Resonance free lattices for A.G. machines

A part of an alternating gradient circular machine composed of a number of identical cells N/sub c/ will not contribute to the excitation of most of the non-linear resonances to first order in multipole strength, if the two phase advances per cell take the values 2/spl pi/k/sub 1//N/sub c/ and 2/spl pi/k/sub 2//N/sub c/. k/sub 1/ and k/sub 2/ are any integers and k/sub 1//spl ne/k/sub 2/. This property is demonstrated here. Its application to synchrotron light sources and colliders is discussed.