Left: LISA orbit. Right: LISA’s equilateral triangle constellation. (Not to scale.)
LISA arm scheme. The distance between the PMs must be measured at the pico meter level in the milli-Hertz range in order to ensure GW detection. x = 0.6 m, d OB–PM ≃ 0.05 m and d OB–OB ≃ 5 Gm (OB stands for optical bench). Distance fluctuations between the two mirrors of the telescope translate directly into path-length noise and thus spoil the LISA sensitivity. The noise budget assigned to this effect is given by Eq. (5).
Scheme of the LISA telescope current baseline design. The cylinder-shaped spacer (0.55 m diameter and 1 m length) is made of CFRP.10
Setup used to determine the relative dimensional stability of the CFRP cavity. All the lasers of the setup are Nd:YAG with a wavelength of 1064 nm. Each laser is locked to its respective cavity using the PDH technique. In this manner, the frequency of the laser tracks the length fluctuations of the cavity. EOM: electro-optical modulator, BS: power beam splitter, PBS: polarizing beam splitter, PD: photo-detector, and λ/4: quarter-wave plate.
Setup used to determine the absolute length changes of the CFRP cavity during the outgassing process. All the lasers of the setup are Nd:YAG with a wavelength of 1064 nm. Laser 3 is locked to a hyperfine transition of the iodine molecule using the frequency modulation Doppler-free saturation spectroscopy technique to provide an absolute frequency reference. Laser 2 is locked to the CFRP cavity using the PDH technique. DM: dichroic mirror, AOM: acoustic-optical modulator, LIA: lock-in amplifier, λ/2: half-wave plate, I2: iodine molecules, and 2F is a nonlinear crystal (Pp:MgLNO) that creates the second harmonic of the Nd:YAG laser.
Completed CFRP cavity with Zerodur/mirror plugs epoxied into place. The structure is 230 mm long. The outer shell is 200 mm in diameter and 5.5 mm thick. The inner tube has 45 mm outer diameter and 30 mm inner diameter. The struts are 4.2 mm thick.
Left: laboratory temperature fluctuations (black trace) and cavity temperature fluctuations (gray trace). Right: transfer function between laboratory and cavity temperature fluctuations. The solid black trace is the theoretical one—see Appendix. The gray trace is the measured one and the dashed black one is the required to meet the requirements. The pink area shows the frequency range where the temperature stability is not good enough for our experiments in the LISA band.
Measured length fluctuations (black trace) and predicted ones due to temperature fluctuations (dashed black trace) using the estimated CTE.
Expansion/contraction of the mirrors due to the power build up in the cavity. L 1 is the length of the cavity at a given temperature and in absence of light. L 2 is the length of the cavity when the laser is in resonance with the cavity. The temperature of the mirrors increases due to absorption and, consequently, they expand due to their CTE. The length of the mirrors of the cavity (and the cavity itself) reaches a steady-state for a given power built up in the cavity. If the power fluctuates the length of the mirrors fluctuates accordingly.
Coherence function between transmitted power, P τ, and beat-note for P τ = 60 μW and P τ = 1.2 mW.
Left: linear spectral density of the transmitted light power. Right: linear spectral density of the length fluctuations of the cavity. The noise in the mid-frequency range is significantly reduced when using low power.
Left: beat-note response after changing power going into the cavity by 1.14 mW. Right: Once the drift of the beat-note (caused by low-frequency temperature fluctuations) is removed a first-order response is clearly seen. The black trace is the measured signal while the gray trace is the fit—see Eq. (13).
Stability results for two different power levels: 1.2 mW (red trace, or (b) trace) and 60 μW (magenta trace or (d) trace). The predicted stability using Eq. (14) is also shown for the two different measurements (black (c) and green (e) traces). The blue-dashed line (a) is the LISA telescope requirement. The discrepancy for f ≲ 0.1 mHz is because the temperature and the beat-note data were not measured simultaneously and the temperature fluctuations during the beat-note measurement were lower than the ones during the temperature measurements. The dashed yellow trace (f) shows the Zerodur cavity stability measurements which sets the noise levels of the CFRP stability measurements.
Red trace (b): the measured length change of the CFRP cavity. Black (c) and magenta (d) traces: length change in the cavity due to outgassing, i.e., after removing the effect of the temperature (blue trace (a)). The temperature data and total length change traces correspond to the outgassing data given by the black trace (c). The same process was done to the magenta trace (d) although the temperature and total length change are not shown in the plot for clarity.
Thermal insulator concept. The cavity is placed inside the tank sitting on top of a stand and surrounded by PET shields. The PET shields are closed cylinders. Idem for the Zerodur cavity but with stainless-steel gold coated shields instead of PET ones.
Theoretical transfer functions for the CFRP (solid lines) and Zerodur (dashed lines) tanks.
Parameters used to calculate f cut-off for the CFRP tank and Zerodur tank.
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