ON THE COMPUTATION OF RESONANT MODES IN CYLINDRICALLY SYMMETRIC CAVITIES

Abstract Intense bunches of charged particles in accelerators excite transverse higher modes in accelerating cavities. These higher modes lead to an interaction between widely seperated bunches. Such multi-bunch or multi-turn instabilities due to long range forces can be described by the cavity mode frequencies and field patterns. For structures of cylindrical symmetry a computer code named URMEL is described which calculates resonant modes of any azimuthal mode number m = 0, 1, 2… (monopole, dipole, quadrupole, etc.). The eigenfrequencies are found as linear eigenvalues of a large matrix and simple mathematical procedures guarantee that no modes are missed. The combined use of URMEL in the frequency domain and of the complementary code TBCI in the time domain enables a complete analysis of long range — low frequency — forces (narrow band impedances) and short range — high frequency — forces (broad band impedances.