVE
We exposed our sample test mass to the ESD electrodes at ± 600 V for two weeks, followed by two weeks with the ESD feedthroughs grounded, followed by two more weeks with the 600 V terminals reversed. We used LabView to automate scans of the test mass every 12 h. Each scan consisted of 21 measurements at 1 mm intervals along a line perpendicular to the ESD electrodes. The initial scan is subtracted from each to give the change in probe signal since the beginning of the experiment. Figure 3 shows the results of a scan near the end of the initial two-week charging period. The scan shows three peaks, two positive and one negative, at 7 mm intervals, precisely what we would expect from 3 mm wide electrodes spaced 4 mm apart at alternating voltages (the other three peaks are outside of our available scan range). We first calculated the difference in probe signal between neighboring peaks, represented by the two solid black arrows in Figure 3. Averaging these two numbers gave us a measure of the magnitude of charge accumulation at that time. Figure 4 shows the charge magnitude as a function of time. Fitting a line to each region of the plot gives the following charging rates:
r ESD active: 8 × 10−16 C/cm2 /h; r ESD off: (−8 ± 1) × 10−17 C/cm2 /h; r ESD polarity reversed: −1.2 × 10−15 C/cm2 /h.
FIG. 2. Cross-sectional view of experimental setup (not to scale).
Charge relaxation due to surface conductivity should cause the initial charging rate (which is working against the relaxation) to be slower than the discharging rate with the
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FIG. 4. Test mass charge magnitude versus ESD exposure time.
ESD polarity reversed (which is working with the relaxation), and that the difference should be twice the discharging rate with the ESD off. The rate with polarity reversed is in fact faster, but the difference is more than four times the discharge rate with the ESD off, suggesting another physical effect may be present. An exponential fit to the charge data with the ESD off yields a relaxation time constant of 3700 ± 900 h. This is a factor of three smaller than the time constant measured by Prokhorov and Mitrofanov, but this ratio and the time constant value are consistent with previous measurements of our test mass.7 The discrepancy is due to differing methods of cleaning the test mass prior to measurements, which cause different levels of surface conductivity; the Prokhorov/Mitrofanov sample was cleaned in an ultrasound bath with acetone, producing a cleanliness on par with an Advanced LIGO optic at installation, while our sample is dry-wiped, arguably a better representation of the surface cleanliness after months or years of use. The average charging/discharging rate is 10−15 C/cm2 /h, roughly an order of magnitude less than the previous measurement by Prokhorov and Mitrofanov.11 The higher surface conductivity of our sample should result in a slower charging rate, but not by a full factor of ten. Coating differences are unlikely to contribute, since we have previously measured similar discharging rates on coated and uncoated surfaces of the same substrate.12 One possible explanation is that the charging rate is a strong function of the separation between ESD and sample, since we would expect the effect of the ESD to be greater when it is close to the sample. This would also explain the difference in peak amplitudes in Figure 3, if the sample were not perfectly parallel to the ESD, than an electrode that was slightly closer to the sample would generate a larger peak. IV. DISCHARGING WITH IONIZED NITROGEN
We began by determining the optimal nitrogen flow rate for ion generation. Gas from a cylinder of compressed nitrogen flowed through a metering valve into our vacuum chamber. By adjusting the metering valve while pumping on the
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FIG. 5. Ion flux as a function of steady-state pressure (proportional to flow rate).
system, we reached a steady-state pressure proportional to the nitrogen flow rate. We then measured the ion flux with the sampling electrometer as a function of pressure, with the results shown in Figure 5. Ion generation was a maximum between 50 and 60 mTorr. This result was insensitive to the spacing between the two electrometer wires and to the height of the high voltage pins above the sampling electrometer, so we do not believe recombination downstream of the pins affected the measurement at higher pressures. At 55 mTorr, when the turbopump was shut off, the pressure increased at 13 mTorr per second. Given an approximate volume of 0.02 m3 for our system, this corresponds to a nitrogen flow rate of 3.4 × 10−4 L/s, or about 4 × 10−7 kg/s. We use this flow rate for the remainder of our measurements. With the two-pin feedthrough, ion production was evenly balanced between positive and negative ions. But with the eight-pin feedthrough at voltages as low as 75% of the maximum, nitrogen gas discharge occurs, characterized by a large increase in positive ion production and a decrease in negative ions almost to zero. Since the two-pin feedthrough never exhibited this behavior, we used it exclusively for the subsequent measurements. We also measured ion generation versus pin length by starting with an unmodified feedthrough, shortening the pins by approximately 20 mm at a time, reinstalling in the system, and measuring the relative ion production with the sampling electrometer at a fixed nitrogen flow rate. The results are shown in Figure 6. Recall from Figure 2 that the feedthrough is installed on one end of a cross; the central region of the cross extends from 43 mm to 83 mm away from each end. The ion flux appears to increase linearly as the pin extends across this region, implying that ions are being generated along the full length of the pin, not just the tip. The peak at a length of 100 mm may imply that ion production is greater at the tip than elsewhere, and decreases when the tip is no longer in direct line-of-sight to the nitrogen inlet. For each measurement of discharge rate, the test mass was charged by wiping vigorously with a Kimwipe and then pumping down to vacuum. The nitrogen metering valve was
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FIG. 6. Ion production versus pin length. The region between the dashed lines is where the nitrogen inlet is directly above the end of the pin.
FIG. 8. Measured (diamonds) and predicted (solid line) test mass charge versus ionized nitrogen exposure time.
set to give a steady-state pressure of 55 mTorr. The charge level was measured at 64 points in an 8 × 8 grid with 3 mm spacing between points, and the absolute value of these readings were summed to obtain an overall surface charge level. The test mass was then moved under the ESD and voltage was applied to the ionizing pins for 10 min intervals. After each exposure the high voltage was shut off and the test mass was moved back to the Kelvin probe for another measurement. Figure 7 shows a result common to all our measurements—the rate of discharge was exponentially related to the amount of charge on the test mass surface:
A typical example of discharging a test mass is shown in Figure 8. The points represent charge density measurements, while the solid curve is a least-squares fit of Eq. (2) to the data. The fit matches well until the data sharply levels off at a charge density of 3 × 10−14 C/cm2 , or 30 times the minimum sensitivity of our Kelvin probe. The fitted values of a and b imply that even with a large starting charge density of 10−11 C/cm2 , the test mass will reach minimum charge density in under 2 h.
dQ = aQ0 e−bQ/Q0 , − dt
In summary, we have verified charge accumulation from an electrostatic drive at a rate of 8 × 10−16 C/cm2 /h. We have demonstrated charge mitigation with nitrogen ionized by high voltage pins, with the nitrogen flow perpendicular to the pins and generating ions along the entire pin length. We have derived an equation for charge magnitude as a function of time which is an excellent fit to the data, and which predicts discharging from 10−11 C/cm2 to below 3 × 10−14 C/cm2 in under 2 h. By using only minor variations on commercially available vacuum hardware, this ionizing system should be easier to service and replace at gravitational-wave observatories. Absorption measurements of the test mass are still required to ensure the reflective coating is not being damaged by the ion flow.
(1)
where Q0 is the initial charge level, Q is the current charge level, and a and b are unitless positive constants insensitive to the choice of Q0 . Treating Q as a function of time, this differential equation can be solved to yield: Q(t) = −
Q0 ln abt + e−b . b
(2)
V. CONCLUSIONS
ACKNOWLEDGMENTS
The authors would like to thank Valery Mitrofanov, Stuart Reid, and Rai Weiss for their advice, suggestions, and assistance. This work was supported by the National Science Foundation under Grant No. PHY-1068760. This article has been assigned LIGO Document No. LIGO-P1300108. 1 R.
FIG. 7. Measured exponential dependence of discharge rate on charge density.
Weiss, LIGO Technical Note LIGO-T960137 (1996), see http://www. ligo.caltech.edu/docs/T/T960137-00.pdf. 2 S. Rowan, S. M. Twyford, R. Hutchins, and J. Hough, Class. Quantum Grav. 14, 1537 (1997). 3 P. Bender, A. Brillet, I. Ciufolini, A. M. Cruise, C. Cutler, K. Danzmann, F. Fidecaro, W. M. Folkner, J. Hough, P. McNamara, M. Peterseim, D. Robertson, M. Rodrigues, A. Rüdiger, M. Sandford, G. Schäfer, R.
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