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in 10 steps Advanced Virgo Passive seismic attenuation as applied in gravitational wave detection 2. VIRGO Einstein 1. Albert Einstein predicted the existence of gravitational waves as ripples of space-time moving with the speed of light. They are caused by acceleration of massive objects, for example neutron stars, orbiting closely around each other The gravitational wave detector VIRGO (near Pisa, Italy) operates a Michelson interferometer measuring the length difference of its 3 kilometer long arms. A passing gravitational wave makes one arm longer and the other shorter or vice versa. These length fluctuations are typically 1018 meters: 10000 times smaller than an atomic nuclear diameter! The detector is sensitive in the range 10Hz -10 kHz. Orbiting neutron stars emitting gravitational waves 3. Seismic vibrations Micro-seismic vibrations shake the ground typically at 10-7 m (0.1 µm) in all directions. They disturb the measurements of gravitational waves and need strong attenuation VIRGO gravitational waves detector near Pisa, Italy 5. Natural frequencies 4. Mechanical oscillators Key elements of our vibration isolation technique are simple one-dimensional oscillators: β’ pendulum for horizontal motion (length L) β’ mass-spring system for vertical motion, stiffness k. In 1673 Christiaan Huygens published the first mathematical relation ever applied in natural sciences : the formula for the period of a pendulum. We still benefit from it today: Pendulum period Mass-spring system k L m x x ππ πππ π ππ Pendulum frequency : ππππ = π»π» = πππ π x0 x0 : π»π»ππ = βΆ ππππ = ππ ππ πππ π π³π³ ππ ππ π³π³ ππ ππ Christaan Hyugens m Typical ground displacement noise spectrum at the VIRGO site, recorded at different times 6. Passive vibration isolation Any oscillator attenuates, by nature, vibrations above its resonance frequency. Notice that: β’ Attenuation is better at higher frequencies (red line). β’ Vibrations at for instance 10 Hz are attenuated 100 times more by a 10 times slower oscillator (green line) Therefore we try to make ultra-slow oscillatorsβ¦. 10. Compact 6-D high-performance isolation 7. Inverted pendulum Nikhef has designed and built MultiSAS, a multi-stage 6-dof attenuator suspending a 320 kg optical bench from a single wire. It includes three inverted pendulums (blue) and two pendulums (red) for horizontal isolation, and a chain of two GAS filters (yellow) for vertical isolation, all inside a vacuum tank. Above 2 Hz the attenuation is completely passive. Voice coils, LVDT sensors and geophones are employed in a feed-back scheme for DC positioning and suppression of resonances. 5 of these will be installed in Advanced VIRGO. The mass of an inverted pendulum is supported by a stiff rod. The pivot at the lower end is an elastic flexure. This flexure provides stiffness (k) preventing the mass from falling down. The frequency, typically tuned to 100 mHz, is given by: x F m Fanti ππππ = ππ ππ ππ β πππ π ππ π³π³ L mg elastic flexure 8. Vertical anti-Spring principle 9. Geometric Anti-Spring filter A vertical spring (stiffness k) is combined with two or more horizontal compressed springs. At any deflection y the compression forces Fc contribute oppositely to the restoring force βk y. As a result the natural frequency can be tuned close to zero: ππππ ππ ππ β ππ π«π« ππππ = πππ π ππ In a geometric anti-spring the vertical and horizontal (compressive) springs are combined in a single pre-stressed elastic element , a triangular blade spring. Up to 12 blades can be assembled in a GAS filter. The natural frequency is typically tuned to 200 mHz. The blades are made of maraging steel. The maximum surface stress is 1.7 GPa. (GAS) MultiSAS
