M. Todd, S. Dwyer
As derived in previous alogs, we are able to relate the HOM spacing observed in each arm to the surface defocus of the test masses -- which is a combination of self-heating and ring heater power (ignoring CO2 affects on the ITM RoC). From the fits we've made of the HOM spacing / surface defocus change as a function of ring heater power we can get a value for the ring heater to surface defocus coupling factor.
Theoretically from this we should be able to solve for the self heating contribution in the test masses as well -- allowing us to constrain things like the coupling of absorbed power to surface defocus at the ITMs if we assume to know the arm power and absorption values (from HWS).
Upper Limits
If we assume no absorption in ETMs (obviously not physical), and we assume the HWS values for the ITM absorptions are correct, then with a HOM spacing measurement from each arm we can get an upper limit of the coupling factor of self-heating to surface defocus for each ITM (they shouldn't be different but this is a good exercise).
Assuming alpha is the absorption coefficient, i subscript is for the ITM, and x/y is which arm. P_y,i_rh is the itmy ring-heater. G-factors are the product of ITM and ETM g-factors. Then from the formula in section 1.2 of the notes file : Gy = Gyc - B*L*gyic*(Pyerh+Pyirh) - L*(Ai*alpha_yi*Pyarm*gyec + beta*Ai*alpha_e*Pyarm*gyic), we can solve for Ai which is the coupling factor of self-heating to surface defocus.
| Parameter | Value | Notes |
| alpha_x,i | 430 ppm | from alog 76937 |
| alpha_y,i | 375 ppm | from alog 76937 |
| alpha_x,e | 0 ppm | |
| alpha_y,e | 0 ppm | |
| P_y,i_rh | 0.000 W | T0 = 1417899757 |
| P_x,i_rh | 0.850 W | |
| P_x,e_rh | 1.950 W | |
| P_y,e_rh | 2.146 W | |
| P_yarm |
385159 W
|
T0 = 1417899757 |
| P_xarm | 385159 | T0 = 1417899757 |
| Gx | 0.8149 | T0 = 1417899757 |
| Gy | 0.8198 |
TMS * pi G = cos2 ( ---------------- ) FSR |
| Ai_y | -26 uD/W | |
| Ai_x | -39 uD/W |
Middling Values
If we assume quoted absorption in ETMs (measured by LIGO, on galaxy), and we assume the HWS values for the ITM absorptions are correct, then with a HOM spacing measurement from each arm we can get a more realistic value of the coupling factor of self-heating to surface defocus for each ITM (they shouldn't be different but this is a good exercise).
Assuming alpha is the absorption coefficient, i subscript is for the ITM, and x/y is which arm. P_y,i_rh is the itmy ring-heater. G-factors are the product of ITM and ETM g-factors. Then from the formula in the notes file : Gy = Gyc - B*L*gyic*(Pyerh+Pyirh) - L*(Ai*alpha_yi*Pyarm*gyec + beta*Ai*alpha_e*Pyarm*gyic), we can solve for Ai which is the coupling factor of self-heating to surface defocus.
| Parameter | Value | Notes |
| alpha_x,i | 430 ppm | from alog 76937 |
| alpha_y,i | 375 ppm | from alog 76937 |
| alpha_x,e | 200 ppm | |
| alpha_y,e | 210 ppm | |
| P_y,i_rh | 0.000 W | T0 = 1417899757 |
| P_x,i_rh | 0.850 W | |
| P_x,e_rh | 1.950 W | |
| P_y,e_rh | 2.146 W | |
| P_yarm |
385159 W
|
T0 = 1417899757 |
| P_xarm | 385159 | T0 = 1417899757 |
| Gx | 0.8149 | T0 = 1417899757 |
| Gy | 0.8198 |
TMS * pi G = cos2 ( ---------------- ) FSR |
| Ai_y | -16 uD/W | |
| Ai_x | -26 uD/W |
Summary
Both of these values indicate there is certainly an overestimation of the self-heating impact on surface defocus.
For reference, the current TCS-SIM values for this coupling factor are Ai_y = Ai_x = -36.5 uD/W. More examination is required into this.
Links to previous alogs:
- Estimating HOM spacing shift from self-heating alone: https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=84172
