Compensation Plate performances

I analized the performances of the correction due to CP, as usual in terms of coupling losses. I applied a heating profile à la Vinet shown in the next figure



The analitycal expression is in the form

I(r)=cosh(r²/wc²)-exp(-2*r²/w²)

wc is a parameter that I changed ranging from 0.11m to 0.2m, while I kept w costant at the value of 0.06m, the same as the waist of the heating pattern on the TM. In this preliminary analisys I neglected the heat exchange btw TM and CP due to radiation (as if CP and TM are far apart). Moreover, there is no ring heater around the TM to correct the ROC.

The first figure shows the Log of the coupling losses as a function of wc and the CO₂ power for a CP that is 0.065m thick.



The second image is the same calculation, but using a profile given by an AXICON. In this case wc represents the Inner Radius of the ring, the outer radius being fixed at 0.13m.



We can see that in both cases it is possible to achieve coupling losses of the order of 10⁴ ppm.

I repeated the analysis in the case of an AXICON profile with the complete TCS set-up: TM+CP+RH. The ring heater is placed in the position that minimizes the power to correct ROC errors and is emitting circa 15W in all directions. The distance btw CP and TM is 1cm and the CP is 0.065m thick. Results are shown in the next figure as usual.



The results do not differ very much from those found when the RH is not present, meaning that it's contribution is rather negligible. Again the best coupling losses is in the 10⁴ppm region. It may be worth increasing the outer radius of the annular pattern to 0.14m (next analisys).

Alessio wrote:The results do not differ very much from those found when the RH is not present, meaning that it's contribution is rather negligible.

I must correct myself: the ring heater contribution is not negligible, it is correcting the lensing due to the heat radiated from the CP to the TM.

I repeated the analisys of the complete setup with an AXICON pattern, but I increased the outer radius of the profile to 0.14m, so to heat the CP all the way to the edge.



The result is just a little bit better than with R_out=0.13m, still the best coupling losses are around 10⁴ppm. I want to try to increase the radius of the CP to 0.15m...

I simply increased the power and R_in resolution. Now the power ranges from 3.5W to 10.25W in steps of 0.25W (before it was 0.5W), while R_in goes from 30mm to 75mm in steps of 5mm (before it was 10mm). Results do not change much. The minimum is for R_in between 40mm and 45mm and P is around 7.0W-7.25W.

Triggered by Viviana, I tried to see what happens if the CP is far away from the TM (heated by the RH). So, I made the usual simulations (R_in from 35mm to 75mm by 5mm and P_CO2 from 3.25W to 10.25W by 0.25W). I analized two cases: CP is 0.065m or 0.1m thick. Here hare the results in the usual form.

CP is 0.065m thick...



... and CP is 0.1m thick



As it is clear from the plot, a thinner CP is better. In the case of the 0.065m CP it is possible to achieve coupling losses as low as 10³ppm. We can finally say, by comparing the case of the complete setup and the case of the "far-away" 0.065m CP, that having the CP close to the test mass is increasing coupling losses by a factor of 10.

To have an idea of what is happening where we have the minima of the couplig losses, I calculated the related OPL increase.

Figure 1 shows the OPL of the complete setup (RH+TM+CP, CP and TM are close to each other) the corresponding coupling losses are 10⁴ppm, figure 2 show the same quantity for the case of a CP 0.065m thick, far away from the TM, corresponding coupling losses are 1300ppm. Third figure is the same as figure 2, but the CP is 0.1m thick, coupling losses are about 10⁴ppm.







From the figures 2 and 3 it is possible to notice very clearly the contribution of the RH to the TM OPL. On figure 1, the RH contribution is almost negligible, this may be due to the heating of the TM by the radiation from the CP. Since it is clear that a thick CP is worse than a thin CP, the LIGO need for gold coating of the TM barrel could be explained by the fact that their CP is 0.13m thick.

In the simulations done with the TM heated by the RH and the CP far away with thicknesses of 0.065m and 0.1m it is clearly visible that coupling losse tend to decrease as the CP thickness decreases. So I wanted to verify this and I made simulations for different CP thicknesses. Each time, I recorded the minimum coupling losses, that occurs for different CO₂ powers and profile's inner radius. Figure shows the results.



It seems that with a CP 3.5cm thick, it is possible to reach coupling losses as low as 540ppm, astonishing! Next picture shows the usual Log(Losses) vs CO₂ power and R_in

It is now clear to everybody, that putting CPs close to the test mass is making TCS almost ineffective. The question is: where to put them? Our first proposition was to hang them from the BS tower: it was said it is impossible. Now it seems that this "impossibility" has been relaxed. So I wanted to check possible interactions between CPs and the BS. The system is not axisimmetrical anymore, so I hat to make a full 3D simulation. First figure shows the ANSYS model.



The BS is heated by the IFO beam, while the CPs are heated by the CO₂ laser with a power equal to 4.5W, which is giving the nice 540ppm losses. Next figure shows the temperature map of the BS.



So the BS is heated by the heat radiated by the CPs, the BS RM might mitigate this effect. Anyway, I wanted to see if thi is an issue or not in terms of coupling losses.
The following pictures show the OPL increases from the various sources: TM heated by the YAG and RH, CP heated by the CO₂ and the BS heated by the YAG and by the heat from the CPs. Since the BS is at 45° wrt to the YAG beam, I calculated the OPL increase in the vertical (Y) and horizontal (X) directions. The Y direction is not affected by the heat oming from the CPs, only X is.



Next figure shows the residual OPL increase in the X and Y, sum of all contributions.



Corresponding coupling losses are 600ppm in X and 3000ppm in Y (but this could be decreased by applying a little bit more of CO₂ power on the CPs). I think this is a strong support to the idea of suspending the CPs from the BS tower.

Alessio wrote:It seems that with a CP 3.5cm thick, it is possible to reach coupling losses as low as 540ppm, astonishing! Next picture shows the usual Log(Losses) vs CO₂ power and R_in

So I decided to increase the R_in resolution from 5mm to 1.25mm. In this case, keeping the same resolution on the CO₂ power, the number of simulations increase from 280 to 1036! ANSYS took several hours to complete and Matlab took something like 40min to analyze the data. But the result is very good. Next picture is the same LogLosses map.



And this is the corresponding OPL for the lowest losses...



To make it short, we could get coupling losses as low as 300ppm!

I simply included the effect of the BS on the overall performances of the TCS. As in the previous calculations including the BS, I show results for the X and Y directions.

Usual Log(L) map for the X direction.



Same map for the Y drection.



Average of the two maps.



Results:

	Coupling Losses (ppm)
X direction	330
Y direction	740
Average	1630