Mode coupling in the modified betatron

The effects of quadratic nonlinearities in the single-particle equations of motion on electron orbits in the modified betatron are studied. Strong coupling of the two modes of betatron oscillation is found to occur for a particular value of the ratio Bsub(theta)Bsub(z) unless the gradient in the field index takes a certain value. In general, the mode coupling appears to be quite harmless in the azimuthally symmetric case. When field or focusing errors are present the mode coupling reduces the effect on the orbit of the l = 1 orbital resonance but does not do so sufficiently so that the l = 1 resonance could be safely passed through in a practical device. (author)