FORCES AND FORCE GRADIENTS DUE TO PATCH FIELDS AND CONTACT-POTENTIAL DIFFERENCES

We derive expressions for the forces and force gradients which exist b etween infinite parallel metallic surfaces in terms of the spatial dis tributions of the surface potentials. The main motivation for this is to enable the forces and force gradients to be calculated from electri cal measurements of the surface potentials. However, by making some wo rst-case assumptions about the potential distributions, we establish a limit for the relative displacement delta of the spacecraft and proof mass in the LISA mission of delta less than or equal to 8 x 10(-10) ( Delta a/10(-15) m s(2) Hz(-1/2)) (rho/20 g cm(-3)) (d/4 cm) (a/1 mm)(3 ) (0.1 V/v)(2) m Hz(-1/2) where Delta a is the target acceleration sen sitivity, rho is the proof-mass density, d is the dimension of the pro of mass (assumed cubic) and a is the spacing between the proof mass an d the surrounding electrodes. The magnitude of the patch-potential var iations or contact-potential differences between the plates is paramet rized as v.