Pre-Phase A Report - Lisa - Nasa

92 Chapter 4 Measurement Sensitivity
disturbance corresponding to δQ, namely
Sa ≈ 1
m
2 e ˙ Q
2 πf (v×B) (ms−2 / √ Hz) . (4.12)
Putting in numbers, and imposing a limit of 10−16 ms−2 / √ Hz for the acceleration, yields
an upper limit of 2×10−12 C/s for the mean charge rate. This is almost six orders of
magnitude above the expected charge rate, and so this effect can be neglected.
For the final term in Eq. 4.8, recent measurements of the interplanetary magnetic field
variations (from the Ulysses spacecraft at 1 AU) have been used to derive δB and place
limits on the allowable charge at which 10 % of the acceleration noise budget is reached.
These are shown, versus frequency, in Figure 4.7 . Also shown is the time taken to reach
these limits, assuming the charging rates computed by GEANT (with a factor of two
margin). It is clear that for low frequencies (10−4 Hz) the charge build-up exceeds the
Charge limit (electrons/protons)
10 14
10 13
10 12
10 11
10 10
10 9
10 8
10 7
10 6
10 -4
10 -3
10 -2
Frequency (Hz)
Figure 4.7 Limit on allowable charge due to the Lorentz force disturbance as
a function of frequency.
allowable levels after an hour or so (the situation is less severe at higher frequencies),
which means that the charge must be removed rather frequently. In principle this limit
could be relaxed somewhat by employing closed electromagnetic shielding around the
accelerometer. The precise extent to which this can be done is unclear but it is certainly
reasonable to expect to be able to obtain an order of magnitude reduction in charge
sensitivity. In fact it turns out that additional constraints on the charge level become the
limiting factors beyond this level of shielding anyway. These are explored in the following
sections.
Coulomb forces. Electrically the conducting proof mass surrounded by electrodes can
be thought of as a bank of capacitors with the proof mass forming a common central
3-3-1999 9:33 Corrected version 2.08
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