On Maximum FODO Acceptance

Abstract

This note illustrates maximum acceptance of FODO quadrupole focusing channel. Acceptance is the largest Floquet ellipse of a matched beam: A = $\frac{a^2}{β}$$_{max}$ where a is the aperture of the channel and β max is the largest value of beta-function in the channel. If aperture of the channel is restricted by a circle of radius a, the s-s acceptance is available for particles oscillating at median plane, y=0. Particles outside median plane will occupy smaller phase space area. In x-y plane, cross section of the accepted beam has a shape of ellipse with truncated boundaries.