First order tune shift calculations for transverse betatron dynamics

An effective Hamiltonian, with non-linear magnetic multipole terms and momentum dispersion contributions, is used to obtain the first order tune-shift results for transverse betatron motion for protons in the Superconducting Super Collider (SSC). This Hamiltonian is represented in terms of action angle variables, and analytical results are obtained using symbolic algebra methods. Mathematical derivations of the transverse multipole expansion and of the transverse betatron equations, using an invariant action and curvilinear coordinates, are given in the appendices. Numerical and graphical tune-space results are given that illustrate the dependence of tune-shifts on injection amplitude and momentum spread. 10 refs., 7 figs