Beam-Beam deflection feedback

Beam-beam deflection feedback acting within the
crossing time of a single bunch train may be needed to
keep linear collider beams colliding at high luminosity. In
a short-pulse machine such as the Next Linear Collider
(NLC) this feedback must converge quickly to be useful.
The non-linear nature of beam-beam deflection vs. beam-
beam offset in these machines precludes obtaining both
rapid convergence and a stable steady-state lock to beam
offsets with a linear feedback algorithm. We show that a
simply realizable programmable non-linear amplifier in
the feedback loop can linearize the feedback loop,
approximately compensating the beam-beam deflection
non-linearity. Performance of a prototype non-linear
amplifier is shown. Improvement of convergence and
stability of the beam-beam feedback loop is simulated
Beam-Beam deflection feedback