  A high-precision intra-bunch-train beam orbit feedback correction system has
been developed and tested in the ATF2 beamline of the Accelerator Test Facility
at the High Energy Accelerator Research Organization in Japan. The system uses
the vertical position of the bunch measured at two beam position monitors
(BPMs) to calculate a pair of kicks which are applied to the next bunch using
two upstream kickers, thereby correcting both the vertical position and
trajectory angle. Using trains of two electron bunches separated in time by
187.6~ns, the system was optimised so as to stabilize the beam offset at the
feedback BPMs to better than 350~nm, yielding a local trajectory angle
correction to within 250~nrad. The quality of the correction was verified using
three downstream witness BPMs and the results were found to be in agreement
with the predictions of a linear lattice model used to propagate the beam
trajectory from the feedback region. This same model predicts a corrected beam
jitter of c.~1~nm at the focal point of the accelerator. Measurements with a
beam size monitor at this location demonstrate that reducing the trajectory
jitter of the beam by a factor of 4 also reduces the increase in the measured
beam size as a function of beam charge by a factor of c.~1.6.
