摘要：Higher harmonic cavity used in the third generation synchrotron light source increases the Touschek lifetime. The higher harmonic cavity of Shanghai Synchrotron Radiation Facility （SSrf） is a 1.5 GHz passive superconducting cavity. Its higher order modes （HOM） are extracted by a ferrite HOM damper out of the cryostat. Multi-cell cavity is chosen concerning the voltage. The harmonic cavity dynamics, beam dynamics with passive harmonic cavity and the design of single cell cavity are included in this paper.