The ET-FIBER project is a collaborative R&D initiative,
focused on developing silicon fibers for suspending
a 70 kg monocrystalline silicon test mass
in the ET-CRISTAL prototype.

ET-CRISTAL serves as a critical cryogenic prototype
for the Einstein Telescope, which operates
a large monocrystalline silicon mirror cooled
radiatively to 20–25 K, while achieving low seismic noise
below 10 Hz through advanced vibration isolation.

In this context, ET-FIBER aims to design,
manufacture, and characterize silicon fibers
capable of supporting these large test masses
under cryogenic conditions, while meeting
the stringent mechanical and thermal noise
requirements of next-generation detectors.

For this project, two different designs
are currently considered.
The first one is a classic suspension system
with tensional elements only [1].
This is what has been done in gravitational
wave detectors of previous generation.

In this case, the main challenge
is the manufacturing of the rods.
Indeed, those are long and thin
which is problematic.
Vibrations are induced in the machining process
which leads to defects or even structural failure
since silicon is brittle.

To address this problem,
the possibility to weld multiple smaller parts
is being studied.
The machining process itself
is also under development
by the concerned partner.

The second design is composed
of tensional and compressive parts
as seen in figure 2.
The starting point of this design
is the fact that silicon exhibits
a higher mechanical strength
in compression [2].

This could be used by making
the flexible parts of the design
compressive and very thin,
which would improve the isolation
and reduce the thermal noise
of the structure by improving
its dilution factor.

This solution has as advantage
the fact that the flexible parts
are smaller.
There is then no problem
for the machining.

The longer parts of the design
are thicker,
then less subjected to vibration
during machining.
Also, they do not necessarily
need to be in silicon.

The thermal noise is mostly located
in parts subjected to strain
which is not the case
for those tensional bars.

Using FEM and analytical models,
it is possible to do a projection
of the possible performances,
either in terms of vibration
or thermal noise.

The comparison that is presented here
has been performed using similar size
for the flexible parts in both designs.

The vibration isolation is shown
in figure 3 using FEM
for the two types of design.
This curve is the amplification
at the location of the mirror
of a movement located
at the top of the suspension.

It can be seen that
the compressional design
is less competitive
between 2 Hz and 200 Hz.
However, this could be mitigated
by modifying the tensional bars design.

Indeed, lowering their moment of inertia
would improve the performances.

The comparison of the two designs
can also be done for the thermal noise
[3], [4] in figure 4.

Both designs have very close performances.
Also, they are in line
with the wanted sensitivity
of the Einstein Telescope.

1. X. Koroveshi et al.,
   “Cryogenic payloads for the Einstein Telescope:
   Baseline design with heat extraction,
   suspension thermal noise modeling,
   and sensitivity analyses,”
   Phys. Rev. D,
   vol. 108,
   no. 12,
   p. 123009,
   Dec. 2023,
   doi: 10.1103/PhysRevD.108.123009.
2. F. E. P. Arellano et al.,
   “A cryogenic test-mass suspension
   with flexures operating in compression
   for third-generation gravitational-wave detectors”.
3. P. R. Saulson,
   “Thermal noise in mechanical experiments,”
   Phys. Rev. D,
   vol. 42,
   no. 8,
   pp. 2437–2445,
   Oct. 1990,
   doi: 10.1103/PhysRevD.42.2437.
4. A. V. Cumming et al.,
   “Silicon mirror suspensions
   for gravitational wave detectors,”
   Class. Quantum Gravity,
   vol. 31,
   no. 2,
   p. 025017,
   Jan. 2014,
   doi: 10.1088/0264-9381/31/2/025017.