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- 1. + Lamiya Mowla Cool Mirrors to Adviser: Prof. Rainer Weiss Detect Gravity Waves Prof. Robbie Berg
- 2. + Overview Background Gravitational waves and LIGO Cryogenic detector is cool The experiment What – cool mirrors Why - to reduce thermal noise How – I’ll explain When – good question
- 3. + Gravitational Waves Ripples in the fabric of space- time due to large amounts of accelerating mass. Predicted by Einstein in 1916 as part of Theory of General Relativity. First evidence from the Hulse- Taylor Pulsar experiment 1974.
- 4. + Gravity Waves Gravity waves: Stretch and squeeze space. Slow down and speed up rate of flow of time. Two polarizations, axis rotated at 45 degree Plus polarization Cross polarization
- 5. + Gravitational Wave Spectrum Sources Present Detectors Future Detectors Strain h Wavelength λ
- 6. + Astrophysical sources for LIGO h Strain = ΔL/L 10 -21 λ
- 7. + Laser Interferometer Gravitational wave Detector (LIGO) LIGO Hanford LIGO Livingston
- 8. + Michelson Interferometer
- 9. + Thermal Noise Fluctuation due to Brownian motion of particles. Fluctuation Dissipation Theorem The admittance of fluctuation in a system is proportional to the dissipation in the system. Lower thermal noise Lower dissipation Higher Mechanical Q
- 10. + Mechanical Q Q is the ratio of elastic restoring force to dissipative force. Measured by ring-down time of vibration. How to achieve high Q? Q = π f0τ
- 11. + Fluctuation Dissipation Theorem Q related to “loss angle” υ by υ(ω) = υ(ω)viscous + υstructural + υ(ω)thermoelastic Vacuum Clever designing Brownian Motion
- 12. + Silicon at 120 K Linear expansion coefficient 0 at 120 K. No Brownian Motion hence no thermoelastic damping at 120 K. Improves mechanical Q of the mirror. Linear Expansion = 0 120 K
- 13. + Third Generation LIGO Proposed to be operated at 120 K. Silicon mirrors and pendulum suspension to be used. Mirror and fiber to be cooled down radiatively to 120 K using : Liquid nitrogen High emissivity coating. Is this feasible?
- 14. + The Experiment Measure the emissivity of a cooled silicon mirror, with and without using high emissivity coating. Dielectric Measure the mechanical Coating Q of the silicon with and without the coating. High-emissivity coating
- 15. + The Silicon Wafer Single-crystal Prime CZ Silicon wafer. 2-inch diameter and 0.05 inch thick. Double-side polished.
- 16. +The Vibrational Mode 6 holes drilled around the nodal line of radius 0.68” using Poisson ratio f0,1 = 7.3 kHz
- 17. + The Dewar • Double chambered He dewar. • Both chambers filled with liquid N2. • Pumped down to 10-7 Torr (10-5 Pa).
- 18. + Suspending the Wafer 8 mm Insulators
- 19. + The Setup Si Diode Al Ring Dale Resistor Si Wafer Teflon Film Resistor Tube Steel Electrode Nylon Wire Screw
- 20. + The Setup
- 21. + Temperature Control Temperature Micro- controller For “Boot- Dale Resistor Strapping” Film Resistor Si Diode PRA D ε(λ) = PRAD / 4σA (ΔTSi-LN) TLN3
- 22. + Measuring the emissivity of the wafer PRAD = σAε(TSi4 – TLN4) Where, PRAD = Power input of the film resistor A = Surface area of the wafer TLN = 77 K Tsi = 120 K σ = Stefan-Boltzmann Constant = 5.670373(21)×10−8 W m−2 K−4
- 23. + Measuring the Q Al Ring x d ~ 8 mm VPlateαVSense Q-circuit Q = π f0 τ
- 24. + Q - Circuit d x VPlateαVSense
- 25. + Coating
- 26. + Picture of the whole setup
- 27. + Acknowledgement
- 28. + Heat Transfer PGas Conduction = 8 x 10-6 W PNylon = 6 x 10-6 W PRadiation = 3 x 10-4 W PGas Conduction =8 x 10-6 W
Editor's Notes
- Thank you all for coming out here this morning. Today I’ll be talking about my thesis research that I started over the summer. My project is to investigate the radiative cooling of silicon mirror for the third generation LIGO, and during the next 25 minutes I’ll explain what that means.
- I’ll first give a brief overview of the background on gravitational wave, LIGO and why a cryogenic gravity detector is cool. For the interest of time, I’ll keep this discussion short, but I’ll be happy to answer any questions, so please feel free to interrupt me. Next I’ll talk about the project itself, what progress I’ve made so far and what I hope to accomplish within April.
- GW are distortions in the space-time curvature created by large amounts of accelerating masses, or energy.It was first predicted by Einstein in the Theory of General in 1916. So we are still within a century of the prediction, and hopefully it’ll be detected before the century is over. Evidence of GW was found from HTP experiment, where the decay of the orbit of the two neutron stars, once of which is a pulsar, gave evidence of energy being carried away by GW. The neutron stars are about 1.4 solar mass each, and you can see the ripples being created due to their motion. And that’s what the GW does.
- GW stretches and squeezes space, and slows down or speeds up rate of flow of time.The gravitational waves have 2 polarizations, plus and cross. Here you can see what will happen to this circular arrangement of mass if GW passes through it.Now what gives rise to these waves in our sky.
- This graph shows the spectrum of our known sources of GWs, and the field of view of the possible detectors.The horizontal axis shows the wavelength of the GWs, and the vertical axis shows their strain, which is the fractional change in length that’ll be caused the wave.Now I’ll zoom into the window of LIGO.
- You see the sources for LIGO are black hole binaries, neutron star binaries, and neutron stars. (MRI – mass ratio inspirals).But notice the strain that these GWs will produce – it’s a part in 10^21. That’s mind-blowingly tiny. It means the GW from a NSB will change the length of a meter scale by less than a millionth of a size of a proton. And LIGO is promising that it’ll detect just that tiny tiny distortion.
- Behold the LIGO, laser interferometer gravitational wave detector. There are 3 detectors in 2 observatories, 2 in Livingston, 1 in Hanford separated by a few thousand miles. The reason for having 2 observatories is have confidence in detection, and also to locate source by triangulation.
- These detectors are Michelson interferometers with 4km long arms. These partial end mirrors create a cavity, which allows multipass of beams increasing the effective length the laser beam is travelling. The laser beam comes out from here, splits at the beam splitter, gets reflected from the end mirrors and comes back. Now when the two arms have equal length, they just cancel each other and no light is detected at the photodetector.However, when GW passes, one arm gets bigger and the other shortens and vice versa, so the light now travels different length, and is no longer cancelled out when it reaches this point, and a signal is detected by the photodetector. Now is detection depends strictly on the change in length between surfaces of the mirrors, and any other factor which might cause the surface to move will give rise to noise preventing the GW from getting detected. And one such noise is thermal noise.
- Thermal noise is the fundamental inevitable kind of noise due to brownian motion of particles. The external air particles, or the movement of the particles within the mirror itself. Now, one way of reducing this is, is as the name suggests, to go to lower temperature. But there is another beautiful way of doing it, by utilizing the fluctuation dissipation theorem. It states that the admittance of mechanical vibration in a system is proportional to the dissipation in the system. Hence the strength of thermal noise depends on the dissipation in the system. Now we know that a system with high mechanical Q has low dissipation, so we want a system with high Q. What does that mean?
- Q is the ratio of elastic restoring force to dissipative force. So it’s a measure of how fast a system will restore to its original after it has been hit by sth. It can be measured by ring-down time of vibration.If it takes long to die down, then it means low damping, which means high Q. Well that brings us back to FDT.
- Q related to “loss angle” φ by, which is a damping factor. Phi has 3 components, viscous damping, which is due to air molecules hitting. Can be reduced by going to better vacuum. The other is structural, which depends on the geometry of the material, and can be reduced by clever designing. The other is the thermoelastic damping, which is the contraction or expansion of the mirror surface by brownian motion of the particles inside the mirror themselves, due to the sign of the thermal expansion coefficient. And the only way this brownian motion will stop is when the thermal expansion coefficient of the material goes to 0. Now turns out Silicon has such a sweet spot at 120K.
- So if silicon can be used for mirror and the suspension fibers of the pendullum, then the thermoelastic damping can be avoided. And that’s what ranaAdhikari of Caltech has proposed for the 3rd generation LIGO.
- Radiative cooling since it is in vacuum, and you don’t want any cold finger touching it since that’ll mess up the Q.Use high emissivity coating for efficient emission. Now is this feasible? And that’s what I’m trying to find out.
- Now the worry is that putting on the coating will distort the structural damping and hence lower the Q and that’s what we are trying to find out. So now I’ll talk about the actual experiment, which is what you are most interested in. So I’m performing the test on small silicon wafer.
- Finding the right kind of wafer took a while. What we have here is a single crystal wafer, double side polished.2 inch in diameter, 0.05 inch thick. We drilled 6 holes by some company that Rai found.
- The holes are on the nodal line of the mode at which we will be driving our wafer for the Q measurement. We chose to drive our the wafer at this simple circular mode at 7 kHz. In this model I built the part in SolidWorks, and then used Comsolmultiphysics software to model the vibrational mode of the wafer. I learnt using these two softwares over the summer. I used a poisson ratio of 0.68 to find the radius of the nodal line.Now to cool this wafer to 120 K we are using a nitrogen dewar.
- That is the outer shroud, this thing is upside down. This shroud is attached to this, and then the whole thing goes inside the big shroud. You can’t see them in this picture, but a number of modifications were made to the dewar. Over the summer I leak tested it with He Leak detector, an outlet was made on this side to attach a micropirani gauge. The pump station is attached here and LN2 goes in through the top. This attached portion here is the suspension system for the wafer. It was machined by Rai last month, and I assembled it over the break.
- The wafer is suspended through 3 of the hoels at 120 degree to one another. I inserted teflon tubes through the holes to make, so that the wire doesn’t touch the wafer. The wires then ass through holes in the side of the al ring. The al ring is attached to the bottom plate of the dewar with small plastic legs, so there is no thermal contact. Heat shrink tubes pass through the holes in the ring, and using these screws the position of the wafer can be adjusted. These two electrodes act as capacitors for driving the wafer for the Q measurement, which I’ll explain later.
- This is the top view of the setup. There are two dale resistors and a silicon diode temp sensor on the Al ring to maintain its temp at 120K.A film resistor and silicon diode on the wafer, maintains the temp of wafer at 120K. These will be sodered on using indium soder on the silicon. This wire here puts a bias on the wafer to charge,adn I’ll explain why that is.A silicon diode to be connected to the silicon wafer and another to the aluminum ringResistors on the wafer and the ring will hold it at 120K.
- A silicon diode to be connected to the silicon wafer and another to the aluminum ringResistors on the wafer and the ring will hold it at 120K.
- The two dale resistors are connected to the temp sensors on both the silicon and the al ring, and a microcontroller will hold both of them at 120K. We want the ring to be at 120K as well, so that no heat is conducted by the nylon fibre and the wires. This will ensure only radiative cooling of the wafer.The resistor and sensor together will be connected to another controller, which will hold the temp of wafer at 120K. The power used by the wafer to maintain its temp at 120K in the 77K enviroment will tell us the emissivity of the Si.The process will be repeated with putting the coating on as well.
- Where Prad is the amount of power being put into the film resistor.We have found that at a pressure of 10^-7 torres, heat transfer by radiation dominates over convective heat transfer.
- The second part of the experiment is to measure the mechanical Q of the circuit. To measure the Q, I’ll drive the wafer at frequency of the mentioned vibrational mode of the circuit. Once sufficiently driven, I’ll turn off the drive force and let the wafer ring-down. I’ll calculate the Q by measuring the decay time of the slope.Here is the details of the Q circuit.
- To detect the motion of the wave a 50 kHz source will be put on the electrodes, which will act as capacitors. A DC voltage will be put on the wafer to make it charged so that a force is applied on it when it moves. As the wafer moves its motion can be seen in the scope through the LI. The amplitude of this signal is proportional to the distance x, so as the wafer rings down, we’ll see the signal dropping. Frpm the driver part, the wafer’ll be driven at 7.3 kHz and we can see the circular vibrational mode.
- Black gold compound. At 120 K, peak wavelength ~ 35 microns. Around 10-20% reflectance at that wavelength. From the analytical model of Rai, the wafer itself has an emissivity of ~ 8%. Putting the coating on will bring up the emissivity to ~90%.