Understanding the properties of fused silica fibers for
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1. appear to be greater during the day Shedding even more light on the situation alternating the current by switching the above laboratory lights on and off produced sudden spikes in the Vallen Visual AE diagrams If this alternation endured for a significant amount of time then consistent streams of background noise emerged This inductive coupling originated from the proximity of cables carrying high AC currents Current spikes coming from quickly switched circuits and other high frequency currents may also produce this source of electromagnetic interference Fortunately this emergence dissipates over a given period of time However this dissipation period constricted accurate data analysis to a minimal acquisition period As a cleaning tool the pulsing capability of this particular piezoelectric accelerometer enables one to actively reduce these false signatures After proactively inducing an electromagnetic interference initiating pulses from either channel will automatically counter this EMI For future tests magnetic shielding should be taken into consideration Figure 9 A Vallen Visual AE diagram depicting a 20 hour acquisition run with an 11 hour optimal silence period as a result of an absence in light and human activity 2 7 Pulse Method Vallen Visual AE data showed echoes in most diagrams while pulses were emitt2. posses ultra high vacuum compatibility and non dissipative Adjoining the fiber and the mirror an intercessor is used This intermediary is more commonly known as the ear of the construct As seen below in figure 11 the ear serves as a supporting block Reconfiguring the Si O bonds in SiO chains the silicate bonding procedure is the alternate method for attaching or gluing silica fibers This bonding procedure uses extremely pure components such as flat surfaces ultra pure water and the catalyst potassium hydroxide KOH The procedure begins with hydration where a drop of a pure diluter KOH solution is used to wet the surface being glued Next etching occurs from the KOH solution because of the presence of the OH groups As a result of this presence Si O bonds are broken and SiO3 are produced in the solution The last step involves dehydration OH strips the H from the silanol group on the surface forming water Si OH groups dehydration produces Si O Si bridges Ultimately the SiO3 chains connect the two surfaces completing the gluing procedure Figure 13 Images of interferometer mirror with fused silica fibers attached 3 Experimental Results 3 1 Speed of sound Using the Vallen Visual AE diagram time measurements were made during preliminary tests Pulses were sent through the given fiber As pulses were received from the non pulsating piezoelectric accelerometer reception times were recorded These differences in t
3. several designs were tested The design of these fibers are constructed with extreme care and accuracy Virgo in collaboration with Mcintosh from the GEO600 group at Glasgow constructed the required machine for the production of such fibers Mechanically and deliberately the fiber is pulled from a previously synthetically fused silica rod The fiber is heated from pure oxygen and hydrogen gas Fibers constructed in this way have been geometrically characterized with a computerized microscope However this mechanical design for producing fibers has been modified in order to produce current fused silica fibers for testing After producing the fused silica fiber certain tests must be run in order to understand the behavior of the fiber For instance due to the sensitivity of the fiber s surface any significant scratch can dramatically reduce the breaking strength of the fiber In fact the slightest contact with the fiber can break the fiber These fibers must be handled with extreme care This sensitivity was held in mind throughout the entire fused silica fiber installation process performed during this project Another important aspect of these fibers behavior is the events that lead up to a complete break in the material Although having high degree of durability it is important to understand the imperfections that accompany this system of suspension In correlation to the fibers breaking point understanding the effectiveness of the silica bo
4. data file shows six isolated disturbances within the fiber during an overnight test run Figure 7 Vallen Visual Acoustic Emission diagram showing six incidences of possible internal a SS SS SS S ES S SS SE SS SS S ee aT aie oOo Oo oOo D nN uw t on i 5 i Eo H 5 ye i 2 i a EE SS ee 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000 65000 disturbance Using the wave applet feature of the Vallen Acoustic Emission system a particular Vallen Visual AE diagram was analyzed and converted into a 3 dimensional image of the respective hit s frequency These images consisting of 4 peculiar hits illustrates a possible micro crack detection Upon reviewing these graphs there exists a slight difference in the wavelet coefficient and the intensity of the 3D graphs in direct correlation to their respective energies This correlation in future tests may establish a way for determining deformations within the fused silica fiber In addition to verifying these deformations it may be possible to determine the crack width geometry and location Although crack length and geometry may prove to be most challenging within the allotted programs finding the source of propagation can be achieved by analyzing the recorded hit energy If the energy appears to be greater near a particular accelerometer then the disturbance originated close to that particular piezoelectric In this ca
5. 0 56 2 250 0 11414 4 163E02 40 0 oo i 462 2565 462 256500 94 5 6 6 114 6 17 167E0O4 40 0 oo i 461 9797 461 979700 56 2 280 0 11302 4 161E02 40 0 00 05 462 6638 462 663800 94 5 6 8 114 6 17 167E04 40 0 00 05 462 3869 462 386900 56 2 260 0 10252 8 156E02 40 0 oo 463 0710 463 071000 94 5 72 0 114 6 i7 167EO4 40 0 oo e 462 7940 462 794000 56 2 280 0 11587 2 162E02 40 0 oo 463 4782 463 476200 94 5 6 8 114 6 17 167E04 40 0 00 05 463 2013 463 201300 56 5 20030 11372 8 163E02 40 0 oo 463 8853 463 885300 40 4 0 2 0 2 329E 1 40 0 00 05 483 1449 483 144900 94 5 6 8 114 6 167E04 40 0 A 00 05 463 6085 463 608500 att N 4 e N Sb HPH N CE CES eE E chek Eer Ne Ne Ne Ne DY P DY WW Oot CRo sas ies T on O N H Ht 2 Fa ip m ONE Se he Be foot AO feo Arei CESCE ct ct ict ct sch ct sch ck ict ct e NN HFN HPN PDN PD pe nOwdoOnoOoOanaoendgn oa Nw B W hb WB B bh A bh bh Figure 12 Vallen Visual AE display of a hit chart indicating the amplitude count energy and time 2 8 Silica Bonding As a component of understanding the fiber s behavior exploring the bonding capabilities is required as the fiber is too fragile for any type of welding Gluing the fibers as a means of attaching the fiber to the interferometer mirror is the better option Similar to the fused silica fiber the bonding agent must be a clean solution
6. Aaron D Spooner Louisiana State University 26 July 2011 University of Florida International REU for Gravitational Wave Physics Host Institution Sapienza Rome Italy Mentor Paola Puppo Project Understanding the properties of fused silica fibers for Virgo s current Gravitational Wave interferometer mirror suspensions Abstract The purpose of this project is to understand the intrinsic properties of the fused silica fibers are installed in Virgo s current interferometric detector Virgo experiment These fibers will provide suspension for the Virgo interferometer mirrors Significantly reducing thermal noise emissions these fused silica fibers are highly implemented Currently the properties of the silica fiber are under further investigation Utilizing various techniques to monitor the fiber s properties investigational results will be analyzed and recorded prior to the fiber s installation Additionally realizing bonding methods for the fiber mirror connection is another behavioral priority 1 Introduction 1 1 Gravitational Waves Introduced in 1916 and emerging from Einstein s general theory of relativity gravitational waves are disturbances or perturbations in space time These propagations occur from accelerating non symmetric mass distributors such as orbiting pulsars and black holes However these ripples in space time are practically infinitesimal in length Although indirectly verified as a result of discrepanc
7. Fourier Transform Two fast Fourier transform FFT plots were produced using the Vallen acoustic emissions program FFT avg applet The first plot figure 13 represents pulses emitted from channel 2 and the output as denoted by channel 1 is seen through the second plot figure 13 Another set of plots were taken in the same fashion however the pulses were sent through channel 1 and received by channel 2 A ratio of these two scenarios were taken and are being analyzed by researchers at the University of Rome Vallen TR FFT Averager 82010 202 Ji a0 100 no 120 File E Data Acquistion TFB tra Sets 1 to 10 Date 23 07 2011 Figure 15 Image of FFT depicting waveform produced by pulses sent through channel 2 b e gt TIE v we va TFT mag ET coy i i 7 sae ert urma PTA UNT Figure 16 Image of FFT depicting waveform produced by pulses received through channel 1 4 Conclusion The acoustic emission analysis of silica fibers described in this report has several applications for understanding the properties of the fused silica fiber With further investigations deformations as well as events that occur prior to a possible break in the fiber can be isolated and studied After shielding the piezoelectric from electromagnetic disturbances properly securing the cables attached to these accelerometers and establish an even smoot
8. ad to be dealt with on a constant basis Initially using metallic clamps to keep the accelerometers in place the surface contact of the accelerometers were appropriate and extra noise was nonexistent at that moment in time Realistically the test load mounting design prevents the implementation of any externally attached mechanism such as a clamp Additionally the added weight would produce an unbalanced system for the test load However for that particular moment in time the configuration was suitable for preliminary test runs These tests allowed for further insight into the sensitivity of the accelerometer To pause for a moment it is important to comprehend the mechanics of the accelerometers used in this experiment An accelerometer measures the respective or proper acceleration For the purpose of this experiment piezoelectric accelerometers are implemented in order to study dynamic mechanical changes Piezoelectric accelerometers are well known transducers for their remarkable ability to measure the exact vibrations of a given system In this experiment vibration within the given fiber can be detected with these piezoelectric instruments An accelerometer also senses the surrounding seismic activity Through electronic integration and computer interfacing these piezoelectric devices can provide information pertaining to the velocity as well as displacement of any disturbance With no external power supply or movable components these i
9. by channel 1 bottom Figure 11 Vallen Visual AE diagram showing hit depicting echoes from both channel 2 and channel 1 counterparts respectively a ae a TD ny Ts Sy ee ea ee 85 Aq asion SWH Echo s produced with channel 2 as 40 95 dB Echo s produced with channel 1 as source or pulse producer source or pulse producer 2D1 CHAN 1 m CHAN 2 7 CHAN 3 CHAN 4 CHAN 5 CHAN 6 CHAN 6 _CHAN 5 _CHAN 4 _ CHAN 3 CHAN 2 CHAN 1 2 A R D CNIS E TE THR FLAG HHMMSS MSEC NSEC dB us us eu dB MRSFXCTAEDN hhrmss ms ps ms ps 56 5 280 0 10256 0 875 155802 40 0 R c 00 05 24 459 8134 459 613400 94 5 7 0 114 8 17 167E04 40 0 00 05 25 4595364 459 53 6400 S6 5 279 868 1136976 669 162E02 40 0 00 05 25 460 2207 460 220700 94 5 7 0 114 6 17 167E04 40 0 00 05 26 459 9436 459 943600 S655 260 2 ti372 6 913 164E02 40 0 00 05 26 460 6276 460 627600 94 5 7 0 114 8 17 167E04 40 0 00 05 27 460 3506 460 350800 56 5 260 0 11256 4 904 160E02 40 0 00 05 27 461 0350 461 035000 94 5 6 8 114 6 17 167E04 40 0 00 05 28 460 7581 460 758100 56 2 279 8 11356 8 868 159E02 40 0 oo 28 461 4424 461 442400 94 5 6 65 114 6 17 167E04 40 0 oo 29 461 1653 461 165300 56 2 279 8 11372 6 696 162E02 40 0 oo i 461 8494 461 849400 4074 0 2 0 2 I 2 amp lEzl 40 0 0 313 00 9 29 486 8716 466 871600 94 5 7 0 114 6 17 167E04 40 0 00 05 461 5724 461 57240
10. ed from channel 1 and channel 2 If the acquisition recorded pulses for an extended period of time then several echoes emerged These echoes or receiver counterparts proved to be quite useful for analyzing particular aspects of how the pulse effected the fiber In reference to the existence of cracks in the material these pulses led to further deformation investigations Using these pulses established a method that could be controlled and monitored With this Pulse Method in order to identify external disturbances pulses were sent through both channels and studied The echoes hit energy time delay and amplitudes were recorded Pulsing also illustrates the direction of the wave propagation In reference to the figure indicate below if pulses are input from the test load then the difference in amplitude between the two sensors appears greater than pulses emitted from the sensor attached to the mounting bracket Record amplitude diff Also during this particular run refer to graph the reception of pulses at the top showed displayed hits of slightly different amplitudes and energies The pulses received at the base followed a more linearly consistent pattern record amp and at what time duration Vallen TR Viewer Wata Acquisition Wulse Method tra Fie Edt Heb oo 4 Sampled Signal Amplitude jmV Amplitude mV b gt Figure 10 Image of a Vallen Visual TR Viewer graph of a pulse sent through channel 2 top and recieved
11. ficient for the purposes of the experiment Figure 4 Picture of pipe set up with air inlet left and Vacuum gauge sensor right attached Prior to configuration as an effort to optimize the vacuum and eliminate all leaks the Leak Detector was implemented This process incorporates He as a method of determining if there are any porous areas that could serve as potential air inlets As a result of Helium s low mass and low percentage in atmosphere this element is used in order to bombard a given area as a means of detecting a leak Referred to as the outside inside helium leak testing technique the component being tested is connected to the detector and vacuum sealed After establishing a vacuum within the attached component Helium is sorayed over the entire surface Within the detector there lies a mass spectrometer If the Helium penetrates any portion of the component being tested then the mass spectrometer will detect the leaked Helium As this system can detect leak rates up to 1 8x10 mbar the detector was most favorable for the desired 1x10 vacuum 4 Figure 5 Image of leak detector 2 4 LED lighting system design for proper illumination After assembling the vacuum chamber it soon became apparent that the inside of the chamber was extremely dark In response to this lack of visibility a LED lighting system was designed in order to monitor the preliminary Aluminum fiber The components of this system were quite s
12. h wax distribution or the contact surface proper silent runs can be achieved With an insulated system fibers can be analyzed thoroughly and efficiently Also in order to reduce mechanical noise an apparatus that allows for a dually decoupled system may reduce virtually all sources of external noise This dually decoupled set up would detach both piezoelectric accelerometers from the mounting frame Therefore with a decoubled system future fused silica fibers can be analyzed in complete silence Acknowledgements would like to thank the National Science Foundation for funding this summer IREU program the University of Florida Physics Department for offering me this incredible opportunity and the University of Rome Sapienza in Rome Italy Also would like to thank Paola Puppo Andrea Conte Maurizio Perciballi Ettore Majorana for helping me throughout the course of this summer Finally would like to send a special thank you to Andrew Dwayne Spooner for scientific inspiration 5 References Bruel amp Kjaer Piezoelectric Accelerometers and Vibration Preamplifiers The Vallen system AMSY 5 User Manual P Amico L Bosi L Carbone L Gammaitoni F Marchesoni Michele Punturo F Travasso H Vocca Monolithic fused silica suspension for Virgo gravitational waves detector Vol 73 No 9 September 2002 Leak Detector Methods A comparative Study of Technologies and Techniques Short Version Michele Punturo Monolithic Suspensio
13. he difference in time between channel 1 and channel 2 cannot be measured for values less than 100 micro seconds Additionally the zoom feature breaks down at a certain point and displays inaccurate scales As the scale approaches set intervals of 100 micro seconds the linear spacing of the chart fails to produce proportionality After understanding the vallen acquisition system the next step involved establishing a suitable contact without the use of metallic clamps As the provided magnetic clamping mechanism did not provide for a balanced system nor a suitable contact as a result of the material s weak magnetic attraction wax was the appropriate and non invasive option The applied wax must be uniformly distributed between the accelerometer and the surface on which it is being applied Failure to establish a smooth even contact results in extra noise in the Vallen Visual Acoustic Emission diagrams Even though in most cases this noise was confined to a certain amplitude range the interference inhibited proper analysis In order to detect isolated incidences within and around the fiber the system must maintain silence at all times In reference to figure 2 the noise was confined to amplitudes ranging from 40 to 43 5 dB This confinement allowed for proper background noise extraction Knowing the set range of interference it was possible to properly adjust the accelerometer Eventually with practice and small evenly spaced coatings of wax the s
14. ies in pulsar 1916 13 predicted period gravitational waves have not been detected as of date Unlike electromagnetic waves gravitational waves propagate throughout the universe seamlessly These waves do not interact with matter From an experimental view point such a detection may seem impossible or too improbable for accurate findings On the contrary several sites have been established to detect these perturbations in space time Using a Michelson Morley Interferometer design such sites known as LIGO GEO600 and VIRGO have been constructed in order to accomplish this task A shared concern for these detectors is the existence of external noises that inhibit instrument sensitivity and accurate detection The subject of this report is based ona particular gravitational wave interferometer located in Cascina Italy known as VIRGO The Virgo interferometer houses a monolithic suspension design that encompasses a fused silica fiber as a means of reducing thermal noise activity 1 2 Silica Fiber As metallic wires produce thermal noise due to internal friction the monolithic suspension design proved to be highly favorable In more concrete detail a low dissipation material such as fused silica fibers are implemented in the Virgo gravitational wave detector as a more appropriate solution In conjunction with the lack of thermal noise production the material s breaking strength is highly trustworthy In the early stages of the fiber s development
15. ime were displayed on the Vallen Visual AE value chart The measured Steel wire length was 7938 m Using the equation for velocity and with this given length and a time delay of number the resultant velocity for the speed of wire within the Steel wire was number Ax om ee The expected value as calculated by using the young s modulus and fused silica density v Young s modulus equation Y 7 Density p Likewise this method of measurement was applied to the fused silica fiber The fiber length average time delay resultant velocity were the following 8m 00029s 2758 m s Id DSETCHAN A R D CNTS E TE RMS THR PAO FLAG HHMMSS MSEC NSEC dB us us eu uV dB mV MRSFXCTAEDN hhmmss ms us ms us La Label 1 12 58 Resume DT giovedi 9 giugno 2011 Host Time 12 58 La Label 2 12 59 Pulsing channel 1 167 4 9 8 344 5 345601 2 840 0 0 000 C 00 00 51 376 0556 376 055600 249 0 78 8 1088 0 70 752E00 8 940 0 0 000 c 00 00 51 376 3215 376 321500 167 4 9 8 344 5 346601 2 740 0 0 313 C 00 00 52 376 4628 376 462800 249 0 55 6 1078 4 72 754E00 8 940 0 0 313 R c 00 00 52 376 7518 376 751800 167 4 9 8 344 5 345601 2 840 0 0 000 C 00 00 53 376 8700 376 870000 249 0 75 8 1109 2 71 770E00 8 940 0 0 000 c 00 00 53 377 1390 377 139000 Figure 14 Vallen Visual Acoustic Emission AE hit information display chart As indicated above these hits are a result of pulsating the accelerometer by pulsing channel 1 3 2 Fast
16. imple Using only a basic resistor switch 9 volt battery and LED a light source was established and attached underneath the top mounting bracket Figure 6 LED lighting system control box 2 5 Tests for the fused silica fiber On July 4 2011 installation day occurred The fused silica wire was installed and setup tests were run in order to calibrate the accelerometers With the surface under the attached accelerometer partially missing due to a gap within silica fiber s mounting ring a poor contact was established Despite the lack of surface area in contact background noise did not appear as the accelerometer was properly aligned with a smooth even wax coating Several test were run after this installation Also at the end of most days the Vallen Acoustic Emission system remained running throughout the night in order to detect any disturbances within or around the fiber After compiling data for two weeks in this way certain diagrams registered several disturbances These disturbances were predicted to be micro crack detections A micro crack can be defined as any microscopic crack or fracture within the given material Deformations could appear as slits or a rip with a wide assortment of geometries Despite the impeccability of the material these deformations could readily appear at any given moment in time as a result of a diminishing bonding strength in the material Supporting the existence of micro cracks Vallen Acoustic Emission
17. n S Rowan J Hough amp C A Cantley Bonding amp visual inspection of preliminary test ears July 2005
18. nd with current Virgo interferometer mirrors must also be taken into consideration 2 Experimental Methods 2 1 Experiment set up The apparatus and layout of the entire experiment has been confined to a vacuum chamber monitored via PC utilizing Vallen Acoustic Emission systems and programs A specially designed mounting unit has been established to run preliminary tests on a 79 38 cm long Aluminum fiber Attached above the mounting bracket and in direct contact with the given fiber there rests an accelerometer with a denoted channel number Likewise another accelerometer with a different denoted channel number is attached to the top of a 5 6 kg test load The designation of weight for the given test load was a direct result of proportionality to the interferometer s mirror weight in conjunction with its mounting system The weight has been slightly adjusted to test the fiber at a greater strain As testing practices improved and installation procedures mastered the silica fiber was analyzed under this mounting mechanism The purpose of this design is welcomed as it is required to simulate the expected hang length of the silica fiber as well as support its distinct vacuum chamber design The chamber design or hat has incorporated a metal with properties that appear to be closely related to most aluminum alloys as it is not magnetic The mechanism stands at 1 1 m and has a base with a diameter of 60 m which supports the framework of the mechani
19. nstruments are incredibly compact and durable As spherical wave propagation registers at different moments in time between the two separately placed accelerometers the detectors will record these distinct moments in time With this statement in mind the preliminary experiments consisted of hitting or tapping the test load in an effort to calculate the velocity of sound through the given metal At this stage in the experiment channel 2 was assigned to set a top the mounting bracket and channel 1 was placed on the test load hanging directly below The Vallen Acquisition system was set to record as a metallic pressure vessel with the standard factory default settings With the distance set at 13 5 centimeter which proved quite acceptable as it was chosen to be well within the diameter of the test load vibrations were induced in five distinct isolated hits The hits or taps were oriented at certain corners of the surfaces in order to understand how the accelerometer would register the hits As predicted hits closer to the accelerometer appeared first with a greater amplitude and energy In similar fashion hits farther away produced shorter amplitudes and weaker energies Using this information the preset distance was divided by the difference in time of the two channels in order to produce the rate of propagation or speed After reviewing the results apparently the sensitivity of the Vallen Visual AE system is insufficient The problem emerges as t
20. se the energy appeared higher near the test mass In similar response the energy appeared diminished near the mounting bracket or red sensor Disturbance prior to micro crack event Micro crack intiated near test mass 3D Representation of WT Coefficients 3D Representation of WT Coefficients SEAS RN VT Me ys i enis D D f Z O Micro crack detected by red sensor 3D Representation of WT Coefficients Tv pe WT Coefficfents Figure 8 Possible micro crack detection as depicted by this 3 dimensional progression 2 6 Electromagnetic interference EMI When using piezoelectric accelerometers several factors must be taken into consideration in order to eliminate as much background noise as possible To name a few extracurricular inputs not pertaining to vibration related outputs transverse vibrations poor mounting base bending high sound levels humidity high and low temperatures x rays gamma rays and electromagnetic fields all contribute to false vibration measurements Eliminating several known erroneous inputs the remaining false input that shall be discussed as it is one of few verified false signatures pertains to electromagnetic fields This electromagnetic interference or EMI emanates from laboratory lighting as denoted by several Vallen Visual AE diagrams Reviewing the data and comparing the densities of hit points the amount of vibrations recorded within the system
21. sm s mounting bracket The circular base has inscribed within its surface a secondary ring that is required for O ring insertion This secondary ring is required for establishing a vacuum once the O ring has been inserted If the O ring is not properly aligned with this inscribed ring then a proper vacuum cannot be achieved After lowering the chamber the apparatus is contained and the inside is only visible through a single viewing port 68 m above the ground Fortunately it is possible to see everything within the chamber Unfortunately a light source is required for better illumination and construction of this lighting system will be discussed at a later point in this report Figure 1 mounting mechanism designed to support fiber left and the chamber right used to create a suitable vacuum to simulate Virgo conditions 2 2 Early test with Aluminum fiber To begin understanding how to monitor the fused silica fiber was the main concern in the early stages of this project Testing the sensitivity of the accelerometers and deriving a method of disturbance isolation served as the first challenge In addition to the sensitivity of the accelerometer initiating a direct even contact served as another task Second isolating the minute deformations within the wire proved to be extremely troublesome Lastly establishing a consistently stable platform as well as environment for the detectors provided an unwanted challenge that nevertheless h
22. ystem achieved an adequate silence level As it was extremely difficult to eliminate all forms of background noise at this stage in testing the elimination of interference induced by an uneven contact was a considerable achievement Figure 2 Image of 5 6 kg test load with channel piezoelectric accelerometer attached and designated as channel 1 or green sensor Figure 3 Diagram illustrating improper wax distribution as indicated by an uneven surface or un balanced accelerometer Amp dB i E 2 3 Assembly of Vacuum Chamber Preliminary tests were run on the Aluminum fiber with the Vallen Acoustic Emission system assembly of the vacuum chamber began with locating and allocating special pipes Next while wearing latex gloves pipes must be thoroughly cleaned with alcohol before any connections are made When every component has been properly cleaned pipes are adjoined with O rings After inserting these O rings into the rim of the pipe clamps known as ties were attached around the adjoined pipes in order to establish an air tight system Following pipe assembly certain monitoring instruments were attached to open ended portions of the pipe Specifically the left port was designated as the air inlet and the right port functioned as a conduit to the Vacuum Gauge controller The Vacuum Gauge provided digital readings of the pressure within the chamber This device allowed one to determine whether or not the vacuum was suf
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