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| The displacement of the left mirror is ~0.2 nm. So the sensitivity of the cavity length to vertical acceleration is 4 x 10^-10 (dL/L) / g. Next we have to consider the limited vibration isolation characteristics of the reference cavities stack and spring pendulum. | The displacement of the left mirror is ~0.17 nm. The overall cavity length gets shorter by ~0.35 nm making a strain of dL/L = (3.5e-10)/0.20 = 1.7 x 10^-9^. So the sensitivity of the cavity length to vertical acceleration is ~2 x 10^-10^ / (m/s^2^) or 53 kHz / (m/s^2^). Next we have to consider the limited vibration isolation characteristics of the reference cavities stack and spring pendulum. For comparison, the Ye/Hall vertical football cavities have a sensitivity of 10-20 kHz/(m/s^2^). Not such a big difference if it turns out that the measured sensitivity is as good as the model. |
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The sensitivity of the cavity to [[/Horizontal Accelerations]] (beamline (X) and non-beamline (Y)) are much smaller than the vertical direction. === Thermal Noise === === Temperature Noise === The reference cavity's vacuum can is actively stabilized with a PID loop of ?? Hz BW. Is it an integrator? The sensor noise of the AD590 temperature sensors is 40 pA/rHz (according to the data sheet) which corresponds to 40 uK/rHz. If were able to stabilize to this level (which I doubt), the inside temperature fluctuations would then be in the 10 nK/rHz regime because of the passive filtering of the can. IF true, the strain noise of the cavity spacer would be (10 nK/rHz)*(5e-7 (dL/L)/K) = 5e-15 / rHz. ''This is a LOT more than either the coating thermal noise or seismic noise''. Here's the measured temperature noise at some random room at the AEI attachment:tempnoise.pdf. We can assume that the 'ambient' line is typical of a basic room. |
We have done some analysis of the Reference Cavity using COMSOL. We got the design parameters for the reference cavity from [http://www.ligo.caltech.edu/docs/D/D980670-00.pdf D980670]
Basic Model Parameters
T = 273 + 38 K (reference cavity can is kept at 38 C)
- Spacer and mirrors made of Corning Fused Silica (7940) - in reality its probably 7980?
Uses: Structural Mechanics module, Heat Transfer module, & Materials Library
Eigenmodes
- Remove gravity
- No constraints (as if there's no wire)
Vertical Sensitivity
- Constrain the grooves on the bottom in all 3 DOF.
- Add a load force on the spacer. F/V = -9.81 * 2200 (comsol likes a force/volume)
Deformation of the cylinder shows the actual shape. Color indicates displacement along the cavity axis.
The displacement of the left mirror is ~0.17 nm. The overall cavity length gets shorter by ~0.35 nm making a strain of dL/L = (3.5e-10)/0.20 = 1.7 x 10-9. So the sensitivity of the cavity length to vertical acceleration is ~2 x 10-10 / (m/s2) or 53 kHz / (m/s2). Next we have to consider the limited vibration isolation characteristics of the reference cavities stack and spring pendulum.
For comparison, the Ye/Hall vertical football cavities have a sensitivity of 10-20 kHz/(m/s2). Not such a big difference if it turns out that the measured sensitivity is as good as the model.
The sensitivity of the cavity to /Horizontal Accelerations (beamline (X) and non-beamline (Y)) are much smaller than the vertical direction.
Thermal Noise
Temperature Noise
The reference cavity's vacuum can is actively stabilized with a PID loop of ?? Hz BW. Is it an integrator?
The sensor noise of the AD590 temperature sensors is 40 pA/rHz (according to the data sheet) which corresponds to 40 uK/rHz. If were able to stabilize to this level (which I doubt), the inside temperature fluctuations would then be in the 10 nK/rHz regime because of the passive filtering of the can.
IF true, the strain noise of the cavity spacer would be (10 nK/rHz)*(5e-7 (dL/L)/K) = 5e-15 / rHz. This is a LOT more than either the coating thermal noise or seismic noise.
Here's the measured temperature noise at some random room at the AEI attachment:tempnoise.pdf. We can assume that the 'ambient' line is typical of a basic room.