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