Experimental results of the betatron sum resonance

The experimental observations of motion near the betatron sum resonance, νx + 2νz = 13, are presented. A fast quadrupole (Panofsky-style ferrite picture-frame magnet with a pulsed power supplier) producing a betatron tune shift of the order of 0.03 at rise time of 1 μs was used. This quadrupole was used to produce betatron tunes which jumped past and then crossed back through a betatron sum resonance line. The beam response as function of initial betatron amplitudes were recorded turn by turn. The correlated growth of the action variables, Jx and Jz, was observed. The phase space plots in the resonance frame reveal the features of particle motion near the nonlinear sum resonance region