The accretion of electrostatic charge in the isolated LISA test masses due to energetic particles in the space environment hinders the drag-free operation of the gravitational inertial sensors. Robust predictions of charging rates and associated stochastic fluctuations are therefore required for the exposure scenarios expected throughout the mission. We report on detailed charging simulations with the
Geant4 toolkit, using comprehensive geometry and physics models, for
galactic cosmic-ray protons and helium nuclei. These predict net charging rates of up to +100 elementary charges per second during the solar minimum period, decreasing by half at solar maximum. Charging from sporadic solar events involving energetic protons was also investigated. Other physical processes hitherto overlooked as potential charging mechanisms have been assessed. Significantly, the kinetic emission of very low-energy secondary electrons due to bombardment of the inertial sensors by primary cosmic rays and their secondaries can produce charging currents comparable with the Monte Carlo rates.
LISA employs a capacitive sensing and positioning system to maintain the drag free environment of the test masses acting as interferometer mirror elements. The need for detailed electrostatic modelling of the test mass environment arises because any electric field gradient or variation associated with test mass motion can couple the test mass to its housing, and ultimately the spacecraft. Cross-couplings between components in the system can introduce direct couplings between sensing signals, sensing axes and the drive signal. A variation in cross-couplings or asymmetry in the system can introduce capacitance gradients and second derivatives, giving rise to unwanted forces and spring constant modifications. These effects will vary dependent on the precise geometry of the system and will also tend to increase the sensitivity to accumulated charge on the test-mass. Presented are the results of a systematic study of the effect of the principal geometry elements (e.g. machining imperfections, the caging mechanism) on the test mass electrostatic environment, using the finite element code ANSYS. This work is part of an ongoing ESA study into drag-free control for LISA and the LTP on SMART 2 and ultimately aims to eliminate geometries that introduce too large a disturbance and optimise the electrostatic design.