  We report on electrostatic measurements made on board the European Space
Agency mission LISA Pathfinder. Detailed measurements of the charge-induced
electrostatic forces exerted on free-falling test masses (TMs) inside the
capacitive gravitational reference sensor are the first made in a relevant
environment for a space-based gravitational wave detector. Employing a
combination of charge control and electric-field compensation, we show that the
level of charge-induced acceleration noise on a single TM can be maintained at
a level close to 1.0 fm/s^2/sqrt(Hz) across the 0.1-100 mHz frequency band that
is crucial to an observatory such as LISA. Using dedicated measurements that
detect these effects in the differential acceleration between the two test
masses, we resolve the stochastic nature of the TM charge build up due to
interplanetary cosmic rays and the TM charge-to-force coupling through stray
electric fields in the sensor. All our measurements are in good agreement with
predictions based on a relatively simple electrostatic model of the LISA
Pathfinder instrument.
