Effects of the Passive Harmonic Cavity on the Beam Bunch

In this paper, we present a computer tracking code, which can investigate the bunch length, energy spread and the threshold current of Robinson instability under the influence of the passive harmonic cavity. The effects of the radiation damping, quantum excitation and the beam loading of the harmonic cavity are included in the computation. The calculated result shows that the beam has a constant energy spread and blows up as the beam current increases from below to over the threshold current of the Robinson instability. It also indicates that the shunt impedance of the harmonic cavity is critical for whether the harmonic cavity can reach the designed goal, a stable and lengthening beam at the design beam current.