Pre-Phase A Report - Lisa - Nasa

90 Chapter 4 Measurement Sensitivity
results of this convolution are shown in Figure 4.6 . It can be seen that the charging is
charge per [sec−MeV]
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
H+
He++
−0.005
0 200 400 600 800 1000 1200 1400 1600 1800 2000
incident energy (MeV)
Figure 4.6 Computed cosmic ray charging spectrum for the LISA proof mass.
The results shown are for solar minimum, (and should be reduced by a factor
of 4 for solar maximum).
significant for incident particle energies up to 1000 MeV. To shield against these would
require in excess of 25 cm tungsten, totally impractical for a space mission.
Integrating over energy yields a total charge rate of 11 protons/s (2×10−18 C/s) at solar
minimum, with a discrepancy of ±10% corresponding to the effects of low-energy electrons.
Additional errors come from uncertainties in the cosmic ray spectra (error bars
in Figure 4.4) which amount to ±30 % in computed charge rate. Therefore, the actual
charge rate can be expected somewhere between 6 and 16 protons/s for solar minimum
(and between 1 and 4 protons/s for solar maximum). It is interesting to note that although
helium accounts for only 10 % of the cosmic ray incident flux, it is found to produce
30 % of the charging, owing to the comparatively high numbers of secondaries generated.
Another interesting quantity is the ratio of stopped charge to the total rate of charges
entering the proof mass if it were exposed directly to the cosmic ray flux. This ratio turns
out to be 1:20 which shows that, (very) roughly speaking, 95 % percent of the cosmic rays
pass straight through without any effect.
The cosmic rays are the dominant species only when the Sun is inactive. When it is active,
an average solar flare will send out protons with sufficient energy to produce a charging
of about 4×107 protons integrated over the event (calculated using GEANT with solar
proton flux models from [101]). An anomalously large flare leads to 4×1010 protons. As
discussed in [99], the frequency of flare events is skewed and asymmetric with respect to
the solar cycle. In the seven-year neighbourhood of solar maximum, about eight average
flares per year can be expected. In the three-year neighbourhood of solar minimum, the
3-3-1999 9:33 Corrected version 2.08