Charging of free-falling test masses in orbit due to cosmic rays: Results from LISA Pathfinder

A comprehensive summary of the measurements made to characterize test-mass charging due to the space environment during the LISA Pathfinder mission is presented. Measurements of the residual charge of the test mass after release by the grabbing and positioning mechanism show that the initial charge of the test masses was negative after all releases, leaving the test mass with a potential in the range from $-12$ to $-512$. Variations in the neutral test-mass charging rate between 21.7 and $30.7e{\mathrm{s}}^{-1}$ were observed over the course of the 17-month science operations produced by cosmic ray flux changes including a Forbush decrease associated with a small solar energetic particle event. A dependence of the cosmic ray charging rate on the test-mass potential between $-30.2$ and $-40.3e{\mathrm{s}}^{-1}{\mathrm{V}}^{-1}$ was observed resulting in an equilibrium test-mass potential between 670 and 960 mV, and this is attributed to a contribution to charging from low-energy electrons emitted from the gold surfaces of the gravitational reference sensor. Data from the onboard particle detector show a reliable correlation with the charging rate and with other environmental monitors of the cosmic ray flux. This correlation is exploited to extrapolate test-mass charging rates to a 20-year period giving useful insight into the expected range of charging rate that may be observed in the LISA mission.

Figure 1

Diagram of LISA Pathfinder GRS showing 46 mm cubic test mass surrounded by capacitive-sensing bias injection electrodes in blue, $x/\varphi$ sensing and actuation electrodes in red, $y/\theta$ in green and $z/\eta$ in yellow.

Figure 2

LPF test-mass charge as function of time throughout the mission. Dashed lines indicate the upper and lower limits for the charge during nominal operations at $3\times {10}^{7}e\approx 140\mathrm{mV}$. Abrupt decreases in the test-mass charge are the result of charge control operations using the onboard UV illumination system. Large excursions of the charge occurred at day 152, 425 and 567 during test-mass charging and noise investigations.

Figure 3

LPF charging rate measurement for both test masses with minimum force and torque actuation authority and $V_{\mathrm{MOD}}=50\mathrm{mV}$ starting at June 22, 2017 at $02:12:00$ UTC, the left-hand axis indicates the test-mass charge and the right-hand axis the equivalent test-mass potential with $C_T=34.1\mathrm{pF}$. The inset shows an expanded plot of the data around $V_{\mathrm{TM}}\approx -808\mathrm{mV}$ with linear best-fit lines. The charging rates from the fitted lines are $+53.4\pm 1.2e{\mathrm{s}}^{-1}$ (${\chi }_{\mathrm{red}}^2=0.99$) and $52.4\pm 1.2e{\mathrm{s}}^{-1}$ (${\chi }_{\mathrm{red}}^2=1.2$) for TM 1 and 2, respectively.

Figure 4

The variation in the test-mass charging rates observed with varying test-mass potential for the two measurements described in the text. The upper panel shows the results from January 30, 2017 and the lower panel from June 22, 2017.

Figure 5

The test-mass charge measured with $V_{\mathrm{MOD}}=50\mathrm{mV}$ during the change in test-mass force and torque authority at May 13, 2016 $07:30$ UTC ($t=0$). Dashed lines indicate the best fit to the charge trend at $t<0$ in high-authority mode and dash-dotted lines show the trend at $t>0$ in minimum-authority mode.

Figure 6

LPF test-mass charging rates as a function radiation monitor count rate for selected measurements with $V_{\mathrm{TM}}$ close to 0 V and ac actuation voltages in minimum-authority mode. Solid lines show the weighted best fit to the data, dashed lines indicate the unweighted fit.

Figure 7

LPF test-mass charging rates plotted against radiation monitor count rate over a 3-day period beginning April 20, 2016 $08:00:00$ UTC. The measurement was performed with $V_{\mathrm{MOD}}=3\mathrm{V}$ and ac actuation voltages in high-authority mode but with reduced amplitudes on the $x$ electrodes. Charging and radiation monitor count rates are evaluated over 1-hr periods. Solid lines show the best fit to the data.

Figure 8

Test-mass charge and radiation monitor measurements made during the Forbush decrease beginning at July 15, 2017 $01:00$ UTC. The measurement was performed with $V_{\mathrm{MOD}}=10\mathrm{mV}$ and ac actuation voltages in minimum-authority mode. Charging and radiation monitor count rates are evaluated over 2-hr periods.

Figure 9

Scatter plot of the data shown in Fig. 8 showing the correspondence between the test-mass charging rate and radiation monitor count rate during the Forbush decrease. Solid lines show the best fit to the data.

Figure 10

Charging rate of the LISA Pathfinder test masses extrapolated over the 20-year observation range of the INTEGRAL mission by correlation with the IREM count rate as described in the text. The shaded region shows the duration of the LISA Pathfinder mission.