Effects of magnet non-linearities on betatron oscillation frequencies for the 300 bev proton synchrotron

Abstract

The purpose of this note is to study the effects on betatron frequencies -- in particular, their variation with particle energy — due to non-linear magnet fields. The idea is to determine whether non- linearities can be introduced deliberately in such a way that ν, the number of betatron wavelengths in the circumference, is independent of particle energy for energies near the equilibrium energy. The result is that non-linearities of a magnitude such that the field index n varies by about 1 per cent per cm will suffice.