Non-linear longitudinal beam dynamics with harmonic RF systems for bunch lengthening

Harmonic cavities have been installed on various storage ring light sources to increase the Touschek lifetime by a factor of 2 to 4 by lengthening bunches. Several side effects have been observed, which limit the gain in lifetime. In the worst case, the beam stability can be altered, but harmonic cavities can also provide Landau damping of coherent motion. A multibunch multiparticle tracking code has been developed to evaluate the performance of harmonic RF systems under consideration of all longitudinal beam dynamics issues. Bunches with high intensities are already elongated by the interaction with the ring impedance. The computations indicate that a harmonic RF system provide significant additional lengthening. The application to the ESRF shows that an active superconducting harmonic system would constitute the only appropriate solution. Such a system would be useful in single bunch and sixteen-bunch operation to improve the beam lifetime by a factor of 2 and 3, respectively