Transverse mode coupling instability with a double rf system

摘要

Effects on a transverse mode coupling instability in a storage ring by a strongly deformed rf bucket in a double rf system are studied. An eigenvalue equation, respectively the vanishing of the determinant of an infinite matrix, is derived from a Hamiltonian formalism. Truncation of th is determinant permits solution of the problem on a computer, and a code MOSDRF has been written which finds the complex mode frequencies. The stability limits are determined by equating the imaginary part of the solution to the radiation damping rate. The theory was applied to LEP with third higher-harmonic cavities, and the results were compared with those obtained by the Multi-particle simulation program FEDBAK. They agree well, and show that the threshold current will be reduced rather than improved.