Experimental results of the betatron sum resonance

The experimental observations of motion near the betatron sum resonance, /spl nusub x/+2/spl nusub z/=13, are presented. A fast quadrupole (Panofsky-style ferrite picture-frame magnet with 8 pulsed power supplies) producing a betatron tune shift of the order of 0.03 at rise time of 1 /spl mu/s 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, J/sub x/ and J/sub z/, was observed. The phase space plots in the resonance frame reveal the features of particle motion near the nonlinear sum resonance region.<
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