1. Topology comparison RSE vs. SAGNAC using GWINC
S. Chelkowski, H. Müller-Ebhardt, S. Hild
21/09/2009
S. Chelkowski
ET Workshop, Erice, 10/2009

2. Overview Intro & Motivation Noise coupling differences & similarities
Displacement noise in a 2- & 4-mirror cavity
Beam geometry influence on thermal noise
GWINC model
Results
Conclusion
S. Chelkowski
ET Workshop, Erice, 10/2009

3. ET note on QND review
Conclusion
Sagnac Topology seems to give the best quantum noise performance
S. Chelkowski
ET Workshop, Erice, 10/2009

4. More realistic comparison of Sagnac and RSE topology
S. Chelkowski
ET Workshop, Erice, 10/2009

5. Noise coupling – Sagnac compared to RSE
Quantum noise characteristic change
How do various displacement noises couple more due to four mirror cavities, e.g. TN, Seismic noise, etc...
Beam geometry changes and influences TN further
Higher losses in four mirror arm cavity
Etc...
S. Chelkowski
ET Workshop, Erice, 10/2009

6. Coupling of displacement noises
Cavity Design
Signal
Noise
For two mirrors
of the 4 mirror
cavity:
Signal:
Noise:
S. Chelkowski
ET Workshop, Erice, 10/2009

7. Beam geometry changes affect the TN
Beam geometry on mirror surface depends on incidence angle
Initial beam shape defined by:
changes into:
Note
Take clipping loss into account in the following analysis
S. Chelkowski
ET Workshop, Erice, 10/2009

8. Beam geometry in the 4 mirror cavity
Mirror sizes used: r=31cm
Round beam with w=12cm has clipping loss of 1ppm
Beam size on one of the four arm cavity mirrors
Resulting Beam
wx = 12cm & wy = 10cm
S. Chelkowski
ET Workshop, Erice, 10/2009

9. Consequences for the thermal noise
Coating Brownian thermal noise:
CBTN adaptation to elliptical beam:
with
PSD: ,
with
&
we find
Bessel function of 0. order
Beam intensity distribution:
Analytically not solvable!
Numerical integration
S. Chelkowski
ET Workshop, Erice, 10/2009

10. The same was done for the Substrate Brownian thermal noise!
Result for CBTN
CBTN for elliptical beam shape using the minor beam width
with CBTN correction factor
The same was done for the Substrate Brownian thermal noise!
S. Chelkowski
ET Workshop, Erice, 10/2009

11. CBTN for elliptical beam shape using the minor beam width
Result for SBTN
CBTN for elliptical beam shape using the minor beam width
with SBTN correction factor
S. Chelkowski
ET Workshop, Erice, 10/2009

12. Result for our specific case
Topology wx
[cm] wy
CBTN
cor. factor
SBTN
ET RSE 12 1
ET Sagnac 10
1.189
1.089
S. Chelkowski
ET Workshop, Erice, 10/2009

13. Current model status Single detector Underground
L = 10km
Underground
Seismic noise reduced
Gravity gradient noise reduced
Adapted thermal noises & suspension model
Optimisation parameters
Input laser power P
SR, ITM & PRM transmissivity
Tuning of SRM
Readout quadrature with homodyne detector
S. Chelkowski
ET Workshop, Erice, 10/2009

14. Things to keep in mind
This is a topology analysis and there is no intension to create a new baseline sensitivity curve
Following sensitivities are lower than the ones presented on the ET webpage
No magical factor used e.g. for the grav. gradient noise
No squeezing used
No cryogenic techniques
Nevertheless the following comparison is valid
The model can be changed later and a higher performing configuration can be found via optimisation
S. Chelkowski
ET Workshop, Erice, 10/2009

15. Figure of merit and optimisation
BHBH and NSNS inspiral ranges
Give parameters of standard candles.
BHBH: Mass each 30Msol, Distance 10Mpc, merger at ~5Hz
NSNS: Mass each 1.4Msol, Distance 23Mpc, merger at ~2.3kHz
5D parameter space is scanned automatically for the optimal configuration with an adaptive resolution
S. Chelkowski
ET Workshop, Erice, 10/2009

16. RSE topology results – tuned configuration
BHBH: 9736Mpc
NSNS: 871Mpc
S. Chelkowski
ET Workshop, Erice, 10/2009

17. RSE topology results – 5D - auto optimisation
BHBH optimisation
BHBH: 11776Mpc
NSNS optimisation
NSNS: 949Mpc
S. Chelkowski
ET Workshop, Erice, 10/2009

18. SAGNAC topology results – 5D - auto optimisation
BHBH: 14836Mpc
NSNS: 1282Mpc
S. Chelkowski
ET Workshop, Erice, 10/2009

19. Comparison of results – BHBH optimisation - I
RSE – tuned SR
SAGNAC-optimised
BHBH inspiral range for Sagnac topology 52% larger
Event rate increased by a factor of 3.5
S. Chelkowski
ET Workshop, Erice, 10/2009

20. Comparison of results – BHBH optimisation - II
RSE – optimised
SAGNAC-optimised
BHBH inspiral range for Sagnac topology 26% larger
Event rate increased by a factor of 2.0
S. Chelkowski
ET Workshop, Erice, 10/2009

21. Comparison of results – NSNS optimisation - I
RSE – tuned SR
SAGNAC-optimised
BHBH inspiral range for Sagnac topology 47% larger
Event rate increased by a factor of 3.2
S. Chelkowski
ET Workshop, Erice, 10/2009

22. Comparison of results – NSNS optimisation - II
RSE – optimised
SAGNAC-optimised
BHBH inspiral range for Sagnac topology 35% larger
Event rate increased by a factor of 2.5
S. Chelkowski
ET Workshop, Erice, 10/2009

23. Conclusion Sagnac topology performs better than RSE in this analysis
BHBH inspiral range increase by 26%-52%
NSNS inspiral range increase by 35%-47%
Next steps:
Use Markov Chain Monte Carlo method for the optimisation, first tests already done
How does it perform?
Useful for comparison of other topologies in the future
Write ET note about this topology analysis
S. Chelkowski
ET Workshop, Erice, 10/2009

24. THE END...
S. Chelkowski
ET Workshop, Erice, 10/2009

25. Additional slides
S. Chelkowski
ET Workshop, Erice, 10/2009

26. PRM transmissivity algorithm check - I
Tuning Tprm for a fixed config
S. Chelkowski
ET Workshop, Erice, 10/2009

27. PRM transmissivity algorithm check - I
Auto optimisation
Manual optimisation
S. Chelkowski
ET Workshop, Erice, 10/2009