HIGH PERFORMANCE VIBRATION ISOLATION FOR GRAVITATIONAL WAVE DETECTION

By C. MIMIS

CONTENTS 1 INTRODUCTION 1 2 EULER SPRING VERTICAL ISOLATION 52 3 PASSIVELY SELF DAMPED CHAIN 86 4 SCOTT RUSSEL HORIZONTAL PRE ISOLATOR 116 5 TORSION CRANK VERTICAL PRE ISOLATOR 140 6 INVERSE PENDULUM HORIZONTAL PRE ISOLATORS 158 7 DOUBLE PRE ISOLATION AND TILT SUPPRESSION 180 8 ANALYSIS METHODS AND EXAMPLES 210 1 INTRODUCTION 1 1 VIBRATION ISOLATION BASIC PHILOSOPHY THE ESSENCE OF VIBRATION IN THIS THESIS IS THE UNDESIRABLE MOTION PRODUCED IN A BODY DUE TO VARYING FORCES ACTING ON IT WHILE THE TERM IS USUALLY APPLIED TO PERIODIC MOTION IN A FREQUENCY RANGE FROM A FEW HERTZ THROUGH TENS OF HERTZ HERE IT IS USED OF MORE RANDOM MOTION INCLUDING FREQUENCIES WELL ABOVE AND BELOW THIS RANGE THE PRIMARY SOURCE OF THESE FORCES AND THIS MOTION IS FROM SOUND WAVES IN THE ATMOSPHERE AND FROM THE CONTINUOUS BACKGROUND SEISMIC ACTIVITY IN THE SURFACE OF THE EARTH ON WHICH OUR EQUIPMENT NEEDS TO BE MOUNTED THIS MOTION IS OF ORDER MICRONS AND USUALLY GOES UNNOTICED UNTIL A VERY SENSITIVE MEASUREMENT IS MADE OR A STRONG EARTHQUAKE OCCURS NEARBY AN IDEALLY ISOLATED BODY IS ONE WHICH IS IN A STATE OF FREE FALL SUCH THAT THERE ARE NO FORCES AT ALL ACTING ON IT TO DISTURB ITS FREE FALL IN ANY WAY FOR AN EARTH BASED SYSTEM THIS CAN BE WELL APPROXIMATED FOR FREQUENCIES ABOVE DC BY OPERATING IN A HIGH VACUUM ENCLOSURE TO ISOLATE FROM SOUND WAVES AND BY MEANS OF A SOPHISTICATED SUSPENSION SYSTEM TO ISOLATE FROM SEISMIC MOTION WHICH IS THE TOPIC OF THIS THESIS EARTH S DC GRAVITATIONAL FIELD MUST BE COUNTERACTED BY A CONSTANT FORCE IN THE VERTICAL DIRECTION AND THE BODY CAN ONLY BE FREE TO DRIFT OVER A VERY LIMITED DISTANCE BEFORE IT MUST BE ACTED UPON BY A VARIABLE FORCE TO KEEP IT WITHIN THE ENCLOSURE THIS DISTANCE COULD BE MADE SOME TENS OF CENTIMETRES BUT SINCE SEISMIC MOTION IN THE ABSENCE OF EARTHQUAKES IS ONLY MICRONS THIS FREE DRIFT DISTANCE MAY BE LIMITED TO A MILLIMETRE OR LESS IN ORDER TO CONSTRAIN THE BODY TO AN APPROXIMATE POSITION WITHIN THE ENCLOSURE A RESTORING FORCE NEEDS TO BE APPLIED WHEN THE MASS MOVES AWAY FROM ITS IDEAL POSITION SINCE THE ENCLOSURE IS CONTINUALLY MOVING UNDER SEISMIC MOTION THIS MEANS THAT A VARYING FORCE WILL CONTINUALLY BE APPLIED TO THE BODY AS A RESULT OF THIS MOTION REDUCING THE VIBRATIONAL MOTION OF THE BODY RESULTING FROM THIS FORCE TO A MINIMUM IS THE PRIMARY PURPOSE OF THE VIBRATION ISOLATION AND SUSPENSION SYSTEM ONE MIGHT IMAGINE A FORCE VERSUS DISPLACEMENT SCHEME IN WHICH ALMOST NO FORCE IS APPLIED TO THE BODY FOR SMALL OFFSETS FROM ITS IDEAL POSITION BUT WHICH IS STRONGLY INCREASED FOR LARGE OFFSETS THE PROBLEM WITH A NONLINEAR SCHEME LIKE THIS IS THAT IT UP CONVERTS PERMISSIBLE LOW FREQUENCY MOTION TO UNACCEPTABLE HIGH FREQUENCY MOTION 1 THIS IS OBVIOUS IF WE TAKE THE SCHEME TO ITS LIMIT BY APPLYING THE NONLINEARITY OF A BRICK WALL A SLOW DRIFT COMES TO A SUDDEN HALT AND REVERSES SO WE ARE LIMITED TO APPLYING A RESTORING FORCE WHICH IS LINEARLY RELATED TO DISPLACEMENT AND INCLUDES A DAMPING EFFECT TO PREVENT OSCILLATING FOREVER THIS DESCRIBES A DAMPED HARMONIC OSCILLATOR AND SUSPENSION SYSTEMS NECESSARILY CONSIST OF SUCH SECOND ORDER STAGES OFTEN REALISED WITH MASSES AND SPRINGS OR PENDULUMS FOR HORIZONTAL MOTION ACTIVE TECHNIQUES MAY ALSO BE APPLIED SUCH AS MEASURING ACCELERATION INERTIALLY AND APPLYING FORCES TO INCREASE THE APPARENT MASS OR MEASURING THE POSITION AND APPLYING FORCES TO CHANGE THE APPARENT SPRING RATE OR EVEN SIMULATING ENTIRE MASS AND SPRING STAGES WITH ELECTRONIC SENSING AND ACTUATION MULTIPLE STAGES ARE NEEDED IN ORDER TO ACHIEVE THE REQUIRED ISOLATION AND THEY ACT AS A MULTI STAGE LOW PASS FILTER PREVENTING THE HIGHER FREQUENCY SEISMIC MOTION FROM AFFECTING THE ISOLATED BODY BUT CONSTRAINING ITS POSITION WITHIN THE ENCLOSURE OR FRAMEWORK AT LOW FREQUENCIES 1 2 GRAVITATIONAL WAVE DETECTION 1 2 1 METHODS OF DETECTION THE BASIC METHOD OF DETECTING GRAVITATIONAL WAVES IS TO SUSPEND A LARGE ELASTIC BODY RESONANT BAR OR A WIDELY SEPARATED PAIR OF TEST MASSES INTERFEROMETER IN SUCH A WAY THAT THEY CANNOT BE ACTED UPON BY ANY WELL KNOWN AND MUNDANE FORCES THE LENGTH OF THE ELASTIC BODY OR THE SEPARATION BETWEEN THE TEST MASSES IS MONITORED BY A VERY SENSITIVE MOTION SENSOR TO DETECT ANY UNEXPECTED MOTION THERE ARE SOME FORCES SUCH AS IMPACTS FROM COSMIC RAY SHOWERS WHICH CANNOT BE ISOLATED FROM BUT WHICH ARE SELDOM ENOUGH TO BE DETECTED BY OTHER MEANS AND VETOED WHEN ALL MUNDANE DISTURBANCES HAVE BEEN PREVENTED OR VETOED ANY INEXPLICABLE SUDDEN MOTION MUST BE CAUSED BY UNEXPLORED FORCES GRAVITATIONAL WAVES FROM ASTRONOMICAL EVENTS BEING THE ONLY CANDIDATES EXPECTED IN THE CASE OF RESONANT BAR DETECTORS INCLUDING THE MODERN SPHERICAL BARS THE PASSAGE OF A GRAVITATIONAL WAVE CAUSES A MOMENTARY STRETCHING AND RELAXING OF THE ELASTIC MATERIAL OF THE BAR WHICH CAUSES A RINGING OR A CHANGE IN THE RINGING AT THE RESONANT FREQUENCY OF LONGITUDINAL STRETCH OF THE BAR THE RINGING MOTION IS DETECTED BY A VERY SENSITIVE MOTION SENSOR BETWEEN ONE END OF THE BAR AND A SMALL TUNED SPRING MASS ASSEMBLY ATTACHED TO THAT END FOR VARIOUS REASONS THIS FREQUENCY IS USUALLY IN THE REGION OF SEVERAL HUNDRED HZ TO 1 KHZ AND THESE DETECTORS ARE USUALLY ONLY SENSITIVE TO HIGH PERFORMANCE VIBRATION ISOLATION 2 COMPONENTS OF THE GRAVITATIONAL WAVE AT FREQUENCIES CLOSE TO THIS RESONANCE AS A RESULT OF THE HIGH FREQUENCY AND NARROW BAND OF DETECTION SENSITIVITY THESE DEVICES ARE RELATIVELY STRAIGHTFORWARD TO ISOLATE FROM SEISMIC DISTURBANCE IN CONTRAST THE LASER INTERFEROMETER DETECTORS ARE A BROADBAND DETECTOR AND RELY ON THE ISOLATION SYSTEMS TO PREVENT THE SEPARATION BETWEEN INDIVIDUALLY ISOLATED TEST MASSES SEVERAL KILOMETRES APART FROM BEING DISTURBED WITHIN THIS BANDWIDTH WHICH IS A MUCH MORE CHALLENGING ENDEAVOUR IN ITS SIMPLEST CONCEPTION AN INTERFEROMETER DETECTOR USES THREE FREELY SUSPENDED TEST MASSES ARRANGED AS A VERY LARGE MICHELSON INTERFEROMETER AS SHOWN IN FIGURE 1 1 A PASSING GRAVITATIONAL WAVE OF A SUITABLE POLARISATION WILL CAUSE SPACE TO BE WARPED OR OSCILLATING GRAVITATIONAL FORCES TO APPEAR SUCH THAT DISTANCES BETWEEN FREELY SUSPENDED TEST MASSES CHANGE AS INDICATED BY THE RING OF BLOCKS IN THE FIGURE THE INTERFEROMETER IS IDEALLY SUITED TO DETECTING THIS TYPE OF MOTION AND WORKS AS FOLLOWS A POWERFUL LASER BEAM IS SENT THROUGH A BEAM SPLITTER MOUNTED ON A CENTRAL TEST MASS AND TRAVELS DOWN TWO PERPENDICULAR ARMS TO BE REFLECTED BACK AGAIN FROM MIRRORS ON TEST MASSES AT THE REMOTE ENDS OF THE ARMS THE DIFFERENCE IN PATH LENGTH TRAVELLED BY THE BEAMS IN THE TWO ARMS DETERMINES THEIR RELATIVE PHASE WHEN THEY RECOMBINE AT THE BEAM SPLITTER AND THIS IN TURN DETERMINES HOW MUCH OF THE RECOMBINED LIGHT EXITS TOWARDS THE PHOTO DETECTOR AND HOW MUCH TOWARDS THE LASER A CHANGE IN PATH LENGTH DIFFERENCE OF ONE HALF OF A WAVELENGTH I E 0 5 M IN SEVERAL KM IS SUFFICIENT TO REDIRECT ALL THE LIGHT FROM THE LASER EXIT TO THE PHOTO DETECTOR EXIT AND THEREIN LIES THE SENSITIVITY OF THE DEVICE PHOTO DETECTOR LASER SOFT SUSPENSION BEAM SPLITTER MIRROR MIRROR TEST MASS TEST MASS TEST MASS 1 2 3 4 5 EFFECT OF A GRAVITATIONAL WAVE ON SUSPENDED MASSES FIGURE 1 1 APPLICATION OF A LASER INTERFEROMETER TO GRAVITY WAVE DETECTION HIGH PERFORMANCE VIBRATION ISOLATION 3 1 2 2 SENSITIVITY A SIMPLE MICHELSON SUCH AS DESCRIBED IS STILL NOT SENSITIVE ENOUGH BY MANY ORDERS OF MAGNITUDE AND VARIOUS SCHEMES ARE USED TO INCREASE THE SENSITIVITY WHICH IS FOUND TO BE DETERMINED BY THE LIGHT ENERGY STORED IN THE ARMS THE MOST COMMON APPROACH IS TO PUT ADDITIONAL MIRRORS THAT ARE SLIGHTLY TRANSPARENT JUST AFTER THE BEAM SPLITTER SO THAT THE SPLIT LIGHT PASSES THROUGH THE BACK OF THE EXTRA MIRRORS AND HAS TO REFLECT MANY TIMES BETWEEN THEM AND THE END MIRRORS BEFORE IT CAN ESCAPE FROM THIS CAVITY TO RECOMBINE AT THE BEAM SPLITTER THIS INCREASES THE SENSITIVITY OF THE BASIC INSTRUMENT BY THE AVERAGE NUMBER OF TIMES THE LIGHT RE TRAVELS THE ARMS HOWEVER WITH THIS ARRANGEMENT THE LASER LIGHT ONLY RESONATES IN THE ARM CAVITIES FOR ROUND TRIP CAVITY LENGTHS WHICH ARE WITHIN A VERY SMALL FRACTION 1 RE TRAVEL TIMES OF AN EXACT INTEGER NUMBER OF WAVELENGTHS THIS POSES A TOUGH PROBLEM FOR THE CONTROL SYSTEM TO INITIALLY ALIGN AND OBTAIN LOCK IN THE PRESENCE OF EVEN VERY SMALL AMOUNTS OF RESIDUAL LOW FREQUENCY SEISMIC INDUCED MOTION THERE ARE ALSO ADDITIONAL SCHEMES WHICH MAY BE EMPLOYED TO RECYCLE AND THUS INCREASE THE LASER AND SIGNAL POWER WHICH DO NOT IMPACT THE SUSPENSION ARRANGEMENTS AND SO ARE BEYOND THE SCOPE OF THIS SIMPLE INTRODUCTION THE BOTTOM LINE IS THAT IN ORDER TO STAND A REASONABLE CHANCE OF DETECTING GRAVITATIONAL RADIATION FROM PREDICTED SOURCES WITHIN THE LIFETIME OF AN EXPERIMENT MOTION SENSITIVITIES OF ORDER 10 20 M HZ ARE REQUIRED AT THIS SENSITIVITY MANY FUNDAMENTAL SOURCES OF NOISE DOMINATE THE SPECTRUM FREQ HZ DISPLACEMENT NOISE M HZ 10K 1K 100 10 10 22 10 20 10 18 10 16 10 14 10 12 10 8 10 10 PENDULUM THERMAL NOISE MEASURED SENSITIVITY MIRROR THERMAL NOISE SEISMIC NOISE TYPICAL URBAN SEISMIC LEVEL 10 6 F 2 SHOT NOISE PREDICTED SOURCES NS NS INSPIRAL SUPER NOVAE FIGURE 1 2 TAMA 300 NOISE FLOORS AND SENSITIVITY ATTAINED IN SEPTEMBER 2000 HIGH PERFORMANCE VIBRATION ISOLATION 4