1. Considerations about triangular and L-shaped detectors
Riccardo DeSalvo
University of Sannio and Riclab LLC

2. Two configurations were conmpared for ET
Double traditional L-shape and triangular

3. Two configurations compared
Same length of tunnels and of vacuum pipes
Each tunnel houses 2 warm interferometers and 2 low-frequency cryo ones.
Both geometries optimized to make complete detection of both polarizations
The 86% lower sensitivity/km from the 60o of the triangular configuration is exactly compensated by the shorter arms and the √2 from the twin interferometers in each of the L- shape interferometers at 45o.
Same cost

4. The most obvious problems with the triangular design is the Beam Splitter

5. Beam Splitter problems with the triangular design
Entering the beam splitter at more than 45o has a dramatic effect on the beam splitter size;
At 60o needs to be 1.6 x as wide as at 45o
2 x the distance travelled in glass
6 x times as heavy
If the beam size is not reduced by baffling or optical means it ends up being larger than the main mirrors

6. Present solution to reduce the beam size of the triangular configuration
Spherical lensing on outer surface of Input Test Mass
Problems:
Transforms translations into angles
Does not provide position and mode matching tools for the two spots at the recombination point

7. How to solve the large Beam Splitter problem?

8. Proposed solution to reduce the beam size: (solution useful to both triangular and L-configuration)
Move the (injection and detection) beam expanding telescopes inside the Michelson interferometer
Requirement:
Use two parabolic telescope mirrors angled 7.5o (for the triangular configuration, small angle for “L”)
Multiple advantages:

9. Proposed solution to reduce the beam size:
Smaller beam splitter is required
ITM with a flat back surface simpler to manufacture
Independent control of the two mirrors for best lateral and angular overlap of spots on the beam splitter
Beams can cross at 90o also in triangular configuration

10. Proposed solution to reduce the beam size: both configurations
Thermal compensation on the telescope mirrors allow to precisely match the sizes of the two beam spots on the beam splitter
Dynamical correction for power-dependent aberrations in the main mirrors may allow elimination of the compensation plates
heat

11. Proposed solution to reduce the beam size: both configurations
Beams from multiple detectors can be sequentially extracted from the main tunnel with beam splitters naturally located in well separated halls

12. Proposed solution to reduce the beam size: both configurations
The longer distances offer the opportunity to cleanly separate the ghost images of the ITM wedge for diagnostic and control use.
They can be extracted with the additional advantage of smaller ITM wedge angles.

13. Advantages of the L-shaped interferometers
There are 8 interferometers in the “L” instead of 6 in the triangular
There are several operational advantages from the fact that the two GW detectors oriented at 45o are in completely separate tunnels.
Star-watch mode observation can be maintained in one during maintenance of the other
The construction can be staged in time and is more flexible. Example:
The second tunnel pair can be completed while a first detector is implemented in the first tunnel pair.
Debugged detectors can be installed in the second pair of tunnels
The second detector is installed in the first tunnel
More flexibility is available for a staged installation of the cryogenic LF detectors

14. Advantages of the L-shaped interferometers
There are several observational advantages
Maintenance in the “x” detectors can be performed
while the “+” detectors run in star-watch mode.
In the triangular configuration access to any angle station may perturb all detectors and impede all detections.
The two pairs of identical interferometer in the “x”, ”+” configuration tunnels are ideal for stochastic background detection.
L-shaped detectors can be extended with longer arms.