International Nuclear Information System (INIS)

Japanese Mar 1999 p. 371-372 Japan Shi, Dequan Yamazaki, Takashi

International Nuclear Information System (INIS)

One of the hallmarks of linear coupling is the resonant exchange of oscillation amplitude between the horizontal and vertical planes when the difference between the unperturbed tunes is close to an integer. The standard derivation of this phenomenon (known as the difference resonance) can be found, for example, in the classic papers of Guignard [1, 2]. One starts with an uncoupled lattice and adds a linear perturbation that couples the two planes. The equations of motion are expressed in hamiltonian form. As the difference between the unperturbed tunes approaches an integer, one finds that the perturbing terms in the hamiltonian can be divided into terms that oscillate slowly and ones that oscillate rapidly. The rapidly oscillating terms are discarded or transformed to higher order with an appropriate canonical transformation. The resulting approximate hamiltonian gives equations of motion that clearly exhibit the exchange of oscillation amplitude between the two planes. If, instead of ...