This log is duplicated in LLO alog 25563.

Summary

Further to my alog 25932, I have calculated approximate TCS power levels for O2, this time including the effect of the ring heaters. The results are presented in tabular form.

The bottom line:

1. the RHs are used predominantly to correct the surface deformation on the test masses.
2. The CO2 lasers are used to correct the residual lens in the test mass after the RHs have been applied. 
3. We might need to commission annular heating on CO2Y at LHO.
4. ETMY_RH at LLO requires a larger increase in power due to the relatively high absorption in ETMY

Calculation:

Surface curvature

To correct the surface curvature errors, we use the RH. It is straightforward to show that the required change in RH power is given by:

dP_RH = - (absorb*dParm) * dSD/dP_self / (dSD/dP_RH),

where 'absorb' is the absorption in the surface of the optic, dParm is the change in the power in the arm, dSD/dP_self (H1:TCS-SIM__SURF_DEFOCUS_SELF_GAIN) is the steady-state change in the surface deformation in diopters per Watt absorbed power, and dSD/dP_RH (H1:TCS-SIM__SURF_DEFOCUS_RH_GAIN) is the steady-state change in the surface deformation per Watt power from the RH. These values are available on the TCS SIM MEDM page.

Substrate thermal lens

The same calculation can be done for the CO2 laser power:

dP_CO2 = - [ (absorb*dParm) * dS/dP_self + dP_RH * dS/dP_RH ] / (dS/dP_CO2),

where dS/dP_self, dS/dP_RH, dS/dP_CO2 are the change in the substrate lens defocus per Watt for self-heating, RH and central heating CO2 laser respectively. Note that the RH power has, nominally, been fixed by correcting the surface curvature in the previous step.

Note the distinction between the responses for the surface deformation, dSD/dP and the substrate lens, dS/dP.

LHO settings:

Based on the best estimates for the absorption in the test masses, the changes in actuator settings are:

Obviously, we can't apply negative power with central heating on CO2Y. The reason CO2Y was set to 0W for O1 was because it wasn't working during that science run - therefore, this is probably not the best operating power for CO2Y at 100kW of arm power.

• A recommended commissioning activity would be to optimize CO2Y at 100kW in the arms and then recalculate the required TCS at 200kW in the arms.
• If we find we do need more negative lensing in the substrates of the ITMs we can do one of two things:
  • Use more RH power and move the ITM surface curvature away from the nominal operating point
  • Or, commission an annular heating mask with the CO2 lasers.

LLO settings:

Notice the relatively large increase required for ETMY - this is due to our measurements indicating an absorption on there of the order of 1.6ppm, or about 5 or 6 times larger than the average of the other optics.