Pre-Phase A Report - Lisa - Nasa

64 Chapter 3 Experiment Description
be described [82] by a spectral density with a shallow frequency dependence:
1.75×
f
1mHz
−1/3 Wm −2 / √ Hz .
To quantify the effects of solar and electrical variations, a simple thermal model for the
spacecraft was formed with single nodes for the spacecraft body, solar panels, optical
bench, telescope, laser radiator and electronics disk. The temperature fluctuations of
the optical bench due to solar fluctuations were found to be well under the value of
10−6 K/ √ Hz at 1 mHz used in the analysis of the laser phase noise. To keep the power
variations from producing thermal noise in excess of this, the power dissipation of the payload
electronics will have to be controlled to 10 mW/ √ Hz and the power dissipation of the
photodiodes on the optical bench will have to be controlled to better than 50 µW/ √ Hz .
The needed control can be achieved with small heaters and voltage and current sensors.
The spacecraft electronics do not need to be controlled to better than the 0.1 % typical
of flight-qualified units.
The secondary mirror of the telescope is supported from the primary by a graphiteepoxy
spider with length 40 cm and thermal coefficient of expansion 0.4×10−6 /K. The
thermally-induced path-length variations using the thermal model were found to be less
than 2 pm/ √ Hz at 1 mHz, and so are not a major source of noise.
The accelerations caused by changes in the mass distribution of the payload were assessed.
The primary payload masses are the optical bench, the telescope, the payload electronics,
and the laser/radiator combination. The proof-mass acceleration noise caused by
solar fluctuations was found to be less than 1×10−16 ms−2 / √ Hz at 1 mHz. The acceleration
noise due to thermal variations in the dimensions and component positions of the
spacecraft body has not yet been assessed.
3.1.8 Pointing stability
The requirements of the interferometry place constraints on the allowed angular fluctuations
of the various interfering beams. The level of pointing control required of each
spacecraft is set by the level of phase front distortion in a transmitted beam. If the beam
deviates from having perfect spherical wavefronts centred on the transmitting craft, then
angular changes of the transmitting craft produce changes in the phase of the received
light, and hence apparent gravitational wave signals. From diffraction arguments the
largest effect is from a first order curvature error of the wavefront (equivalent to a defocus
in one or the other dimension). In this case the apparent phase change, δφ, due to
movement of the beam in the far field is given by:
δφ = 1
32
3 2π
d · D
λ
2 θdcδθ , (3.6)
where D is the diameter of the mirror, d is the amplitude of curvature error in the
wavefront, θdc is the static offset error in the pointing and δθ is the angular fluctuation.
In this case with an allowed phase error from this source of δφ =(2π/λ) ×10 −12 rad/ √ Hz
3-3-1999 9:33 Corrected version 2.08