Resonance families and their action on betatron motion

The present paper takes one step beyond the single-resonance theory for betatron motion by summing all the members of a given resonance family and expressing the joint influence in a single driving term. As a demonstration and confirmation of this work, the family driving terms are used to derive the classic closed-orbit and betatron- modulation equations of Courant and Snyder (1958). A more serious demonstration is made by applying the family driving terms to the compensation of linear coupling and showing how numerical matrix- based and resonance compensation schemes are related. In a final phase, the Henon map is used to compare the efficiency of different coupling compensation schemes with respect to dynamic aperture. (23 refs).