ASTROD I Charging Simulation and Disturbances

1
ASTROD I Charging Simulation and Disturbances
Gang Bao(1,2), D N A Shaul(3), H M Araujo (3)
,Wei-Tou Ni(1,2), T J Sumner(3) and Lei Liu(1)
(1)Purple Mountain Observatory, Chinese Academy
of Sciences, Nanjing 210008 (2)National
Astronomical Observatories, The Chinese Academy
of Sciences, Beijing 100012 (3)Department of
Physics, Imperial College London, London, SW7
2BZ, UK
ASTROD I is planned as single spacecraft mission
and aims to perform interferometric and pulse
ranging with ground stations (ODSN Optical Deep
Space Network) to measure the solar system
parameters and to test relativistic gravity to
high precision. At the heart of the spacecraft is
a test mass, which the spacecraft will follow
using a drag-free control system. The mission
critically depends on maintaining the geodesic
motion of the test mass. Charging of the test
mass due to cosmic rays and solar particles and
the interaction of this charge with the
interplanetary magnetic field or any conducting
surfaces surrounding the test mass will disturb
its geodesic motion. We have estimated the amount
of charge deposited per second on the ASTROD I
test mass by cosmic ray protons and alpha
particles at solar minimum. This has been
simulated using the Geant4 toolkit and a
simplified, geometrical model. A positive
charging rate of 24.2 0.7 e/s was obtained.
Based on this charging rate, the magnitude of the
acceleration noise and the coherent signals
associated with charging are estimated.
ASTROD I
Orbit
Table 1. Characteristics of each material
layer (the radius in table 1 is the distance from
the center of the test mass to the outer surface
of each layer)
The ASTROD I mission concept is based around a
single spacecraft and laser interferometric
pulse ranging with ground stations. It is the
first step towards the ASTROD (Astrodynamical
Space Test of Relativity using Optical Devices)
1. The scientific goals of ASTROD I include
measuring the relativistic parameters with better
accuracy, improving the sensitivity achieved in
using the optical Doppler tracking method for
detecting gravitational waves, and measuring many
solar system parameters more precisely 2.
ASTROD I geometry model The geometry model used
in this study is sketched in the figure. The test
mass is a 505035 mm3 Au-Pt alloy (density 20
g/cm3) rectangular parallelepiped at the center
of the model, surrounded by 3 concentric,
spherical shells. The material of the innermost
shell is molybdenum (used to simulate the
electrodes) that of the middle shell is titanium
(used to simulate the house which enclosure the
test mass and sensor) that of the outermost
shell is carbon (used to simulate the structure
of spacecraft, equipment, battery etc.) The blank
region between the test mass and molybdenum shell
in figure 2 is vacuum (1.010-25 g/cm3). The
thicknesses and densities of the 3 material
shells used in the model are reported in table 1.
A comparison of noise curve of ASTROD I with LTP
and LISA. The solid line is for ASTROD I, the
dotted line is for LTP and the dashed line is for
LISA . The overall acceleration noise budget for
ASTROD I is
ms-2Hz-1/2,
where (frequency). The
ASTROD I bandwidth is 0.1 mHz100 mHz.
Differential energy spectra for cosmic ray
protons and alpha particles at solar minimum. In
the figure for alpha particles, the green line is
for the 3He and red line for the 4He 5. In our
simulation, cosmic rays are emitted
isotropically, irradiating the entire spacecraft
uniformly, from an outer spherical shell (radius
99 mm). The primary energies are sampled in the
range of 0.01-1000 GeV/nucleon, from the
distributions plotted in figure, corresponding to
the proton and helium fluxes at solar minimum.

The charging timeline for 3He
The charging timeline for protons
The charging timeline for 4He
The blue curves in figures above are the
timelines for the test mass net charge and the
black lines correspond to a least squares fit of
this data, giving the mean net charging rates.
The charging rates attributable to the proton,
3He and 4He fluxes are 19.2 0.5 e/s, 0.7
0.05 e/s and 4.3 0.2 e/s, respectively. The
MC uncertainty is calculated by combining the
Poisson variances for the occurrence of each net
event charge, to which we must add an estimated
error margin of 30 on the Geant cosmic ray
charging simulation and a contribution to the
charging rate of 28.4 e/s for kinetic low-energy
secondary electron emission based on the LISA
studies 6.
Charging disturbances The accumulation of
charge on the test mass will give rise to
acceleration noise and the corresponding
stiffness in the measurement bandwidth, through
both Coulomb and Lorentz interactions. These are
evaluated in our study. The magnitude of the
associated acceleration noise (due to random
fluctuations of the test mass position relative
to the spacecraft, of the potentials of the
conductors that surround the test mass and of the
charge) increases with decreasing frequency. They
are estimated at 0.1 mHz to be 4.9710-15 ms-2Hz
-1/2 for displacement noise, 5.2910-15 ms-2Hz
-1/2 for voltage noise, 3.9810-15 ms-2Hz -1/2
for charge noise and 2.3110-15 ms-2Hz-1/2 for
Lorentz noise. The stiffness is 7.0810-8 s-2 at
0.1 mHz. These figures were derived assuming
worst case charging conditions they have
included both an error margin of 30 for the
cosmic-ray flux plus extra systematics from
modelling implementation and a contribution to
the net charging rate of 28.4 e/s for kinetic
low-energy secondary electron emission (that is
likely to almost cancel in the actual sensor)
8. The charge noise therein mentioned above
increases with decreasing f as f -1. All these
noises due to charging fall well below the noise
target 10-13 ms-2Hz -1/2 at 0.1 mHz for ASTROD I.
The steady build up of charge on the test mass
will give rise to coherent Fourier components in
the ASTROD I frequency bandwidth 9. Taking the
mean charging rate as constant and assuming that
the test mass is discharged once every 24 hours,
the spectral densities of the coherent Coulomb
(fk(t), ek(t)) and Lorentz (lk(t)) signals are
plotted in the figure to the left. The Coulomb
signals, fk(t) and ek(t), are estimated to
exceed the ASTROD I acceleration noise limit at
low frequencies. Several schemes have been
suggested to minimize the potential loss of the
ASTROD I science data 9 and studies are
underway to develop methods for coping with these
signals for LISA. By comparison with LISA, ASTROD
Is relaxed noise limt means that it is expected
to be easier to remove these signals for ASTROD
I.
References 1 W.-T. Ni, S. Shiomi and A.-C.
Liao, ASTROD, ASTROD?and their
gravitational-wave sensitivities. Class.
Quantum Grav. 21, S641-S646, 2004. 2 W.-T. Ni,
G. Bao, Y. Bao, H. Dittus et al. ASTROD?,Test of
Relativity, Solar-System Measurement
and G-Wave Detection. Journal of Korean Physical
Society, Vol.45, pp.S118-S123, 2004. 3 S.
Shiomi and W.-T. Ni, Acceleration disturbances
and requirements for ASTROD I, gr-qc/050612
(submitted to Class. Quantum Gravity) 4 H.
Araujo, A. Howard, D. Shaul and T. Sumner,
Electrostatic charging of cubic test masses in
the LISA mission. Class. Quantum Grav.
20, S201-S209, 2003. 5 C. Grimani, H. Vocca, M.
Barone et al. Cosmic ray spectra near the LISA
orbit. Class. Quantum Grav. 21,
S629-S633, 2004. 6 H. Araujo, P. Wass, D. Shaul
G. Rochester, T. Sumner, Detailed calculation of
test-mass charging in the LISA mission.
Astroparticle Physics, Vol 22, p 451 - 469,
2005. 7 C. Grimani, H. Vocca, G.. Bagni et al.
LISA test-mass charging process due to cosmic-ray
nuclei and electrons. Class. Quantum
Grav. 22, S327-S332, 2005. 8 D. Shaul, H.
Araujo, G. Rochester, T. Sumner, P. Wass,
Evaluation of disturbances due to test mass
charging for LISA. Class. Quantum Grav., 22,
S297-S309, 2005. 9 D. Shaul, T. Sumner, G.
Rochester, Coherent Fourier components in the
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International Journal of Modern
Physics D14, 51-71 (2005)