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The predominant source of nonlinearity in most existing accelerators aresextupoles, which introduce nonlinear resonances. When the horizontal tune ofan accelerator is near such a resonance line ($n\nu_x$), stable fixed points(SFPs) may appear in the horizontal phase space to form a second closed orbitdifferent from the "zero" closed orbit. The stable islands in phase spacesurrounding the SFPs are also referred as transverse resonance island "buckets"(TRIBs). However, the TRIBs are not always present near a resonance line in astorage ring. Necessary conditions for TRIBs formation will be discussed inthis paper. A 6-GeV lattice with the horizontal tune near a 3rd-order resonanceline at $3\nu_{x}$=50 is then designed for the Cornell Electron Storage Ring(CESR). After loading this lattice into CESR, the TRIBs are observed whileadjusting the horizontal tune near the 3rd-order resonance, consistent withparticle tracking simulations. TRIBs rotation in the horizontal phase space arealso experimentally demonstrated with adjustment of a sextupole knob. Theseresults are in good agreement with the theoretical calculation.

Lattice design and experimental studies of nonlinear resonance at the Cornell Electron Storage Ring